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API Documentation

+

opt_einsum.contract

+ + +
+ + + + +
+ +

Contains the primary optimization and contraction routines.

+ + + +
+ + + + + + + + +
+ + + +

+ ContractExpression + + +

+ + +
+ + +

Helper class for storing an explicit contraction_list which can +then be repeatedly called solely with the array arguments.

+ +
+ Source code in opt_einsum/contract.py + 
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class ContractExpression:
+    """Helper class for storing an explicit ``contraction_list`` which can
+    then be repeatedly called solely with the array arguments.
+    """
+
+    def __init__(
+        self,
+        contraction: str,
+        contraction_list: ContractionListType,
+        constants_dict: Dict[int, ArrayType],
+        **einsum_kwargs: Any,
+    ):
+        self.contraction_list = contraction_list
+        self.einsum_kwargs = einsum_kwargs
+        self.contraction = format_const_einsum_str(contraction, constants_dict.keys())
+
+        # need to know _full_num_args to parse constants with, and num_args to call with
+        self._full_num_args = contraction.count(",") + 1
+        self.num_args = self._full_num_args - len(constants_dict)
+
+        # likewise need to know full contraction list
+        self._full_contraction_list = contraction_list
+
+        self._constants_dict = constants_dict
+        self._evaluated_constants: Dict[str, Any] = {}
+        self._backend_expressions: Dict[str, Any] = {}
+
+    def evaluate_constants(self, backend: Optional[str] = "auto") -> None:
+        """Convert any constant operands to the correct backend form, and
+        perform as many contractions as possible to create a new list of
+        operands, stored in ``self._evaluated_constants[backend]``. This also
+        makes sure ``self.contraction_list`` only contains the remaining,
+        non-const operations.
+        """
+        # prepare a list of operands, with `None` for non-consts
+        tmp_const_ops = [self._constants_dict.get(i, None) for i in range(self._full_num_args)]
+        backend = parse_backend(tmp_const_ops, backend)
+
+        # get the new list of operands with constant operations performed, and remaining contractions
+        try:
+            new_ops, new_contraction_list = backends.evaluate_constants(backend, tmp_const_ops, self)
+        except KeyError:
+            new_ops, new_contraction_list = self(*tmp_const_ops, backend=backend, evaluate_constants=True)
+
+        self._evaluated_constants[backend] = new_ops
+        self.contraction_list = new_contraction_list
+
+    def _get_evaluated_constants(self, backend: str) -> List[Optional[ArrayType]]:
+        """Retrieve or generate the cached list of constant operators (mixed
+        in with None representing non-consts) and the remaining contraction
+        list.
+        """
+        try:
+            return self._evaluated_constants[backend]
+        except KeyError:
+            self.evaluate_constants(backend)
+            return self._evaluated_constants[backend]
+
+    def _get_backend_expression(self, arrays: Sequence[ArrayType], backend: str) -> Any:
+        try:
+            return self._backend_expressions[backend]
+        except KeyError:
+            fn = backends.build_expression(backend, arrays, self)
+            self._backend_expressions[backend] = fn
+            return fn
+
+    def _contract(
+        self,
+        arrays: Sequence[ArrayType],
+        out: Optional[ArrayType] = None,
+        backend: Optional[str] = "auto",
+        evaluate_constants: bool = False,
+    ) -> ArrayType:
+        """The normal, core contraction."""
+        contraction_list = self._full_contraction_list if evaluate_constants else self.contraction_list
+
+        return _core_contract(
+            list(arrays),
+            contraction_list,
+            out=out,
+            backend=backend,
+            evaluate_constants=evaluate_constants,
+            **self.einsum_kwargs,
+        )
+
+    def _contract_with_conversion(
+        self,
+        arrays: Sequence[ArrayType],
+        out: Optional[ArrayType],
+        backend: str,
+        evaluate_constants: bool = False,
+    ) -> ArrayType:
+        """Special contraction, i.e., contraction with a different backend
+        but converting to and from that backend. Retrieves or generates a
+        cached expression using ``arrays`` as templates, then calls it
+        with ``arrays``.
+
+        If ``evaluate_constants=True``, perform a partial contraction that
+        prepares the constant tensors and operations with the right backend.
+        """
+        # convert consts to correct type & find reduced contraction list
+        if evaluate_constants:
+            return backends.evaluate_constants(backend, arrays, self)
+
+        result = self._get_backend_expression(arrays, backend)(*arrays)
+
+        if out is not None:
+            out[()] = result
+            return out
+
+        return result
+
+    def __call__(self, *arrays: ArrayType, **kwargs: Any) -> ArrayType:
+        """Evaluate this expression with a set of arrays.
+
+        Parameters
+        ----------
+        arrays : seq of array
+            The arrays to supply as input to the expression.
+        out : array, optional (default: ``None``)
+            If specified, output the result into this array.
+        backend : str, optional  (default: ``numpy``)
+            Perform the contraction with this backend library. If numpy arrays
+            are supplied then try to convert them to and from the correct
+            backend array type.
+        """
+        out = kwargs.pop("out", None)
+        backend = parse_backend(arrays, kwargs.pop("backend", "auto"))
+        evaluate_constants = kwargs.pop("evaluate_constants", False)
+
+        if kwargs:
+            raise ValueError(
+                "The only valid keyword arguments to a `ContractExpression` "
+                "call are `out=` or `backend=`. Got: {}.".format(kwargs)
+            )
+
+        correct_num_args = self._full_num_args if evaluate_constants else self.num_args
+
+        if len(arrays) != correct_num_args:
+            raise ValueError(
+                "This `ContractExpression` takes exactly {} array arguments "
+                "but received {}.".format(self.num_args, len(arrays))
+            )
+
+        if self._constants_dict and not evaluate_constants:
+            # fill in the missing non-constant terms with newly supplied arrays
+            ops_var, ops_const = iter(arrays), self._get_evaluated_constants(backend)
+            ops: Sequence[ArrayType] = [next(ops_var) if op is None else op for op in ops_const]
+        else:
+            ops = arrays
+
+        try:
+            # Check if the backend requires special preparation / calling
+            #   but also ignore non-numpy arrays -> assume user wants same type back
+            if backends.has_backend(backend) and all(infer_backend(x) == "numpy" for x in arrays):
+                return self._contract_with_conversion(ops, out, backend, evaluate_constants=evaluate_constants)
+
+            return self._contract(ops, out, backend, evaluate_constants=evaluate_constants)
+
+        except ValueError as err:
+            original_msg = str(err.args) if err.args else ""
+            msg = (
+                "Internal error while evaluating `ContractExpression`. Note that few checks are performed"
+                " - the number and rank of the array arguments must match the original expression. "
+                "The internal error was: '{}'".format(original_msg),
+            )
+            err.args = msg
+            raise
+
+    def __repr__(self) -> str:
+        if self._constants_dict:
+            constants_repr = ", constants={}".format(sorted(self._constants_dict))
+        else:
+            constants_repr = ""
+        return "<ContractExpression('{}'{})>".format(self.contraction, constants_repr)
+
+    def __str__(self) -> str:
+        s = [self.__repr__()]
+        for i, c in enumerate(self.contraction_list):
+            s.append("\n  {}.  ".format(i + 1))
+            s.append("'{}'".format(c[2]) + (" [{}]".format(c[-1]) if c[-1] else ""))
+        if self.einsum_kwargs:
+            s.append("\neinsum_kwargs={}".format(self.einsum_kwargs))
+        return "".join(s)
+
+
+ + + +
+ + + + + + + + + + +
+ + + +

+ __call__(*arrays, **kwargs) + +

+ + +
+ +

Evaluate this expression with a set of arrays.

+
Parameters
+

arrays : seq of array + The arrays to supply as input to the expression. +out : array, optional (default: None) + If specified, output the result into this array. +backend : str, optional (default: numpy) + Perform the contraction with this backend library. If numpy arrays + are supplied then try to convert them to and from the correct + backend array type.

+ +
+ Source code in opt_einsum/contract.py + 
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def __call__(self, *arrays: ArrayType, **kwargs: Any) -> ArrayType:
+    """Evaluate this expression with a set of arrays.
+
+    Parameters
+    ----------
+    arrays : seq of array
+        The arrays to supply as input to the expression.
+    out : array, optional (default: ``None``)
+        If specified, output the result into this array.
+    backend : str, optional  (default: ``numpy``)
+        Perform the contraction with this backend library. If numpy arrays
+        are supplied then try to convert them to and from the correct
+        backend array type.
+    """
+    out = kwargs.pop("out", None)
+    backend = parse_backend(arrays, kwargs.pop("backend", "auto"))
+    evaluate_constants = kwargs.pop("evaluate_constants", False)
+
+    if kwargs:
+        raise ValueError(
+            "The only valid keyword arguments to a `ContractExpression` "
+            "call are `out=` or `backend=`. Got: {}.".format(kwargs)
+        )
+
+    correct_num_args = self._full_num_args if evaluate_constants else self.num_args
+
+    if len(arrays) != correct_num_args:
+        raise ValueError(
+            "This `ContractExpression` takes exactly {} array arguments "
+            "but received {}.".format(self.num_args, len(arrays))
+        )
+
+    if self._constants_dict and not evaluate_constants:
+        # fill in the missing non-constant terms with newly supplied arrays
+        ops_var, ops_const = iter(arrays), self._get_evaluated_constants(backend)
+        ops: Sequence[ArrayType] = [next(ops_var) if op is None else op for op in ops_const]
+    else:
+        ops = arrays
+
+    try:
+        # Check if the backend requires special preparation / calling
+        #   but also ignore non-numpy arrays -> assume user wants same type back
+        if backends.has_backend(backend) and all(infer_backend(x) == "numpy" for x in arrays):
+            return self._contract_with_conversion(ops, out, backend, evaluate_constants=evaluate_constants)
+
+        return self._contract(ops, out, backend, evaluate_constants=evaluate_constants)
+
+    except ValueError as err:
+        original_msg = str(err.args) if err.args else ""
+        msg = (
+            "Internal error while evaluating `ContractExpression`. Note that few checks are performed"
+            " - the number and rank of the array arguments must match the original expression. "
+            "The internal error was: '{}'".format(original_msg),
+        )
+        err.args = msg
+        raise
+
+
+
+ +
+ + +
+ + + +

+ evaluate_constants(backend='auto') + +

+ + +
+ +

Convert any constant operands to the correct backend form, and +perform as many contractions as possible to create a new list of +operands, stored in self._evaluated_constants[backend]. This also +makes sure self.contraction_list only contains the remaining, +non-const operations.

+ +
+ Source code in opt_einsum/contract.py + 
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def evaluate_constants(self, backend: Optional[str] = "auto") -> None:
+    """Convert any constant operands to the correct backend form, and
+    perform as many contractions as possible to create a new list of
+    operands, stored in ``self._evaluated_constants[backend]``. This also
+    makes sure ``self.contraction_list`` only contains the remaining,
+    non-const operations.
+    """
+    # prepare a list of operands, with `None` for non-consts
+    tmp_const_ops = [self._constants_dict.get(i, None) for i in range(self._full_num_args)]
+    backend = parse_backend(tmp_const_ops, backend)
+
+    # get the new list of operands with constant operations performed, and remaining contractions
+    try:
+        new_ops, new_contraction_list = backends.evaluate_constants(backend, tmp_const_ops, self)
+    except KeyError:
+        new_ops, new_contraction_list = self(*tmp_const_ops, backend=backend, evaluate_constants=True)
+
+    self._evaluated_constants[backend] = new_ops
+    self.contraction_list = new_contraction_list
+
+
+
+ +
+ + + +
+ +
+ + +
+ +
+ + + +

+ PathInfo + + +

+ + +
+ + +

A printable object to contain information about a contraction path.

+

Attributes:

+
    +
  • naive_cost - (int) The estimate FLOP cost of a naive einsum contraction.
    • +
  • opt_cost - (int) The estimate FLOP cost of this optimized contraction path.
    • +
  • largest_intermediate - (int) The number of elements in the largest intermediate array that will be produced during the contraction.
    • +
+ +
+ Source code in opt_einsum/contract.py + 
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class PathInfo:
+    """A printable object to contain information about a contraction path.
+
+    **Attributes:**
+
+    - **naive_cost** - *(int)* The estimate FLOP cost of a naive einsum contraction.
+    - **opt_cost** - *(int)* The estimate FLOP cost of this optimized contraction path.
+    - **largest_intermediate** - *(int)* The number of elements in the largest intermediate array that will be produced during the contraction.
+    """
+
+    def __init__(
+        self,
+        contraction_list: ContractionListType,
+        input_subscripts: str,
+        output_subscript: str,
+        indices: ArrayIndexType,
+        path: PathType,
+        scale_list: Sequence[int],
+        naive_cost: int,
+        opt_cost: int,
+        size_list: Sequence[int],
+        size_dict: Dict[str, int],
+    ):
+        self.contraction_list = contraction_list
+        self.input_subscripts = input_subscripts
+        self.output_subscript = output_subscript
+        self.path = path
+        self.indices = indices
+        self.scale_list = scale_list
+        self.naive_cost = Decimal(naive_cost)
+        self.opt_cost = Decimal(opt_cost)
+        self.speedup = self.naive_cost / self.opt_cost
+        self.size_list = size_list
+        self.size_dict = size_dict
+
+        self.shapes = [tuple(size_dict[k] for k in ks) for ks in input_subscripts.split(",")]
+        self.eq = "{}->{}".format(input_subscripts, output_subscript)
+        self.largest_intermediate = Decimal(max(size_list))
+
+    def __repr__(self) -> str:
+        # Return the path along with a nice string representation
+        header = ("scaling", "BLAS", "current", "remaining")
+
+        path_print = [
+            "  Complete contraction:  {}\n".format(self.eq),
+            "         Naive scaling:  {}\n".format(len(self.indices)),
+            "     Optimized scaling:  {}\n".format(max(self.scale_list)),
+            "      Naive FLOP count:  {:.3e}\n".format(self.naive_cost),
+            "  Optimized FLOP count:  {:.3e}\n".format(self.opt_cost),
+            "   Theoretical speedup:  {:.3e}\n".format(self.speedup),
+            "  Largest intermediate:  {:.3e} elements\n".format(self.largest_intermediate),
+            "-" * 80 + "\n",
+            "{:>6} {:>11} {:>22} {:>37}\n".format(*header),
+            "-" * 80,
+        ]
+
+        for n, contraction in enumerate(self.contraction_list):
+            _, _, einsum_str, remaining, do_blas = contraction
+
+            if remaining is not None:
+                remaining_str = ",".join(remaining) + "->" + self.output_subscript
+            else:
+                remaining_str = "..."
+            size_remaining = max(0, 56 - max(22, len(einsum_str)))
+
+            path_run = (
+                self.scale_list[n],
+                do_blas,
+                einsum_str,
+                remaining_str,
+                size_remaining,
+            )
+            path_print.append("\n{:>4} {:>14} {:>22}    {:>{}}".format(*path_run))
+
+        return "".join(path_print)
+
+
+ + + +
+ + + + + + + + + + + +
+ +
+ + +
+ + + +
+ + + +

+ contract(*operands_, **kwargs) + +

+ + +
+ +

Evaluates the Einstein summation convention on the operands. A drop in +replacement for NumPy's einsum function that optimizes the order of contraction +to reduce overall scaling at the cost of several intermediate arrays.

+ + + +

Parameters:

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NameTypeDescriptionDefault
subscripts + +
+

(str) Specifies the subscripts for summation.

+
+ 		+ required +
\*operands + +
+

(list of array_like) hese are the arrays for the operation.

+
+ 		+ required +
out + +
+

(array_like) A output array in which set the sresulting output.

+
+ 		+ required +
optimize + - *(str, list or bool, optional (default + +
+

auto))* Choose the type of path. +- if a list is given uses this as the path. +- 'optimal' An algorithm that explores all possible ways of +contracting the listed tensors. Scales factorially with the number of +terms in the contraction. +- 'dp' A faster (but essentially optimal) algorithm that uses +dynamic programming to exhaustively search all contraction paths +without outer-products. +- 'greedy' An cheap algorithm that heuristically chooses the best +pairwise contraction at each step. Scales linearly in the number of +terms in the contraction. +- 'random-greedy' Run a randomized version of the greedy algorithm +32 times and pick the best path. +- 'random-greedy-128' Run a randomized version of the greedy +algorithm 128 times and pick the best path. +- 'branch-all' An algorithm like optimal but that restricts itself +to searching 'likely' paths. Still scales factorially. +- 'branch-2' An even more restricted version of 'branch-all' that +only searches the best two options at each step. Scales exponentially +with the number of terms in the contraction. +- 'auto' Choose the best of the above algorithms whilst aiming to +keep the path finding time below 1ms. +- 'auto-hq' Aim for a high quality contraction, choosing the best +of the above algorithms whilst aiming to keep the path finding time +below 1sec.

+
+ 		+ required +
memory_limit + - *({None, int, 'max_input'} (default + +
+

None))* - Give the upper bound of the largest intermediate tensor contract will build. +- None or -1 means there is no limit +- max_input means the limit is set as largest input tensor +- a positive integer is taken as an explicit limit on the number of elements

+

The default is None. Note that imposing a limit can make contractions +exponentially slower to perform.

+
+ 		+ required +
- + backend - *(str, optional (default + +
+

auto))* Which library to use to perform the required tensordot, transpose +and einsum calls. Should match the types of arrays supplied, See +:func:contract_expression for generating expressions which convert +numpy arrays to and from the backend library automatically.

+
+ 		+ required +
+ + + +

Returns:

+ + + + + + + + + + + + + +
TypeDescription
+ ArrayType + +
+

The result of the einsum expression.

+
+
+ +
+ Notes +

This function should produce a result identical to that of NumPy's einsum +function. The primary difference is contract will attempt to form +intermediates which reduce the overall scaling of the given einsum contraction. +By default the worst intermediate formed will be equal to that of the largest +input array. For large einsum expressions with many input arrays this can +provide arbitrarily large (1000 fold+) speed improvements.

+

For contractions with just two tensors this function will attempt to use +NumPy's built-in BLAS functionality to ensure that the given operation is +performed optimally. When NumPy is linked to a threaded BLAS, potential +speedups are on the order of 20-100 for a six core machine.

+
+
+ Source code in opt_einsum/contract.py + 
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def contract(*operands_: Any, **kwargs: Any) -> ArrayType:
+    """
+    Evaluates the Einstein summation convention on the operands. A drop in
+    replacement for NumPy's einsum function that optimizes the order of contraction
+    to reduce overall scaling at the cost of several intermediate arrays.
+
+    Parameters:
+        subscripts: *(str)* Specifies the subscripts for summation.
+        \\*operands: *(list of array_like)* hese are the arrays for the operation.
+        out: *(array_like)* A output array in which set the sresulting output.
+        dtype - *(str)* The dtype of the given contraction, see np.einsum.
+        order - *(str)* The order of the resulting contraction, see np.einsum.
+        casting - *(str)* The casting procedure for operations of different dtype, see np.einsum.
+        use_blas - *(bool)* Do you use BLAS for valid operations, may use extra memory for more intermediates.
+        optimize - *(str, list or bool, optional (default: ``auto``))* Choose the type of path.
+            - if a list is given uses this as the path.
+            - `'optimal'` An algorithm that explores all possible ways of
+            contracting the listed tensors. Scales factorially with the number of
+            terms in the contraction.
+            - `'dp'` A faster (but essentially optimal) algorithm that uses
+            dynamic programming to exhaustively search all contraction paths
+            without outer-products.
+            - `'greedy'` An cheap algorithm that heuristically chooses the best
+            pairwise contraction at each step. Scales linearly in the number of
+            terms in the contraction.
+            - `'random-greedy'` Run a randomized version of the greedy algorithm
+            32 times and pick the best path.
+            - `'random-greedy-128'` Run a randomized version of the greedy
+            algorithm 128 times and pick the best path.
+            - `'branch-all'` An algorithm like optimal but that restricts itself
+            to searching 'likely' paths. Still scales factorially.
+            - `'branch-2'` An even more restricted version of 'branch-all' that
+            only searches the best two options at each step. Scales exponentially
+            with the number of terms in the contraction.
+            - `'auto'` Choose the best of the above algorithms whilst aiming to
+            keep the path finding time below 1ms.
+            - `'auto-hq'` Aim for a high quality contraction, choosing the best
+            of the above algorithms whilst aiming to keep the path finding time
+            below 1sec.
+
+        memory_limit - *({None, int, 'max_input'} (default: `None`))* - Give the upper bound of the largest intermediate tensor contract will build.
+            - None or -1 means there is no limit
+            - `max_input` means the limit is set as largest input tensor
+            - a positive integer is taken as an explicit limit on the number of elements
+
+            The default is None. Note that imposing a limit can make contractions
+            exponentially slower to perform.
+
+        - backend - *(str, optional (default: ``auto``))* Which library to use to perform the required ``tensordot``, ``transpose``
+            and ``einsum`` calls. Should match the types of arrays supplied, See
+            :func:`contract_expression` for generating expressions which convert
+            numpy arrays to and from the backend library automatically.
+
+    Returns:
+        The result of the einsum expression.
+
+    Notes:
+        This function should produce a result identical to that of NumPy's einsum
+        function. The primary difference is ``contract`` will attempt to form
+        intermediates which reduce the overall scaling of the given einsum contraction.
+        By default the worst intermediate formed will be equal to that of the largest
+        input array. For large einsum expressions with many input arrays this can
+        provide arbitrarily large (1000 fold+) speed improvements.
+
+        For contractions with just two tensors this function will attempt to use
+        NumPy's built-in BLAS functionality to ensure that the given operation is
+        performed optimally. When NumPy is linked to a threaded BLAS, potential
+        speedups are on the order of 20-100 for a six core machine.
+    """
+    optimize_arg = kwargs.pop("optimize", True)
+    if optimize_arg is True:
+        optimize_arg = "auto"
+
+    valid_einsum_kwargs = ["out", "dtype", "order", "casting"]
+    einsum_kwargs = {k: v for (k, v) in kwargs.items() if k in valid_einsum_kwargs}
+
+    # If no optimization, run pure einsum
+    if optimize_arg is False:
+        return _einsum(*operands_, **einsum_kwargs)
+
+    # Grab non-einsum kwargs
+    use_blas = kwargs.pop("use_blas", True)
+    memory_limit = kwargs.pop("memory_limit", None)
+    backend = kwargs.pop("backend", "auto")
+    gen_expression = kwargs.pop("_gen_expression", False)
+    constants_dict = kwargs.pop("_constants_dict", {})
+
+    # Make sure remaining keywords are valid for einsum
+    unknown_kwargs = [k for (k, v) in kwargs.items() if k not in valid_einsum_kwargs]
+    if len(unknown_kwargs):
+        raise TypeError("Did not understand the following kwargs: {}".format(unknown_kwargs))
+
+    if gen_expression:
+        full_str = operands_[0]
+
+    # Build the contraction list and operand
+    operands: Sequence[ArrayType]
+    contraction_list: ContractionListType
+    operands, contraction_list = contract_path(  # type: ignore
+        *operands_, optimize=optimize_arg, memory_limit=memory_limit, einsum_call=True, use_blas=use_blas
+    )
+
+    # check if performing contraction or just building expression
+    if gen_expression:
+        return ContractExpression(full_str, contraction_list, constants_dict, **einsum_kwargs)
+
+    return _core_contract(operands, contraction_list, backend=backend, **einsum_kwargs)
+
+
+
+ +
+ + +
+ + + +

+ contract_expression(subscripts, *shapes, **kwargs) + +

+ + +
+ +

Generate a reusable expression for a given contraction with +specific shapes, which can, for example, be cached.

+

Parameters:

+
    +
  • subscripts - (str) Specifies the subscripts for summation.
    • +
  • shapes - (sequence of integer tuples) Shapes of the arrays to optimize the contraction for.
    • +
  • constants - (sequence of int, optional) The indices of any constant arguments in shapes, in which case the + actual array should be supplied at that position rather than just a + shape. If these are specified, then constant parts of the contraction + between calls will be reused. Additionally, if a GPU-enabled backend is + used for example, then the constant tensors will be kept on the GPU, + minimizing transfers.
    • +
  • kwargs - Passed on to contract_path or einsum. See contract.
    • +
+

Returns:

+
    +
  • expr - (ContractExpression) Callable with signature expr(*arrays, out=None, backend='numpy') where the array's shapes should match shapes.
    • +
+

Notes:

+
    +
  • The out keyword argument should be supplied to the generated expression + rather than this function.
    • +
  • The backend keyword argument should also be supplied to the generated + expression. If numpy arrays are supplied, if possible they will be + converted to and back from the correct backend array type.
    • +
  • The generated expression will work with any arrays which have + the same rank (number of dimensions) as the original shapes, however, if + the actual sizes are different, the expression may no longer be optimal.
    • +
  • Constant operations will be computed upon the first call with a particular + backend, then subsequently reused.
    • +
+

Examples:

+

Basic usage:

+
expr = contract_expression("ab,bc->ac", (3, 4), (4, 5))
+a, b = np.random.rand(3, 4), np.random.rand(4, 5)
+c = expr(a, b)
+np.allclose(c, a @ b)
+#> True
+
+

Supply a as a constant:

+
expr = contract_expression("ab,bc->ac", a, (4, 5), constants=[0])
+expr
+#> <ContractExpression('[ab],bc->ac', constants=[0])>
+
+c = expr(b)
+np.allclose(c, a @ b)
+#> True
+
+ +
+ Source code in opt_einsum/contract.py + 
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def contract_expression(subscripts: str, *shapes: PathType, **kwargs: Any) -> Any:
+    """Generate a reusable expression for a given contraction with
+    specific shapes, which can, for example, be cached.
+
+    **Parameters:**
+
+    - **subscripts** - *(str)* Specifies the subscripts for summation.
+    - **shapes** - *(sequence of integer tuples)* Shapes of the arrays to optimize the contraction for.
+    - **constants** - *(sequence of int, optional)* The indices of any constant arguments in `shapes`, in which case the
+        actual array should be supplied at that position rather than just a
+        shape. If these are specified, then constant parts of the contraction
+        between calls will be reused. Additionally, if a GPU-enabled backend is
+        used for example, then the constant tensors will be kept on the GPU,
+        minimizing transfers.
+    - **kwargs** - Passed on to `contract_path` or `einsum`. See `contract`.
+
+    **Returns:**
+
+    - **expr** - *(ContractExpression)* Callable with signature `expr(*arrays, out=None, backend='numpy')` where the array's shapes should match `shapes`.
+
+    **Notes:**
+
+    - The `out` keyword argument should be supplied to the generated expression
+      rather than this function.
+    - The `backend` keyword argument should also be supplied to the generated
+      expression. If numpy arrays are supplied, if possible they will be
+      converted to and back from the correct backend array type.
+    - The generated expression will work with any arrays which have
+      the same rank (number of dimensions) as the original shapes, however, if
+      the actual sizes are different, the expression may no longer be optimal.
+    - Constant operations will be computed upon the first call with a particular
+      backend, then subsequently reused.
+
+    **Examples:**
+
+    Basic usage:
+
+    ```python
+    expr = contract_expression("ab,bc->ac", (3, 4), (4, 5))
+    a, b = np.random.rand(3, 4), np.random.rand(4, 5)
+    c = expr(a, b)
+    np.allclose(c, a @ b)
+    #> True
+    ```
+
+    Supply `a` as a constant:
+
+    ```python
+    expr = contract_expression("ab,bc->ac", a, (4, 5), constants=[0])
+    expr
+    #> <ContractExpression('[ab],bc->ac', constants=[0])>
+
+    c = expr(b)
+    np.allclose(c, a @ b)
+    #> True
+    ```
+
+    """
+    if not kwargs.get("optimize", True):
+        raise ValueError("Can only generate expressions for optimized contractions.")
+
+    for arg in ("out", "backend"):
+        if kwargs.get(arg, None) is not None:
+            raise ValueError(
+                "'{}' should only be specified when calling a "
+                "`ContractExpression`, not when building it.".format(arg)
+            )
+
+    if not isinstance(subscripts, str):
+        subscripts, shapes = parser.convert_interleaved_input((subscripts,) + shapes)
+
+    kwargs["_gen_expression"] = True
+
+    # build dict of constant indices mapped to arrays
+    constants = kwargs.pop("constants", ())
+    constants_dict = {i: shapes[i] for i in constants}
+    kwargs["_constants_dict"] = constants_dict
+
+    # apart from constant arguments, make dummy arrays
+    dummy_arrays = [s if i in constants else shape_only(s) for i, s in enumerate(shapes)]
+
+    return contract(subscripts, *dummy_arrays, **kwargs)
+
+
+
+ +
+ + +
+ + + +

+ contract_path(*operands_, **kwargs) + +

+ + +
+ +

Find a contraction order path, without performing the contraction.

+

Parameters:

+
    +
  • subscripts - (str) Specifies the subscripts for summation.
    • +
  • *operands - (list of array_like) these are the arrays for the operation.
    • +
  • use_blas - (bool) Do you use BLAS for valid operations, may use extra memory for more intermediates.
    • +
  • +

    optimize - (str, list or bool, optional (default: auto)) Choose the type of path.

    +
      +
    • if a list is given uses this as the path.
      • +
    • 'optimal' An algorithm that explores all possible ways of + contracting the listed tensors. Scales factorially with the number of + terms in the contraction.
      • +
    • 'dp' A faster (but essentially optimal) algorithm that uses + dynamic programming to exhaustively search all contraction paths + without outer-products.
      • +
    • 'greedy' An cheap algorithm that heuristically chooses the best + pairwise contraction at each step. Scales linearly in the number of + terms in the contraction.
      • +
    • 'random-greedy' Run a randomized version of the greedy algorithm + 32 times and pick the best path.
      • +
    • 'random-greedy-128' Run a randomized version of the greedy + algorithm 128 times and pick the best path.
      • +
    • 'branch-all' An algorithm like optimal but that restricts itself + to searching 'likely' paths. Still scales factorially.
      • +
    • 'branch-2' An even more restricted version of 'branch-all' that + only searches the best two options at each step. Scales exponentially + with the number of terms in the contraction.
      • +
    • 'auto' Choose the best of the above algorithms whilst aiming to + keep the path finding time below 1ms.
      • +
    • 'auto-hq' Aim for a high quality contraction, choosing the best + of the above algorithms whilst aiming to keep the path finding time + below 1sec.
      • +
    +
    • +
  • +

    memory_limit - ({None, int, 'max_input'} (default: None)) - Give the upper bound of the largest intermediate tensor contract will build.

    +
      +
    • None or -1 means there is no limit
      • +
    • max_input means the limit is set as largest input tensor
      • +
    • a positive integer is taken as an explicit limit on the number of elements
      • +
    +

    The default is None. Note that imposing a limit can make contractions +exponentially slower to perform.

    +
    • +
  • +

    shapes - (bool, optional) Whether contract_path should assume arrays (the default) or array shapes have been supplied.

    +
    • +
+

Returns:

+
    +
  • path - (list of tuples) The einsum path
    • +
  • PathInfo - (str) A printable object containing various information about the path found.
    • +
+

Notes:

+

The resulting path indicates which terms of the input contraction should be +contracted first, the result of this contraction is then appended to the end of +the contraction list.

+

Examples:

+

We can begin with a chain dot example. In this case, it is optimal to +contract the b and c tensors represented by the first element of the path (1, +2). The resulting tensor is added to the end of the contraction and the +remaining contraction, (0, 1), is then executed.

+
a = np.random.rand(2, 2)
+b = np.random.rand(2, 5)
+c = np.random.rand(5, 2)
+path_info = opt_einsum.contract_path('ij,jk,kl->il', a, b, c)
+print(path_info[0])
+#> [(1, 2), (0, 1)]
+print(path_info[1])
+#>   Complete contraction:  ij,jk,kl->il
+#>          Naive scaling:  4
+#>      Optimized scaling:  3
+#>       Naive FLOP count:  1.600e+02
+#>   Optimized FLOP count:  5.600e+01
+#>    Theoretical speedup:  2.857
+#>   Largest intermediate:  4.000e+00 elements
+#> -------------------------------------------------------------------------
+#> scaling                  current                                remaining
+#> -------------------------------------------------------------------------
+#>    3                   kl,jk->jl                                ij,jl->il
+#>    3                   jl,ij->il                                   il->il
+
+

A more complex index transformation example.

+
I = np.random.rand(10, 10, 10, 10)
+C = np.random.rand(10, 10)
+path_info = oe.contract_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C)
+
+print(path_info[0])
+#> [(0, 2), (0, 3), (0, 2), (0, 1)]
+print(path_info[1])
+#>   Complete contraction:  ea,fb,abcd,gc,hd->efgh
+#>          Naive scaling:  8
+#>      Optimized scaling:  5
+#>       Naive FLOP count:  8.000e+08
+#>   Optimized FLOP count:  8.000e+05
+#>    Theoretical speedup:  1000.000
+#>   Largest intermediate:  1.000e+04 elements
+#> --------------------------------------------------------------------------
+#> scaling                  current                                remaining
+#> --------------------------------------------------------------------------
+#>    5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+#>    5               bcde,fb->cdef                         gc,hd,cdef->efgh
+#>    5               cdef,gc->defg                            hd,defg->efgh
+#>    5               defg,hd->efgh                               efgh->efgh
+
+ +
+ Source code in opt_einsum/contract.py + 
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def contract_path(*operands_: Any, **kwargs: Any) -> Tuple[PathType, PathInfo]:
+    """
+    Find a contraction order `path`, without performing the contraction.
+
+    **Parameters:**
+
+    - **subscripts** - *(str)* Specifies the subscripts for summation.
+    - **\\*operands** - *(list of array_like)* these are the arrays for the operation.
+    - **use_blas** - *(bool)* Do you use BLAS for valid operations, may use extra memory for more intermediates.
+    - **optimize** - *(str, list or bool, optional (default: `auto`))* Choose the type of path.
+
+        - if a list is given uses this as the path.
+        - `'optimal'` An algorithm that explores all possible ways of
+          contracting the listed tensors. Scales factorially with the number of
+          terms in the contraction.
+        - `'dp'` A faster (but essentially optimal) algorithm that uses
+          dynamic programming to exhaustively search all contraction paths
+          without outer-products.
+        - `'greedy'` An cheap algorithm that heuristically chooses the best
+          pairwise contraction at each step. Scales linearly in the number of
+          terms in the contraction.
+        - `'random-greedy'` Run a randomized version of the greedy algorithm
+          32 times and pick the best path.
+        - `'random-greedy-128'` Run a randomized version of the greedy
+          algorithm 128 times and pick the best path.
+        - `'branch-all'` An algorithm like optimal but that restricts itself
+          to searching 'likely' paths. Still scales factorially.
+        - `'branch-2'` An even more restricted version of 'branch-all' that
+          only searches the best two options at each step. Scales exponentially
+          with the number of terms in the contraction.
+        - `'auto'` Choose the best of the above algorithms whilst aiming to
+          keep the path finding time below 1ms.
+        - `'auto-hq'` Aim for a high quality contraction, choosing the best
+          of the above algorithms whilst aiming to keep the path finding time
+          below 1sec.
+
+    - **memory_limit** - *({None, int, 'max_input'} (default: `None`))* - Give the upper bound of the largest intermediate tensor contract will build.
+
+        - None or -1 means there is no limit
+        - `max_input` means the limit is set as largest input tensor
+        - a positive integer is taken as an explicit limit on the number of elements
+
+        The default is None. Note that imposing a limit can make contractions
+        exponentially slower to perform.
+
+    - **shapes** - *(bool, optional)* Whether ``contract_path`` should assume arrays (the default) or array shapes have been supplied.
+
+    **Returns:**
+
+    - **path** - *(list of tuples)* The einsum path
+    - **PathInfo** - *(str)* A printable object containing various information about the path found.
+
+    **Notes:**
+
+    The resulting path indicates which terms of the input contraction should be
+    contracted first, the result of this contraction is then appended to the end of
+    the contraction list.
+
+    **Examples:**
+
+    We can begin with a chain dot example. In this case, it is optimal to
+    contract the b and c tensors represented by the first element of the path (1,
+    2). The resulting tensor is added to the end of the contraction and the
+    remaining contraction, `(0, 1)`, is then executed.
+
+    ```python
+    a = np.random.rand(2, 2)
+    b = np.random.rand(2, 5)
+    c = np.random.rand(5, 2)
+    path_info = opt_einsum.contract_path('ij,jk,kl->il', a, b, c)
+    print(path_info[0])
+    #> [(1, 2), (0, 1)]
+    print(path_info[1])
+    #>   Complete contraction:  ij,jk,kl->il
+    #>          Naive scaling:  4
+    #>      Optimized scaling:  3
+    #>       Naive FLOP count:  1.600e+02
+    #>   Optimized FLOP count:  5.600e+01
+    #>    Theoretical speedup:  2.857
+    #>   Largest intermediate:  4.000e+00 elements
+    #> -------------------------------------------------------------------------
+    #> scaling                  current                                remaining
+    #> -------------------------------------------------------------------------
+    #>    3                   kl,jk->jl                                ij,jl->il
+    #>    3                   jl,ij->il                                   il->il
+    ```
+
+    A more complex index transformation example.
+
+    ```python
+    I = np.random.rand(10, 10, 10, 10)
+    C = np.random.rand(10, 10)
+    path_info = oe.contract_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C)
+
+    print(path_info[0])
+    #> [(0, 2), (0, 3), (0, 2), (0, 1)]
+    print(path_info[1])
+    #>   Complete contraction:  ea,fb,abcd,gc,hd->efgh
+    #>          Naive scaling:  8
+    #>      Optimized scaling:  5
+    #>       Naive FLOP count:  8.000e+08
+    #>   Optimized FLOP count:  8.000e+05
+    #>    Theoretical speedup:  1000.000
+    #>   Largest intermediate:  1.000e+04 elements
+    #> --------------------------------------------------------------------------
+    #> scaling                  current                                remaining
+    #> --------------------------------------------------------------------------
+    #>    5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+    #>    5               bcde,fb->cdef                         gc,hd,cdef->efgh
+    #>    5               cdef,gc->defg                            hd,defg->efgh
+    #>    5               defg,hd->efgh                               efgh->efgh
+    ```
+    """
+
+    # Make sure all keywords are valid
+    unknown_kwargs = set(kwargs) - _VALID_CONTRACT_KWARGS
+    if len(unknown_kwargs):
+        raise TypeError("einsum_path: Did not understand the following kwargs: {}".format(unknown_kwargs))
+
+    path_type = kwargs.pop("optimize", "auto")
+
+    memory_limit = kwargs.pop("memory_limit", None)
+    shapes = kwargs.pop("shapes", False)
+
+    # Hidden option, only einsum should call this
+    einsum_call_arg = kwargs.pop("einsum_call", False)
+    use_blas = kwargs.pop("use_blas", True)
+
+    # Python side parsing
+    input_subscripts, output_subscript, operands = parser.parse_einsum_input(operands_, shapes=shapes)
+
+    # Build a few useful list and sets
+    input_list = input_subscripts.split(",")
+    input_sets = [frozenset(x) for x in input_list]
+    if shapes:
+        input_shapes = operands
+    else:
+        input_shapes = [x.shape for x in operands]
+    output_set = frozenset(output_subscript)
+    indices = frozenset(input_subscripts.replace(",", ""))
+
+    # Get length of each unique dimension and ensure all dimensions are correct
+    size_dict: Dict[str, int] = {}
+    for tnum, term in enumerate(input_list):
+        sh = input_shapes[tnum]
+
+        if len(sh) != len(term):
+            raise ValueError(
+                "Einstein sum subscript '{}' does not contain the "
+                "correct number of indices for operand {}.".format(input_list[tnum], tnum)
+            )
+        for cnum, char in enumerate(term):
+            dim = int(sh[cnum])
+
+            if char in size_dict:
+                # For broadcasting cases we always want the largest dim size
+                if size_dict[char] == 1:
+                    size_dict[char] = dim
+                elif dim not in (1, size_dict[char]):
+                    raise ValueError(
+                        "Size of label '{}' for operand {} ({}) does not match previous "
+                        "terms ({}).".format(char, tnum, size_dict[char], dim)
+                    )
+            else:
+                size_dict[char] = dim
+
+    # Compute size of each input array plus the output array
+    size_list = [helpers.compute_size_by_dict(term, size_dict) for term in input_list + [output_subscript]]
+    memory_arg = _choose_memory_arg(memory_limit, size_list)
+
+    num_ops = len(input_list)
+
+    # Compute naive cost
+    # This is not quite right, need to look into exactly how einsum does this
+    # indices_in_input = input_subscripts.replace(',', '')
+
+    inner_product = (sum(len(x) for x in input_sets) - len(indices)) > 0
+    naive_cost = helpers.flop_count(indices, inner_product, num_ops, size_dict)
+
+    # Compute the path
+    if not isinstance(path_type, (str, paths.PathOptimizer)):
+        # Custom path supplied
+        path = path_type
+    elif num_ops <= 2:
+        # Nothing to be optimized
+        path = [tuple(range(num_ops))]
+    elif isinstance(path_type, paths.PathOptimizer):
+        # Custom path optimizer supplied
+        path = path_type(input_sets, output_set, size_dict, memory_arg)
+    else:
+        path_optimizer = paths.get_path_fn(path_type)
+        path = path_optimizer(input_sets, output_set, size_dict, memory_arg)
+
+    cost_list = []
+    scale_list = []
+    size_list = []
+    contraction_list = []
+
+    # Build contraction tuple (positions, gemm, einsum_str, remaining)
+    for cnum, contract_inds in enumerate(path):
+        # Make sure we remove inds from right to left
+        contract_inds = tuple(sorted(list(contract_inds), reverse=True))
+
+        contract_tuple = helpers.find_contraction(contract_inds, input_sets, output_set)
+        out_inds, input_sets, idx_removed, idx_contract = contract_tuple
+
+        # Compute cost, scale, and size
+        cost = helpers.flop_count(idx_contract, bool(idx_removed), len(contract_inds), size_dict)
+        cost_list.append(cost)
+        scale_list.append(len(idx_contract))
+        size_list.append(helpers.compute_size_by_dict(out_inds, size_dict))
+
+        tmp_inputs = [input_list.pop(x) for x in contract_inds]
+        tmp_shapes = [input_shapes.pop(x) for x in contract_inds]
+
+        if use_blas:
+            do_blas = blas.can_blas(tmp_inputs, "".join(out_inds), idx_removed, tmp_shapes)
+        else:
+            do_blas = False
+
+        # Last contraction
+        if (cnum - len(path)) == -1:
+            idx_result = output_subscript
+        else:
+            # use tensordot order to minimize transpositions
+            all_input_inds = "".join(tmp_inputs)
+            idx_result = "".join(sorted(out_inds, key=all_input_inds.find))
+
+        shp_result = parser.find_output_shape(tmp_inputs, tmp_shapes, idx_result)
+
+        input_list.append(idx_result)
+        input_shapes.append(shp_result)
+
+        einsum_str = ",".join(tmp_inputs) + "->" + idx_result
+
+        # for large expressions saving the remaining terms at each step can
+        # incur a large memory footprint - and also be messy to print
+        if len(input_list) <= 20:
+            remaining: Optional[Tuple[str, ...]] = tuple(input_list)
+        else:
+            remaining = None
+
+        contraction = (contract_inds, idx_removed, einsum_str, remaining, do_blas)
+        contraction_list.append(contraction)
+
+    opt_cost = sum(cost_list)
+
+    if einsum_call_arg:
+        return operands, contraction_list  # type: ignore
+
+    path_print = PathInfo(
+        contraction_list,
+        input_subscripts,
+        output_subscript,
+        indices,
+        path,
+        scale_list,
+        naive_cost,
+        opt_cost,
+        size_list,
+        size_dict,
+    )
+
+    return path, path_print
+
+
+
+ +
+ + +
+ + + +

+ format_const_einsum_str(einsum_str, constants) + +

+ + +
+ +

Add brackets to the constant terms in einsum_str. For example:

+
>>> format_const_einsum_str('ab,bc,cd->ad', [0, 2])
+'bc,[ab,cd]->ad'
+
+ +

No-op if there are no constants.

+ +
+ Source code in opt_einsum/contract.py + 
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def format_const_einsum_str(einsum_str: str, constants: Iterable[int]) -> str:
+    """Add brackets to the constant terms in ``einsum_str``. For example:
+
+        >>> format_const_einsum_str('ab,bc,cd->ad', [0, 2])
+        'bc,[ab,cd]->ad'
+
+    No-op if there are no constants.
+    """
+    if not constants:
+        return einsum_str
+
+    if "->" in einsum_str:
+        lhs, rhs = einsum_str.split("->")
+        arrow = "->"
+    else:
+        lhs, rhs, arrow = einsum_str, "", ""
+
+    wrapped_terms = ["[{}]".format(t) if i in constants else t for i, t in enumerate(lhs.split(","))]
+
+    formatted_einsum_str = "{}{}{}".format(",".join(wrapped_terms), arrow, rhs)
+
+    # merge adjacent constants
+    formatted_einsum_str = formatted_einsum_str.replace("],[", ",")
+    return formatted_einsum_str
+
+
+
+ +
+ + +
+ + + +

+ parse_backend(arrays, backend) + +

+ + +
+ +

Find out what backend we should use, dipatching based on the first +array if backend='auto' is specified.

+ +
+ Source code in opt_einsum/contract.py + 
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def parse_backend(arrays: Sequence[ArrayType], backend: Optional[str]) -> str:
+    """Find out what backend we should use, dipatching based on the first
+    array if ``backend='auto'`` is specified.
+    """
+    if (backend != "auto") and (backend is not None):
+        return backend
+    backend = infer_backend(arrays[0])
+
+    # some arrays will be defined in modules that don't implement tensordot
+    # etc. so instead default to numpy
+    if not backends.has_tensordot(backend):
+        return "numpy"
+
+    return backend
+
+
+
+ +
+ + +
+ + + +

+ shape_only(shape) + +

+ + +
+ +

Dummy numpy.ndarray which has a shape only - for generating +contract expressions.

+ +
+ Source code in opt_einsum/contract.py + 
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def shape_only(shape: PathType) -> Shaped:
+    """Dummy ``numpy.ndarray`` which has a shape only - for generating
+    contract expressions.
+    """
+    return Shaped(shape)
+
+
+
+ +
+ + + +
+ +
+ +

opt_einsum.contract_path

+ + + +
+ + + + + +
+ +

Find a contraction order path, without performing the contraction.

+

Parameters:

+
    +
  • subscripts - (str) Specifies the subscripts for summation.
    • +
  • *operands - (list of array_like) these are the arrays for the operation.
    • +
  • use_blas - (bool) Do you use BLAS for valid operations, may use extra memory for more intermediates.
    • +
  • +

    optimize - (str, list or bool, optional (default: auto)) Choose the type of path.

    +
      +
    • if a list is given uses this as the path.
      • +
    • 'optimal' An algorithm that explores all possible ways of + contracting the listed tensors. Scales factorially with the number of + terms in the contraction.
      • +
    • 'dp' A faster (but essentially optimal) algorithm that uses + dynamic programming to exhaustively search all contraction paths + without outer-products.
      • +
    • 'greedy' An cheap algorithm that heuristically chooses the best + pairwise contraction at each step. Scales linearly in the number of + terms in the contraction.
      • +
    • 'random-greedy' Run a randomized version of the greedy algorithm + 32 times and pick the best path.
      • +
    • 'random-greedy-128' Run a randomized version of the greedy + algorithm 128 times and pick the best path.
      • +
    • 'branch-all' An algorithm like optimal but that restricts itself + to searching 'likely' paths. Still scales factorially.
      • +
    • 'branch-2' An even more restricted version of 'branch-all' that + only searches the best two options at each step. Scales exponentially + with the number of terms in the contraction.
      • +
    • 'auto' Choose the best of the above algorithms whilst aiming to + keep the path finding time below 1ms.
      • +
    • 'auto-hq' Aim for a high quality contraction, choosing the best + of the above algorithms whilst aiming to keep the path finding time + below 1sec.
      • +
    +
    • +
  • +

    memory_limit - ({None, int, 'max_input'} (default: None)) - Give the upper bound of the largest intermediate tensor contract will build.

    +
      +
    • None or -1 means there is no limit
      • +
    • max_input means the limit is set as largest input tensor
      • +
    • a positive integer is taken as an explicit limit on the number of elements
      • +
    +

    The default is None. Note that imposing a limit can make contractions +exponentially slower to perform.

    +
    • +
  • +

    shapes - (bool, optional) Whether contract_path should assume arrays (the default) or array shapes have been supplied.

    +
    • +
+

Returns:

+
    +
  • path - (list of tuples) The einsum path
    • +
  • PathInfo - (str) A printable object containing various information about the path found.
    • +
+

Notes:

+

The resulting path indicates which terms of the input contraction should be +contracted first, the result of this contraction is then appended to the end of +the contraction list.

+

Examples:

+

We can begin with a chain dot example. In this case, it is optimal to +contract the b and c tensors represented by the first element of the path (1, +2). The resulting tensor is added to the end of the contraction and the +remaining contraction, (0, 1), is then executed.

+
a = np.random.rand(2, 2)
+b = np.random.rand(2, 5)
+c = np.random.rand(5, 2)
+path_info = opt_einsum.contract_path('ij,jk,kl->il', a, b, c)
+print(path_info[0])
+#> [(1, 2), (0, 1)]
+print(path_info[1])
+#>   Complete contraction:  ij,jk,kl->il
+#>          Naive scaling:  4
+#>      Optimized scaling:  3
+#>       Naive FLOP count:  1.600e+02
+#>   Optimized FLOP count:  5.600e+01
+#>    Theoretical speedup:  2.857
+#>   Largest intermediate:  4.000e+00 elements
+#> -------------------------------------------------------------------------
+#> scaling                  current                                remaining
+#> -------------------------------------------------------------------------
+#>    3                   kl,jk->jl                                ij,jl->il
+#>    3                   jl,ij->il                                   il->il
+
+

A more complex index transformation example.

+
I = np.random.rand(10, 10, 10, 10)
+C = np.random.rand(10, 10)
+path_info = oe.contract_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C)
+
+print(path_info[0])
+#> [(0, 2), (0, 3), (0, 2), (0, 1)]
+print(path_info[1])
+#>   Complete contraction:  ea,fb,abcd,gc,hd->efgh
+#>          Naive scaling:  8
+#>      Optimized scaling:  5
+#>       Naive FLOP count:  8.000e+08
+#>   Optimized FLOP count:  8.000e+05
+#>    Theoretical speedup:  1000.000
+#>   Largest intermediate:  1.000e+04 elements
+#> --------------------------------------------------------------------------
+#> scaling                  current                                remaining
+#> --------------------------------------------------------------------------
+#>    5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+#>    5               bcde,fb->cdef                         gc,hd,cdef->efgh
+#>    5               cdef,gc->defg                            hd,defg->efgh
+#>    5               defg,hd->efgh                               efgh->efgh
+
+ +
+ Source code in opt_einsum/contract.py + 
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def contract_path(*operands_: Any, **kwargs: Any) -> Tuple[PathType, PathInfo]:
+    """
+    Find a contraction order `path`, without performing the contraction.
+
+    **Parameters:**
+
+    - **subscripts** - *(str)* Specifies the subscripts for summation.
+    - **\\*operands** - *(list of array_like)* these are the arrays for the operation.
+    - **use_blas** - *(bool)* Do you use BLAS for valid operations, may use extra memory for more intermediates.
+    - **optimize** - *(str, list or bool, optional (default: `auto`))* Choose the type of path.
+
+        - if a list is given uses this as the path.
+        - `'optimal'` An algorithm that explores all possible ways of
+          contracting the listed tensors. Scales factorially with the number of
+          terms in the contraction.
+        - `'dp'` A faster (but essentially optimal) algorithm that uses
+          dynamic programming to exhaustively search all contraction paths
+          without outer-products.
+        - `'greedy'` An cheap algorithm that heuristically chooses the best
+          pairwise contraction at each step. Scales linearly in the number of
+          terms in the contraction.
+        - `'random-greedy'` Run a randomized version of the greedy algorithm
+          32 times and pick the best path.
+        - `'random-greedy-128'` Run a randomized version of the greedy
+          algorithm 128 times and pick the best path.
+        - `'branch-all'` An algorithm like optimal but that restricts itself
+          to searching 'likely' paths. Still scales factorially.
+        - `'branch-2'` An even more restricted version of 'branch-all' that
+          only searches the best two options at each step. Scales exponentially
+          with the number of terms in the contraction.
+        - `'auto'` Choose the best of the above algorithms whilst aiming to
+          keep the path finding time below 1ms.
+        - `'auto-hq'` Aim for a high quality contraction, choosing the best
+          of the above algorithms whilst aiming to keep the path finding time
+          below 1sec.
+
+    - **memory_limit** - *({None, int, 'max_input'} (default: `None`))* - Give the upper bound of the largest intermediate tensor contract will build.
+
+        - None or -1 means there is no limit
+        - `max_input` means the limit is set as largest input tensor
+        - a positive integer is taken as an explicit limit on the number of elements
+
+        The default is None. Note that imposing a limit can make contractions
+        exponentially slower to perform.
+
+    - **shapes** - *(bool, optional)* Whether ``contract_path`` should assume arrays (the default) or array shapes have been supplied.
+
+    **Returns:**
+
+    - **path** - *(list of tuples)* The einsum path
+    - **PathInfo** - *(str)* A printable object containing various information about the path found.
+
+    **Notes:**
+
+    The resulting path indicates which terms of the input contraction should be
+    contracted first, the result of this contraction is then appended to the end of
+    the contraction list.
+
+    **Examples:**
+
+    We can begin with a chain dot example. In this case, it is optimal to
+    contract the b and c tensors represented by the first element of the path (1,
+    2). The resulting tensor is added to the end of the contraction and the
+    remaining contraction, `(0, 1)`, is then executed.
+
+    ```python
+    a = np.random.rand(2, 2)
+    b = np.random.rand(2, 5)
+    c = np.random.rand(5, 2)
+    path_info = opt_einsum.contract_path('ij,jk,kl->il', a, b, c)
+    print(path_info[0])
+    #> [(1, 2), (0, 1)]
+    print(path_info[1])
+    #>   Complete contraction:  ij,jk,kl->il
+    #>          Naive scaling:  4
+    #>      Optimized scaling:  3
+    #>       Naive FLOP count:  1.600e+02
+    #>   Optimized FLOP count:  5.600e+01
+    #>    Theoretical speedup:  2.857
+    #>   Largest intermediate:  4.000e+00 elements
+    #> -------------------------------------------------------------------------
+    #> scaling                  current                                remaining
+    #> -------------------------------------------------------------------------
+    #>    3                   kl,jk->jl                                ij,jl->il
+    #>    3                   jl,ij->il                                   il->il
+    ```
+
+    A more complex index transformation example.
+
+    ```python
+    I = np.random.rand(10, 10, 10, 10)
+    C = np.random.rand(10, 10)
+    path_info = oe.contract_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C)
+
+    print(path_info[0])
+    #> [(0, 2), (0, 3), (0, 2), (0, 1)]
+    print(path_info[1])
+    #>   Complete contraction:  ea,fb,abcd,gc,hd->efgh
+    #>          Naive scaling:  8
+    #>      Optimized scaling:  5
+    #>       Naive FLOP count:  8.000e+08
+    #>   Optimized FLOP count:  8.000e+05
+    #>    Theoretical speedup:  1000.000
+    #>   Largest intermediate:  1.000e+04 elements
+    #> --------------------------------------------------------------------------
+    #> scaling                  current                                remaining
+    #> --------------------------------------------------------------------------
+    #>    5               abcd,ea->bcde                      fb,gc,hd,bcde->efgh
+    #>    5               bcde,fb->cdef                         gc,hd,cdef->efgh
+    #>    5               cdef,gc->defg                            hd,defg->efgh
+    #>    5               defg,hd->efgh                               efgh->efgh
+    ```
+    """
+
+    # Make sure all keywords are valid
+    unknown_kwargs = set(kwargs) - _VALID_CONTRACT_KWARGS
+    if len(unknown_kwargs):
+        raise TypeError("einsum_path: Did not understand the following kwargs: {}".format(unknown_kwargs))
+
+    path_type = kwargs.pop("optimize", "auto")
+
+    memory_limit = kwargs.pop("memory_limit", None)
+    shapes = kwargs.pop("shapes", False)
+
+    # Hidden option, only einsum should call this
+    einsum_call_arg = kwargs.pop("einsum_call", False)
+    use_blas = kwargs.pop("use_blas", True)
+
+    # Python side parsing
+    input_subscripts, output_subscript, operands = parser.parse_einsum_input(operands_, shapes=shapes)
+
+    # Build a few useful list and sets
+    input_list = input_subscripts.split(",")
+    input_sets = [frozenset(x) for x in input_list]
+    if shapes:
+        input_shapes = operands
+    else:
+        input_shapes = [x.shape for x in operands]
+    output_set = frozenset(output_subscript)
+    indices = frozenset(input_subscripts.replace(",", ""))
+
+    # Get length of each unique dimension and ensure all dimensions are correct
+    size_dict: Dict[str, int] = {}
+    for tnum, term in enumerate(input_list):
+        sh = input_shapes[tnum]
+
+        if len(sh) != len(term):
+            raise ValueError(
+                "Einstein sum subscript '{}' does not contain the "
+                "correct number of indices for operand {}.".format(input_list[tnum], tnum)
+            )
+        for cnum, char in enumerate(term):
+            dim = int(sh[cnum])
+
+            if char in size_dict:
+                # For broadcasting cases we always want the largest dim size
+                if size_dict[char] == 1:
+                    size_dict[char] = dim
+                elif dim not in (1, size_dict[char]):
+                    raise ValueError(
+                        "Size of label '{}' for operand {} ({}) does not match previous "
+                        "terms ({}).".format(char, tnum, size_dict[char], dim)
+                    )
+            else:
+                size_dict[char] = dim
+
+    # Compute size of each input array plus the output array
+    size_list = [helpers.compute_size_by_dict(term, size_dict) for term in input_list + [output_subscript]]
+    memory_arg = _choose_memory_arg(memory_limit, size_list)
+
+    num_ops = len(input_list)
+
+    # Compute naive cost
+    # This is not quite right, need to look into exactly how einsum does this
+    # indices_in_input = input_subscripts.replace(',', '')
+
+    inner_product = (sum(len(x) for x in input_sets) - len(indices)) > 0
+    naive_cost = helpers.flop_count(indices, inner_product, num_ops, size_dict)
+
+    # Compute the path
+    if not isinstance(path_type, (str, paths.PathOptimizer)):
+        # Custom path supplied
+        path = path_type
+    elif num_ops <= 2:
+        # Nothing to be optimized
+        path = [tuple(range(num_ops))]
+    elif isinstance(path_type, paths.PathOptimizer):
+        # Custom path optimizer supplied
+        path = path_type(input_sets, output_set, size_dict, memory_arg)
+    else:
+        path_optimizer = paths.get_path_fn(path_type)
+        path = path_optimizer(input_sets, output_set, size_dict, memory_arg)
+
+    cost_list = []
+    scale_list = []
+    size_list = []
+    contraction_list = []
+
+    # Build contraction tuple (positions, gemm, einsum_str, remaining)
+    for cnum, contract_inds in enumerate(path):
+        # Make sure we remove inds from right to left
+        contract_inds = tuple(sorted(list(contract_inds), reverse=True))
+
+        contract_tuple = helpers.find_contraction(contract_inds, input_sets, output_set)
+        out_inds, input_sets, idx_removed, idx_contract = contract_tuple
+
+        # Compute cost, scale, and size
+        cost = helpers.flop_count(idx_contract, bool(idx_removed), len(contract_inds), size_dict)
+        cost_list.append(cost)
+        scale_list.append(len(idx_contract))
+        size_list.append(helpers.compute_size_by_dict(out_inds, size_dict))
+
+        tmp_inputs = [input_list.pop(x) for x in contract_inds]
+        tmp_shapes = [input_shapes.pop(x) for x in contract_inds]
+
+        if use_blas:
+            do_blas = blas.can_blas(tmp_inputs, "".join(out_inds), idx_removed, tmp_shapes)
+        else:
+            do_blas = False
+
+        # Last contraction
+        if (cnum - len(path)) == -1:
+            idx_result = output_subscript
+        else:
+            # use tensordot order to minimize transpositions
+            all_input_inds = "".join(tmp_inputs)
+            idx_result = "".join(sorted(out_inds, key=all_input_inds.find))
+
+        shp_result = parser.find_output_shape(tmp_inputs, tmp_shapes, idx_result)
+
+        input_list.append(idx_result)
+        input_shapes.append(shp_result)
+
+        einsum_str = ",".join(tmp_inputs) + "->" + idx_result
+
+        # for large expressions saving the remaining terms at each step can
+        # incur a large memory footprint - and also be messy to print
+        if len(input_list) <= 20:
+            remaining: Optional[Tuple[str, ...]] = tuple(input_list)
+        else:
+            remaining = None
+
+        contraction = (contract_inds, idx_removed, einsum_str, remaining, do_blas)
+        contraction_list.append(contraction)
+
+    opt_cost = sum(cost_list)
+
+    if einsum_call_arg:
+        return operands, contraction_list  # type: ignore
+
+    path_print = PathInfo(
+        contraction_list,
+        input_subscripts,
+        output_subscript,
+        indices,
+        path,
+        scale_list,
+        naive_cost,
+        opt_cost,
+        size_list,
+        size_dict,
+    )
+
+    return path, path_print
+
+
+
+ +

opt_einsum.contract_expression

+ + + +
+ + + + + +
+ +

Generate a reusable expression for a given contraction with +specific shapes, which can, for example, be cached.

+

Parameters:

+
    +
  • subscripts - (str) Specifies the subscripts for summation.
    • +
  • shapes - (sequence of integer tuples) Shapes of the arrays to optimize the contraction for.
    • +
  • constants - (sequence of int, optional) The indices of any constant arguments in shapes, in which case the + actual array should be supplied at that position rather than just a + shape. If these are specified, then constant parts of the contraction + between calls will be reused. Additionally, if a GPU-enabled backend is + used for example, then the constant tensors will be kept on the GPU, + minimizing transfers.
    • +
  • kwargs - Passed on to contract_path or einsum. See contract.
    • +
+

Returns:

+
    +
  • expr - (ContractExpression) Callable with signature expr(*arrays, out=None, backend='numpy') where the array's shapes should match shapes.
    • +
+

Notes:

+
    +
  • The out keyword argument should be supplied to the generated expression + rather than this function.
    • +
  • The backend keyword argument should also be supplied to the generated + expression. If numpy arrays are supplied, if possible they will be + converted to and back from the correct backend array type.
    • +
  • The generated expression will work with any arrays which have + the same rank (number of dimensions) as the original shapes, however, if + the actual sizes are different, the expression may no longer be optimal.
    • +
  • Constant operations will be computed upon the first call with a particular + backend, then subsequently reused.
    • +
+

Examples:

+

Basic usage:

+
expr = contract_expression("ab,bc->ac", (3, 4), (4, 5))
+a, b = np.random.rand(3, 4), np.random.rand(4, 5)
+c = expr(a, b)
+np.allclose(c, a @ b)
+#> True
+
+

Supply a as a constant:

+
expr = contract_expression("ab,bc->ac", a, (4, 5), constants=[0])
+expr
+#> <ContractExpression('[ab],bc->ac', constants=[0])>
+
+c = expr(b)
+np.allclose(c, a @ b)
+#> True
+
+ +
+ Source code in opt_einsum/contract.py + 
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def contract_expression(subscripts: str, *shapes: PathType, **kwargs: Any) -> Any:
+    """Generate a reusable expression for a given contraction with
+    specific shapes, which can, for example, be cached.
+
+    **Parameters:**
+
+    - **subscripts** - *(str)* Specifies the subscripts for summation.
+    - **shapes** - *(sequence of integer tuples)* Shapes of the arrays to optimize the contraction for.
+    - **constants** - *(sequence of int, optional)* The indices of any constant arguments in `shapes`, in which case the
+        actual array should be supplied at that position rather than just a
+        shape. If these are specified, then constant parts of the contraction
+        between calls will be reused. Additionally, if a GPU-enabled backend is
+        used for example, then the constant tensors will be kept on the GPU,
+        minimizing transfers.
+    - **kwargs** - Passed on to `contract_path` or `einsum`. See `contract`.
+
+    **Returns:**
+
+    - **expr** - *(ContractExpression)* Callable with signature `expr(*arrays, out=None, backend='numpy')` where the array's shapes should match `shapes`.
+
+    **Notes:**
+
+    - The `out` keyword argument should be supplied to the generated expression
+      rather than this function.
+    - The `backend` keyword argument should also be supplied to the generated
+      expression. If numpy arrays are supplied, if possible they will be
+      converted to and back from the correct backend array type.
+    - The generated expression will work with any arrays which have
+      the same rank (number of dimensions) as the original shapes, however, if
+      the actual sizes are different, the expression may no longer be optimal.
+    - Constant operations will be computed upon the first call with a particular
+      backend, then subsequently reused.
+
+    **Examples:**
+
+    Basic usage:
+
+    ```python
+    expr = contract_expression("ab,bc->ac", (3, 4), (4, 5))
+    a, b = np.random.rand(3, 4), np.random.rand(4, 5)
+    c = expr(a, b)
+    np.allclose(c, a @ b)
+    #> True
+    ```
+
+    Supply `a` as a constant:
+
+    ```python
+    expr = contract_expression("ab,bc->ac", a, (4, 5), constants=[0])
+    expr
+    #> <ContractExpression('[ab],bc->ac', constants=[0])>
+
+    c = expr(b)
+    np.allclose(c, a @ b)
+    #> True
+    ```
+
+    """
+    if not kwargs.get("optimize", True):
+        raise ValueError("Can only generate expressions for optimized contractions.")
+
+    for arg in ("out", "backend"):
+        if kwargs.get(arg, None) is not None:
+            raise ValueError(
+                "'{}' should only be specified when calling a "
+                "`ContractExpression`, not when building it.".format(arg)
+            )
+
+    if not isinstance(subscripts, str):
+        subscripts, shapes = parser.convert_interleaved_input((subscripts,) + shapes)
+
+    kwargs["_gen_expression"] = True
+
+    # build dict of constant indices mapped to arrays
+    constants = kwargs.pop("constants", ())
+    constants_dict = {i: shapes[i] for i in constants}
+    kwargs["_constants_dict"] = constants_dict
+
+    # apart from constant arguments, make dummy arrays
+    dummy_arrays = [s if i in constants else shape_only(s) for i, s in enumerate(shapes)]
+
+    return contract(subscripts, *dummy_arrays, **kwargs)
+
+
+
+ +

opt_einsum.contract.ContractExpression

+ + +
+ + + + +
+ + +

Helper class for storing an explicit contraction_list which can +then be repeatedly called solely with the array arguments.

+ +
+ Source code in opt_einsum/contract.py + 
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class ContractExpression:
+    """Helper class for storing an explicit ``contraction_list`` which can
+    then be repeatedly called solely with the array arguments.
+    """
+
+    def __init__(
+        self,
+        contraction: str,
+        contraction_list: ContractionListType,
+        constants_dict: Dict[int, ArrayType],
+        **einsum_kwargs: Any,
+    ):
+        self.contraction_list = contraction_list
+        self.einsum_kwargs = einsum_kwargs
+        self.contraction = format_const_einsum_str(contraction, constants_dict.keys())
+
+        # need to know _full_num_args to parse constants with, and num_args to call with
+        self._full_num_args = contraction.count(",") + 1
+        self.num_args = self._full_num_args - len(constants_dict)
+
+        # likewise need to know full contraction list
+        self._full_contraction_list = contraction_list
+
+        self._constants_dict = constants_dict
+        self._evaluated_constants: Dict[str, Any] = {}
+        self._backend_expressions: Dict[str, Any] = {}
+
+    def evaluate_constants(self, backend: Optional[str] = "auto") -> None:
+        """Convert any constant operands to the correct backend form, and
+        perform as many contractions as possible to create a new list of
+        operands, stored in ``self._evaluated_constants[backend]``. This also
+        makes sure ``self.contraction_list`` only contains the remaining,
+        non-const operations.
+        """
+        # prepare a list of operands, with `None` for non-consts
+        tmp_const_ops = [self._constants_dict.get(i, None) for i in range(self._full_num_args)]
+        backend = parse_backend(tmp_const_ops, backend)
+
+        # get the new list of operands with constant operations performed, and remaining contractions
+        try:
+            new_ops, new_contraction_list = backends.evaluate_constants(backend, tmp_const_ops, self)
+        except KeyError:
+            new_ops, new_contraction_list = self(*tmp_const_ops, backend=backend, evaluate_constants=True)
+
+        self._evaluated_constants[backend] = new_ops
+        self.contraction_list = new_contraction_list
+
+    def _get_evaluated_constants(self, backend: str) -> List[Optional[ArrayType]]:
+        """Retrieve or generate the cached list of constant operators (mixed
+        in with None representing non-consts) and the remaining contraction
+        list.
+        """
+        try:
+            return self._evaluated_constants[backend]
+        except KeyError:
+            self.evaluate_constants(backend)
+            return self._evaluated_constants[backend]
+
+    def _get_backend_expression(self, arrays: Sequence[ArrayType], backend: str) -> Any:
+        try:
+            return self._backend_expressions[backend]
+        except KeyError:
+            fn = backends.build_expression(backend, arrays, self)
+            self._backend_expressions[backend] = fn
+            return fn
+
+    def _contract(
+        self,
+        arrays: Sequence[ArrayType],
+        out: Optional[ArrayType] = None,
+        backend: Optional[str] = "auto",
+        evaluate_constants: bool = False,
+    ) -> ArrayType:
+        """The normal, core contraction."""
+        contraction_list = self._full_contraction_list if evaluate_constants else self.contraction_list
+
+        return _core_contract(
+            list(arrays),
+            contraction_list,
+            out=out,
+            backend=backend,
+            evaluate_constants=evaluate_constants,
+            **self.einsum_kwargs,
+        )
+
+    def _contract_with_conversion(
+        self,
+        arrays: Sequence[ArrayType],
+        out: Optional[ArrayType],
+        backend: str,
+        evaluate_constants: bool = False,
+    ) -> ArrayType:
+        """Special contraction, i.e., contraction with a different backend
+        but converting to and from that backend. Retrieves or generates a
+        cached expression using ``arrays`` as templates, then calls it
+        with ``arrays``.
+
+        If ``evaluate_constants=True``, perform a partial contraction that
+        prepares the constant tensors and operations with the right backend.
+        """
+        # convert consts to correct type & find reduced contraction list
+        if evaluate_constants:
+            return backends.evaluate_constants(backend, arrays, self)
+
+        result = self._get_backend_expression(arrays, backend)(*arrays)
+
+        if out is not None:
+            out[()] = result
+            return out
+
+        return result
+
+    def __call__(self, *arrays: ArrayType, **kwargs: Any) -> ArrayType:
+        """Evaluate this expression with a set of arrays.
+
+        Parameters
+        ----------
+        arrays : seq of array
+            The arrays to supply as input to the expression.
+        out : array, optional (default: ``None``)
+            If specified, output the result into this array.
+        backend : str, optional  (default: ``numpy``)
+            Perform the contraction with this backend library. If numpy arrays
+            are supplied then try to convert them to and from the correct
+            backend array type.
+        """
+        out = kwargs.pop("out", None)
+        backend = parse_backend(arrays, kwargs.pop("backend", "auto"))
+        evaluate_constants = kwargs.pop("evaluate_constants", False)
+
+        if kwargs:
+            raise ValueError(
+                "The only valid keyword arguments to a `ContractExpression` "
+                "call are `out=` or `backend=`. Got: {}.".format(kwargs)
+            )
+
+        correct_num_args = self._full_num_args if evaluate_constants else self.num_args
+
+        if len(arrays) != correct_num_args:
+            raise ValueError(
+                "This `ContractExpression` takes exactly {} array arguments "
+                "but received {}.".format(self.num_args, len(arrays))
+            )
+
+        if self._constants_dict and not evaluate_constants:
+            # fill in the missing non-constant terms with newly supplied arrays
+            ops_var, ops_const = iter(arrays), self._get_evaluated_constants(backend)
+            ops: Sequence[ArrayType] = [next(ops_var) if op is None else op for op in ops_const]
+        else:
+            ops = arrays
+
+        try:
+            # Check if the backend requires special preparation / calling
+            #   but also ignore non-numpy arrays -> assume user wants same type back
+            if backends.has_backend(backend) and all(infer_backend(x) == "numpy" for x in arrays):
+                return self._contract_with_conversion(ops, out, backend, evaluate_constants=evaluate_constants)
+
+            return self._contract(ops, out, backend, evaluate_constants=evaluate_constants)
+
+        except ValueError as err:
+            original_msg = str(err.args) if err.args else ""
+            msg = (
+                "Internal error while evaluating `ContractExpression`. Note that few checks are performed"
+                " - the number and rank of the array arguments must match the original expression. "
+                "The internal error was: '{}'".format(original_msg),
+            )
+            err.args = msg
+            raise
+
+    def __repr__(self) -> str:
+        if self._constants_dict:
+            constants_repr = ", constants={}".format(sorted(self._constants_dict))
+        else:
+            constants_repr = ""
+        return "<ContractExpression('{}'{})>".format(self.contraction, constants_repr)
+
+    def __str__(self) -> str:
+        s = [self.__repr__()]
+        for i, c in enumerate(self.contraction_list):
+            s.append("\n  {}.  ".format(i + 1))
+            s.append("'{}'".format(c[2]) + (" [{}]".format(c[-1]) if c[-1] else ""))
+        if self.einsum_kwargs:
+            s.append("\neinsum_kwargs={}".format(self.einsum_kwargs))
+        return "".join(s)
+
+
+ + + +
+ + + + + + + + + + +
+ + + +

+ __call__(*arrays, **kwargs) + +

+ + +
+ +

Evaluate this expression with a set of arrays.

+

Parameters

+

arrays : seq of array + The arrays to supply as input to the expression. +out : array, optional (default: None) + If specified, output the result into this array. +backend : str, optional (default: numpy) + Perform the contraction with this backend library. If numpy arrays + are supplied then try to convert them to and from the correct + backend array type.

+ +
+ Source code in opt_einsum/contract.py + 
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def __call__(self, *arrays: ArrayType, **kwargs: Any) -> ArrayType:
+    """Evaluate this expression with a set of arrays.
+
+    Parameters
+    ----------
+    arrays : seq of array
+        The arrays to supply as input to the expression.
+    out : array, optional (default: ``None``)
+        If specified, output the result into this array.
+    backend : str, optional  (default: ``numpy``)
+        Perform the contraction with this backend library. If numpy arrays
+        are supplied then try to convert them to and from the correct
+        backend array type.
+    """
+    out = kwargs.pop("out", None)
+    backend = parse_backend(arrays, kwargs.pop("backend", "auto"))
+    evaluate_constants = kwargs.pop("evaluate_constants", False)
+
+    if kwargs:
+        raise ValueError(
+            "The only valid keyword arguments to a `ContractExpression` "
+            "call are `out=` or `backend=`. Got: {}.".format(kwargs)
+        )
+
+    correct_num_args = self._full_num_args if evaluate_constants else self.num_args
+
+    if len(arrays) != correct_num_args:
+        raise ValueError(
+            "This `ContractExpression` takes exactly {} array arguments "
+            "but received {}.".format(self.num_args, len(arrays))
+        )
+
+    if self._constants_dict and not evaluate_constants:
+        # fill in the missing non-constant terms with newly supplied arrays
+        ops_var, ops_const = iter(arrays), self._get_evaluated_constants(backend)
+        ops: Sequence[ArrayType] = [next(ops_var) if op is None else op for op in ops_const]
+    else:
+        ops = arrays
+
+    try:
+        # Check if the backend requires special preparation / calling
+        #   but also ignore non-numpy arrays -> assume user wants same type back
+        if backends.has_backend(backend) and all(infer_backend(x) == "numpy" for x in arrays):
+            return self._contract_with_conversion(ops, out, backend, evaluate_constants=evaluate_constants)
+
+        return self._contract(ops, out, backend, evaluate_constants=evaluate_constants)
+
+    except ValueError as err:
+        original_msg = str(err.args) if err.args else ""
+        msg = (
+            "Internal error while evaluating `ContractExpression`. Note that few checks are performed"
+            " - the number and rank of the array arguments must match the original expression. "
+            "The internal error was: '{}'".format(original_msg),
+        )
+        err.args = msg
+        raise
+
+
+
+ +
+ + +
+ + + +

+ evaluate_constants(backend='auto') + +

+ + +
+ +

Convert any constant operands to the correct backend form, and +perform as many contractions as possible to create a new list of +operands, stored in self._evaluated_constants[backend]. This also +makes sure self.contraction_list only contains the remaining, +non-const operations.

+ +
+ Source code in opt_einsum/contract.py + 
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def evaluate_constants(self, backend: Optional[str] = "auto") -> None:
+    """Convert any constant operands to the correct backend form, and
+    perform as many contractions as possible to create a new list of
+    operands, stored in ``self._evaluated_constants[backend]``. This also
+    makes sure ``self.contraction_list`` only contains the remaining,
+    non-const operations.
+    """
+    # prepare a list of operands, with `None` for non-consts
+    tmp_const_ops = [self._constants_dict.get(i, None) for i in range(self._full_num_args)]
+    backend = parse_backend(tmp_const_ops, backend)
+
+    # get the new list of operands with constant operations performed, and remaining contractions
+    try:
+        new_ops, new_contraction_list = backends.evaluate_constants(backend, tmp_const_ops, self)
+    except KeyError:
+        new_ops, new_contraction_list = self(*tmp_const_ops, backend=backend, evaluate_constants=True)
+
+    self._evaluated_constants[backend] = new_ops
+    self.contraction_list = new_contraction_list
+
+
+
+ +
+ + + +
+ +
+ + +

opt_einsum.contract.PathInfo

+ + +
+ + + + +
+ + +

A printable object to contain information about a contraction path.

+

Attributes:

+
    +
  • naive_cost - (int) The estimate FLOP cost of a naive einsum contraction.
    • +
  • opt_cost - (int) The estimate FLOP cost of this optimized contraction path.
    • +
  • largest_intermediate - (int) The number of elements in the largest intermediate array that will be produced during the contraction.
    • +
+ +
+ Source code in opt_einsum/contract.py + 
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class PathInfo:
+    """A printable object to contain information about a contraction path.
+
+    **Attributes:**
+
+    - **naive_cost** - *(int)* The estimate FLOP cost of a naive einsum contraction.
+    - **opt_cost** - *(int)* The estimate FLOP cost of this optimized contraction path.
+    - **largest_intermediate** - *(int)* The number of elements in the largest intermediate array that will be produced during the contraction.
+    """
+
+    def __init__(
+        self,
+        contraction_list: ContractionListType,
+        input_subscripts: str,
+        output_subscript: str,
+        indices: ArrayIndexType,
+        path: PathType,
+        scale_list: Sequence[int],
+        naive_cost: int,
+        opt_cost: int,
+        size_list: Sequence[int],
+        size_dict: Dict[str, int],
+    ):
+        self.contraction_list = contraction_list
+        self.input_subscripts = input_subscripts
+        self.output_subscript = output_subscript
+        self.path = path
+        self.indices = indices
+        self.scale_list = scale_list
+        self.naive_cost = Decimal(naive_cost)
+        self.opt_cost = Decimal(opt_cost)
+        self.speedup = self.naive_cost / self.opt_cost
+        self.size_list = size_list
+        self.size_dict = size_dict
+
+        self.shapes = [tuple(size_dict[k] for k in ks) for ks in input_subscripts.split(",")]
+        self.eq = "{}->{}".format(input_subscripts, output_subscript)
+        self.largest_intermediate = Decimal(max(size_list))
+
+    def __repr__(self) -> str:
+        # Return the path along with a nice string representation
+        header = ("scaling", "BLAS", "current", "remaining")
+
+        path_print = [
+            "  Complete contraction:  {}\n".format(self.eq),
+            "         Naive scaling:  {}\n".format(len(self.indices)),
+            "     Optimized scaling:  {}\n".format(max(self.scale_list)),
+            "      Naive FLOP count:  {:.3e}\n".format(self.naive_cost),
+            "  Optimized FLOP count:  {:.3e}\n".format(self.opt_cost),
+            "   Theoretical speedup:  {:.3e}\n".format(self.speedup),
+            "  Largest intermediate:  {:.3e} elements\n".format(self.largest_intermediate),
+            "-" * 80 + "\n",
+            "{:>6} {:>11} {:>22} {:>37}\n".format(*header),
+            "-" * 80,
+        ]
+
+        for n, contraction in enumerate(self.contraction_list):
+            _, _, einsum_str, remaining, do_blas = contraction
+
+            if remaining is not None:
+                remaining_str = ",".join(remaining) + "->" + self.output_subscript
+            else:
+                remaining_str = "..."
+            size_remaining = max(0, 56 - max(22, len(einsum_str)))
+
+            path_run = (
+                self.scale_list[n],
+                do_blas,
+                einsum_str,
+                remaining_str,
+                size_remaining,
+            )
+            path_print.append("\n{:>4} {:>14} {:>22}    {:>{}}".format(*path_run))
+
+        return "".join(path_print)
+
+
+ + + +
+ + + + + + + + + + + +
+ +
+ + +

opt_einsum.get_symbol

+ + + +
+ + + + + +
+ +

Get the symbol corresponding to int i - runs through the usual 52 +letters before resorting to unicode characters, starting at chr(192) and skipping surrogates.

+

Examples:

+
get_symbol(2)
+#> 'c'
+
+get_symbol(200)
+#> 'Ŕ'
+
+get_symbol(20000)
+#> '京'
+
+ +
+ Source code in opt_einsum/parser.py + 
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def get_symbol(i: int) -> str:
+    """Get the symbol corresponding to int ``i`` - runs through the usual 52
+    letters before resorting to unicode characters, starting at ``chr(192)`` and skipping surrogates.
+
+    **Examples:**
+
+    ```python
+    get_symbol(2)
+    #> 'c'
+
+    get_symbol(200)
+    #> 'Ŕ'
+
+    get_symbol(20000)
+    #> '京'
+    ```
+    """
+    if i < 52:
+        return _einsum_symbols_base[i]
+    elif i >= 55296:
+        # Skip chr(57343) - chr(55296) as surrogates
+        return chr(i + 2048)
+    else:
+        return chr(i + 140)
+
+
+
+ +

opt_einsum.shared_intermediates

+ + + +
+ + + + + +
+ +

Context in which contract intermediate results are shared.

+

Note that intermediate computations will not be garbage collected until +1. this context exits, and +2. the yielded cache is garbage collected (if it was captured).

+

Parameters:

+
    +
  • cache - (dict) If specified, a user-stored dict in which intermediate results will be stored. This can be used to interleave sharing contexts.
    • +
+

Returns:

+
    +
  • cache - (dict) A dictionary in which sharing results are stored. If ignored, + sharing results will be garbage collected when this context is + exited. This dict can be passed to another context to resume + sharing.
    • +
+ +
+ Source code in opt_einsum/sharing.py + 
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@contextlib.contextmanager
+def shared_intermediates(
+    cache: Optional[CacheType] = None,
+) -> Generator[CacheType, None, None]:
+    """Context in which contract intermediate results are shared.
+
+    Note that intermediate computations will not be garbage collected until
+    1. this context exits, and
+    2. the yielded cache is garbage collected (if it was captured).
+
+    **Parameters:**
+
+    - **cache** - *(dict)* If specified, a user-stored dict in which intermediate results will be stored. This can be used to interleave sharing contexts.
+
+    **Returns:**
+
+    - **cache** - *(dict)* A dictionary in which sharing results are stored. If ignored,
+        sharing results will be garbage collected when this context is
+        exited. This dict can be passed to another context to resume
+        sharing.
+    """
+    if cache is None:
+        cache = {}
+    _add_sharing_cache(cache)
+    try:
+        yield cache
+    finally:
+        _remove_sharing_cache()
+
+
+
+ +

opt_einsum.paths.optimal

+ + + +
+ + + + + +
+ +

Computes all possible pair contractions in a depth-first recursive manner, +sieving results based on memory_limit and the best path found so far. +Returns: the lowest cost path. This algorithm scales factoriallly with +respect to the elements in the list input_sets.

+

Parameters:

+
    +
  • inputs - (list) List of sets that represent the lhs side of the einsum subscript.
    • +
  • output - (set) Set that represents the rhs side of the overall einsum subscript.
    • +
  • size_dict - (dictionary) Dictionary of index sizes.
    • +
  • memory_limit - (int) The maximum number of elements in a temporary array.
    • +
+

Returns:

+
    +
  • path - (list) The optimal contraction order within the memory limit constraint.
    • +
+

Examples:

+
isets = [set('abd'), set('ac'), set('bdc')]
+oset = set('')
+idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+optimal(isets, oset, idx_sizes, 5000)
+#> [(0, 2), (0, 1)]
+
+ +
+ Source code in opt_einsum/paths.py + 
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def optimal(
+    inputs: List[ArrayIndexType],
+    output: ArrayIndexType,
+    size_dict: Dict[str, int],
+    memory_limit: Optional[int] = None,
+) -> PathType:
+    """
+    Computes all possible pair contractions in a depth-first recursive manner,
+    sieving results based on `memory_limit` and the best path found so far.
+    **Returns:** the lowest cost path. This algorithm scales factoriallly with
+    respect to the elements in the list `input_sets`.
+
+    **Parameters:**
+
+    - **inputs** - *(list)* List of sets that represent the lhs side of the einsum subscript.
+    - **output** - *(set)* Set that represents the rhs side of the overall einsum subscript.
+    - **size_dict** - *(dictionary)* Dictionary of index sizes.
+    - **memory_limit** - *(int)* The maximum number of elements in a temporary array.
+
+    **Returns:**
+
+    - **path** - *(list)* The optimal contraction order within the memory limit constraint.
+
+    **Examples:**
+
+    ```python
+    isets = [set('abd'), set('ac'), set('bdc')]
+    oset = set('')
+    idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    optimal(isets, oset, idx_sizes, 5000)
+    #> [(0, 2), (0, 1)]
+    ```
+    """
+    inputs_set = tuple(map(frozenset, inputs))
+    output_set = frozenset(output)
+
+    best_flops = {"flops": float("inf")}
+    best_ssa_path = {"ssa_path": (tuple(range(len(inputs))),)}
+    size_cache: Dict[FrozenSet[str], int] = {}
+    result_cache: Dict[Tuple[ArrayIndexType, ArrayIndexType], Tuple[FrozenSet[str], int]] = {}
+
+    def _optimal_iterate(path, remaining, inputs, flops):
+
+        # reached end of path (only ever get here if flops is best found so far)
+        if len(remaining) == 1:
+            best_flops["flops"] = flops
+            best_ssa_path["ssa_path"] = path
+            return
+
+        # check all possible remaining paths
+        for i, j in itertools.combinations(remaining, 2):
+            if i > j:
+                i, j = j, i
+            key = (inputs[i], inputs[j])
+            try:
+                k12, flops12 = result_cache[key]
+            except KeyError:
+                k12, flops12 = result_cache[key] = calc_k12_flops(inputs, output_set, remaining, i, j, size_dict)
+
+            # sieve based on current best flops
+            new_flops = flops + flops12
+            if new_flops >= best_flops["flops"]:
+                continue
+
+            # sieve based on memory limit
+            if memory_limit not in _UNLIMITED_MEM:
+                try:
+                    size12 = size_cache[k12]
+                except KeyError:
+                    size12 = size_cache[k12] = compute_size_by_dict(k12, size_dict)
+
+                # possibly terminate this path with an all-terms einsum
+                if size12 > memory_limit:
+                    new_flops = flops + _compute_oversize_flops(inputs, remaining, output_set, size_dict)
+                    if new_flops < best_flops["flops"]:
+                        best_flops["flops"] = new_flops
+                        best_ssa_path["ssa_path"] = path + (tuple(remaining),)
+                    continue
+
+            # add contraction and recurse into all remaining
+            _optimal_iterate(
+                path=path + ((i, j),),
+                inputs=inputs + (k12,),
+                remaining=remaining - {i, j} | {len(inputs)},
+                flops=new_flops,
+            )
+
+    _optimal_iterate(path=(), inputs=inputs_set, remaining=set(range(len(inputs))), flops=0)
+
+    return ssa_to_linear(best_ssa_path["ssa_path"])
+
+
+
+ +

opt_einsum.paths.greedy

+ + + +
+ + + + + +
+ +

Finds the path by a three stage algorithm:

+
    +
  1. Eagerly compute Hadamard products.
    2. +
  2. Greedily compute contractions to maximize removed_size
    3. +
  3. Greedily compute outer products.
    4. +
+

This algorithm scales quadratically with respect to the +maximum number of elements sharing a common dim.

+

Parameters:

+
    +
  • inputs - (list) List of sets that represent the lhs side of the einsum subscript
    • +
  • output - (set) Set that represents the rhs side of the overall einsum subscript
    • +
  • size_dict - (dictionary) Dictionary of index sizes
    • +
  • memory_limit - (int) The maximum number of elements in a temporary array
    • +
  • choose_fn - (callable, optional) A function that chooses which contraction to perform from the queue
    • +
  • cost_fn - (callable, optional) A function that assigns a potential contraction a cost.
    • +
+

Returns:

+
    +
  • path - (list) The contraction order (a list of tuples of ints).
    • +
+

Examples:

+
isets = [set('abd'), set('ac'), set('bdc')]
+oset = set('')
+idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+greedy(isets, oset, idx_sizes)
+#> [(0, 2), (0, 1)]
+
+ +
+ Source code in opt_einsum/paths.py + 
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def greedy(
+    inputs: List[ArrayIndexType],
+    output: ArrayIndexType,
+    size_dict: Dict[str, int],
+    memory_limit: Optional[int] = None,
+    choose_fn: Any = None,
+    cost_fn: str = "memory-removed",
+) -> PathType:
+    """
+    Finds the path by a three stage algorithm:
+
+    1. Eagerly compute Hadamard products.
+    2. Greedily compute contractions to maximize `removed_size`
+    3. Greedily compute outer products.
+
+    This algorithm scales quadratically with respect to the
+    maximum number of elements sharing a common dim.
+
+    **Parameters:**
+
+    - **inputs** - *(list)* List of sets that represent the lhs side of the einsum subscript
+    - **output** - *(set)* Set that represents the rhs side of the overall einsum subscript
+    - **size_dict** - *(dictionary)* Dictionary of index sizes
+    - **memory_limit** - *(int)* The maximum number of elements in a temporary array
+    - **choose_fn** - *(callable, optional)* A function that chooses which contraction to perform from the queue
+    - **cost_fn** - *(callable, optional)* A function that assigns a potential contraction a cost.
+
+    **Returns:**
+
+    - **path** - *(list)* The contraction order (a list of tuples of ints).
+
+    **Examples:**
+
+    ```python
+    isets = [set('abd'), set('ac'), set('bdc')]
+    oset = set('')
+    idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    greedy(isets, oset, idx_sizes)
+    #> [(0, 2), (0, 1)]
+    ```
+    """
+    if memory_limit not in _UNLIMITED_MEM:
+        return branch(inputs, output, size_dict, memory_limit, nbranch=1, cost_fn=cost_fn)  # type: ignore
+
+    ssa_path = ssa_greedy_optimize(inputs, output, size_dict, cost_fn=cost_fn, choose_fn=choose_fn)
+    return ssa_to_linear(ssa_path)
+
+
+
+ +

opt_einsum.paths.branch

+ + + +
+ + + + + +
+ +
+ Source code in opt_einsum/paths.py + 
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def branch(
+    inputs: List[ArrayIndexType],
+    output: ArrayIndexType,
+    size_dict: Dict[str, int],
+    memory_limit: Optional[int] = None,
+    **optimizer_kwargs: Dict[str, Any],
+) -> PathType:
+    optimizer = BranchBound(**optimizer_kwargs)
+    return optimizer(inputs, output, size_dict, memory_limit)
+
+
+
+ +

opt_einsum.paths.PathOptimizer

+ + +
+ + + + +
+ + +

Base class for different path optimizers to inherit from.

+

Subclassed optimizers should define a call method with signature:

+
def __call__(self, inputs, output, size_dict, memory_limit=None):
+    """
+    **Parameters:**
+    ----------
+    inputs : list[set[str]]
+        The indices of each input array.
+    outputs : set[str]
+        The output indices
+    size_dict : dict[str, int]
+        The size of each index
+    memory_limit : int, optional
+        If given, the maximum allowed memory.
+    """
+    # ... compute path here ...
+    return path
+
+

where path is a list of int-tuples specifying a contraction order.

+ +
+ Source code in opt_einsum/paths.py + 
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class PathOptimizer:
+    """Base class for different path optimizers to inherit from.
+
+    Subclassed optimizers should define a call method with signature:
+
+    ```python
+    def __call__(self, inputs, output, size_dict, memory_limit=None):
+        \"\"\"
+        **Parameters:**
+        ----------
+        inputs : list[set[str]]
+            The indices of each input array.
+        outputs : set[str]
+            The output indices
+        size_dict : dict[str, int]
+            The size of each index
+        memory_limit : int, optional
+            If given, the maximum allowed memory.
+        \"\"\"
+        # ... compute path here ...
+        return path
+    ```
+
+    where `path` is a list of int-tuples specifying a contraction order.
+    """
+
+    def _check_args_against_first_call(
+        self,
+        inputs: List[ArrayIndexType],
+        output: ArrayIndexType,
+        size_dict: Dict[str, int],
+    ) -> None:
+        """Utility that stateful optimizers can use to ensure they are not
+        called with different contractions across separate runs.
+        """
+        args = (inputs, output, size_dict)
+        if not hasattr(self, "_first_call_args"):
+            # simply set the attribute as currently there is no global PathOptimizer init
+            self._first_call_args = args
+        elif args != self._first_call_args:
+            raise ValueError(
+                "The arguments specifying the contraction that this path optimizer "
+                "instance was called with have changed - try creating a new instance."
+            )
+
+    def __call__(
+        self,
+        inputs: List[ArrayIndexType],
+        output: ArrayIndexType,
+        size_dict: Dict[str, int],
+        memory_limit: Optional[int] = None,
+    ) -> PathType:
+        raise NotImplementedError
+
+
+ + + +
+ + + + + + + + + + + +
+ +
+ + +

opt_einsum.paths.BranchBound

+ + +
+ + + + +
+

+ Bases: PathOptimizer

+ + +

Explores possible pair contractions in a depth-first recursive manner like +the optimal approach, but with extra heuristic early pruning of branches +as well sieving by memory_limit and the best path found so far. Returns: +the lowest cost path. This algorithm still scales factorially with respect +to the elements in the list input_sets if nbranch is not set, but it +scales exponentially like nbranch**len(input_sets) otherwise.

+

Parameters:

+
    +
  • nbranch - (None or int, optional) How many branches to explore at each contraction step. If None, explore + all possible branches. If an integer, branch into this many paths at + each step. Defaults to None.
    • +
  • cutoff_flops_factor - (float, optional) If at any point, a path is doing this much worse than the best path + found so far was, terminate it. The larger this is made, the more paths + will be fully explored and the slower the algorithm. Defaults to 4.
    • +
  • minimize - ({'flops', 'size'}, optional) Whether to optimize the path with regard primarily to the total + estimated flop-count, or the size of the largest intermediate. The + option not chosen will still be used as a secondary criterion.
    • +
  • cost_fn - (callable, optional) A function that returns a heuristic 'cost' of a potential contraction + with which to sort candidates. Should have signature + cost_fn(size12, size1, size2, k12, k1, k2).
    • +
+ +
+ Source code in opt_einsum/paths.py + 
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class BranchBound(PathOptimizer):
+    """
+    Explores possible pair contractions in a depth-first recursive manner like
+    the `optimal` approach, but with extra heuristic early pruning of branches
+    as well sieving by `memory_limit` and the best path found so far. **Returns:**
+    the lowest cost path. This algorithm still scales factorially with respect
+    to the elements in the list `input_sets` if `nbranch` is not set, but it
+    scales exponentially like `nbranch**len(input_sets)` otherwise.
+
+    **Parameters:**
+
+    - **nbranch** - *(None or int, optional)* How many branches to explore at each contraction step. If None, explore
+        all possible branches. If an integer, branch into this many paths at
+        each step. Defaults to None.
+    - **cutoff_flops_factor** - *(float, optional)* If at any point, a path is doing this much worse than the best path
+        found so far was, terminate it. The larger this is made, the more paths
+        will be fully explored and the slower the algorithm. Defaults to 4.
+    - **minimize** - *({'flops', 'size'}, optional)* Whether to optimize the path with regard primarily to the total
+        estimated flop-count, or the size of the largest intermediate. The
+        option not chosen will still be used as a secondary criterion.
+    - **cost_fn** - *(callable, optional)* A function that returns a heuristic 'cost' of a potential contraction
+        with which to sort candidates. Should have signature
+        `cost_fn(size12, size1, size2, k12, k1, k2)`.
+    """
+
+    def __init__(
+        self,
+        nbranch=None,
+        cutoff_flops_factor=4,
+        minimize="flops",
+        cost_fn="memory-removed",
+    ):
+        if (nbranch is not None) and nbranch < 1:
+            raise ValueError(f"The number of branches must be at least one, `nbranch={nbranch}`.")
+
+        self.nbranch = nbranch
+        self.cutoff_flops_factor = cutoff_flops_factor
+        self.minimize = minimize
+        self.cost_fn = _COST_FNS.get(cost_fn, cost_fn)
+
+        self.better = get_better_fn(minimize)
+        self.best = {"flops": float("inf"), "size": float("inf")}
+        self.best_progress = defaultdict(lambda: float("inf"))
+
+    @property
+    def path(self) -> PathType:
+        return ssa_to_linear(self.best["ssa_path"])
+
+    def __call__(
+        self,
+        inputs_: List[ArrayIndexType],
+        output_: ArrayIndexType,
+        size_dict: Dict[str, int],
+        memory_limit: Optional[int] = None,
+    ) -> PathType:
+        """
+
+        **Parameters:**
+
+        - **input_sets** - *(list)* List of sets that represent the lhs side of the einsum subscript
+        - **output_set** - *(set)* Set that represents the rhs side of the overall einsum subscript
+        - **idx_dict** - *(dictionary)* Dictionary of index sizes
+        - **memory_limit** - *(int)* The maximum number of elements in a temporary array
+
+        **Returns:**
+
+        - **path** - *(list)* The contraction order within the memory limit constraint.
+
+        **Examples:**
+
+        ```python
+        isets = [set('abd'), set('ac'), set('bdc')]
+        oset = set('')
+        idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+        optimal(isets, oset, idx_sizes, 5000)
+        #> [(0, 2), (0, 1)]
+        """
+        self._check_args_against_first_call(inputs_, output_, size_dict)
+
+        inputs: Tuple[FrozenSet[str]] = tuple(map(frozenset, inputs_))  # type: ignore
+        output: FrozenSet[str] = frozenset(output_)
+
+        size_cache = {k: compute_size_by_dict(k, size_dict) for k in inputs}
+        result_cache: Dict[Tuple[FrozenSet[str], FrozenSet[str]], Tuple[FrozenSet[str], int]] = {}
+
+        def _branch_iterate(path, inputs, remaining, flops, size):
+
+            # reached end of path (only ever get here if flops is best found so far)
+            if len(remaining) == 1:
+                self.best["size"] = size
+                self.best["flops"] = flops
+                self.best["ssa_path"] = path
+                return
+
+            def _assess_candidate(k1: FrozenSet[str], k2: FrozenSet[str], i: int, j: int) -> Any:
+                # find resulting indices and flops
+                try:
+                    k12, flops12 = result_cache[k1, k2]
+                except KeyError:
+                    k12, flops12 = result_cache[k1, k2] = calc_k12_flops(inputs, output, remaining, i, j, size_dict)
+
+                try:
+                    size12 = size_cache[k12]
+                except KeyError:
+                    size12 = size_cache[k12] = compute_size_by_dict(k12, size_dict)
+
+                new_flops = flops + flops12
+                new_size = max(size, size12)
+
+                # sieve based on current best i.e. check flops and size still better
+                if not self.better(new_flops, new_size, self.best["flops"], self.best["size"]):
+                    return None
+
+                # compare to how the best method was doing as this point
+                if new_flops < self.best_progress[len(inputs)]:
+                    self.best_progress[len(inputs)] = new_flops
+                # sieve based on current progress relative to best
+                elif new_flops > self.cutoff_flops_factor * self.best_progress[len(inputs)]:
+                    return None
+
+                # sieve based on memory limit
+                if (memory_limit not in _UNLIMITED_MEM) and (size12 > memory_limit):  # type: ignore
+                    # terminate path here, but check all-terms contract first
+                    new_flops = flops + _compute_oversize_flops(inputs, remaining, output_, size_dict)
+                    if new_flops < self.best["flops"]:
+                        self.best["flops"] = new_flops
+                        self.best["ssa_path"] = path + (tuple(remaining),)
+                    return None
+
+                # set cost heuristic in order to locally sort possible contractions
+                size1, size2 = size_cache[inputs[i]], size_cache[inputs[j]]
+                cost = self.cost_fn(size12, size1, size2, k12, k1, k2)
+
+                return cost, flops12, new_flops, new_size, (i, j), k12
+
+            # check all possible remaining paths
+            candidates = []
+            for i, j in itertools.combinations(remaining, 2):
+                if i > j:
+                    i, j = j, i
+                k1, k2 = inputs[i], inputs[j]
+
+                # initially ignore outer products
+                if k1.isdisjoint(k2):
+                    continue
+
+                candidate = _assess_candidate(k1, k2, i, j)
+                if candidate:
+                    heapq.heappush(candidates, candidate)
+
+            # assess outer products if nothing left
+            if not candidates:
+                for i, j in itertools.combinations(remaining, 2):
+                    if i > j:
+                        i, j = j, i
+                    k1, k2 = inputs[i], inputs[j]
+                    candidate = _assess_candidate(k1, k2, i, j)
+                    if candidate:
+                        heapq.heappush(candidates, candidate)
+
+            # recurse into all or some of the best candidate contractions
+            bi = 0
+            while (self.nbranch is None or bi < self.nbranch) and candidates:
+                _, _, new_flops, new_size, (i, j), k12 = heapq.heappop(candidates)
+                _branch_iterate(
+                    path=path + ((i, j),),
+                    inputs=inputs + (k12,),
+                    remaining=(remaining - {i, j}) | {len(inputs)},
+                    flops=new_flops,
+                    size=new_size,
+                )
+                bi += 1
+
+        _branch_iterate(path=(), inputs=inputs, remaining=set(range(len(inputs))), flops=0, size=0)
+
+        return self.path
+
+
+ + + +
+ + + + + + + + + + +
+ + + +

+ __call__(inputs_, output_, size_dict, memory_limit=None) + +

+ + +
+ +

Parameters:

+
    +
  • input_sets - (list) List of sets that represent the lhs side of the einsum subscript
    • +
  • output_set - (set) Set that represents the rhs side of the overall einsum subscript
    • +
  • idx_dict - (dictionary) Dictionary of index sizes
    • +
  • memory_limit - (int) The maximum number of elements in a temporary array
    • +
+

Returns:

+
    +
  • path - (list) The contraction order within the memory limit constraint.
    • +
+

Examples:

+

```python +isets = [set('abd'), set('ac'), set('bdc')] +oset = set('') +idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4} +optimal(isets, oset, idx_sizes, 5000)

+

> [(0, 2), (0, 1)]

+ +
+ Source code in opt_einsum/paths.py + 
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def __call__(
+    self,
+    inputs_: List[ArrayIndexType],
+    output_: ArrayIndexType,
+    size_dict: Dict[str, int],
+    memory_limit: Optional[int] = None,
+) -> PathType:
+    """
+
+    **Parameters:**
+
+    - **input_sets** - *(list)* List of sets that represent the lhs side of the einsum subscript
+    - **output_set** - *(set)* Set that represents the rhs side of the overall einsum subscript
+    - **idx_dict** - *(dictionary)* Dictionary of index sizes
+    - **memory_limit** - *(int)* The maximum number of elements in a temporary array
+
+    **Returns:**
+
+    - **path** - *(list)* The contraction order within the memory limit constraint.
+
+    **Examples:**
+
+    ```python
+    isets = [set('abd'), set('ac'), set('bdc')]
+    oset = set('')
+    idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
+    optimal(isets, oset, idx_sizes, 5000)
+    #> [(0, 2), (0, 1)]
+    """
+    self._check_args_against_first_call(inputs_, output_, size_dict)
+
+    inputs: Tuple[FrozenSet[str]] = tuple(map(frozenset, inputs_))  # type: ignore
+    output: FrozenSet[str] = frozenset(output_)
+
+    size_cache = {k: compute_size_by_dict(k, size_dict) for k in inputs}
+    result_cache: Dict[Tuple[FrozenSet[str], FrozenSet[str]], Tuple[FrozenSet[str], int]] = {}
+
+    def _branch_iterate(path, inputs, remaining, flops, size):
+
+        # reached end of path (only ever get here if flops is best found so far)
+        if len(remaining) == 1:
+            self.best["size"] = size
+            self.best["flops"] = flops
+            self.best["ssa_path"] = path
+            return
+
+        def _assess_candidate(k1: FrozenSet[str], k2: FrozenSet[str], i: int, j: int) -> Any:
+            # find resulting indices and flops
+            try:
+                k12, flops12 = result_cache[k1, k2]
+            except KeyError:
+                k12, flops12 = result_cache[k1, k2] = calc_k12_flops(inputs, output, remaining, i, j, size_dict)
+
+            try:
+                size12 = size_cache[k12]
+            except KeyError:
+                size12 = size_cache[k12] = compute_size_by_dict(k12, size_dict)
+
+            new_flops = flops + flops12
+            new_size = max(size, size12)
+
+            # sieve based on current best i.e. check flops and size still better
+            if not self.better(new_flops, new_size, self.best["flops"], self.best["size"]):
+                return None
+
+            # compare to how the best method was doing as this point
+            if new_flops < self.best_progress[len(inputs)]:
+                self.best_progress[len(inputs)] = new_flops
+            # sieve based on current progress relative to best
+            elif new_flops > self.cutoff_flops_factor * self.best_progress[len(inputs)]:
+                return None
+
+            # sieve based on memory limit
+            if (memory_limit not in _UNLIMITED_MEM) and (size12 > memory_limit):  # type: ignore
+                # terminate path here, but check all-terms contract first
+                new_flops = flops + _compute_oversize_flops(inputs, remaining, output_, size_dict)
+                if new_flops < self.best["flops"]:
+                    self.best["flops"] = new_flops
+                    self.best["ssa_path"] = path + (tuple(remaining),)
+                return None
+
+            # set cost heuristic in order to locally sort possible contractions
+            size1, size2 = size_cache[inputs[i]], size_cache[inputs[j]]
+            cost = self.cost_fn(size12, size1, size2, k12, k1, k2)
+
+            return cost, flops12, new_flops, new_size, (i, j), k12
+
+        # check all possible remaining paths
+        candidates = []
+        for i, j in itertools.combinations(remaining, 2):
+            if i > j:
+                i, j = j, i
+            k1, k2 = inputs[i], inputs[j]
+
+            # initially ignore outer products
+            if k1.isdisjoint(k2):
+                continue
+
+            candidate = _assess_candidate(k1, k2, i, j)
+            if candidate:
+                heapq.heappush(candidates, candidate)
+
+        # assess outer products if nothing left
+        if not candidates:
+            for i, j in itertools.combinations(remaining, 2):
+                if i > j:
+                    i, j = j, i
+                k1, k2 = inputs[i], inputs[j]
+                candidate = _assess_candidate(k1, k2, i, j)
+                if candidate:
+                    heapq.heappush(candidates, candidate)
+
+        # recurse into all or some of the best candidate contractions
+        bi = 0
+        while (self.nbranch is None or bi < self.nbranch) and candidates:
+            _, _, new_flops, new_size, (i, j), k12 = heapq.heappop(candidates)
+            _branch_iterate(
+                path=path + ((i, j),),
+                inputs=inputs + (k12,),
+                remaining=(remaining - {i, j}) | {len(inputs)},
+                flops=new_flops,
+                size=new_size,
+            )
+            bi += 1
+
+    _branch_iterate(path=(), inputs=inputs, remaining=set(range(len(inputs))), flops=0, size=0)
+
+    return self.path
+
+
+
+ +
+ + + +
+ +
+ + +

opt_einsum.path_random.RandomOptimizer

+ + +
+ + + + +
+

+ Bases: PathOptimizer

+ + +

Base class for running any random path finder that benefits +from repeated calling, possibly in a parallel fashion. Custom random +optimizers should subclass this, and the setup method should be +implemented with the following signature:

+
def setup(self, inputs, output, size_dict):
+    # custom preparation here ...
+    return trial_fn, trial_args
+
+

Where trial_fn itself should have the signature::

+
def trial_fn(r, *trial_args):
+    # custom computation of path here
+    return ssa_path, cost, size
+
+

Where r is the run number and could for example be used to seed a +random number generator. See RandomGreedy for an example.

+

Parameters:

+
    +
  • max_repeats - (int, optional) The maximum number of repeat trials to have.
    • +
  • max_time - (float, optional) The maximum amount of time to run the algorithm for.
    • +
  • minimize - ({'flops', 'size'}, optional) Whether to favour paths that minimize the total estimated flop-count or + the size of the largest intermediate created.
    • +
  • parallel - ({bool, int, or executor-pool like}, optional) Whether to parallelize the random trials, by default False. If + True, use a concurrent.futures.ProcessPoolExecutor with the same + number of processes as cores. If an integer is specified, use that many + processes instead. Finally, you can supply a custom executor-pool which + should have an API matching that of the python 3 standard library + module concurrent.futures. Namely, a submit method that returns + Future objects, themselves with result and cancel methods.
    • +
  • pre_dispatch - (int, optional) If running in parallel, how many jobs to pre-dispatch so as to avoid + submitting all jobs at once. Should also be more than twice the number + of workers to avoid under-subscription. Default: 128.
    • +
+

Attributes:

+
    +
  • path - (list[tuple[int]]) The best path found so far.
    • +
  • costs - (list[int]) The list of each trial's costs found so far.
    • +
  • sizes - (list[int]) The list of each trial's largest intermediate size so far.
    • +
+ +
+ Source code in opt_einsum/path_random.py + 
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class RandomOptimizer(paths.PathOptimizer):
+    """Base class for running any random path finder that benefits
+    from repeated calling, possibly in a parallel fashion. Custom random
+    optimizers should subclass this, and the `setup` method should be
+    implemented with the following signature:
+
+    ```python
+    def setup(self, inputs, output, size_dict):
+        # custom preparation here ...
+        return trial_fn, trial_args
+    ```
+
+    Where `trial_fn` itself should have the signature::
+
+    ```python
+    def trial_fn(r, *trial_args):
+        # custom computation of path here
+        return ssa_path, cost, size
+    ```
+
+    Where `r` is the run number and could for example be used to seed a
+    random number generator. See `RandomGreedy` for an example.
+
+
+    **Parameters:**
+
+    - **max_repeats** - *(int, optional)* The maximum number of repeat trials to have.
+    - **max_time** - *(float, optional)* The maximum amount of time to run the algorithm for.
+    - **minimize** - *({'flops', 'size'}, optional)* Whether to favour paths that minimize the total estimated flop-count or
+        the size of the largest intermediate created.
+    - **parallel** - *({bool, int, or executor-pool like}, optional)* Whether to parallelize the random trials, by default `False`. If
+        `True`, use a `concurrent.futures.ProcessPoolExecutor` with the same
+        number of processes as cores. If an integer is specified, use that many
+        processes instead. Finally, you can supply a custom executor-pool which
+        should have an API matching that of the python 3 standard library
+        module `concurrent.futures`. Namely, a `submit` method that returns
+        `Future` objects, themselves with `result` and `cancel` methods.
+    - **pre_dispatch** - *(int, optional)* If running in parallel, how many jobs to pre-dispatch so as to avoid
+        submitting all jobs at once. Should also be more than twice the number
+        of workers to avoid under-subscription. Default: 128.
+
+    **Attributes:**
+
+    - **path** - *(list[tuple[int]])* The best path found so far.
+    - **costs** - *(list[int])* The list of each trial's costs found so far.
+    - **sizes** - *(list[int])* The list of each trial's largest intermediate size so far.
+    """
+
+    def __init__(
+        self,
+        max_repeats: int = 32,
+        max_time: Optional[float] = None,
+        minimize: str = "flops",
+        parallel: bool = False,
+        pre_dispatch: int = 128,
+    ):
+
+        if minimize not in ("flops", "size"):
+            raise ValueError("`minimize` should be one of {'flops', 'size'}.")
+
+        self.max_repeats = max_repeats
+        self.max_time = max_time
+        self.minimize = minimize
+        self.better = paths.get_better_fn(minimize)
+        self._parallel = False
+        self.parallel = parallel
+        self.pre_dispatch = pre_dispatch
+
+        self.costs: List[int] = []
+        self.sizes: List[int] = []
+        self.best: Dict[str, Any] = {"flops": float("inf"), "size": float("inf")}
+
+        self._repeats_start = 0
+        self._executor: Any
+        self._futures: Any
+
+    @property
+    def path(self) -> PathType:
+        """The best path found so far."""
+        return paths.ssa_to_linear(self.best["ssa_path"])
+
+    @property
+    def parallel(self) -> bool:
+        return self._parallel
+
+    @parallel.setter
+    def parallel(self, parallel: bool) -> None:
+        # shutdown any previous executor if we are managing it
+        if getattr(self, "_managing_executor", False):
+            self._executor.shutdown()
+
+        self._parallel = parallel
+        self._managing_executor = False
+
+        if parallel is False:
+            self._executor = None
+            return
+
+        if parallel is True:
+            from concurrent.futures import ProcessPoolExecutor
+
+            self._executor = ProcessPoolExecutor()
+            self._managing_executor = True
+            return
+
+        if isinstance(parallel, numbers.Number):
+            from concurrent.futures import ProcessPoolExecutor
+
+            self._executor = ProcessPoolExecutor(parallel)
+            self._managing_executor = True
+            return
+
+        # assume a pool-executor has been supplied
+        self._executor = parallel
+
+    def _gen_results_parallel(self, repeats: Iterable[int], trial_fn: Any, args: Any) -> Generator[Any, None, None]:
+        """Lazily generate results from an executor without submitting all jobs at once."""
+        self._futures = deque()
+
+        # the idea here is to submit at least ``pre_dispatch`` jobs *before* we
+        # yield any results, then do both in tandem, before draining the queue
+        for r in repeats:
+            if len(self._futures) < self.pre_dispatch:
+                self._futures.append(self._executor.submit(trial_fn, r, *args))
+                continue
+            yield self._futures.popleft().result()
+
+        while self._futures:
+            yield self._futures.popleft().result()
+
+    def _cancel_futures(self) -> None:
+        if self._executor is not None:
+            for f in self._futures:
+                f.cancel()
+
+    def setup(
+        self,
+        inputs: List[ArrayIndexType],
+        output: ArrayIndexType,
+        size_dict: Dict[str, int],
+    ) -> Tuple[Any, Any]:
+        raise NotImplementedError
+
+    def __call__(
+        self,
+        inputs: List[ArrayIndexType],
+        output: ArrayIndexType,
+        size_dict: Dict[str, int],
+        memory_limit: Optional[int] = None,
+    ) -> PathType:
+        self._check_args_against_first_call(inputs, output, size_dict)
+
+        # start a timer?
+        if self.max_time is not None:
+            t0 = time.time()
+
+        trial_fn, trial_args = self.setup(inputs, output, size_dict)
+
+        r_start = self._repeats_start + len(self.costs)
+        r_stop = r_start + self.max_repeats
+        repeats = range(r_start, r_stop)
+
+        # create the trials lazily
+        if self._executor is not None:
+            trials = self._gen_results_parallel(repeats, trial_fn, trial_args)
+        else:
+            trials = (trial_fn(r, *trial_args) for r in repeats)
+
+        # assess the trials
+        for ssa_path, cost, size in trials:
+
+            # keep track of all costs and sizes
+            self.costs.append(cost)
+            self.sizes.append(size)
+
+            # check if we have found a new best
+            found_new_best = self.better(cost, size, self.best["flops"], self.best["size"])
+
+            if found_new_best:
+                self.best["flops"] = cost
+                self.best["size"] = size
+                self.best["ssa_path"] = ssa_path
+
+            # check if we have run out of time
+            if (self.max_time is not None) and (time.time() > t0 + self.max_time):
+                break
+
+        self._cancel_futures()
+        return self.path
+
+    def __del__(self):
+        # if we created the parallel pool-executor, shut it down
+        if getattr(self, "_managing_executor", False):
+            self._executor.shutdown()
+
+
+ + + +
+ + + + + + + +
+ + + +

+ path: PathType + + + property + + +

+ + +
+ +

The best path found so far.

+
+ +
+ + + + + +
+ +
+ + +

opt_einsum.path_random.RandomGreedy

+ + +
+ + + + +
+

+ Bases: RandomOptimizer

+ + +

Parameters:

+
    +
  • cost_fn - (callable, optional) A function that returns a heuristic 'cost' of a potential contraction + with which to sort candidates. Should have signature + cost_fn(size12, size1, size2, k12, k1, k2).
    • +
  • temperature - (float, optional) When choosing a possible contraction, its relative probability will be + proportional to exp(-cost / temperature). Thus the larger + temperature is, the further random paths will stray from the normal + 'greedy' path. Conversely, if set to zero, only paths with exactly the + same cost as the best at each step will be explored.
    • +
  • rel_temperature - (bool, optional) Whether to normalize the temperature at each step to the scale of + the best cost. This is generally beneficial as the magnitude of costs + can vary significantly throughout a contraction. If False, the + algorithm will end up branching when the absolute cost is low, but + stick to the 'greedy' path when the cost is high - this can also be + beneficial.
    • +
  • nbranch - (int, optional) How many potential paths to calculate probability for and choose from at each step.
    • +
  • kwargs - Supplied to RandomOptimizer.
    • +
+ +
+ Source code in opt_einsum/path_random.py + 
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class RandomGreedy(RandomOptimizer):
+    """
+
+    **Parameters:**
+
+    - **cost_fn** - *(callable, optional)* A function that returns a heuristic 'cost' of a potential contraction
+        with which to sort candidates. Should have signature
+        `cost_fn(size12, size1, size2, k12, k1, k2)`.
+    - **temperature** - *(float, optional)* When choosing a possible contraction, its relative probability will be
+        proportional to `exp(-cost / temperature)`. Thus the larger
+        `temperature` is, the further random paths will stray from the normal
+        'greedy' path. Conversely, if set to zero, only paths with exactly the
+        same cost as the best at each step will be explored.
+    - **rel_temperature** - *(bool, optional)* Whether to normalize the ``temperature`` at each step to the scale of
+        the best cost. This is generally beneficial as the magnitude of costs
+        can vary significantly throughout a contraction. If False, the
+        algorithm will end up branching when the absolute cost is low, but
+        stick to the 'greedy' path when the cost is high - this can also be
+        beneficial.
+    - **nbranch** - *(int, optional)* How many potential paths to calculate probability for and choose from at each step.
+    - **kwargs** - Supplied to RandomOptimizer.
+    """
+
+    def __init__(
+        self,
+        cost_fn: str = "memory-removed-jitter",
+        temperature: float = 1.0,
+        rel_temperature: bool = True,
+        nbranch: int = 8,
+        **kwargs: Any,
+    ):
+        self.cost_fn = cost_fn
+        self.temperature = temperature
+        self.rel_temperature = rel_temperature
+        self.nbranch = nbranch
+        super().__init__(**kwargs)
+
+    @property
+    def choose_fn(self) -> Any:
+        """The function that chooses which contraction to take - make this a
+        property so that ``temperature`` and ``nbranch`` etc. can be updated
+        between runs.
+        """
+        if self.nbranch == 1:
+            return None
+
+        return functools.partial(
+            thermal_chooser,
+            temperature=self.temperature,
+            nbranch=self.nbranch,
+            rel_temperature=self.rel_temperature,
+        )
+
+    def setup(
+        self,
+        inputs: List[ArrayIndexType],
+        output: ArrayIndexType,
+        size_dict: Dict[str, int],
+    ) -> Tuple[Any, Any]:
+        fn = _trial_greedy_ssa_path_and_cost
+        args = (inputs, output, size_dict, self.choose_fn, self.cost_fn)
+        return fn, args
+
+
+ + + +
+ + + + + + + +
+ + + +

+ choose_fn: Any + + + property + + +

+ + +
+ +

The function that chooses which contraction to take - make this a +property so that temperature and nbranch etc. can be updated +between runs.

+
+ +
+ + + + + +
+ +
+ + +

opt_einsum.paths.DynamicProgramming

+ + +
+ + + + +
+

+ Bases: PathOptimizer

+ + +

Finds the optimal path of pairwise contractions without intermediate outer +products based a dynamic programming approach presented in +Phys. Rev. E 90, 033315 (2014) (the corresponding preprint is publicly +available at https://arxiv.org/abs/1304.6112). This method is especially +well-suited in the area of tensor network states, where it usually +outperforms all the other optimization strategies.

+

This algorithm shows exponential scaling with the number of inputs +in the worst case scenario (see example below). If the graph to be +contracted consists of disconnected subgraphs, the algorithm scales +linearly in the number of disconnected subgraphs and only exponentially +with the number of inputs per subgraph.

+

Parameters:

+
    +
  • +

    minimize - ({'flops', 'size', 'write', 'combo', 'limit', callable}, optional) What to minimize:

    +
      +
    • 'flops' - minimize the number of flops
      • +
    • 'size' - minimize the size of the largest intermediate
      • +
    • 'write' - minimize the size of all intermediate tensors
      • +
    • 'combo' - minimize flops + alpha * write summed over intermediates, a default ratio of alpha=64 + is used, or it can be customized with f'combo-{alpha}'
      • +
    • 'limit' - minimize max(flops, alpha * write) summed over intermediates, a default ratio of alpha=64 + is used, or it can be customized with f'limit-{alpha}'
      • +
    • callable - a custom local cost function
      • +
    +
    • +
  • +

    cost_cap - ({True, False, int}, optional) How to implement cost-capping:

    +
      +
    • True - iteratively increase the cost-cap
      • +
    • False - implement no cost-cap at all
      • +
    • int - use explicit cost cap
      • +
    +
    • +
  • +

    search_outer - (bool, optional) In rare circumstances the optimal contraction may involve an outer + product, this option allows searching such contractions but may well + slow down the path finding considerably on all but very small graphs.

    +
    • +
+ +
+ Source code in opt_einsum/paths.py + 
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class DynamicProgramming(PathOptimizer):
+    """
+    Finds the optimal path of pairwise contractions without intermediate outer
+    products based a dynamic programming approach presented in
+    Phys. Rev. E 90, 033315 (2014) (the corresponding preprint is publicly
+    available at https://arxiv.org/abs/1304.6112). This method is especially
+    well-suited in the area of tensor network states, where it usually
+    outperforms all the other optimization strategies.
+
+    This algorithm shows exponential scaling with the number of inputs
+    in the worst case scenario (see example below). If the graph to be
+    contracted consists of disconnected subgraphs, the algorithm scales
+    linearly in the number of disconnected subgraphs and only exponentially
+    with the number of inputs per subgraph.
+
+    **Parameters:**
+
+    - **minimize** - *({'flops', 'size', 'write', 'combo', 'limit', callable}, optional)* What to minimize:
+
+        - 'flops' - minimize the number of flops
+        - 'size' - minimize the size of the largest intermediate
+        - 'write' - minimize the size of all intermediate tensors
+        - 'combo' - minimize `flops + alpha * write` summed over intermediates, a default ratio of alpha=64
+          is used, or it can be customized with `f'combo-{alpha}'`
+        - 'limit' - minimize `max(flops, alpha * write)` summed over intermediates, a default ratio of alpha=64
+          is used, or it can be customized with `f'limit-{alpha}'`
+        - callable - a custom local cost function
+
+    - **cost_cap** - *({True, False, int}, optional)* How to implement cost-capping:
+
+        - True - iteratively increase the cost-cap
+        - False - implement no cost-cap at all
+        - int - use explicit cost cap
+
+    - **search_outer** - *(bool, optional)* In rare circumstances the optimal contraction may involve an outer
+        product, this option allows searching such contractions but may well
+        slow down the path finding considerably on all but very small graphs.
+    """
+
+    def __init__(self, minimize: str = "flops", cost_cap: bool = True, search_outer: bool = False) -> None:
+        self.minimize = minimize
+        self.search_outer = search_outer
+        self.cost_cap = cost_cap
+
+    def __call__(
+        self,
+        inputs_: List[ArrayIndexType],
+        output_: ArrayIndexType,
+        size_dict_: Dict[str, int],
+        memory_limit: Optional[int] = None,
+    ) -> PathType:
+        """
+        **Parameters:**
+
+        - **inputs** - *(list)* List of sets that represent the lhs side of the einsum subscript
+        - **output** - *(set)* Set that represents the rhs side of the overall einsum subscript
+        - **size_dict** - *(dictionary)* Dictionary of index sizes
+        - **memory_limit** - *(int)* The maximum number of elements in a temporary array
+
+        **Returns:**
+
+        - **path** - *(list)* The contraction order (a list of tuples of ints).
+
+        **Examples:**
+
+        ```python
+        n_in = 3  # exponential scaling
+        n_out = 2 # linear scaling
+        s = dict()
+        i_all = []
+        for _ in range(n_out):
+            i = [set() for _ in range(n_in)]
+            for j in range(n_in):
+                for k in range(j+1, n_in):
+                    c = oe.get_symbol(len(s))
+                    i[j].add(c)
+                    i[k].add(c)
+                    s[c] = 2
+            i_all.extend(i)
+        o = DynamicProgramming()
+        o(i_all, set(), s)
+        #> [(1, 2), (0, 4), (1, 2), (0, 2), (0, 1)]
+        ```
+        """
+        _check_contraction, naive_scale = _parse_minimize(self.minimize)
+        _check_outer = (lambda x: True) if self.search_outer else (lambda x: x)
+
+        ind_counts = Counter(itertools.chain(*inputs_, output_))
+        all_inds = tuple(ind_counts)
+
+        # convert all indices to integers (makes set operations ~10 % faster)
+        symbol2int = {c: j for j, c in enumerate(all_inds)}
+        inputs = [frozenset(symbol2int[c] for c in i) for i in inputs_]
+        output = frozenset(symbol2int[c] for c in output_)
+        size_dict_canonical = {symbol2int[c]: v for c, v in size_dict_.items() if c in symbol2int}
+        size_dict = [size_dict_canonical[j] for j in range(len(size_dict_canonical))]
+        naive_cost = naive_scale * len(inputs) * functools.reduce(operator.mul, size_dict, 1)
+
+        inputs, inputs_done, inputs_contractions = _dp_parse_out_single_term_ops(inputs, all_inds, ind_counts)
+
+        if not inputs:
+            # nothing left to do after single axis reductions!
+            return _tree_to_sequence(simple_tree_tuple(inputs_done))
+
+        # a list of all necessary contraction expressions for each of the
+        # disconnected subgraphs and their size
+        subgraph_contractions = inputs_done
+        subgraph_contractions_size = [1] * len(inputs_done)
+
+        if self.search_outer:
+            # optimize everything together if we are considering outer products
+            subgraphs = [frozenset(range(len(inputs)))]
+        else:
+            subgraphs = _find_disconnected_subgraphs(inputs, output)
+
+        # the bitmap set of all tensors is computed as it is needed to
+        # compute set differences: s1 - s2 transforms into
+        # s1 & (all_tensors ^ s2)
+        all_tensors = (1 << len(inputs)) - 1
+
+        for g in subgraphs:
+
+            # dynamic programming approach to compute x[n] for subgraph g;
+            # x[n][set of n tensors] = (indices, cost, contraction)
+            # the set of n tensors is represented by a bitmap: if bit j is 1,
+            # tensor j is in the set, e.g. 0b100101 = {0,2,5}; set unions
+            # (intersections) can then be computed by bitwise or (and);
+            x: List[Any] = [None] * 2 + [dict() for j in range(len(g) - 1)]
+            x[1] = OrderedDict((1 << j, (inputs[j], 0, inputs_contractions[j])) for j in g)
+
+            # convert set of tensors g to a bitmap set:
+            bitmap_g = functools.reduce(lambda x, y: x | y, (1 << j for j in g))
+
+            # try to find contraction with cost <= cost_cap and increase
+            # cost_cap successively if no such contraction is found;
+            # this is a major performance improvement; start with product of
+            # output index dimensions as initial cost_cap
+            subgraph_inds = frozenset.union(*_bitmap_select(bitmap_g, inputs))
+            if self.cost_cap is True:
+                cost_cap = compute_size_by_dict(subgraph_inds & output, size_dict)
+            elif self.cost_cap is False:
+                cost_cap = float("inf")  # type: ignore
+            else:
+                cost_cap = self.cost_cap
+            # set the factor to increase the cost by each iteration (ensure > 1)
+            if len(subgraph_inds) == 0:
+                cost_increment = 2
+            else:
+                cost_increment = max(min(map(size_dict.__getitem__, subgraph_inds)), 2)
+
+            while len(x[-1]) == 0:
+                for n in range(2, len(x[1]) + 1):
+                    xn = x[n]
+
+                    # try to combine solutions from x[m] and x[n-m]
+                    for m in range(1, n // 2 + 1):
+                        for s1, (i1, cost1, contract1) in x[m].items():
+                            for s2, (i2, cost2, contract2) in x[n - m].items():
+
+                                # can only merge if s1 and s2 are disjoint
+                                # and avoid e.g. s1={0}, s2={1} and s1={1}, s2={0}
+                                if (not s1 & s2) and (m != n - m or s1 < s2):
+                                    i1_cut_i2_wo_output = (i1 & i2) - output
+
+                                    # maybe ignore outer products:
+                                    if _check_outer(i1_cut_i2_wo_output):
+
+                                        i1_union_i2 = i1 | i2
+                                        _check_contraction(
+                                            cost1,
+                                            cost2,
+                                            i1_union_i2,
+                                            size_dict,
+                                            cost_cap,
+                                            s1,
+                                            s2,
+                                            xn,
+                                            bitmap_g,
+                                            all_tensors,
+                                            inputs,
+                                            i1_cut_i2_wo_output,
+                                            memory_limit,
+                                            contract1,
+                                            contract2,
+                                        )
+
+                if (cost_cap > naive_cost) and (len(x[-1]) == 0):
+                    raise RuntimeError("No contraction found for given `memory_limit`.")
+
+                # increase cost cap for next iteration:
+                cost_cap = cost_increment * cost_cap
+
+            i, cost, contraction = list(x[-1].values())[0]
+            subgraph_contractions.append(contraction)
+            subgraph_contractions_size.append(compute_size_by_dict(i, size_dict))
+
+        # sort the subgraph contractions by the size of the subgraphs in
+        # ascending order (will give the cheapest contractions); note that
+        # outer products should be performed pairwise (to use BLAS functions)
+        subgraph_contractions = [
+            subgraph_contractions[j]
+            for j in sorted(
+                range(len(subgraph_contractions_size)),
+                key=subgraph_contractions_size.__getitem__,
+            )
+        ]
+
+        # build the final contraction tree
+        tree = simple_tree_tuple(subgraph_contractions)
+        return _tree_to_sequence(tree)
+
+
+ + + +
+ + + + + + + + + + +
+ + + +

+ __call__(inputs_, output_, size_dict_, memory_limit=None) + +

+ + +
+ +

Parameters:

+
    +
  • inputs - (list) List of sets that represent the lhs side of the einsum subscript
    • +
  • output - (set) Set that represents the rhs side of the overall einsum subscript
    • +
  • size_dict - (dictionary) Dictionary of index sizes
    • +
  • memory_limit - (int) The maximum number of elements in a temporary array
    • +
+

Returns:

+
    +
  • path - (list) The contraction order (a list of tuples of ints).
    • +
+

Examples:

+
n_in = 3  # exponential scaling
+n_out = 2 # linear scaling
+s = dict()
+i_all = []
+for _ in range(n_out):
+    i = [set() for _ in range(n_in)]
+    for j in range(n_in):
+        for k in range(j+1, n_in):
+            c = oe.get_symbol(len(s))
+            i[j].add(c)
+            i[k].add(c)
+            s[c] = 2
+    i_all.extend(i)
+o = DynamicProgramming()
+o(i_all, set(), s)
+#> [(1, 2), (0, 4), (1, 2), (0, 2), (0, 1)]
+
+ +
+ Source code in opt_einsum/paths.py + 
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def __call__(
+    self,
+    inputs_: List[ArrayIndexType],
+    output_: ArrayIndexType,
+    size_dict_: Dict[str, int],
+    memory_limit: Optional[int] = None,
+) -> PathType:
+    """
+    **Parameters:**
+
+    - **inputs** - *(list)* List of sets that represent the lhs side of the einsum subscript
+    - **output** - *(set)* Set that represents the rhs side of the overall einsum subscript
+    - **size_dict** - *(dictionary)* Dictionary of index sizes
+    - **memory_limit** - *(int)* The maximum number of elements in a temporary array
+
+    **Returns:**
+
+    - **path** - *(list)* The contraction order (a list of tuples of ints).
+
+    **Examples:**
+
+    ```python
+    n_in = 3  # exponential scaling
+    n_out = 2 # linear scaling
+    s = dict()
+    i_all = []
+    for _ in range(n_out):
+        i = [set() for _ in range(n_in)]
+        for j in range(n_in):
+            for k in range(j+1, n_in):
+                c = oe.get_symbol(len(s))
+                i[j].add(c)
+                i[k].add(c)
+                s[c] = 2
+        i_all.extend(i)
+    o = DynamicProgramming()
+    o(i_all, set(), s)
+    #> [(1, 2), (0, 4), (1, 2), (0, 2), (0, 1)]
+    ```
+    """
+    _check_contraction, naive_scale = _parse_minimize(self.minimize)
+    _check_outer = (lambda x: True) if self.search_outer else (lambda x: x)
+
+    ind_counts = Counter(itertools.chain(*inputs_, output_))
+    all_inds = tuple(ind_counts)
+
+    # convert all indices to integers (makes set operations ~10 % faster)
+    symbol2int = {c: j for j, c in enumerate(all_inds)}
+    inputs = [frozenset(symbol2int[c] for c in i) for i in inputs_]
+    output = frozenset(symbol2int[c] for c in output_)
+    size_dict_canonical = {symbol2int[c]: v for c, v in size_dict_.items() if c in symbol2int}
+    size_dict = [size_dict_canonical[j] for j in range(len(size_dict_canonical))]
+    naive_cost = naive_scale * len(inputs) * functools.reduce(operator.mul, size_dict, 1)
+
+    inputs, inputs_done, inputs_contractions = _dp_parse_out_single_term_ops(inputs, all_inds, ind_counts)
+
+    if not inputs:
+        # nothing left to do after single axis reductions!
+        return _tree_to_sequence(simple_tree_tuple(inputs_done))
+
+    # a list of all necessary contraction expressions for each of the
+    # disconnected subgraphs and their size
+    subgraph_contractions = inputs_done
+    subgraph_contractions_size = [1] * len(inputs_done)
+
+    if self.search_outer:
+        # optimize everything together if we are considering outer products
+        subgraphs = [frozenset(range(len(inputs)))]
+    else:
+        subgraphs = _find_disconnected_subgraphs(inputs, output)
+
+    # the bitmap set of all tensors is computed as it is needed to
+    # compute set differences: s1 - s2 transforms into
+    # s1 & (all_tensors ^ s2)
+    all_tensors = (1 << len(inputs)) - 1
+
+    for g in subgraphs:
+
+        # dynamic programming approach to compute x[n] for subgraph g;
+        # x[n][set of n tensors] = (indices, cost, contraction)
+        # the set of n tensors is represented by a bitmap: if bit j is 1,
+        # tensor j is in the set, e.g. 0b100101 = {0,2,5}; set unions
+        # (intersections) can then be computed by bitwise or (and);
+        x: List[Any] = [None] * 2 + [dict() for j in range(len(g) - 1)]
+        x[1] = OrderedDict((1 << j, (inputs[j], 0, inputs_contractions[j])) for j in g)
+
+        # convert set of tensors g to a bitmap set:
+        bitmap_g = functools.reduce(lambda x, y: x | y, (1 << j for j in g))
+
+        # try to find contraction with cost <= cost_cap and increase
+        # cost_cap successively if no such contraction is found;
+        # this is a major performance improvement; start with product of
+        # output index dimensions as initial cost_cap
+        subgraph_inds = frozenset.union(*_bitmap_select(bitmap_g, inputs))
+        if self.cost_cap is True:
+            cost_cap = compute_size_by_dict(subgraph_inds & output, size_dict)
+        elif self.cost_cap is False:
+            cost_cap = float("inf")  # type: ignore
+        else:
+            cost_cap = self.cost_cap
+        # set the factor to increase the cost by each iteration (ensure > 1)
+        if len(subgraph_inds) == 0:
+            cost_increment = 2
+        else:
+            cost_increment = max(min(map(size_dict.__getitem__, subgraph_inds)), 2)
+
+        while len(x[-1]) == 0:
+            for n in range(2, len(x[1]) + 1):
+                xn = x[n]
+
+                # try to combine solutions from x[m] and x[n-m]
+                for m in range(1, n // 2 + 1):
+                    for s1, (i1, cost1, contract1) in x[m].items():
+                        for s2, (i2, cost2, contract2) in x[n - m].items():
+
+                            # can only merge if s1 and s2 are disjoint
+                            # and avoid e.g. s1={0}, s2={1} and s1={1}, s2={0}
+                            if (not s1 & s2) and (m != n - m or s1 < s2):
+                                i1_cut_i2_wo_output = (i1 & i2) - output
+
+                                # maybe ignore outer products:
+                                if _check_outer(i1_cut_i2_wo_output):
+
+                                    i1_union_i2 = i1 | i2
+                                    _check_contraction(
+                                        cost1,
+                                        cost2,
+                                        i1_union_i2,
+                                        size_dict,
+                                        cost_cap,
+                                        s1,
+                                        s2,
+                                        xn,
+                                        bitmap_g,
+                                        all_tensors,
+                                        inputs,
+                                        i1_cut_i2_wo_output,
+                                        memory_limit,
+                                        contract1,
+                                        contract2,
+                                    )
+
+            if (cost_cap > naive_cost) and (len(x[-1]) == 0):
+                raise RuntimeError("No contraction found for given `memory_limit`.")
+
+            # increase cost cap for next iteration:
+            cost_cap = cost_increment * cost_cap
+
+        i, cost, contraction = list(x[-1].values())[0]
+        subgraph_contractions.append(contraction)
+        subgraph_contractions_size.append(compute_size_by_dict(i, size_dict))
+
+    # sort the subgraph contractions by the size of the subgraphs in
+    # ascending order (will give the cheapest contractions); note that
+    # outer products should be performed pairwise (to use BLAS functions)
+    subgraph_contractions = [
+        subgraph_contractions[j]
+        for j in sorted(
+            range(len(subgraph_contractions_size)),
+            key=subgraph_contractions_size.__getitem__,
+        )
+    ]
+
+    # build the final contraction tree
+    tree = simple_tree_tuple(subgraph_contractions)
+    return _tree_to_sequence(tree)
+
+
+
+ +
+ + + +
+ +
+ + +
+ + + + + + + + + + + + + +
+
+ + + +
+ +
+ + + +
+
+
+
+ + + + + + + + + + + + + + + + \ No newline at end of file diff --git a/assets/_mkdocstrings.css b/assets/_mkdocstrings.css new file mode 100644 index 00000000..85449ec7 --- /dev/null +++ b/assets/_mkdocstrings.css @@ -0,0 +1,119 @@ + +/* Avoid breaking parameter names, etc. in table cells. */ +.doc-contents td code { + word-break: normal !important; +} + +/* No line break before first paragraph of descriptions. */ +.doc-md-description, +.doc-md-description>p:first-child { + display: inline; +} + +/* Max width for docstring sections tables. */ +.doc .md-typeset__table, +.doc .md-typeset__table table { + display: table !important; + width: 100%; +} + +.doc .md-typeset__table tr { + display: table-row; +} + +/* Defaults in Spacy table style. */ +.doc-param-default { + float: right; +} + +/* Backward-compatibility: docstring section titles in bold. */ +.doc-section-title { + font-weight: bold; +} + +/* Symbols in Navigation and ToC. */ +:root, +[data-md-color-scheme="default"] { + 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bold; +} + +code.doc-symbol-attribute { + color: var(--doc-symbol-attribute-fg-color); + background-color: var(--doc-symbol-attribute-bg-color); +} + +code.doc-symbol-attribute::after { + content: "attr"; +} + +code.doc-symbol-function { + color: var(--doc-symbol-function-fg-color); + background-color: var(--doc-symbol-function-bg-color); +} + +code.doc-symbol-function::after { + content: "func"; +} + +code.doc-symbol-method { + color: var(--doc-symbol-method-fg-color); + background-color: var(--doc-symbol-method-bg-color); +} + +code.doc-symbol-method::after { + content: "meth"; +} + +code.doc-symbol-class { + color: var(--doc-symbol-class-fg-color); + background-color: var(--doc-symbol-class-bg-color); +} + +code.doc-symbol-class::after { + content: "class"; +} + +code.doc-symbol-module { + color: var(--doc-symbol-module-fg-color); + background-color: var(--doc-symbol-module-bg-color); +} + +code.doc-symbol-module::after { + content: "mod"; +} + +.doc-signature .autorefs { + color: inherit; + border-bottom: 1px dotted currentcolor; +} diff --git a/assets/images/favicon.png b/assets/images/favicon.png new file mode 100644 index 00000000..1cf13b9f Binary files /dev/null and b/assets/images/favicon.png differ diff --git a/assets/javascripts/bundle.a7c05c9e.min.js b/assets/javascripts/bundle.a7c05c9e.min.js new file mode 100644 index 00000000..31d74078 --- /dev/null +++ b/assets/javascripts/bundle.a7c05c9e.min.js @@ -0,0 +1,29 @@ +"use strict";(()=>{var Fi=Object.create;var gr=Object.defineProperty;var ji=Object.getOwnPropertyDescriptor;var Wi=Object.getOwnPropertyNames,Dt=Object.getOwnPropertySymbols,Ui=Object.getPrototypeOf,xr=Object.prototype.hasOwnProperty,no=Object.prototype.propertyIsEnumerable;var oo=(e,t,r)=>t in e?gr(e,t,{enumerable:!0,configurable:!0,writable:!0,value:r}):e[t]=r,R=(e,t)=>{for(var r in t||(t={}))xr.call(t,r)&&oo(e,r,t[r]);if(Dt)for(var r of Dt(t))no.call(t,r)&&oo(e,r,t[r]);return e};var io=(e,t)=>{var r={};for(var o in 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circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead path{fill:var(--md-mermaid-sequence-message-line-color);stroke:none}.loopLine{fill:var(--md-mermaid-sequence-loop-bg-color);stroke:var(--md-mermaid-sequence-loop-border-color)}.labelBox{fill:var(--md-mermaid-sequence-label-bg-color);stroke:none}.labelText,.labelText>span{fill:var(--md-mermaid-sequence-label-fg-color);font-family:var(--md-mermaid-font-family)}.sequenceNumber{fill:var(--md-mermaid-sequence-number-fg-color)}rect.rect{fill:var(--md-mermaid-sequence-box-bg-color);stroke:none}rect.rect+text.text{fill:var(--md-mermaid-sequence-box-fg-color)}defs #sequencenumber{fill:var(--md-mermaid-sequence-number-bg-color)!important}";var Br,Da=0;function Va(){return typeof mermaid=="undefined"||mermaid instanceof Element?wt("https://unpkg.com/mermaid@10/dist/mermaid.min.js"):I(void 0)}function In(e){return 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video",e))c.pause()}),tt(e).pipe(v(()=>Na(n)),y(c=>s.next(c)),L(()=>s.complete()),m(c=>R({ref:e},c)))}).pipe(Qe(se))}function Un(e,{viewport$:t,target$:r,print$:o}){return S(...$(".annotate:not(.highlight)",e).map(n=>Cn(n,{target$:r,print$:o})),...$("pre:not(.mermaid) > code",e).map(n=>$n(n,{target$:r,print$:o})),...$("pre.mermaid",e).map(n=>In(n)),...$("table:not([class])",e).map(n=>jn(n)),...$("details",e).map(n=>Pn(n,{target$:r,print$:o})),...$("[data-tabs]",e).map(n=>Wn(n,{viewport$:t,target$:r})),...$("[title]",e).filter(()=>G("content.tooltips")).map(n=>lt(n,{viewport$:t})))}function za(e,{alert$:t}){return t.pipe(v(r=>S(I(!0),I(!1).pipe(Ge(2e3))).pipe(m(o=>({message:r,active:o})))))}function Dn(e,t){let r=P(".md-typeset",e);return C(()=>{let o=new g;return o.subscribe(({message:n,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=n}),za(e,t).pipe(y(n=>o.next(n)),L(()=>o.complete()),m(n=>R({ref:e},n)))})}var qa=0;function Qa(e,t){document.body.append(e);let{width:r}=ce(e);e.style.setProperty("--md-tooltip-width",`${r}px`),e.remove();let o=cr(t),n=typeof o!="undefined"?De(o):I({x:0,y:0}),i=S(et(t),kt(t)).pipe(K());return z([i,n]).pipe(m(([a,s])=>{let{x:p,y:c}=Ue(t),l=ce(t),f=t.closest("table");return f&&t.parentElement&&(p+=f.offsetLeft+t.parentElement.offsetLeft,c+=f.offsetTop+t.parentElement.offsetTop),{active:a,offset:{x:p-s.x+l.width/2-r/2,y:c-s.y+l.height+8}}}))}function Vn(e){let t=e.title;if(!t.length)return M;let r=`__tooltip_${qa++}`,o=Pt(r,"inline"),n=P(".md-typeset",o);return n.innerHTML=t,C(()=>{let i=new g;return i.subscribe({next({offset:a}){o.style.setProperty("--md-tooltip-x",`${a.x}px`),o.style.setProperty("--md-tooltip-y",`${a.y}px`)},complete(){o.style.removeProperty("--md-tooltip-x"),o.style.removeProperty("--md-tooltip-y")}}),S(i.pipe(b(({active:a})=>a)),i.pipe(_e(250),b(({active:a})=>!a))).subscribe({next({active:a}){a?(e.insertAdjacentElement("afterend",o),e.setAttribute("aria-describedby",r),e.removeAttribute("title")):(o.remove(),e.removeAttribute("aria-describedby"),e.setAttribute("title",t))},complete(){o.remove(),e.removeAttribute("aria-describedby"),e.setAttribute("title",t)}}),i.pipe(Le(16,me)).subscribe(({active:a})=>{o.classList.toggle("md-tooltip--active",a)}),i.pipe(ct(125,me),b(()=>!!e.offsetParent),m(()=>e.offsetParent.getBoundingClientRect()),m(({x:a})=>a)).subscribe({next(a){a?o.style.setProperty("--md-tooltip-0",`${-a}px`):o.style.removeProperty("--md-tooltip-0")},complete(){o.style.removeProperty("--md-tooltip-0")}}),Qa(o,e).pipe(y(a=>i.next(a)),L(()=>i.complete()),m(a=>R({ref:e},a)))}).pipe(Qe(se))}function Ka({viewport$:e}){if(!G("header.autohide"))return I(!1);let t=e.pipe(m(({offset:{y:n}})=>n),Ye(2,1),m(([n,i])=>[nMath.abs(i-n.y)>100),m(([,[n]])=>n),K()),o=Ve("search");return z([e,o]).pipe(m(([{offset:n},i])=>n.y>400&&!i),K(),v(n=>n?r:I(!1)),Q(!1))}function Nn(e,t){return C(()=>z([ge(e),Ka(t)])).pipe(m(([{height:r},o])=>({height:r,hidden:o})),K((r,o)=>r.height===o.height&&r.hidden===o.hidden),B(1))}function zn(e,{header$:t,main$:r}){return C(()=>{let o=new g,n=o.pipe(X(),ne(!0));o.pipe(Z("active"),We(t)).subscribe(([{active:a},{hidden:s}])=>{e.classList.toggle("md-header--shadow",a&&!s),e.hidden=s});let i=ue($("[title]",e)).pipe(b(()=>G("content.tooltips")),oe(a=>Vn(a)));return r.subscribe(o),t.pipe(U(n),m(a=>R({ref:e},a)),Pe(i.pipe(U(n))))})}function Ya(e,{viewport$:t,header$:r}){return mr(e,{viewport$:t,header$:r}).pipe(m(({offset:{y:o}})=>{let{height:n}=ce(e);return{active:o>=n}}),Z("active"))}function qn(e,t){return C(()=>{let r=new g;r.subscribe({next({active:n}){e.classList.toggle("md-header__title--active",n)},complete(){e.classList.remove("md-header__title--active")}});let o=fe(".md-content h1");return typeof o=="undefined"?M:Ya(o,t).pipe(y(n=>r.next(n)),L(()=>r.complete()),m(n=>R({ref:e},n)))})}function Qn(e,{viewport$:t,header$:r}){let o=r.pipe(m(({height:i})=>i),K()),n=o.pipe(v(()=>ge(e).pipe(m(({height:i})=>({top:e.offsetTop,bottom:e.offsetTop+i})),Z("bottom"))));return z([o,n,t]).pipe(m(([i,{top:a,bottom:s},{offset:{y:p},size:{height:c}}])=>(c=Math.max(0,c-Math.max(0,a-p,i)-Math.max(0,c+p-s)),{offset:a-i,height:c,active:a-i<=p})),K((i,a)=>i.offset===a.offset&&i.height===a.height&&i.active===a.active))}function Ba(e){let t=__md_get("__palette")||{index:e.findIndex(o=>matchMedia(o.getAttribute("data-md-color-media")).matches)},r=Math.max(0,Math.min(t.index,e.length-1));return I(...e).pipe(oe(o=>d(o,"change").pipe(m(()=>o))),Q(e[r]),m(o=>({index:e.indexOf(o),color:{media:o.getAttribute("data-md-color-media"),scheme:o.getAttribute("data-md-color-scheme"),primary:o.getAttribute("data-md-color-primary"),accent:o.getAttribute("data-md-color-accent")}})),B(1))}function Kn(e){let t=$("input",e),r=E("meta",{name:"theme-color"});document.head.appendChild(r);let o=E("meta",{name:"color-scheme"});document.head.appendChild(o);let n=$t("(prefers-color-scheme: light)");return C(()=>{let i=new g;return i.subscribe(a=>{if(document.body.setAttribute("data-md-color-switching",""),a.color.media==="(prefers-color-scheme)"){let s=matchMedia("(prefers-color-scheme: light)"),p=document.querySelector(s.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: 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Gr=Vt(Yr());function Ga(e){e.setAttribute("data-md-copying","");let t=e.closest("[data-copy]"),r=t?t.getAttribute("data-copy"):e.innerText;return e.removeAttribute("data-md-copying"),r.trimEnd()}function Bn({alert$:e}){Gr.default.isSupported()&&new F(t=>{new Gr.default("[data-clipboard-target], [data-clipboard-text]",{text:r=>r.getAttribute("data-clipboard-text")||Ga(P(r.getAttribute("data-clipboard-target")))}).on("success",r=>t.next(r))}).pipe(y(t=>{t.trigger.focus()}),m(()=>ye("clipboard.copied"))).subscribe(e)}function Gn(e,t){return e.protocol=t.protocol,e.hostname=t.hostname,e}function Ja(e,t){let r=new Map;for(let o of $("url",e)){let n=P("loc",o),i=[Gn(new URL(n.textContent),t)];r.set(`${i[0]}`,i);for(let a of $("[rel=alternate]",o)){let s=a.getAttribute("href");s!=null&&i.push(Gn(new URL(s),t))}}return r}function ur(e){return mn(new URL("sitemap.xml",e)).pipe(m(t=>Ja(t,new URL(e))),ve(()=>I(new Map)))}function Xa(e,t){if(!(e.target instanceof Element))return M;let 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g,o=r.pipe(X(),ne(!0));z([t.pipe(Ae(It)),r],(i,a)=>a).pipe(Z("value")).subscribe(({value:i})=>t.next({type:2,data:i})),r.pipe(Z("focus")).subscribe(({focus:i})=>{i&&Je("search",i)}),d(e.form,"reset").pipe(U(o)).subscribe(()=>e.focus());let n=P("header [for=__search]");return d(n,"click").subscribe(()=>e.focus()),ns(e,{worker$:t}).pipe(y(i=>r.next(i)),L(()=>r.complete()),m(i=>R({ref:e},i)),B(1))}function si(e,{worker$:t,query$:r}){let o=new g,n=tn(e.parentElement).pipe(b(Boolean)),i=e.parentElement,a=P(":scope > :first-child",e),s=P(":scope > :last-child",e);Ve("search").subscribe(l=>s.setAttribute("role",l?"list":"presentation")),o.pipe(ee(r),Ur(t.pipe(Ae(It)))).subscribe(([{items:l},{value:f}])=>{switch(l.length){case 0:a.textContent=f.length?ye("search.result.none"):ye("search.result.placeholder");break;case 1:a.textContent=ye("search.result.one");break;default:let u=sr(l.length);a.textContent=ye("search.result.other",u)}});let 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g,n=Se("search-query"),i=S(d(n,"keydown"),d(n,"focus")).pipe(be(se),m(()=>n.value),K());return o.pipe(We(i),m(([{suggest:s},p])=>{let c=p.split(/([\s-]+)/);if(s!=null&&s.length&&c[c.length-1]){let l=s[s.length-1];l.startsWith(c[c.length-1])&&(c[c.length-1]=l)}else c.length=0;return c})).subscribe(s=>e.innerHTML=s.join("").replace(/\s/g," ")),r.pipe(b(({mode:s})=>s==="search")).subscribe(s=>{switch(s.type){case"ArrowRight":e.innerText.length&&n.selectionStart===n.value.length&&(n.value=e.innerText);break}}),t.pipe(b(dr),m(({data:s})=>s)).pipe(y(s=>o.next(s)),L(()=>o.complete()),m(()=>({ref:e})))}function li(e,{index$:t,keyboard$:r}){let o=Te();try{let n=ni(o.search,t),i=Se("search-query",e),a=Se("search-result",e);d(e,"click").pipe(b(({target:p})=>p instanceof Element&&!!p.closest("a"))).subscribe(()=>Je("search",!1)),r.pipe(b(({mode:p})=>p==="search")).subscribe(p=>{let c=Re();switch(p.type){case"Enter":if(c===i){let l=new Map;for(let f of $(":first-child [href]",a)){let 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z([t,r.pipe(Q(xe()),b(o=>!!o.searchParams.get("h")))]).pipe(m(([o,n])=>oi(o.config)(n.searchParams.get("h"))),m(o=>{var a;let n=new Map,i=document.createNodeIterator(e,NodeFilter.SHOW_TEXT);for(let s=i.nextNode();s;s=i.nextNode())if((a=s.parentElement)!=null&&a.offsetHeight){let p=s.textContent,c=o(p);c.length>p.length&&n.set(s,c)}for(let[s,p]of n){let{childNodes:c}=E("span",null,p);s.replaceWith(...Array.from(c))}return{ref:e,nodes:n}}))}function as(e,{viewport$:t,main$:r}){let o=e.closest(".md-grid"),n=o.offsetTop-o.parentElement.offsetTop;return z([r,t]).pipe(m(([{offset:i,height:a},{offset:{y:s}}])=>(a=a+Math.min(n,Math.max(0,s-i))-n,{height:a,locked:s>=i+n})),K((i,a)=>i.height===a.height&&i.locked===a.locked))}function Jr(e,o){var n=o,{header$:t}=n,r=io(n,["header$"]);let i=P(".md-sidebar__scrollwrap",e),{y:a}=Ue(i);return C(()=>{let s=new g,p=s.pipe(X(),ne(!0)),c=s.pipe(Le(0,me));return c.pipe(ee(t)).subscribe({next([{height:l},{height:f}]){i.style.height=`${l-2*a}px`,e.style.top=`${f}px`},complete(){i.style.height="",e.style.top=""}}),c.pipe(Ae()).subscribe(()=>{for(let l of $(".md-nav__link--active[href]",e)){if(!l.clientHeight)continue;let f=l.closest(".md-sidebar__scrollwrap");if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=ce(f);f.scrollTo({top:u-h/2})}}}),ue($("label[tabindex]",e)).pipe(oe(l=>d(l,"click").pipe(be(se),m(()=>l),U(p)))).subscribe(l=>{let f=P(`[id="${l.htmlFor}"]`);P(`[aria-labelledby="${l.id}"]`).setAttribute("aria-expanded",`${f.checked}`)}),as(e,r).pipe(y(l=>s.next(l)),L(()=>s.complete()),m(l=>R({ref:e},l)))})}function fi(e,t){if(typeof t!="undefined"){let r=`https://api.github.com/repos/${e}/${t}`;return Ct(Ne(`${r}/releases/latest`).pipe(ve(()=>M),m(o=>({version:o.tag_name})),Be({})),Ne(r).pipe(ve(()=>M),m(o=>({stars:o.stargazers_count,forks:o.forks_count})),Be({}))).pipe(m(([o,n])=>R(R({},o),n)))}else{let r=`https://api.github.com/users/${e}`;return Ne(r).pipe(m(o=>({repositories:o.public_repos})),Be({}))}}function ui(e,t){let r=`https://${e}/api/v4/projects/${encodeURIComponent(t)}`;return Ne(r).pipe(ve(()=>M),m(({star_count:o,forks_count:n})=>({stars:o,forks:n})),Be({}))}function di(e){let t=e.match(/^.+github\.com\/([^/]+)\/?([^/]+)?/i);if(t){let[,r,o]=t;return fi(r,o)}if(t=e.match(/^.+?([^/]*gitlab[^/]+)\/(.+?)\/?$/i),t){let[,r,o]=t;return ui(r,o)}return M}var ss;function cs(e){return ss||(ss=C(()=>{let t=__md_get("__source",sessionStorage);if(t)return I(t);if(ae("consent").length){let o=__md_get("__consent");if(!(o&&o.github))return M}return di(e.href).pipe(y(o=>__md_set("__source",o,sessionStorage)))}).pipe(ve(()=>M),b(t=>Object.keys(t).length>0),m(t=>({facts:t})),B(1)))}function hi(e){let t=P(":scope > :last-child",e);return C(()=>{let r=new g;return 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n=t.pipe(m(({offset:{y:a}})=>a),Ye(2,1),m(([a,s])=>a>s&&s>0),K()),i=r.pipe(m(({active:a})=>a));return z([i,n]).pipe(m(([a,s])=>!(a&&s)),K(),U(o.pipe(Ce(1))),ne(!0),st({delay:250}),m(a=>({hidden:a})))}function gi(e,{viewport$:t,header$:r,main$:o,target$:n}){let i=new g,a=i.pipe(X(),ne(!0));return i.subscribe({next({hidden:s}){e.hidden=s,s?(e.setAttribute("tabindex","-1"),e.blur()):e.removeAttribute("tabindex")},complete(){e.style.top="",e.hidden=!0,e.removeAttribute("tabindex")}}),r.pipe(U(a),Z("height")).subscribe(({height:s})=>{e.style.top=`${s+16}px`}),d(e,"click").subscribe(s=>{s.preventDefault(),window.scrollTo({top:0})}),ms(e,{viewport$:t,main$:o,target$:n}).pipe(y(s=>i.next(s)),L(()=>i.complete()),m(s=>R({ref:e},s)))}function xi({document$:e,viewport$:t}){e.pipe(v(()=>$(".md-ellipsis")),oe(r=>tt(r).pipe(U(e.pipe(Ce(1))),b(o=>o),m(()=>r),we(1))),b(r=>r.offsetWidth{let o=r.innerText,n=r.closest("a")||r;return n.title=o,lt(n,{viewport$:t}).pipe(U(e.pipe(Ce(1))),L(()=>n.removeAttribute("title")))})).subscribe(),e.pipe(v(()=>$(".md-status")),oe(r=>lt(r,{viewport$:t}))).subscribe()}function yi({document$:e,tablet$:t}){e.pipe(v(()=>$(".md-toggle--indeterminate")),y(r=>{r.indeterminate=!0,r.checked=!1}),oe(r=>d(r,"change").pipe(Dr(()=>r.classList.contains("md-toggle--indeterminate")),m(()=>r))),ee(t)).subscribe(([r,o])=>{r.classList.remove("md-toggle--indeterminate"),o&&(r.checked=!1)})}function fs(){return/(iPad|iPhone|iPod)/.test(navigator.userAgent)}function Ei({document$:e}){e.pipe(v(()=>$("[data-md-scrollfix]")),y(t=>t.removeAttribute("data-md-scrollfix")),b(fs),oe(t=>d(t,"touchstart").pipe(m(()=>t)))).subscribe(t=>{let r=t.scrollTop;r===0?t.scrollTop=1:r+t.offsetHeight===t.scrollHeight&&(t.scrollTop=r-1)})}function wi({viewport$:e,tablet$:t}){z([Ve("search"),t]).pipe(m(([r,o])=>r&&!o),v(r=>I(r).pipe(Ge(r?400:100))),ee(e)).subscribe(([r,{offset:{y:o}}])=>{if(r)document.body.setAttribute("data-md-scrolllock",""),document.body.style.top=`-${o}px`;else{let n=-1*parseInt(document.body.style.top,10);document.body.removeAttribute("data-md-scrolllock"),document.body.style.top="",n&&window.scrollTo(0,n)}})}Object.entries||(Object.entries=function(e){let t=[];for(let r of Object.keys(e))t.push([r,e[r]]);return t});Object.values||(Object.values=function(e){let t=[];for(let r of Object.keys(e))t.push(e[r]);return t});typeof Element!="undefined"&&(Element.prototype.scrollTo||(Element.prototype.scrollTo=function(e,t){typeof e=="object"?(this.scrollLeft=e.left,this.scrollTop=e.top):(this.scrollLeft=e,this.scrollTop=t)}),Element.prototype.replaceWith||(Element.prototype.replaceWith=function(...e){let t=this.parentNode;if(t){e.length===0&&t.removeChild(this);for(let r=e.length-1;r>=0;r--){let o=e[r];typeof o=="string"?o=document.createTextNode(o):o.parentNode&&o.parentNode.removeChild(o),r?t.insertBefore(this.previousSibling,o):t.replaceChild(o,this)}}}));function us(){return location.protocol==="file:"?wt(`${new URL("search/search_index.js",Xr.base)}`).pipe(m(()=>__index),B(1)):Ne(new URL("search/search_index.json",Xr.base))}document.documentElement.classList.remove("no-js");document.documentElement.classList.add("js");var ot=Yo(),jt=nn(),Ot=cn(jt),Zr=on(),Oe=bn(),hr=$t("(min-width: 960px)"),Si=$t("(min-width: 1220px)"),Oi=pn(),Xr=Te(),Mi=document.forms.namedItem("search")?us():Ke,eo=new g;Bn({alert$:eo});var to=new g;G("navigation.instant")&&Zn({location$:jt,viewport$:Oe,progress$:to}).subscribe(ot);var Ti;((Ti=Xr.version)==null?void 0:Ti.provider)==="mike"&&ii({document$:ot});S(jt,Ot).pipe(Ge(125)).subscribe(()=>{Je("drawer",!1),Je("search",!1)});Zr.pipe(b(({mode:e})=>e==="global")).subscribe(e=>{switch(e.type){case"p":case",":let t=fe("link[rel=prev]");typeof t!="undefined"&&pt(t);break;case"n":case".":let r=fe("link[rel=next]");typeof r!="undefined"&&pt(r);break;case"Enter":let o=Re();o instanceof HTMLLabelElement&&o.click()}});xi({viewport$:Oe,document$:ot});yi({document$:ot,tablet$:hr});Ei({document$:ot});wi({viewport$:Oe,tablet$:hr});var rt=Nn(Se("header"),{viewport$:Oe}),Ft=ot.pipe(m(()=>Se("main")),v(e=>Qn(e,{viewport$:Oe,header$:rt})),B(1)),ds=S(...ae("consent").map(e=>xn(e,{target$:Ot})),...ae("dialog").map(e=>Dn(e,{alert$:eo})),...ae("header").map(e=>zn(e,{viewport$:Oe,header$:rt,main$:Ft})),...ae("palette").map(e=>Kn(e)),...ae("progress").map(e=>Yn(e,{progress$:to})),...ae("search").map(e=>li(e,{index$:Mi,keyboard$:Zr})),...ae("source").map(e=>hi(e))),hs=C(()=>S(...ae("announce").map(e=>gn(e)),...ae("content").map(e=>Un(e,{viewport$:Oe,target$:Ot,print$:Oi})),...ae("content").map(e=>G("search.highlight")?mi(e,{index$:Mi,location$:jt}):M),...ae("header-title").map(e=>qn(e,{viewport$:Oe,header$:rt})),...ae("sidebar").map(e=>e.getAttribute("data-md-type")==="navigation"?Nr(Si,()=>Jr(e,{viewport$:Oe,header$:rt,main$:Ft})):Nr(hr,()=>Jr(e,{viewport$:Oe,header$:rt,main$:Ft}))),...ae("tabs").map(e=>bi(e,{viewport$:Oe,header$:rt})),...ae("toc").map(e=>vi(e,{viewport$:Oe,header$:rt,main$:Ft,target$:Ot})),...ae("top").map(e=>gi(e,{viewport$:Oe,header$:rt,main$:Ft,target$:Ot})))),Li=ot.pipe(v(()=>hs),Pe(ds),B(1));Li.subscribe();window.document$=ot;window.location$=jt;window.target$=Ot;window.keyboard$=Zr;window.viewport$=Oe;window.tablet$=hr;window.screen$=Si;window.print$=Oi;window.alert$=eo;window.progress$=to;window.component$=Li;})(); +//# sourceMappingURL=bundle.a7c05c9e.min.js.map + diff --git a/assets/javascripts/bundle.a7c05c9e.min.js.map b/assets/javascripts/bundle.a7c05c9e.min.js.map new file mode 100644 index 00000000..99cdca1f --- /dev/null +++ b/assets/javascripts/bundle.a7c05c9e.min.js.map @@ -0,0 +1,7 @@ +{ + "version": 3, + "sources": ["node_modules/focus-visible/dist/focus-visible.js", "node_modules/clipboard/dist/clipboard.js", "node_modules/escape-html/index.js", "src/templates/assets/javascripts/bundle.ts", "node_modules/rxjs/node_modules/tslib/tslib.es6.js", "node_modules/rxjs/src/internal/util/isFunction.ts", "node_modules/rxjs/src/internal/util/createErrorClass.ts", "node_modules/rxjs/src/internal/util/UnsubscriptionError.ts", "node_modules/rxjs/src/internal/util/arrRemove.ts", "node_modules/rxjs/src/internal/Subscription.ts", "node_modules/rxjs/src/internal/config.ts", "node_modules/rxjs/src/internal/scheduler/timeoutProvider.ts", "node_modules/rxjs/src/internal/util/reportUnhandledError.ts", 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"node_modules/rxjs/src/internal/scheduler/AsyncAction.ts", "node_modules/rxjs/src/internal/Scheduler.ts", "node_modules/rxjs/src/internal/scheduler/AsyncScheduler.ts", "node_modules/rxjs/src/internal/scheduler/async.ts", "node_modules/rxjs/src/internal/scheduler/QueueAction.ts", "node_modules/rxjs/src/internal/scheduler/QueueScheduler.ts", "node_modules/rxjs/src/internal/scheduler/queue.ts", "node_modules/rxjs/src/internal/scheduler/AnimationFrameAction.ts", "node_modules/rxjs/src/internal/scheduler/AnimationFrameScheduler.ts", "node_modules/rxjs/src/internal/scheduler/animationFrame.ts", "node_modules/rxjs/src/internal/observable/empty.ts", "node_modules/rxjs/src/internal/util/isScheduler.ts", "node_modules/rxjs/src/internal/util/args.ts", "node_modules/rxjs/src/internal/util/isArrayLike.ts", "node_modules/rxjs/src/internal/util/isPromise.ts", "node_modules/rxjs/src/internal/util/isInteropObservable.ts", "node_modules/rxjs/src/internal/util/isAsyncIterable.ts", "node_modules/rxjs/src/internal/util/throwUnobservableError.ts", "node_modules/rxjs/src/internal/symbol/iterator.ts", "node_modules/rxjs/src/internal/util/isIterable.ts", "node_modules/rxjs/src/internal/util/isReadableStreamLike.ts", "node_modules/rxjs/src/internal/observable/innerFrom.ts", "node_modules/rxjs/src/internal/util/executeSchedule.ts", "node_modules/rxjs/src/internal/operators/observeOn.ts", "node_modules/rxjs/src/internal/operators/subscribeOn.ts", "node_modules/rxjs/src/internal/scheduled/scheduleObservable.ts", "node_modules/rxjs/src/internal/scheduled/schedulePromise.ts", "node_modules/rxjs/src/internal/scheduled/scheduleArray.ts", "node_modules/rxjs/src/internal/scheduled/scheduleIterable.ts", "node_modules/rxjs/src/internal/scheduled/scheduleAsyncIterable.ts", "node_modules/rxjs/src/internal/scheduled/scheduleReadableStreamLike.ts", "node_modules/rxjs/src/internal/scheduled/scheduled.ts", "node_modules/rxjs/src/internal/observable/from.ts", "node_modules/rxjs/src/internal/observable/of.ts", "node_modules/rxjs/src/internal/observable/throwError.ts", "node_modules/rxjs/src/internal/util/EmptyError.ts", "node_modules/rxjs/src/internal/util/isDate.ts", "node_modules/rxjs/src/internal/operators/map.ts", "node_modules/rxjs/src/internal/util/mapOneOrManyArgs.ts", "node_modules/rxjs/src/internal/util/argsArgArrayOrObject.ts", "node_modules/rxjs/src/internal/util/createObject.ts", "node_modules/rxjs/src/internal/observable/combineLatest.ts", "node_modules/rxjs/src/internal/operators/mergeInternals.ts", "node_modules/rxjs/src/internal/operators/mergeMap.ts", "node_modules/rxjs/src/internal/operators/mergeAll.ts", "node_modules/rxjs/src/internal/operators/concatAll.ts", "node_modules/rxjs/src/internal/observable/concat.ts", "node_modules/rxjs/src/internal/observable/defer.ts", "node_modules/rxjs/src/internal/observable/fromEvent.ts", "node_modules/rxjs/src/internal/observable/fromEventPattern.ts", "node_modules/rxjs/src/internal/observable/timer.ts", "node_modules/rxjs/src/internal/observable/merge.ts", "node_modules/rxjs/src/internal/observable/never.ts", "node_modules/rxjs/src/internal/util/argsOrArgArray.ts", "node_modules/rxjs/src/internal/operators/filter.ts", "node_modules/rxjs/src/internal/observable/zip.ts", "node_modules/rxjs/src/internal/operators/audit.ts", "node_modules/rxjs/src/internal/operators/auditTime.ts", "node_modules/rxjs/src/internal/operators/bufferCount.ts", "node_modules/rxjs/src/internal/operators/catchError.ts", "node_modules/rxjs/src/internal/operators/scanInternals.ts", "node_modules/rxjs/src/internal/operators/combineLatest.ts", "node_modules/rxjs/src/internal/operators/combineLatestWith.ts", "node_modules/rxjs/src/internal/operators/debounce.ts", "node_modules/rxjs/src/internal/operators/debounceTime.ts", "node_modules/rxjs/src/internal/operators/defaultIfEmpty.ts", "node_modules/rxjs/src/internal/operators/take.ts", "node_modules/rxjs/src/internal/operators/ignoreElements.ts", "node_modules/rxjs/src/internal/operators/mapTo.ts", "node_modules/rxjs/src/internal/operators/delayWhen.ts", "node_modules/rxjs/src/internal/operators/delay.ts", "node_modules/rxjs/src/internal/operators/distinctUntilChanged.ts", "node_modules/rxjs/src/internal/operators/distinctUntilKeyChanged.ts", "node_modules/rxjs/src/internal/operators/throwIfEmpty.ts", "node_modules/rxjs/src/internal/operators/endWith.ts", "node_modules/rxjs/src/internal/operators/finalize.ts", "node_modules/rxjs/src/internal/operators/first.ts", "node_modules/rxjs/src/internal/operators/takeLast.ts", "node_modules/rxjs/src/internal/operators/merge.ts", "node_modules/rxjs/src/internal/operators/mergeWith.ts", "node_modules/rxjs/src/internal/operators/repeat.ts", "node_modules/rxjs/src/internal/operators/scan.ts", "node_modules/rxjs/src/internal/operators/share.ts", "node_modules/rxjs/src/internal/operators/shareReplay.ts", "node_modules/rxjs/src/internal/operators/skip.ts", "node_modules/rxjs/src/internal/operators/skipUntil.ts", "node_modules/rxjs/src/internal/operators/startWith.ts", "node_modules/rxjs/src/internal/operators/switchMap.ts", "node_modules/rxjs/src/internal/operators/takeUntil.ts", "node_modules/rxjs/src/internal/operators/takeWhile.ts", "node_modules/rxjs/src/internal/operators/tap.ts", "node_modules/rxjs/src/internal/operators/throttle.ts", "node_modules/rxjs/src/internal/operators/throttleTime.ts", "node_modules/rxjs/src/internal/operators/withLatestFrom.ts", "node_modules/rxjs/src/internal/operators/zip.ts", "node_modules/rxjs/src/internal/operators/zipWith.ts", "src/templates/assets/javascripts/browser/document/index.ts", "src/templates/assets/javascripts/browser/element/_/index.ts", "src/templates/assets/javascripts/browser/element/focus/index.ts", "src/templates/assets/javascripts/browser/element/hover/index.ts", "src/templates/assets/javascripts/utilities/h/index.ts", "src/templates/assets/javascripts/utilities/round/index.ts", "src/templates/assets/javascripts/browser/script/index.ts", "src/templates/assets/javascripts/browser/element/size/_/index.ts", "src/templates/assets/javascripts/browser/element/size/content/index.ts", "src/templates/assets/javascripts/browser/element/offset/_/index.ts", "src/templates/assets/javascripts/browser/element/offset/content/index.ts", "src/templates/assets/javascripts/browser/element/visibility/index.ts", "src/templates/assets/javascripts/browser/toggle/index.ts", "src/templates/assets/javascripts/browser/keyboard/index.ts", "src/templates/assets/javascripts/browser/location/_/index.ts", "src/templates/assets/javascripts/browser/location/hash/index.ts", "src/templates/assets/javascripts/browser/media/index.ts", "src/templates/assets/javascripts/browser/request/index.ts", "src/templates/assets/javascripts/browser/viewport/offset/index.ts", "src/templates/assets/javascripts/browser/viewport/size/index.ts", "src/templates/assets/javascripts/browser/viewport/_/index.ts", "src/templates/assets/javascripts/browser/viewport/at/index.ts", "src/templates/assets/javascripts/browser/worker/index.ts", "src/templates/assets/javascripts/_/index.ts", "src/templates/assets/javascripts/components/_/index.ts", "src/templates/assets/javascripts/components/announce/index.ts", "src/templates/assets/javascripts/components/consent/index.ts", "src/templates/assets/javascripts/templates/tooltip/index.tsx", "src/templates/assets/javascripts/templates/annotation/index.tsx", "src/templates/assets/javascripts/templates/clipboard/index.tsx", "src/templates/assets/javascripts/templates/search/index.tsx", "src/templates/assets/javascripts/templates/source/index.tsx", "src/templates/assets/javascripts/templates/tabbed/index.tsx", "src/templates/assets/javascripts/templates/table/index.tsx", "src/templates/assets/javascripts/templates/version/index.tsx", "src/templates/assets/javascripts/components/tooltip2/index.ts", "src/templates/assets/javascripts/components/content/annotation/_/index.ts", "src/templates/assets/javascripts/components/content/annotation/list/index.ts", "src/templates/assets/javascripts/components/content/annotation/block/index.ts", "src/templates/assets/javascripts/components/content/code/_/index.ts", "src/templates/assets/javascripts/components/content/details/index.ts", "src/templates/assets/javascripts/components/content/mermaid/index.css", "src/templates/assets/javascripts/components/content/mermaid/index.ts", "src/templates/assets/javascripts/components/content/table/index.ts", "src/templates/assets/javascripts/components/content/tabs/index.ts", "src/templates/assets/javascripts/components/content/_/index.ts", "src/templates/assets/javascripts/components/dialog/index.ts", "src/templates/assets/javascripts/components/tooltip/index.ts", "src/templates/assets/javascripts/components/header/_/index.ts", "src/templates/assets/javascripts/components/header/title/index.ts", "src/templates/assets/javascripts/components/main/index.ts", "src/templates/assets/javascripts/components/palette/index.ts", "src/templates/assets/javascripts/components/progress/index.ts", "src/templates/assets/javascripts/integrations/clipboard/index.ts", "src/templates/assets/javascripts/integrations/sitemap/index.ts", "src/templates/assets/javascripts/integrations/instant/index.ts", "src/templates/assets/javascripts/integrations/search/highlighter/index.ts", "src/templates/assets/javascripts/integrations/search/worker/message/index.ts", "src/templates/assets/javascripts/integrations/search/worker/_/index.ts", "src/templates/assets/javascripts/integrations/version/index.ts", "src/templates/assets/javascripts/components/search/query/index.ts", "src/templates/assets/javascripts/components/search/result/index.ts", "src/templates/assets/javascripts/components/search/share/index.ts", "src/templates/assets/javascripts/components/search/suggest/index.ts", "src/templates/assets/javascripts/components/search/_/index.ts", "src/templates/assets/javascripts/components/search/highlight/index.ts", "src/templates/assets/javascripts/components/sidebar/index.ts", "src/templates/assets/javascripts/components/source/facts/github/index.ts", "src/templates/assets/javascripts/components/source/facts/gitlab/index.ts", "src/templates/assets/javascripts/components/source/facts/_/index.ts", "src/templates/assets/javascripts/components/source/_/index.ts", "src/templates/assets/javascripts/components/tabs/index.ts", "src/templates/assets/javascripts/components/toc/index.ts", "src/templates/assets/javascripts/components/top/index.ts", "src/templates/assets/javascripts/patches/ellipsis/index.ts", "src/templates/assets/javascripts/patches/indeterminate/index.ts", "src/templates/assets/javascripts/patches/scrollfix/index.ts", "src/templates/assets/javascripts/patches/scrolllock/index.ts", "src/templates/assets/javascripts/polyfills/index.ts"], + "sourcesContent": ["(function (global, factory) {\n typeof exports === 'object' && typeof module !== 'undefined' ? factory() :\n typeof define === 'function' && define.amd ? define(factory) :\n (factory());\n}(this, (function () { 'use strict';\n\n /**\n * Applies the :focus-visible polyfill at the given scope.\n * A scope in this case is either the top-level Document or a Shadow Root.\n *\n * @param {(Document|ShadowRoot)} scope\n * @see https://github.com/WICG/focus-visible\n */\n function applyFocusVisiblePolyfill(scope) {\n var hadKeyboardEvent = true;\n var hadFocusVisibleRecently = false;\n var hadFocusVisibleRecentlyTimeout = null;\n\n var inputTypesAllowlist = {\n text: true,\n search: true,\n url: true,\n tel: true,\n email: true,\n password: true,\n number: true,\n date: true,\n month: true,\n week: true,\n time: true,\n datetime: true,\n 'datetime-local': true\n };\n\n /**\n * Helper function for legacy browsers and iframes which sometimes focus\n * elements like document, body, and non-interactive SVG.\n * @param {Element} el\n */\n function isValidFocusTarget(el) {\n if (\n el &&\n el !== document &&\n el.nodeName !== 'HTML' &&\n el.nodeName !== 'BODY' &&\n 'classList' in el &&\n 'contains' in el.classList\n ) {\n return true;\n }\n return false;\n }\n\n /**\n * Computes whether the given element should automatically trigger the\n * `focus-visible` class being added, i.e. whether it should always match\n * `:focus-visible` when focused.\n * @param {Element} el\n * @return {boolean}\n */\n function focusTriggersKeyboardModality(el) {\n var type = el.type;\n var tagName = el.tagName;\n\n if (tagName === 'INPUT' && inputTypesAllowlist[type] && !el.readOnly) {\n return true;\n }\n\n if (tagName === 'TEXTAREA' && !el.readOnly) {\n return true;\n }\n\n if (el.isContentEditable) {\n return true;\n }\n\n return false;\n }\n\n /**\n * Add the `focus-visible` class to the given element if it was not added by\n * the author.\n * @param {Element} el\n */\n function addFocusVisibleClass(el) {\n if (el.classList.contains('focus-visible')) {\n return;\n }\n el.classList.add('focus-visible');\n el.setAttribute('data-focus-visible-added', '');\n }\n\n /**\n * Remove the `focus-visible` class from the given element if it was not\n * originally added by the author.\n * @param {Element} el\n */\n function removeFocusVisibleClass(el) {\n if (!el.hasAttribute('data-focus-visible-added')) {\n return;\n }\n el.classList.remove('focus-visible');\n el.removeAttribute('data-focus-visible-added');\n }\n\n /**\n * If the most recent user interaction was via the keyboard;\n * and the key press did not include a meta, alt/option, or control key;\n * then the modality is keyboard. Otherwise, the modality is not keyboard.\n * Apply `focus-visible` to any current active element and keep track\n * of our keyboard modality state with `hadKeyboardEvent`.\n * @param {KeyboardEvent} e\n */\n function onKeyDown(e) {\n if (e.metaKey || e.altKey || e.ctrlKey) {\n return;\n }\n\n if (isValidFocusTarget(scope.activeElement)) {\n addFocusVisibleClass(scope.activeElement);\n }\n\n hadKeyboardEvent = true;\n }\n\n /**\n * If at any point a user clicks with a pointing device, ensure that we change\n * the modality away from keyboard.\n * This avoids the situation where a user presses a key on an already focused\n * element, and then clicks on a different element, focusing it with a\n * pointing device, while we still think we're in keyboard modality.\n * @param {Event} e\n */\n function onPointerDown(e) {\n hadKeyboardEvent = false;\n }\n\n /**\n * On `focus`, add the `focus-visible` class to the target if:\n * - the target received focus as a result of keyboard navigation, or\n * - the event target is an element that will likely require interaction\n * via the keyboard (e.g. a text box)\n * @param {Event} e\n */\n function onFocus(e) {\n // Prevent IE from focusing the document or HTML element.\n if (!isValidFocusTarget(e.target)) {\n return;\n }\n\n if (hadKeyboardEvent || focusTriggersKeyboardModality(e.target)) {\n addFocusVisibleClass(e.target);\n }\n }\n\n /**\n * On `blur`, remove the `focus-visible` class from the target.\n * @param {Event} e\n */\n function onBlur(e) {\n if (!isValidFocusTarget(e.target)) {\n return;\n }\n\n if (\n e.target.classList.contains('focus-visible') ||\n e.target.hasAttribute('data-focus-visible-added')\n ) {\n // To detect a tab/window switch, we look for a blur event followed\n // rapidly by a visibility change.\n // If we don't see a visibility change within 100ms, it's probably a\n // regular focus change.\n hadFocusVisibleRecently = true;\n window.clearTimeout(hadFocusVisibleRecentlyTimeout);\n hadFocusVisibleRecentlyTimeout = window.setTimeout(function() {\n hadFocusVisibleRecently = false;\n }, 100);\n removeFocusVisibleClass(e.target);\n }\n }\n\n /**\n * If the user changes tabs, keep track of whether or not the previously\n * focused element had .focus-visible.\n * @param {Event} e\n */\n function onVisibilityChange(e) {\n if (document.visibilityState === 'hidden') {\n // If the tab becomes active again, the browser will handle calling focus\n // on the element (Safari actually calls it twice).\n // If this tab change caused a blur on an element with focus-visible,\n // re-apply the class when the user switches back to the tab.\n if (hadFocusVisibleRecently) {\n hadKeyboardEvent = true;\n }\n addInitialPointerMoveListeners();\n }\n }\n\n /**\n * Add a group of listeners to detect usage of any pointing devices.\n * These listeners will be added when the polyfill first loads, and anytime\n * the window is blurred, so that they are active when the window regains\n * focus.\n */\n function addInitialPointerMoveListeners() {\n document.addEventListener('mousemove', onInitialPointerMove);\n document.addEventListener('mousedown', onInitialPointerMove);\n document.addEventListener('mouseup', onInitialPointerMove);\n document.addEventListener('pointermove', onInitialPointerMove);\n document.addEventListener('pointerdown', onInitialPointerMove);\n document.addEventListener('pointerup', onInitialPointerMove);\n document.addEventListener('touchmove', onInitialPointerMove);\n document.addEventListener('touchstart', onInitialPointerMove);\n document.addEventListener('touchend', onInitialPointerMove);\n }\n\n function removeInitialPointerMoveListeners() {\n document.removeEventListener('mousemove', onInitialPointerMove);\n document.removeEventListener('mousedown', onInitialPointerMove);\n document.removeEventListener('mouseup', onInitialPointerMove);\n document.removeEventListener('pointermove', onInitialPointerMove);\n document.removeEventListener('pointerdown', onInitialPointerMove);\n document.removeEventListener('pointerup', onInitialPointerMove);\n document.removeEventListener('touchmove', onInitialPointerMove);\n document.removeEventListener('touchstart', onInitialPointerMove);\n document.removeEventListener('touchend', onInitialPointerMove);\n }\n\n /**\n * When the polfyill first loads, assume the user is in keyboard modality.\n * If any event is received from a pointing device (e.g. mouse, pointer,\n * touch), turn off keyboard modality.\n * This accounts for situations where focus enters the page from the URL bar.\n * @param {Event} e\n */\n function onInitialPointerMove(e) {\n // Work around a Safari quirk that fires a mousemove on whenever the\n // window blurs, even if you're tabbing out of the page. \u00AF\\_(\u30C4)_/\u00AF\n if (e.target.nodeName && e.target.nodeName.toLowerCase() === 'html') {\n return;\n }\n\n hadKeyboardEvent = false;\n removeInitialPointerMoveListeners();\n }\n\n // For some kinds of state, we are interested in changes at the global scope\n // only. For example, global pointer input, global key presses and global\n // visibility change should affect the state at every scope:\n document.addEventListener('keydown', onKeyDown, true);\n document.addEventListener('mousedown', onPointerDown, true);\n document.addEventListener('pointerdown', onPointerDown, true);\n document.addEventListener('touchstart', onPointerDown, true);\n document.addEventListener('visibilitychange', onVisibilityChange, true);\n\n addInitialPointerMoveListeners();\n\n // For focus and blur, we specifically care about state changes in the local\n // scope. This is because focus / blur events that originate from within a\n // shadow root are not re-dispatched from the host element if it was already\n // the active element in its own scope:\n scope.addEventListener('focus', onFocus, true);\n scope.addEventListener('blur', onBlur, true);\n\n // We detect that a node is a ShadowRoot by ensuring that it is a\n // DocumentFragment and also has a host property. This check covers native\n // implementation and polyfill implementation transparently. If we only cared\n // about the native implementation, we could just check if the scope was\n // an instance of a ShadowRoot.\n if (scope.nodeType === Node.DOCUMENT_FRAGMENT_NODE && scope.host) {\n // Since a ShadowRoot is a special kind of DocumentFragment, it does not\n // have a root element to add a class to. So, we add this attribute to the\n // host element instead:\n scope.host.setAttribute('data-js-focus-visible', '');\n } else if (scope.nodeType === Node.DOCUMENT_NODE) {\n document.documentElement.classList.add('js-focus-visible');\n document.documentElement.setAttribute('data-js-focus-visible', '');\n }\n }\n\n // It is important to wrap all references to global window and document in\n // these checks to support server-side rendering use cases\n // @see https://github.com/WICG/focus-visible/issues/199\n if (typeof window !== 'undefined' && typeof document !== 'undefined') {\n // Make the polyfill helper globally available. This can be used as a signal\n // to interested libraries that wish to coordinate with the polyfill for e.g.,\n // applying the polyfill to a shadow root:\n window.applyFocusVisiblePolyfill = applyFocusVisiblePolyfill;\n\n // Notify interested libraries of the polyfill's presence, in case the\n // polyfill was loaded lazily:\n var event;\n\n try {\n event = new CustomEvent('focus-visible-polyfill-ready');\n } catch (error) {\n // IE11 does not support using CustomEvent as a constructor directly:\n event = document.createEvent('CustomEvent');\n event.initCustomEvent('focus-visible-polyfill-ready', false, false, {});\n }\n\n window.dispatchEvent(event);\n }\n\n if (typeof document !== 'undefined') {\n // Apply the polyfill to the global document, so that no JavaScript\n // coordination is required to use the polyfill in the top-level document:\n applyFocusVisiblePolyfill(document);\n }\n\n})));\n", "/*!\n * clipboard.js v2.0.11\n * https://clipboardjs.com/\n *\n * Licensed MIT \u00A9 Zeno Rocha\n */\n(function webpackUniversalModuleDefinition(root, factory) {\n\tif(typeof exports === 'object' && typeof module === 'object')\n\t\tmodule.exports = factory();\n\telse if(typeof define === 'function' && define.amd)\n\t\tdefine([], factory);\n\telse if(typeof exports === 'object')\n\t\texports[\"ClipboardJS\"] = factory();\n\telse\n\t\troot[\"ClipboardJS\"] = factory();\n})(this, function() {\nreturn /******/ (function() { // webpackBootstrap\n/******/ \tvar __webpack_modules__ = ({\n\n/***/ 686:\n/***/ (function(__unused_webpack_module, __webpack_exports__, __webpack_require__) {\n\n\"use strict\";\n\n// EXPORTS\n__webpack_require__.d(__webpack_exports__, {\n \"default\": function() { return /* binding */ clipboard; }\n});\n\n// EXTERNAL MODULE: ./node_modules/tiny-emitter/index.js\nvar tiny_emitter = __webpack_require__(279);\nvar tiny_emitter_default = /*#__PURE__*/__webpack_require__.n(tiny_emitter);\n// EXTERNAL MODULE: ./node_modules/good-listener/src/listen.js\nvar listen = __webpack_require__(370);\nvar listen_default = /*#__PURE__*/__webpack_require__.n(listen);\n// EXTERNAL MODULE: ./node_modules/select/src/select.js\nvar src_select = __webpack_require__(817);\nvar select_default = /*#__PURE__*/__webpack_require__.n(src_select);\n;// CONCATENATED MODULE: ./src/common/command.js\n/**\n * Executes a given operation type.\n * @param {String} type\n * @return {Boolean}\n */\nfunction command(type) {\n try {\n return document.execCommand(type);\n } catch (err) {\n return false;\n }\n}\n;// CONCATENATED MODULE: ./src/actions/cut.js\n\n\n/**\n * Cut action wrapper.\n * @param {String|HTMLElement} target\n * @return {String}\n */\n\nvar ClipboardActionCut = function ClipboardActionCut(target) {\n var selectedText = select_default()(target);\n command('cut');\n return selectedText;\n};\n\n/* harmony default export */ var actions_cut = (ClipboardActionCut);\n;// CONCATENATED MODULE: ./src/common/create-fake-element.js\n/**\n * Creates a fake textarea element with a value.\n * @param {String} value\n * @return {HTMLElement}\n */\nfunction createFakeElement(value) {\n var isRTL = document.documentElement.getAttribute('dir') === 'rtl';\n var fakeElement = document.createElement('textarea'); // Prevent zooming on iOS\n\n fakeElement.style.fontSize = '12pt'; // Reset box model\n\n fakeElement.style.border = '0';\n fakeElement.style.padding = '0';\n fakeElement.style.margin = '0'; // Move element out of screen horizontally\n\n fakeElement.style.position = 'absolute';\n fakeElement.style[isRTL ? 'right' : 'left'] = '-9999px'; // Move element to the same position vertically\n\n var yPosition = window.pageYOffset || document.documentElement.scrollTop;\n fakeElement.style.top = \"\".concat(yPosition, \"px\");\n fakeElement.setAttribute('readonly', '');\n fakeElement.value = value;\n return fakeElement;\n}\n;// CONCATENATED MODULE: ./src/actions/copy.js\n\n\n\n/**\n * Create fake copy action wrapper using a fake element.\n * @param {String} target\n * @param {Object} options\n * @return {String}\n */\n\nvar fakeCopyAction = function fakeCopyAction(value, options) {\n var fakeElement = createFakeElement(value);\n options.container.appendChild(fakeElement);\n var selectedText = select_default()(fakeElement);\n command('copy');\n fakeElement.remove();\n return selectedText;\n};\n/**\n * Copy action wrapper.\n * @param {String|HTMLElement} target\n * @param {Object} options\n * @return {String}\n */\n\n\nvar ClipboardActionCopy = function ClipboardActionCopy(target) {\n var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {\n container: document.body\n };\n var selectedText = '';\n\n if (typeof target === 'string') {\n selectedText = fakeCopyAction(target, options);\n } else if (target instanceof HTMLInputElement && !['text', 'search', 'url', 'tel', 'password'].includes(target === null || target === void 0 ? void 0 : target.type)) {\n // If input type doesn't support `setSelectionRange`. Simulate it. https://developer.mozilla.org/en-US/docs/Web/API/HTMLInputElement/setSelectionRange\n selectedText = fakeCopyAction(target.value, options);\n } else {\n selectedText = select_default()(target);\n command('copy');\n }\n\n return selectedText;\n};\n\n/* harmony default export */ var actions_copy = (ClipboardActionCopy);\n;// CONCATENATED MODULE: ./src/actions/default.js\nfunction _typeof(obj) { \"@babel/helpers - typeof\"; if (typeof Symbol === \"function\" && typeof Symbol.iterator === \"symbol\") { _typeof = function _typeof(obj) { return typeof obj; }; } else { _typeof = function _typeof(obj) { return obj && typeof Symbol === \"function\" && obj.constructor === Symbol && obj !== Symbol.prototype ? \"symbol\" : typeof obj; }; } return _typeof(obj); }\n\n\n\n/**\n * Inner function which performs selection from either `text` or `target`\n * properties and then executes copy or cut operations.\n * @param {Object} options\n */\n\nvar ClipboardActionDefault = function ClipboardActionDefault() {\n var options = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n // Defines base properties passed from constructor.\n var _options$action = options.action,\n action = _options$action === void 0 ? 'copy' : _options$action,\n container = options.container,\n target = options.target,\n text = options.text; // Sets the `action` to be performed which can be either 'copy' or 'cut'.\n\n if (action !== 'copy' && action !== 'cut') {\n throw new Error('Invalid \"action\" value, use either \"copy\" or \"cut\"');\n } // Sets the `target` property using an element that will be have its content copied.\n\n\n if (target !== undefined) {\n if (target && _typeof(target) === 'object' && target.nodeType === 1) {\n if (action === 'copy' && target.hasAttribute('disabled')) {\n throw new Error('Invalid \"target\" attribute. Please use \"readonly\" instead of \"disabled\" attribute');\n }\n\n if (action === 'cut' && (target.hasAttribute('readonly') || target.hasAttribute('disabled'))) {\n throw new Error('Invalid \"target\" attribute. You can\\'t cut text from elements with \"readonly\" or \"disabled\" attributes');\n }\n } else {\n throw new Error('Invalid \"target\" value, use a valid Element');\n }\n } // Define selection strategy based on `text` property.\n\n\n if (text) {\n return actions_copy(text, {\n container: container\n });\n } // Defines which selection strategy based on `target` property.\n\n\n if (target) {\n return action === 'cut' ? actions_cut(target) : actions_copy(target, {\n container: container\n });\n }\n};\n\n/* harmony default export */ var actions_default = (ClipboardActionDefault);\n;// CONCATENATED MODULE: ./src/clipboard.js\nfunction clipboard_typeof(obj) { \"@babel/helpers - typeof\"; if (typeof Symbol === \"function\" && typeof Symbol.iterator === \"symbol\") { clipboard_typeof = function _typeof(obj) { return typeof obj; }; } else { clipboard_typeof = function _typeof(obj) { return obj && typeof Symbol === \"function\" && obj.constructor === Symbol && obj !== Symbol.prototype ? \"symbol\" : typeof obj; }; } return clipboard_typeof(obj); }\n\nfunction _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if (\"value\" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }\n\nfunction _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }\n\nfunction _inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function\"); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, writable: true, configurable: true } }); if (superClass) _setPrototypeOf(subClass, superClass); }\n\nfunction _setPrototypeOf(o, p) { _setPrototypeOf = Object.setPrototypeOf || function _setPrototypeOf(o, p) { o.__proto__ = p; return o; }; return _setPrototypeOf(o, p); }\n\nfunction _createSuper(Derived) { var hasNativeReflectConstruct = _isNativeReflectConstruct(); return function _createSuperInternal() { var Super = _getPrototypeOf(Derived), result; if (hasNativeReflectConstruct) { var NewTarget = _getPrototypeOf(this).constructor; result = Reflect.construct(Super, arguments, NewTarget); } else { result = Super.apply(this, arguments); } return _possibleConstructorReturn(this, result); }; }\n\nfunction _possibleConstructorReturn(self, call) { if (call && (clipboard_typeof(call) === \"object\" || typeof call === \"function\")) { return call; } return _assertThisInitialized(self); }\n\nfunction _assertThisInitialized(self) { if (self === void 0) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return self; }\n\nfunction _isNativeReflectConstruct() { if (typeof Reflect === \"undefined\" || !Reflect.construct) return false; if (Reflect.construct.sham) return false; if (typeof Proxy === \"function\") return true; try { Date.prototype.toString.call(Reflect.construct(Date, [], function () {})); return true; } catch (e) { return false; } }\n\nfunction _getPrototypeOf(o) { _getPrototypeOf = Object.setPrototypeOf ? Object.getPrototypeOf : function _getPrototypeOf(o) { return o.__proto__ || Object.getPrototypeOf(o); }; return _getPrototypeOf(o); }\n\n\n\n\n\n\n/**\n * Helper function to retrieve attribute value.\n * @param {String} suffix\n * @param {Element} element\n */\n\nfunction getAttributeValue(suffix, element) {\n var attribute = \"data-clipboard-\".concat(suffix);\n\n if (!element.hasAttribute(attribute)) {\n return;\n }\n\n return element.getAttribute(attribute);\n}\n/**\n * Base class which takes one or more elements, adds event listeners to them,\n * and instantiates a new `ClipboardAction` on each click.\n */\n\n\nvar Clipboard = /*#__PURE__*/function (_Emitter) {\n _inherits(Clipboard, _Emitter);\n\n var _super = _createSuper(Clipboard);\n\n /**\n * @param {String|HTMLElement|HTMLCollection|NodeList} trigger\n * @param {Object} options\n */\n function Clipboard(trigger, options) {\n var _this;\n\n _classCallCheck(this, Clipboard);\n\n _this = _super.call(this);\n\n _this.resolveOptions(options);\n\n _this.listenClick(trigger);\n\n return _this;\n }\n /**\n * Defines if attributes would be resolved using internal setter functions\n * or custom functions that were passed in the constructor.\n * @param {Object} options\n */\n\n\n _createClass(Clipboard, [{\n key: \"resolveOptions\",\n value: function resolveOptions() {\n var options = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n this.action = typeof options.action === 'function' ? options.action : this.defaultAction;\n this.target = typeof options.target === 'function' ? options.target : this.defaultTarget;\n this.text = typeof options.text === 'function' ? options.text : this.defaultText;\n this.container = clipboard_typeof(options.container) === 'object' ? options.container : document.body;\n }\n /**\n * Adds a click event listener to the passed trigger.\n * @param {String|HTMLElement|HTMLCollection|NodeList} trigger\n */\n\n }, {\n key: \"listenClick\",\n value: function listenClick(trigger) {\n var _this2 = this;\n\n this.listener = listen_default()(trigger, 'click', function (e) {\n return _this2.onClick(e);\n });\n }\n /**\n * Defines a new `ClipboardAction` on each click event.\n * @param {Event} e\n */\n\n }, {\n key: \"onClick\",\n value: function onClick(e) {\n var trigger = e.delegateTarget || e.currentTarget;\n var action = this.action(trigger) || 'copy';\n var text = actions_default({\n action: action,\n container: this.container,\n target: this.target(trigger),\n text: this.text(trigger)\n }); // Fires an event based on the copy operation result.\n\n this.emit(text ? 'success' : 'error', {\n action: action,\n text: text,\n trigger: trigger,\n clearSelection: function clearSelection() {\n if (trigger) {\n trigger.focus();\n }\n\n window.getSelection().removeAllRanges();\n }\n });\n }\n /**\n * Default `action` lookup function.\n * @param {Element} trigger\n */\n\n }, {\n key: \"defaultAction\",\n value: function defaultAction(trigger) {\n return getAttributeValue('action', trigger);\n }\n /**\n * Default `target` lookup function.\n * @param {Element} trigger\n */\n\n }, {\n key: \"defaultTarget\",\n value: function defaultTarget(trigger) {\n var selector = getAttributeValue('target', trigger);\n\n if (selector) {\n return document.querySelector(selector);\n }\n }\n /**\n * Allow fire programmatically a copy action\n * @param {String|HTMLElement} target\n * @param {Object} options\n * @returns Text copied.\n */\n\n }, {\n key: \"defaultText\",\n\n /**\n * Default `text` lookup function.\n * @param {Element} trigger\n */\n value: function defaultText(trigger) {\n return getAttributeValue('text', trigger);\n }\n /**\n * Destroy lifecycle.\n */\n\n }, {\n key: \"destroy\",\n value: function destroy() {\n this.listener.destroy();\n }\n }], [{\n key: \"copy\",\n value: function copy(target) {\n var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {\n container: document.body\n };\n return actions_copy(target, options);\n }\n /**\n * Allow fire programmatically a cut action\n * @param {String|HTMLElement} target\n * @returns Text cutted.\n */\n\n }, {\n key: \"cut\",\n value: function cut(target) {\n return actions_cut(target);\n }\n /**\n * Returns the support of the given action, or all actions if no action is\n * given.\n * @param {String} [action]\n */\n\n }, {\n key: \"isSupported\",\n value: function isSupported() {\n var action = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : ['copy', 'cut'];\n var actions = typeof action === 'string' ? [action] : action;\n var support = !!document.queryCommandSupported;\n actions.forEach(function (action) {\n support = support && !!document.queryCommandSupported(action);\n });\n return support;\n }\n }]);\n\n return Clipboard;\n}((tiny_emitter_default()));\n\n/* harmony default export */ var clipboard = (Clipboard);\n\n/***/ }),\n\n/***/ 828:\n/***/ (function(module) {\n\nvar DOCUMENT_NODE_TYPE = 9;\n\n/**\n * A polyfill for Element.matches()\n */\nif (typeof Element !== 'undefined' && !Element.prototype.matches) {\n var proto = Element.prototype;\n\n proto.matches = proto.matchesSelector ||\n proto.mozMatchesSelector ||\n proto.msMatchesSelector ||\n proto.oMatchesSelector ||\n proto.webkitMatchesSelector;\n}\n\n/**\n * Finds the closest parent that matches a selector.\n *\n * @param {Element} element\n * @param {String} selector\n * @return {Function}\n */\nfunction closest (element, selector) {\n while (element && element.nodeType !== DOCUMENT_NODE_TYPE) {\n if (typeof element.matches === 'function' &&\n element.matches(selector)) {\n return element;\n }\n element = element.parentNode;\n }\n}\n\nmodule.exports = closest;\n\n\n/***/ }),\n\n/***/ 438:\n/***/ (function(module, __unused_webpack_exports, __webpack_require__) {\n\nvar closest = __webpack_require__(828);\n\n/**\n * Delegates event to a selector.\n *\n * @param {Element} element\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @param {Boolean} useCapture\n * @return {Object}\n */\nfunction _delegate(element, selector, type, callback, useCapture) {\n var listenerFn = listener.apply(this, arguments);\n\n element.addEventListener(type, listenerFn, useCapture);\n\n return {\n destroy: function() {\n element.removeEventListener(type, listenerFn, useCapture);\n }\n }\n}\n\n/**\n * Delegates event to a selector.\n *\n * @param {Element|String|Array} [elements]\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @param {Boolean} useCapture\n * @return {Object}\n */\nfunction delegate(elements, selector, type, callback, useCapture) {\n // Handle the regular Element usage\n if (typeof elements.addEventListener === 'function') {\n return _delegate.apply(null, arguments);\n }\n\n // Handle Element-less usage, it defaults to global delegation\n if (typeof type === 'function') {\n // Use `document` as the first parameter, then apply arguments\n // This is a short way to .unshift `arguments` without running into deoptimizations\n return _delegate.bind(null, document).apply(null, arguments);\n }\n\n // Handle Selector-based usage\n if (typeof elements === 'string') {\n elements = document.querySelectorAll(elements);\n }\n\n // Handle Array-like based usage\n return Array.prototype.map.call(elements, function (element) {\n return _delegate(element, selector, type, callback, useCapture);\n });\n}\n\n/**\n * Finds closest match and invokes callback.\n *\n * @param {Element} element\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @return {Function}\n */\nfunction listener(element, selector, type, callback) {\n return function(e) {\n e.delegateTarget = closest(e.target, selector);\n\n if (e.delegateTarget) {\n callback.call(element, e);\n }\n }\n}\n\nmodule.exports = delegate;\n\n\n/***/ }),\n\n/***/ 879:\n/***/ (function(__unused_webpack_module, exports) {\n\n/**\n * Check if argument is a HTML element.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.node = function(value) {\n return value !== undefined\n && value instanceof HTMLElement\n && value.nodeType === 1;\n};\n\n/**\n * Check if argument is a list of HTML elements.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.nodeList = function(value) {\n var type = Object.prototype.toString.call(value);\n\n return value !== undefined\n && (type === '[object NodeList]' || type === '[object HTMLCollection]')\n && ('length' in value)\n && (value.length === 0 || exports.node(value[0]));\n};\n\n/**\n * Check if argument is a string.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.string = function(value) {\n return typeof value === 'string'\n || value instanceof String;\n};\n\n/**\n * Check if argument is a function.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.fn = function(value) {\n var type = Object.prototype.toString.call(value);\n\n return type === '[object Function]';\n};\n\n\n/***/ }),\n\n/***/ 370:\n/***/ (function(module, __unused_webpack_exports, __webpack_require__) {\n\nvar is = __webpack_require__(879);\nvar delegate = __webpack_require__(438);\n\n/**\n * Validates all params and calls the right\n * listener function based on its target type.\n *\n * @param {String|HTMLElement|HTMLCollection|NodeList} target\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listen(target, type, callback) {\n if (!target && !type && !callback) {\n throw new Error('Missing required arguments');\n }\n\n if (!is.string(type)) {\n throw new TypeError('Second argument must be a String');\n }\n\n if (!is.fn(callback)) {\n throw new TypeError('Third argument must be a Function');\n }\n\n if (is.node(target)) {\n return listenNode(target, type, callback);\n }\n else if (is.nodeList(target)) {\n return listenNodeList(target, type, callback);\n }\n else if (is.string(target)) {\n return listenSelector(target, type, callback);\n }\n else {\n throw new TypeError('First argument must be a String, HTMLElement, HTMLCollection, or NodeList');\n }\n}\n\n/**\n * Adds an event listener to a HTML element\n * and returns a remove listener function.\n *\n * @param {HTMLElement} node\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenNode(node, type, callback) {\n node.addEventListener(type, callback);\n\n return {\n destroy: function() {\n node.removeEventListener(type, callback);\n }\n }\n}\n\n/**\n * Add an event listener to a list of HTML elements\n * and returns a remove listener function.\n *\n * @param {NodeList|HTMLCollection} nodeList\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenNodeList(nodeList, type, callback) {\n Array.prototype.forEach.call(nodeList, function(node) {\n node.addEventListener(type, callback);\n });\n\n return {\n destroy: function() {\n Array.prototype.forEach.call(nodeList, function(node) {\n node.removeEventListener(type, callback);\n });\n }\n }\n}\n\n/**\n * Add an event listener to a selector\n * and returns a remove listener function.\n *\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenSelector(selector, type, callback) {\n return delegate(document.body, selector, type, callback);\n}\n\nmodule.exports = listen;\n\n\n/***/ }),\n\n/***/ 817:\n/***/ (function(module) {\n\nfunction select(element) {\n var selectedText;\n\n if (element.nodeName === 'SELECT') {\n element.focus();\n\n selectedText = element.value;\n }\n else if (element.nodeName === 'INPUT' || element.nodeName === 'TEXTAREA') {\n var isReadOnly = element.hasAttribute('readonly');\n\n if (!isReadOnly) {\n element.setAttribute('readonly', '');\n }\n\n element.select();\n element.setSelectionRange(0, element.value.length);\n\n if (!isReadOnly) {\n element.removeAttribute('readonly');\n }\n\n selectedText = element.value;\n }\n else {\n if (element.hasAttribute('contenteditable')) {\n element.focus();\n }\n\n var selection = window.getSelection();\n var range = document.createRange();\n\n range.selectNodeContents(element);\n selection.removeAllRanges();\n selection.addRange(range);\n\n selectedText = selection.toString();\n }\n\n return selectedText;\n}\n\nmodule.exports = select;\n\n\n/***/ }),\n\n/***/ 279:\n/***/ (function(module) {\n\nfunction E () {\n // Keep this empty so it's easier to inherit from\n // (via https://github.com/lipsmack from https://github.com/scottcorgan/tiny-emitter/issues/3)\n}\n\nE.prototype = {\n on: function (name, callback, ctx) {\n var e = this.e || (this.e = {});\n\n (e[name] || (e[name] = [])).push({\n fn: callback,\n ctx: ctx\n });\n\n return this;\n },\n\n once: function (name, callback, ctx) {\n var self = this;\n function listener () {\n self.off(name, listener);\n callback.apply(ctx, arguments);\n };\n\n listener._ = callback\n return this.on(name, listener, ctx);\n },\n\n emit: function (name) {\n var data = [].slice.call(arguments, 1);\n var evtArr = ((this.e || (this.e = {}))[name] || []).slice();\n var i = 0;\n var len = evtArr.length;\n\n for (i; i < len; i++) {\n evtArr[i].fn.apply(evtArr[i].ctx, data);\n }\n\n return this;\n },\n\n off: function (name, callback) {\n var e = this.e || (this.e = {});\n var evts = e[name];\n var liveEvents = [];\n\n if (evts && callback) {\n for (var i = 0, len = evts.length; i < len; i++) {\n if (evts[i].fn !== callback && evts[i].fn._ !== callback)\n liveEvents.push(evts[i]);\n }\n }\n\n // Remove event from queue to prevent memory leak\n // Suggested by https://github.com/lazd\n // Ref: https://github.com/scottcorgan/tiny-emitter/commit/c6ebfaa9bc973b33d110a84a307742b7cf94c953#commitcomment-5024910\n\n (liveEvents.length)\n ? e[name] = liveEvents\n : delete e[name];\n\n return this;\n }\n};\n\nmodule.exports = E;\nmodule.exports.TinyEmitter = E;\n\n\n/***/ })\n\n/******/ \t});\n/************************************************************************/\n/******/ \t// The module cache\n/******/ \tvar __webpack_module_cache__ = {};\n/******/ \t\n/******/ \t// The require function\n/******/ \tfunction __webpack_require__(moduleId) {\n/******/ \t\t// Check if module is in cache\n/******/ \t\tif(__webpack_module_cache__[moduleId]) {\n/******/ \t\t\treturn __webpack_module_cache__[moduleId].exports;\n/******/ \t\t}\n/******/ \t\t// Create a new module (and put it into the cache)\n/******/ \t\tvar module = __webpack_module_cache__[moduleId] = {\n/******/ \t\t\t// no module.id needed\n/******/ \t\t\t// no module.loaded needed\n/******/ \t\t\texports: {}\n/******/ \t\t};\n/******/ \t\n/******/ \t\t// Execute the module function\n/******/ \t\t__webpack_modules__[moduleId](module, module.exports, __webpack_require__);\n/******/ \t\n/******/ \t\t// Return the exports of the module\n/******/ \t\treturn module.exports;\n/******/ \t}\n/******/ \t\n/************************************************************************/\n/******/ \t/* webpack/runtime/compat get default export */\n/******/ \t!function() {\n/******/ \t\t// getDefaultExport function for compatibility with non-harmony modules\n/******/ \t\t__webpack_require__.n = function(module) {\n/******/ \t\t\tvar getter = module && module.__esModule ?\n/******/ \t\t\t\tfunction() { return module['default']; } :\n/******/ \t\t\t\tfunction() { return module; };\n/******/ \t\t\t__webpack_require__.d(getter, { a: getter });\n/******/ \t\t\treturn getter;\n/******/ \t\t};\n/******/ \t}();\n/******/ \t\n/******/ \t/* webpack/runtime/define property getters */\n/******/ \t!function() {\n/******/ \t\t// define getter functions for harmony exports\n/******/ \t\t__webpack_require__.d = function(exports, definition) {\n/******/ \t\t\tfor(var key in definition) {\n/******/ \t\t\t\tif(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {\n/******/ \t\t\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: definition[key] });\n/******/ \t\t\t\t}\n/******/ \t\t\t}\n/******/ \t\t};\n/******/ \t}();\n/******/ \t\n/******/ \t/* webpack/runtime/hasOwnProperty shorthand */\n/******/ \t!function() {\n/******/ \t\t__webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }\n/******/ \t}();\n/******/ \t\n/************************************************************************/\n/******/ \t// module exports must be returned from runtime so entry inlining is disabled\n/******/ \t// startup\n/******/ \t// Load entry module and return exports\n/******/ \treturn __webpack_require__(686);\n/******/ })()\n.default;\n});", "/*!\n * escape-html\n * Copyright(c) 2012-2013 TJ Holowaychuk\n * Copyright(c) 2015 Andreas Lubbe\n * Copyright(c) 2015 Tiancheng \"Timothy\" Gu\n * MIT Licensed\n */\n\n'use strict';\n\n/**\n * Module variables.\n * @private\n */\n\nvar matchHtmlRegExp = /[\"'&<>]/;\n\n/**\n * Module exports.\n * @public\n */\n\nmodule.exports = escapeHtml;\n\n/**\n * Escape special characters in the given string of html.\n *\n * @param {string} string The string to escape for inserting into HTML\n * @return {string}\n * @public\n */\n\nfunction escapeHtml(string) {\n var str = '' + string;\n var match = matchHtmlRegExp.exec(str);\n\n if (!match) {\n return str;\n }\n\n var escape;\n var html = '';\n var index = 0;\n var lastIndex = 0;\n\n for (index = match.index; index < str.length; index++) {\n switch (str.charCodeAt(index)) {\n case 34: // \"\n escape = '"';\n break;\n case 38: // &\n escape = '&';\n break;\n case 39: // '\n escape = ''';\n break;\n case 60: // <\n escape = '<';\n break;\n case 62: // >\n escape = '>';\n break;\n default:\n continue;\n }\n\n if (lastIndex !== index) {\n html += str.substring(lastIndex, index);\n }\n\n lastIndex = index + 1;\n html += escape;\n }\n\n return lastIndex !== index\n ? html + str.substring(lastIndex, index)\n : html;\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath \n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport \"focus-visible\"\n\nimport {\n EMPTY,\n NEVER,\n Observable,\n Subject,\n defer,\n delay,\n filter,\n map,\n merge,\n mergeWith,\n shareReplay,\n switchMap\n} from \"rxjs\"\n\nimport { configuration, feature } from \"./_\"\nimport {\n at,\n getActiveElement,\n getOptionalElement,\n requestJSON,\n setLocation,\n setToggle,\n watchDocument,\n watchKeyboard,\n watchLocation,\n watchLocationTarget,\n watchMedia,\n watchPrint,\n watchScript,\n watchViewport\n} from \"./browser\"\nimport {\n getComponentElement,\n getComponentElements,\n mountAnnounce,\n mountBackToTop,\n mountConsent,\n mountContent,\n mountDialog,\n mountHeader,\n mountHeaderTitle,\n mountPalette,\n mountProgress,\n mountSearch,\n mountSearchHiglight,\n mountSidebar,\n mountSource,\n mountTableOfContents,\n mountTabs,\n watchHeader,\n watchMain\n} from \"./components\"\nimport {\n SearchIndex,\n setupClipboardJS,\n setupInstantNavigation,\n setupVersionSelector\n} from \"./integrations\"\nimport {\n patchEllipsis,\n patchIndeterminate,\n patchScrollfix,\n patchScrolllock\n} from \"./patches\"\nimport \"./polyfills\"\n\n/* ----------------------------------------------------------------------------\n * Functions - @todo refactor\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch search index\n *\n * @returns Search index observable\n */\nfunction fetchSearchIndex(): Observable {\n if (location.protocol === \"file:\") {\n return watchScript(\n `${new URL(\"search/search_index.js\", config.base)}`\n )\n .pipe(\n // @ts-ignore - @todo fix typings\n map(() => __index),\n shareReplay(1)\n )\n } else {\n return requestJSON(\n new URL(\"search/search_index.json\", config.base)\n )\n }\n}\n\n/* ----------------------------------------------------------------------------\n * Application\n * ------------------------------------------------------------------------- */\n\n/* Yay, JavaScript is available */\ndocument.documentElement.classList.remove(\"no-js\")\ndocument.documentElement.classList.add(\"js\")\n\n/* Set up navigation observables and subjects */\nconst document$ = watchDocument()\nconst location$ = watchLocation()\nconst target$ = watchLocationTarget(location$)\nconst keyboard$ = watchKeyboard()\n\n/* Set up media observables */\nconst viewport$ = watchViewport()\nconst tablet$ = watchMedia(\"(min-width: 960px)\")\nconst screen$ = watchMedia(\"(min-width: 1220px)\")\nconst print$ = watchPrint()\n\n/* Retrieve search index, if search is enabled */\nconst config = configuration()\nconst index$ = document.forms.namedItem(\"search\")\n ? fetchSearchIndex()\n : NEVER\n\n/* Set up Clipboard.js integration */\nconst alert$ = new Subject()\nsetupClipboardJS({ alert$ })\n\n/* Set up progress indicator */\nconst progress$ = new Subject()\n\n/* Set up instant navigation, if enabled */\nif (feature(\"navigation.instant\"))\n setupInstantNavigation({ location$, viewport$, progress$ })\n .subscribe(document$)\n\n/* Set up version selector */\nif (config.version?.provider === \"mike\")\n setupVersionSelector({ document$ })\n\n/* Always close drawer and search on navigation */\nmerge(location$, target$)\n .pipe(\n delay(125)\n )\n .subscribe(() => {\n setToggle(\"drawer\", false)\n setToggle(\"search\", false)\n })\n\n/* Set up global keyboard handlers */\nkeyboard$\n .pipe(\n filter(({ mode }) => mode === \"global\")\n )\n .subscribe(key => {\n switch (key.type) {\n\n /* Go to previous page */\n case \"p\":\n case \",\":\n const prev = getOptionalElement(\"link[rel=prev]\")\n if (typeof prev !== \"undefined\")\n setLocation(prev)\n break\n\n /* Go to next page */\n case \"n\":\n case \".\":\n const next = getOptionalElement(\"link[rel=next]\")\n if (typeof next !== \"undefined\")\n setLocation(next)\n break\n\n /* Expand navigation, see https://bit.ly/3ZjG5io */\n case \"Enter\":\n const active = getActiveElement()\n if (active instanceof HTMLLabelElement)\n active.click()\n }\n })\n\n/* Set up patches */\npatchEllipsis({ viewport$, document$ })\npatchIndeterminate({ document$, tablet$ })\npatchScrollfix({ document$ })\npatchScrolllock({ viewport$, tablet$ })\n\n/* Set up header and main area observable */\nconst header$ = watchHeader(getComponentElement(\"header\"), { viewport$ })\nconst main$ = document$\n .pipe(\n map(() => getComponentElement(\"main\")),\n switchMap(el => watchMain(el, { viewport$, header$ })),\n shareReplay(1)\n )\n\n/* Set up control component observables */\nconst control$ = merge(\n\n /* Consent */\n ...getComponentElements(\"consent\")\n .map(el => mountConsent(el, { target$ })),\n\n /* Dialog */\n ...getComponentElements(\"dialog\")\n .map(el => mountDialog(el, { alert$ })),\n\n /* Header */\n ...getComponentElements(\"header\")\n .map(el => mountHeader(el, { viewport$, header$, main$ })),\n\n /* Color palette */\n ...getComponentElements(\"palette\")\n .map(el => mountPalette(el)),\n\n /* Progress bar */\n ...getComponentElements(\"progress\")\n .map(el => mountProgress(el, { progress$ })),\n\n /* Search */\n ...getComponentElements(\"search\")\n .map(el => mountSearch(el, { index$, keyboard$ })),\n\n /* Repository information */\n ...getComponentElements(\"source\")\n .map(el => mountSource(el))\n)\n\n/* Set up content component observables */\nconst content$ = defer(() => merge(\n\n /* Announcement bar */\n ...getComponentElements(\"announce\")\n .map(el => mountAnnounce(el)),\n\n /* Content */\n ...getComponentElements(\"content\")\n .map(el => mountContent(el, { viewport$, target$, print$ })),\n\n /* Search highlighting */\n ...getComponentElements(\"content\")\n .map(el => feature(\"search.highlight\")\n ? mountSearchHiglight(el, { index$, location$ })\n : EMPTY\n ),\n\n /* Header title */\n ...getComponentElements(\"header-title\")\n .map(el => mountHeaderTitle(el, { viewport$, header$ })),\n\n /* Sidebar */\n ...getComponentElements(\"sidebar\")\n .map(el => el.getAttribute(\"data-md-type\") === \"navigation\"\n ? at(screen$, () => mountSidebar(el, { viewport$, header$, main$ }))\n : at(tablet$, () => mountSidebar(el, { viewport$, header$, main$ }))\n ),\n\n /* Navigation tabs */\n ...getComponentElements(\"tabs\")\n .map(el => mountTabs(el, { viewport$, header$ })),\n\n /* Table of contents */\n ...getComponentElements(\"toc\")\n .map(el => mountTableOfContents(el, {\n viewport$, header$, main$, target$\n })),\n\n /* Back-to-top button */\n ...getComponentElements(\"top\")\n .map(el => mountBackToTop(el, { viewport$, header$, main$, target$ }))\n))\n\n/* Set up component observables */\nconst component$ = document$\n .pipe(\n switchMap(() => content$),\n mergeWith(control$),\n shareReplay(1)\n )\n\n/* Subscribe to all components */\ncomponent$.subscribe()\n\n/* ----------------------------------------------------------------------------\n * Exports\n * ------------------------------------------------------------------------- */\n\nwindow.document$ = document$ /* Document observable */\nwindow.location$ = location$ /* Location subject */\nwindow.target$ = target$ /* Location target observable */\nwindow.keyboard$ = keyboard$ /* Keyboard observable */\nwindow.viewport$ = viewport$ /* Viewport observable */\nwindow.tablet$ = tablet$ /* Media tablet observable */\nwindow.screen$ = screen$ /* Media screen observable */\nwindow.print$ = print$ /* Media print observable */\nwindow.alert$ = alert$ /* Alert subject */\nwindow.progress$ = progress$ /* Progress indicator subject */\nwindow.component$ = component$ /* Component observable */\n", "/*! *****************************************************************************\r\nCopyright (c) Microsoft Corporation.\r\n\r\nPermission to use, copy, modify, and/or distribute this software for any\r\npurpose with or without fee is hereby granted.\r\n\r\nTHE SOFTWARE IS PROVIDED \"AS IS\" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH\r\nREGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY\r\nAND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,\r\nINDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM\r\nLOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR\r\nOTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR\r\nPERFORMANCE OF THIS SOFTWARE.\r\n***************************************************************************** */\r\n/* global Reflect, Promise */\r\n\r\nvar extendStatics = function(d, b) {\r\n extendStatics = Object.setPrototypeOf ||\r\n ({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||\r\n function (d, b) { for (var p in b) if (Object.prototype.hasOwnProperty.call(b, p)) d[p] = b[p]; };\r\n return extendStatics(d, b);\r\n};\r\n\r\nexport function __extends(d, b) {\r\n if (typeof b !== \"function\" && b !== null)\r\n throw new TypeError(\"Class extends value \" + String(b) + \" is not a constructor or null\");\r\n extendStatics(d, b);\r\n function __() { this.constructor = d; }\r\n d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());\r\n}\r\n\r\nexport var __assign = function() {\r\n __assign = Object.assign || function __assign(t) {\r\n for (var s, i = 1, n = arguments.length; i < n; i++) {\r\n s = arguments[i];\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p)) t[p] = s[p];\r\n }\r\n return t;\r\n }\r\n return __assign.apply(this, arguments);\r\n}\r\n\r\nexport function __rest(s, e) {\r\n var t = {};\r\n for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p) && e.indexOf(p) < 0)\r\n t[p] = s[p];\r\n if (s != null && typeof Object.getOwnPropertySymbols === \"function\")\r\n for (var i = 0, p = Object.getOwnPropertySymbols(s); i < p.length; i++) {\r\n if (e.indexOf(p[i]) < 0 && Object.prototype.propertyIsEnumerable.call(s, p[i]))\r\n t[p[i]] = s[p[i]];\r\n }\r\n return t;\r\n}\r\n\r\nexport function __decorate(decorators, target, key, desc) {\r\n var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;\r\n if (typeof Reflect === \"object\" && typeof Reflect.decorate === \"function\") r = Reflect.decorate(decorators, target, key, desc);\r\n else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;\r\n return c > 3 && r && Object.defineProperty(target, key, r), r;\r\n}\r\n\r\nexport function __param(paramIndex, decorator) {\r\n return function (target, key) { decorator(target, key, paramIndex); }\r\n}\r\n\r\nexport function __metadata(metadataKey, metadataValue) {\r\n if (typeof Reflect === \"object\" && typeof Reflect.metadata === \"function\") return Reflect.metadata(metadataKey, metadataValue);\r\n}\r\n\r\nexport function __awaiter(thisArg, _arguments, P, generator) {\r\n function adopt(value) { return value instanceof P ? value : new P(function (resolve) { resolve(value); }); }\r\n return new (P || (P = Promise))(function (resolve, reject) {\r\n function fulfilled(value) { try { step(generator.next(value)); } catch (e) { reject(e); } }\r\n function rejected(value) { try { step(generator[\"throw\"](value)); } catch (e) { reject(e); } }\r\n function step(result) { result.done ? resolve(result.value) : adopt(result.value).then(fulfilled, rejected); }\r\n step((generator = generator.apply(thisArg, _arguments || [])).next());\r\n });\r\n}\r\n\r\nexport function __generator(thisArg, body) {\r\n var _ = { label: 0, sent: function() { if (t[0] & 1) throw t[1]; return t[1]; }, trys: [], ops: [] }, f, y, t, g;\r\n return g = { next: verb(0), \"throw\": verb(1), \"return\": verb(2) }, typeof Symbol === \"function\" && (g[Symbol.iterator] = function() { return this; }), g;\r\n function verb(n) { return function (v) { return step([n, v]); }; }\r\n function step(op) {\r\n if (f) throw new TypeError(\"Generator is already executing.\");\r\n while (_) try {\r\n if (f = 1, y && (t = op[0] & 2 ? y[\"return\"] : op[0] ? y[\"throw\"] || ((t = y[\"return\"]) && t.call(y), 0) : y.next) && !(t = t.call(y, op[1])).done) return t;\r\n if (y = 0, t) op = [op[0] & 2, t.value];\r\n switch (op[0]) {\r\n case 0: case 1: t = op; break;\r\n case 4: _.label++; return { value: op[1], done: false };\r\n case 5: _.label++; y = op[1]; op = [0]; continue;\r\n case 7: op = _.ops.pop(); _.trys.pop(); continue;\r\n default:\r\n if (!(t = _.trys, t = t.length > 0 && t[t.length - 1]) && (op[0] === 6 || op[0] === 2)) { _ = 0; continue; }\r\n if (op[0] === 3 && (!t || (op[1] > t[0] && op[1] < t[3]))) { _.label = op[1]; break; }\r\n if (op[0] === 6 && _.label < t[1]) { _.label = t[1]; t = op; break; }\r\n if (t && _.label < t[2]) { _.label = t[2]; _.ops.push(op); break; }\r\n if (t[2]) _.ops.pop();\r\n _.trys.pop(); continue;\r\n }\r\n op = body.call(thisArg, _);\r\n } catch (e) { op = [6, e]; y = 0; } finally { f = t = 0; }\r\n if (op[0] & 5) throw op[1]; return { value: op[0] ? op[1] : void 0, done: true };\r\n }\r\n}\r\n\r\nexport var __createBinding = Object.create ? (function(o, m, k, k2) {\r\n if (k2 === undefined) k2 = k;\r\n Object.defineProperty(o, k2, { enumerable: true, get: function() { return m[k]; } });\r\n}) : (function(o, m, k, k2) {\r\n if (k2 === undefined) k2 = k;\r\n o[k2] = m[k];\r\n});\r\n\r\nexport function __exportStar(m, o) {\r\n for (var p in m) if (p !== \"default\" && !Object.prototype.hasOwnProperty.call(o, p)) __createBinding(o, m, p);\r\n}\r\n\r\nexport function __values(o) {\r\n var s = typeof Symbol === \"function\" && Symbol.iterator, m = s && o[s], i = 0;\r\n if (m) return m.call(o);\r\n if (o && typeof o.length === \"number\") return {\r\n next: function () {\r\n if (o && i >= o.length) o = void 0;\r\n return { value: o && o[i++], done: !o };\r\n }\r\n };\r\n throw new TypeError(s ? \"Object is not iterable.\" : \"Symbol.iterator is not defined.\");\r\n}\r\n\r\nexport function __read(o, n) {\r\n var m = typeof Symbol === \"function\" && o[Symbol.iterator];\r\n if (!m) return o;\r\n var i = m.call(o), r, ar = [], e;\r\n try {\r\n while ((n === void 0 || n-- > 0) && !(r = i.next()).done) ar.push(r.value);\r\n }\r\n catch (error) { e = { error: error }; }\r\n finally {\r\n try {\r\n if (r && !r.done && (m = i[\"return\"])) m.call(i);\r\n }\r\n finally { if (e) throw e.error; }\r\n }\r\n return ar;\r\n}\r\n\r\n/** @deprecated */\r\nexport function __spread() {\r\n for (var ar = [], i = 0; i < arguments.length; i++)\r\n ar = ar.concat(__read(arguments[i]));\r\n return ar;\r\n}\r\n\r\n/** @deprecated */\r\nexport function __spreadArrays() {\r\n for (var s = 0, i = 0, il = arguments.length; i < il; i++) s += arguments[i].length;\r\n for (var r = Array(s), k = 0, i = 0; i < il; i++)\r\n for (var a = arguments[i], j = 0, jl = a.length; j < jl; j++, k++)\r\n r[k] = a[j];\r\n return r;\r\n}\r\n\r\nexport function __spreadArray(to, from, pack) {\r\n if (pack || arguments.length === 2) for (var i = 0, l = from.length, ar; i < l; i++) {\r\n if (ar || !(i in from)) {\r\n if (!ar) ar = Array.prototype.slice.call(from, 0, i);\r\n ar[i] = from[i];\r\n }\r\n }\r\n return to.concat(ar || Array.prototype.slice.call(from));\r\n}\r\n\r\nexport function __await(v) {\r\n return this instanceof __await ? (this.v = v, this) : new __await(v);\r\n}\r\n\r\nexport function __asyncGenerator(thisArg, _arguments, generator) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var g = generator.apply(thisArg, _arguments || []), i, q = [];\r\n return i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i;\r\n function verb(n) { if (g[n]) i[n] = function (v) { return new Promise(function (a, b) { q.push([n, v, a, b]) > 1 || resume(n, v); }); }; }\r\n function resume(n, v) { try { step(g[n](v)); } catch (e) { settle(q[0][3], e); } }\r\n function step(r) { r.value instanceof __await ? Promise.resolve(r.value.v).then(fulfill, reject) : settle(q[0][2], r); }\r\n function fulfill(value) { resume(\"next\", value); }\r\n function reject(value) { resume(\"throw\", value); }\r\n function settle(f, v) { if (f(v), q.shift(), q.length) resume(q[0][0], q[0][1]); }\r\n}\r\n\r\nexport function __asyncDelegator(o) {\r\n var i, p;\r\n return i = {}, verb(\"next\"), verb(\"throw\", function (e) { throw e; }), verb(\"return\"), i[Symbol.iterator] = function () { return this; }, i;\r\n function verb(n, f) { i[n] = o[n] ? function (v) { return (p = !p) ? { value: __await(o[n](v)), done: n === \"return\" } : f ? f(v) : v; } : f; }\r\n}\r\n\r\nexport function __asyncValues(o) {\r\n if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n var m = o[Symbol.asyncIterator], i;\r\n return m ? m.call(o) : (o = typeof __values === \"function\" ? __values(o) : o[Symbol.iterator](), i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i);\r\n function verb(n) { i[n] = o[n] && function (v) { return new Promise(function (resolve, reject) { v = o[n](v), settle(resolve, reject, v.done, v.value); }); }; }\r\n function settle(resolve, reject, d, v) { Promise.resolve(v).then(function(v) { resolve({ value: v, done: d }); }, reject); }\r\n}\r\n\r\nexport function __makeTemplateObject(cooked, raw) {\r\n if (Object.defineProperty) { Object.defineProperty(cooked, \"raw\", { value: raw }); } else { cooked.raw = raw; }\r\n return cooked;\r\n};\r\n\r\nvar __setModuleDefault = Object.create ? (function(o, v) {\r\n Object.defineProperty(o, \"default\", { enumerable: true, value: v });\r\n}) : function(o, v) {\r\n o[\"default\"] = v;\r\n};\r\n\r\nexport function __importStar(mod) {\r\n if (mod && mod.__esModule) return mod;\r\n var result = {};\r\n if (mod != null) for (var k in mod) if (k !== \"default\" && Object.prototype.hasOwnProperty.call(mod, k)) __createBinding(result, mod, k);\r\n __setModuleDefault(result, mod);\r\n return result;\r\n}\r\n\r\nexport function __importDefault(mod) {\r\n return (mod && mod.__esModule) ? mod : { default: mod };\r\n}\r\n\r\nexport function __classPrivateFieldGet(receiver, state, kind, f) {\r\n if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a getter\");\r\n if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot read private member from an object whose class did not declare it\");\r\n return kind === \"m\" ? f : kind === \"a\" ? f.call(receiver) : f ? f.value : state.get(receiver);\r\n}\r\n\r\nexport function __classPrivateFieldSet(receiver, state, value, kind, f) {\r\n if (kind === \"m\") throw new TypeError(\"Private method is not writable\");\r\n if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a setter\");\r\n if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot write private member to an object whose class did not declare it\");\r\n return (kind === \"a\" ? f.call(receiver, value) : f ? f.value = value : state.set(receiver, value)), value;\r\n}\r\n", "/**\n * Returns true if the object is a function.\n * @param value The value to check\n */\nexport function isFunction(value: any): value is (...args: any[]) => any {\n return typeof value === 'function';\n}\n", "/**\n * Used to create Error subclasses until the community moves away from ES5.\n *\n * This is because compiling from TypeScript down to ES5 has issues with subclassing Errors\n * as well as other built-in types: https://github.com/Microsoft/TypeScript/issues/12123\n *\n * @param createImpl A factory function to create the actual constructor implementation. The returned\n * function should be a named function that calls `_super` internally.\n */\nexport function createErrorClass(createImpl: (_super: any) => any): T {\n const _super = (instance: any) => {\n Error.call(instance);\n instance.stack = new Error().stack;\n };\n\n const ctorFunc = createImpl(_super);\n ctorFunc.prototype = Object.create(Error.prototype);\n ctorFunc.prototype.constructor = ctorFunc;\n return ctorFunc;\n}\n", "import { createErrorClass } from './createErrorClass';\n\nexport interface UnsubscriptionError extends Error {\n readonly errors: any[];\n}\n\nexport interface UnsubscriptionErrorCtor {\n /**\n * @deprecated Internal implementation detail. Do not construct error instances.\n * Cannot be tagged as internal: https://github.com/ReactiveX/rxjs/issues/6269\n */\n new (errors: any[]): UnsubscriptionError;\n}\n\n/**\n * An error thrown when one or more errors have occurred during the\n * `unsubscribe` of a {@link Subscription}.\n */\nexport const UnsubscriptionError: UnsubscriptionErrorCtor = createErrorClass(\n (_super) =>\n function UnsubscriptionErrorImpl(this: any, errors: (Error | string)[]) {\n _super(this);\n this.message = errors\n ? `${errors.length} errors occurred during unsubscription:\n${errors.map((err, i) => `${i + 1}) ${err.toString()}`).join('\\n ')}`\n : '';\n this.name = 'UnsubscriptionError';\n this.errors = errors;\n }\n);\n", "/**\n * Removes an item from an array, mutating it.\n * @param arr The array to remove the item from\n * @param item The item to remove\n */\nexport function arrRemove(arr: T[] | undefined | null, item: T) {\n if (arr) {\n const index = arr.indexOf(item);\n 0 <= index && arr.splice(index, 1);\n }\n}\n", "import { isFunction } from './util/isFunction';\nimport { UnsubscriptionError } from './util/UnsubscriptionError';\nimport { SubscriptionLike, TeardownLogic, Unsubscribable } from './types';\nimport { arrRemove } from './util/arrRemove';\n\n/**\n * Represents a disposable resource, such as the execution of an Observable. A\n * Subscription has one important method, `unsubscribe`, that takes no argument\n * and just disposes the resource held by the subscription.\n *\n * Additionally, subscriptions may be grouped together through the `add()`\n * method, which will attach a child Subscription to the current Subscription.\n * When a Subscription is unsubscribed, all its children (and its grandchildren)\n * will be unsubscribed as well.\n *\n * @class Subscription\n */\nexport class Subscription implements SubscriptionLike {\n /** @nocollapse */\n public static EMPTY = (() => {\n const empty = new Subscription();\n empty.closed = true;\n return empty;\n })();\n\n /**\n * A flag to indicate whether this Subscription has already been unsubscribed.\n */\n public closed = false;\n\n private _parentage: Subscription[] | Subscription | null = null;\n\n /**\n * The list of registered finalizers to execute upon unsubscription. Adding and removing from this\n * list occurs in the {@link #add} and {@link #remove} methods.\n */\n private _finalizers: Exclude[] | null = null;\n\n /**\n * @param initialTeardown A function executed first as part of the finalization\n * process that is kicked off when {@link #unsubscribe} is called.\n */\n constructor(private initialTeardown?: () => void) {}\n\n /**\n * Disposes the resources held by the subscription. May, for instance, cancel\n * an ongoing Observable execution or cancel any other type of work that\n * started when the Subscription was created.\n * @return {void}\n */\n unsubscribe(): void {\n let errors: any[] | undefined;\n\n if (!this.closed) {\n this.closed = true;\n\n // Remove this from it's parents.\n const { _parentage } = this;\n if (_parentage) {\n this._parentage = null;\n if (Array.isArray(_parentage)) {\n for (const parent of _parentage) {\n parent.remove(this);\n }\n } else {\n _parentage.remove(this);\n }\n }\n\n const { initialTeardown: initialFinalizer } = this;\n if (isFunction(initialFinalizer)) {\n try {\n initialFinalizer();\n } catch (e) {\n errors = e instanceof UnsubscriptionError ? e.errors : [e];\n }\n }\n\n const { _finalizers } = this;\n if (_finalizers) {\n this._finalizers = null;\n for (const finalizer of _finalizers) {\n try {\n execFinalizer(finalizer);\n } catch (err) {\n errors = errors ?? [];\n if (err instanceof UnsubscriptionError) {\n errors = [...errors, ...err.errors];\n } else {\n errors.push(err);\n }\n }\n }\n }\n\n if (errors) {\n throw new UnsubscriptionError(errors);\n }\n }\n }\n\n /**\n * Adds a finalizer to this subscription, so that finalization will be unsubscribed/called\n * when this subscription is unsubscribed. If this subscription is already {@link #closed},\n * because it has already been unsubscribed, then whatever finalizer is passed to it\n * will automatically be executed (unless the finalizer itself is also a closed subscription).\n *\n * Closed Subscriptions cannot be added as finalizers to any subscription. Adding a closed\n * subscription to a any subscription will result in no operation. (A noop).\n *\n * Adding a subscription to itself, or adding `null` or `undefined` will not perform any\n * operation at all. (A noop).\n *\n * `Subscription` instances that are added to this instance will automatically remove themselves\n * if they are unsubscribed. Functions and {@link Unsubscribable} objects that you wish to remove\n * will need to be removed manually with {@link #remove}\n *\n * @param teardown The finalization logic to add to this subscription.\n */\n add(teardown: TeardownLogic): void {\n // Only add the finalizer if it's not undefined\n // and don't add a subscription to itself.\n if (teardown && teardown !== this) {\n if (this.closed) {\n // If this subscription is already closed,\n // execute whatever finalizer is handed to it automatically.\n execFinalizer(teardown);\n } else {\n if (teardown instanceof Subscription) {\n // We don't add closed subscriptions, and we don't add the same subscription\n // twice. Subscription unsubscribe is idempotent.\n if (teardown.closed || teardown._hasParent(this)) {\n return;\n }\n teardown._addParent(this);\n }\n (this._finalizers = this._finalizers ?? []).push(teardown);\n }\n }\n }\n\n /**\n * Checks to see if a this subscription already has a particular parent.\n * This will signal that this subscription has already been added to the parent in question.\n * @param parent the parent to check for\n */\n private _hasParent(parent: Subscription) {\n const { _parentage } = this;\n return _parentage === parent || (Array.isArray(_parentage) && _parentage.includes(parent));\n }\n\n /**\n * Adds a parent to this subscription so it can be removed from the parent if it\n * unsubscribes on it's own.\n *\n * NOTE: THIS ASSUMES THAT {@link _hasParent} HAS ALREADY BEEN CHECKED.\n * @param parent The parent subscription to add\n */\n private _addParent(parent: Subscription) {\n const { _parentage } = this;\n this._parentage = Array.isArray(_parentage) ? (_parentage.push(parent), _parentage) : _parentage ? [_parentage, parent] : parent;\n }\n\n /**\n * Called on a child when it is removed via {@link #remove}.\n * @param parent The parent to remove\n */\n private _removeParent(parent: Subscription) {\n const { _parentage } = this;\n if (_parentage === parent) {\n this._parentage = null;\n } else if (Array.isArray(_parentage)) {\n arrRemove(_parentage, parent);\n }\n }\n\n /**\n * Removes a finalizer from this subscription that was previously added with the {@link #add} method.\n *\n * Note that `Subscription` instances, when unsubscribed, will automatically remove themselves\n * from every other `Subscription` they have been added to. This means that using the `remove` method\n * is not a common thing and should be used thoughtfully.\n *\n * If you add the same finalizer instance of a function or an unsubscribable object to a `Subscription` instance\n * more than once, you will need to call `remove` the same number of times to remove all instances.\n *\n * All finalizer instances are removed to free up memory upon unsubscription.\n *\n * @param teardown The finalizer to remove from this subscription\n */\n remove(teardown: Exclude): void {\n const { _finalizers } = this;\n _finalizers && arrRemove(_finalizers, teardown);\n\n if (teardown instanceof Subscription) {\n teardown._removeParent(this);\n }\n }\n}\n\nexport const EMPTY_SUBSCRIPTION = Subscription.EMPTY;\n\nexport function isSubscription(value: any): value is Subscription {\n return (\n value instanceof Subscription ||\n (value && 'closed' in value && isFunction(value.remove) && isFunction(value.add) && isFunction(value.unsubscribe))\n );\n}\n\nfunction execFinalizer(finalizer: Unsubscribable | (() => void)) {\n if (isFunction(finalizer)) {\n finalizer();\n } else {\n finalizer.unsubscribe();\n }\n}\n", "import { Subscriber } from './Subscriber';\nimport { ObservableNotification } from './types';\n\n/**\n * The {@link GlobalConfig} object for RxJS. It is used to configure things\n * like how to react on unhandled errors.\n */\nexport const config: GlobalConfig = {\n onUnhandledError: null,\n onStoppedNotification: null,\n Promise: undefined,\n useDeprecatedSynchronousErrorHandling: false,\n useDeprecatedNextContext: false,\n};\n\n/**\n * The global configuration object for RxJS, used to configure things\n * like how to react on unhandled errors. Accessible via {@link config}\n * object.\n */\nexport interface GlobalConfig {\n /**\n * A registration point for unhandled errors from RxJS. These are errors that\n * cannot were not handled by consuming code in the usual subscription path. For\n * example, if you have this configured, and you subscribe to an observable without\n * providing an error handler, errors from that subscription will end up here. This\n * will _always_ be called asynchronously on another job in the runtime. This is because\n * we do not want errors thrown in this user-configured handler to interfere with the\n * behavior of the library.\n */\n onUnhandledError: ((err: any) => void) | null;\n\n /**\n * A registration point for notifications that cannot be sent to subscribers because they\n * have completed, errored or have been explicitly unsubscribed. By default, next, complete\n * and error notifications sent to stopped subscribers are noops. However, sometimes callers\n * might want a different behavior. For example, with sources that attempt to report errors\n * to stopped subscribers, a caller can configure RxJS to throw an unhandled error instead.\n * This will _always_ be called asynchronously on another job in the runtime. This is because\n * we do not want errors thrown in this user-configured handler to interfere with the\n * behavior of the library.\n */\n onStoppedNotification: ((notification: ObservableNotification, subscriber: Subscriber) => void) | null;\n\n /**\n * The promise constructor used by default for {@link Observable#toPromise toPromise} and {@link Observable#forEach forEach}\n * methods.\n *\n * @deprecated As of version 8, RxJS will no longer support this sort of injection of a\n * Promise constructor. If you need a Promise implementation other than native promises,\n * please polyfill/patch Promise as you see appropriate. Will be removed in v8.\n */\n Promise?: PromiseConstructorLike;\n\n /**\n * If true, turns on synchronous error rethrowing, which is a deprecated behavior\n * in v6 and higher. This behavior enables bad patterns like wrapping a subscribe\n * call in a try/catch block. It also enables producer interference, a nasty bug\n * where a multicast can be broken for all observers by a downstream consumer with\n * an unhandled error. DO NOT USE THIS FLAG UNLESS IT'S NEEDED TO BUY TIME\n * FOR MIGRATION REASONS.\n *\n * @deprecated As of version 8, RxJS will no longer support synchronous throwing\n * of unhandled errors. All errors will be thrown on a separate call stack to prevent bad\n * behaviors described above. Will be removed in v8.\n */\n useDeprecatedSynchronousErrorHandling: boolean;\n\n /**\n * If true, enables an as-of-yet undocumented feature from v5: The ability to access\n * `unsubscribe()` via `this` context in `next` functions created in observers passed\n * to `subscribe`.\n *\n * This is being removed because the performance was severely problematic, and it could also cause\n * issues when types other than POJOs are passed to subscribe as subscribers, as they will likely have\n * their `this` context overwritten.\n *\n * @deprecated As of version 8, RxJS will no longer support altering the\n * context of next functions provided as part of an observer to Subscribe. Instead,\n * you will have access to a subscription or a signal or token that will allow you to do things like\n * unsubscribe and test closed status. Will be removed in v8.\n */\n useDeprecatedNextContext: boolean;\n}\n", "import type { TimerHandle } from './timerHandle';\ntype SetTimeoutFunction = (handler: () => void, timeout?: number, ...args: any[]) => TimerHandle;\ntype ClearTimeoutFunction = (handle: TimerHandle) => void;\n\ninterface TimeoutProvider {\n setTimeout: SetTimeoutFunction;\n clearTimeout: ClearTimeoutFunction;\n delegate:\n | {\n setTimeout: SetTimeoutFunction;\n clearTimeout: ClearTimeoutFunction;\n }\n | undefined;\n}\n\nexport const timeoutProvider: TimeoutProvider = {\n // When accessing the delegate, use the variable rather than `this` so that\n // the functions can be called without being bound to the provider.\n setTimeout(handler: () => void, timeout?: number, ...args) {\n const { delegate } = timeoutProvider;\n if (delegate?.setTimeout) {\n return delegate.setTimeout(handler, timeout, ...args);\n }\n return setTimeout(handler, timeout, ...args);\n },\n clearTimeout(handle) {\n const { delegate } = timeoutProvider;\n return (delegate?.clearTimeout || clearTimeout)(handle as any);\n },\n delegate: undefined,\n};\n", "import { config } from '../config';\nimport { timeoutProvider } from '../scheduler/timeoutProvider';\n\n/**\n * Handles an error on another job either with the user-configured {@link onUnhandledError},\n * or by throwing it on that new job so it can be picked up by `window.onerror`, `process.on('error')`, etc.\n *\n * This should be called whenever there is an error that is out-of-band with the subscription\n * or when an error hits a terminal boundary of the subscription and no error handler was provided.\n *\n * @param err the error to report\n */\nexport function reportUnhandledError(err: any) {\n timeoutProvider.setTimeout(() => {\n const { onUnhandledError } = config;\n if (onUnhandledError) {\n // Execute the user-configured error handler.\n onUnhandledError(err);\n } else {\n // Throw so it is picked up by the runtime's uncaught error mechanism.\n throw err;\n }\n });\n}\n", "/* tslint:disable:no-empty */\nexport function noop() { }\n", "import { CompleteNotification, NextNotification, ErrorNotification } from './types';\n\n/**\n * A completion object optimized for memory use and created to be the\n * same \"shape\" as other notifications in v8.\n * @internal\n */\nexport const COMPLETE_NOTIFICATION = (() => createNotification('C', undefined, undefined) as CompleteNotification)();\n\n/**\n * Internal use only. Creates an optimized error notification that is the same \"shape\"\n * as other notifications.\n * @internal\n */\nexport function errorNotification(error: any): ErrorNotification {\n return createNotification('E', undefined, error) as any;\n}\n\n/**\n * Internal use only. Creates an optimized next notification that is the same \"shape\"\n * as other notifications.\n * @internal\n */\nexport function nextNotification(value: T) {\n return createNotification('N', value, undefined) as NextNotification;\n}\n\n/**\n * Ensures that all notifications created internally have the same \"shape\" in v8.\n *\n * TODO: This is only exported to support a crazy legacy test in `groupBy`.\n * @internal\n */\nexport function createNotification(kind: 'N' | 'E' | 'C', value: any, error: any) {\n return {\n kind,\n value,\n error,\n };\n}\n", "import { config } from '../config';\n\nlet context: { errorThrown: boolean; error: any } | null = null;\n\n/**\n * Handles dealing with errors for super-gross mode. Creates a context, in which\n * any synchronously thrown errors will be passed to {@link captureError}. Which\n * will record the error such that it will be rethrown after the call back is complete.\n * TODO: Remove in v8\n * @param cb An immediately executed function.\n */\nexport function errorContext(cb: () => void) {\n if (config.useDeprecatedSynchronousErrorHandling) {\n const isRoot = !context;\n if (isRoot) {\n context = { errorThrown: false, error: null };\n }\n cb();\n if (isRoot) {\n const { errorThrown, error } = context!;\n context = null;\n if (errorThrown) {\n throw error;\n }\n }\n } else {\n // This is the general non-deprecated path for everyone that\n // isn't crazy enough to use super-gross mode (useDeprecatedSynchronousErrorHandling)\n cb();\n }\n}\n\n/**\n * Captures errors only in super-gross mode.\n * @param err the error to capture\n */\nexport function captureError(err: any) {\n if (config.useDeprecatedSynchronousErrorHandling && context) {\n context.errorThrown = true;\n context.error = err;\n }\n}\n", "import { isFunction } from './util/isFunction';\nimport { Observer, ObservableNotification } from './types';\nimport { isSubscription, Subscription } from './Subscription';\nimport { config } from './config';\nimport { reportUnhandledError } from './util/reportUnhandledError';\nimport { noop } from './util/noop';\nimport { nextNotification, errorNotification, COMPLETE_NOTIFICATION } from './NotificationFactories';\nimport { timeoutProvider } from './scheduler/timeoutProvider';\nimport { captureError } from './util/errorContext';\n\n/**\n * Implements the {@link Observer} interface and extends the\n * {@link Subscription} class. While the {@link Observer} is the public API for\n * consuming the values of an {@link Observable}, all Observers get converted to\n * a Subscriber, in order to provide Subscription-like capabilities such as\n * `unsubscribe`. Subscriber is a common type in RxJS, and crucial for\n * implementing operators, but it is rarely used as a public API.\n *\n * @class Subscriber\n */\nexport class Subscriber extends Subscription implements Observer {\n /**\n * A static factory for a Subscriber, given a (potentially partial) definition\n * of an Observer.\n * @param next The `next` callback of an Observer.\n * @param error The `error` callback of an\n * Observer.\n * @param complete The `complete` callback of an\n * Observer.\n * @return A Subscriber wrapping the (partially defined)\n * Observer represented by the given arguments.\n * @nocollapse\n * @deprecated Do not use. Will be removed in v8. There is no replacement for this\n * method, and there is no reason to be creating instances of `Subscriber` directly.\n * If you have a specific use case, please file an issue.\n */\n static create(next?: (x?: T) => void, error?: (e?: any) => void, complete?: () => void): Subscriber {\n return new SafeSubscriber(next, error, complete);\n }\n\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n protected isStopped: boolean = false;\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n protected destination: Subscriber | Observer; // this `any` is the escape hatch to erase extra type param (e.g. R)\n\n /**\n * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n * There is no reason to directly create an instance of Subscriber. This type is exported for typings reasons.\n */\n constructor(destination?: Subscriber | Observer) {\n super();\n if (destination) {\n this.destination = destination;\n // Automatically chain subscriptions together here.\n // if destination is a Subscription, then it is a Subscriber.\n if (isSubscription(destination)) {\n destination.add(this);\n }\n } else {\n this.destination = EMPTY_OBSERVER;\n }\n }\n\n /**\n * The {@link Observer} callback to receive notifications of type `next` from\n * the Observable, with a value. The Observable may call this method 0 or more\n * times.\n * @param {T} [value] The `next` value.\n * @return {void}\n */\n next(value?: T): void {\n if (this.isStopped) {\n handleStoppedNotification(nextNotification(value), this);\n } else {\n this._next(value!);\n }\n }\n\n /**\n * The {@link Observer} callback to receive notifications of type `error` from\n * the Observable, with an attached `Error`. Notifies the Observer that\n * the Observable has experienced an error condition.\n * @param {any} [err] The `error` exception.\n * @return {void}\n */\n error(err?: any): void {\n if (this.isStopped) {\n handleStoppedNotification(errorNotification(err), this);\n } else {\n this.isStopped = true;\n this._error(err);\n }\n }\n\n /**\n * The {@link Observer} callback to receive a valueless notification of type\n * `complete` from the Observable. Notifies the Observer that the Observable\n * has finished sending push-based notifications.\n * @return {void}\n */\n complete(): void {\n if (this.isStopped) {\n handleStoppedNotification(COMPLETE_NOTIFICATION, this);\n } else {\n this.isStopped = true;\n this._complete();\n }\n }\n\n unsubscribe(): void {\n if (!this.closed) {\n this.isStopped = true;\n super.unsubscribe();\n this.destination = null!;\n }\n }\n\n protected _next(value: T): void {\n this.destination.next(value);\n }\n\n protected _error(err: any): void {\n try {\n this.destination.error(err);\n } finally {\n this.unsubscribe();\n }\n }\n\n protected _complete(): void {\n try {\n this.destination.complete();\n } finally {\n this.unsubscribe();\n }\n }\n}\n\n/**\n * This bind is captured here because we want to be able to have\n * compatibility with monoid libraries that tend to use a method named\n * `bind`. In particular, a library called Monio requires this.\n */\nconst _bind = Function.prototype.bind;\n\nfunction bind any>(fn: Fn, thisArg: any): Fn {\n return _bind.call(fn, thisArg);\n}\n\n/**\n * Internal optimization only, DO NOT EXPOSE.\n * @internal\n */\nclass ConsumerObserver implements Observer {\n constructor(private partialObserver: Partial>) {}\n\n next(value: T): void {\n const { partialObserver } = this;\n if (partialObserver.next) {\n try {\n partialObserver.next(value);\n } catch (error) {\n handleUnhandledError(error);\n }\n }\n }\n\n error(err: any): void {\n const { partialObserver } = this;\n if (partialObserver.error) {\n try {\n partialObserver.error(err);\n } catch (error) {\n handleUnhandledError(error);\n }\n } else {\n handleUnhandledError(err);\n }\n }\n\n complete(): void {\n const { partialObserver } = this;\n if (partialObserver.complete) {\n try {\n partialObserver.complete();\n } catch (error) {\n handleUnhandledError(error);\n }\n }\n }\n}\n\nexport class SafeSubscriber extends Subscriber {\n constructor(\n observerOrNext?: Partial> | ((value: T) => void) | null,\n error?: ((e?: any) => void) | null,\n complete?: (() => void) | null\n ) {\n super();\n\n let partialObserver: Partial>;\n if (isFunction(observerOrNext) || !observerOrNext) {\n // The first argument is a function, not an observer. The next\n // two arguments *could* be observers, or they could be empty.\n partialObserver = {\n next: (observerOrNext ?? undefined) as (((value: T) => void) | undefined),\n error: error ?? undefined,\n complete: complete ?? undefined,\n };\n } else {\n // The first argument is a partial observer.\n let context: any;\n if (this && config.useDeprecatedNextContext) {\n // This is a deprecated path that made `this.unsubscribe()` available in\n // next handler functions passed to subscribe. This only exists behind a flag\n // now, as it is *very* slow.\n context = Object.create(observerOrNext);\n context.unsubscribe = () => this.unsubscribe();\n partialObserver = {\n next: observerOrNext.next && bind(observerOrNext.next, context),\n error: observerOrNext.error && bind(observerOrNext.error, context),\n complete: observerOrNext.complete && bind(observerOrNext.complete, context),\n };\n } else {\n // The \"normal\" path. Just use the partial observer directly.\n partialObserver = observerOrNext;\n }\n }\n\n // Wrap the partial observer to ensure it's a full observer, and\n // make sure proper error handling is accounted for.\n this.destination = new ConsumerObserver(partialObserver);\n }\n}\n\nfunction handleUnhandledError(error: any) {\n if (config.useDeprecatedSynchronousErrorHandling) {\n captureError(error);\n } else {\n // Ideal path, we report this as an unhandled error,\n // which is thrown on a new call stack.\n reportUnhandledError(error);\n }\n}\n\n/**\n * An error handler used when no error handler was supplied\n * to the SafeSubscriber -- meaning no error handler was supplied\n * do the `subscribe` call on our observable.\n * @param err The error to handle\n */\nfunction defaultErrorHandler(err: any) {\n throw err;\n}\n\n/**\n * A handler for notifications that cannot be sent to a stopped subscriber.\n * @param notification The notification being sent\n * @param subscriber The stopped subscriber\n */\nfunction handleStoppedNotification(notification: ObservableNotification, subscriber: Subscriber) {\n const { onStoppedNotification } = config;\n onStoppedNotification && timeoutProvider.setTimeout(() => onStoppedNotification(notification, subscriber));\n}\n\n/**\n * The observer used as a stub for subscriptions where the user did not\n * pass any arguments to `subscribe`. Comes with the default error handling\n * behavior.\n */\nexport const EMPTY_OBSERVER: Readonly> & { closed: true } = {\n closed: true,\n next: noop,\n error: defaultErrorHandler,\n complete: noop,\n};\n", "/**\n * Symbol.observable or a string \"@@observable\". Used for interop\n *\n * @deprecated We will no longer be exporting this symbol in upcoming versions of RxJS.\n * Instead polyfill and use Symbol.observable directly *or* use https://www.npmjs.com/package/symbol-observable\n */\nexport const observable: string | symbol = (() => (typeof Symbol === 'function' && Symbol.observable) || '@@observable')();\n", "/**\n * This function takes one parameter and just returns it. Simply put,\n * this is like `(x: T): T => x`.\n *\n * ## Examples\n *\n * This is useful in some cases when using things like `mergeMap`\n *\n * ```ts\n * import { interval, take, map, range, mergeMap, identity } from 'rxjs';\n *\n * const source$ = interval(1000).pipe(take(5));\n *\n * const result$ = source$.pipe(\n * map(i => range(i)),\n * mergeMap(identity) // same as mergeMap(x => x)\n * );\n *\n * result$.subscribe({\n * next: console.log\n * });\n * ```\n *\n * Or when you want to selectively apply an operator\n *\n * ```ts\n * import { interval, take, identity } from 'rxjs';\n *\n * const shouldLimit = () => Math.random() < 0.5;\n *\n * const source$ = interval(1000);\n *\n * const result$ = source$.pipe(shouldLimit() ? take(5) : identity);\n *\n * result$.subscribe({\n * next: console.log\n * });\n * ```\n *\n * @param x Any value that is returned by this function\n * @returns The value passed as the first parameter to this function\n */\nexport function identity(x: T): T {\n return x;\n}\n", "import { identity } from './identity';\nimport { UnaryFunction } from '../types';\n\nexport function pipe(): typeof identity;\nexport function pipe(fn1: UnaryFunction): UnaryFunction;\nexport function pipe(fn1: UnaryFunction, fn2: UnaryFunction): UnaryFunction;\nexport function pipe(fn1: UnaryFunction, fn2: UnaryFunction, fn3: UnaryFunction): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction,\n fn6: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction,\n fn6: UnaryFunction,\n fn7: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction,\n fn6: UnaryFunction,\n fn7: UnaryFunction,\n fn8: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction,\n fn6: UnaryFunction,\n fn7: UnaryFunction,\n fn8: UnaryFunction,\n fn9: UnaryFunction\n): UnaryFunction;\nexport function pipe(\n fn1: UnaryFunction,\n fn2: UnaryFunction,\n fn3: UnaryFunction,\n fn4: UnaryFunction,\n fn5: UnaryFunction,\n fn6: UnaryFunction,\n fn7: UnaryFunction,\n fn8: UnaryFunction,\n fn9: UnaryFunction,\n ...fns: UnaryFunction[]\n): UnaryFunction;\n\n/**\n * pipe() can be called on one or more functions, each of which can take one argument (\"UnaryFunction\")\n * and uses it to return a value.\n * It returns a function that takes one argument, passes it to the first UnaryFunction, and then\n * passes the result to the next one, passes that result to the next one, and so on. \n */\nexport function pipe(...fns: Array>): UnaryFunction {\n return pipeFromArray(fns);\n}\n\n/** @internal */\nexport function pipeFromArray(fns: Array>): UnaryFunction {\n if (fns.length === 0) {\n return identity as UnaryFunction;\n }\n\n if (fns.length === 1) {\n return fns[0];\n }\n\n return function piped(input: T): R {\n return fns.reduce((prev: any, fn: UnaryFunction) => fn(prev), input as any);\n };\n}\n", "import { Operator } from './Operator';\nimport { SafeSubscriber, Subscriber } from './Subscriber';\nimport { isSubscription, Subscription } from './Subscription';\nimport { TeardownLogic, OperatorFunction, Subscribable, Observer } from './types';\nimport { observable as Symbol_observable } from './symbol/observable';\nimport { pipeFromArray } from './util/pipe';\nimport { config } from './config';\nimport { isFunction } from './util/isFunction';\nimport { errorContext } from './util/errorContext';\n\n/**\n * A representation of any set of values over any amount of time. This is the most basic building block\n * of RxJS.\n *\n * @class Observable\n */\nexport class Observable implements Subscribable {\n /**\n * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n */\n source: Observable | undefined;\n\n /**\n * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n */\n operator: Operator | undefined;\n\n /**\n * @constructor\n * @param {Function} subscribe the function that is called when the Observable is\n * initially subscribed to. This function is given a Subscriber, to which new values\n * can be `next`ed, or an `error` method can be called to raise an error, or\n * `complete` can be called to notify of a successful completion.\n */\n constructor(subscribe?: (this: Observable, subscriber: Subscriber) => TeardownLogic) {\n if (subscribe) {\n this._subscribe = subscribe;\n }\n }\n\n // HACK: Since TypeScript inherits static properties too, we have to\n // fight against TypeScript here so Subject can have a different static create signature\n /**\n * Creates a new Observable by calling the Observable constructor\n * @owner Observable\n * @method create\n * @param {Function} subscribe? the subscriber function to be passed to the Observable constructor\n * @return {Observable} a new observable\n * @nocollapse\n * @deprecated Use `new Observable()` instead. Will be removed in v8.\n */\n static create: (...args: any[]) => any = (subscribe?: (subscriber: Subscriber) => TeardownLogic) => {\n return new Observable(subscribe);\n };\n\n /**\n * Creates a new Observable, with this Observable instance as the source, and the passed\n * operator defined as the new observable's operator.\n * @method lift\n * @param operator the operator defining the operation to take on the observable\n * @return a new observable with the Operator applied\n * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n * If you have implemented an operator using `lift`, it is recommended that you create an\n * operator by simply returning `new Observable()` directly. See \"Creating new operators from\n * scratch\" section here: https://rxjs.dev/guide/operators\n */\n lift(operator?: Operator): Observable {\n const observable = new Observable();\n observable.source = this;\n observable.operator = operator;\n return observable;\n }\n\n subscribe(observerOrNext?: Partial> | ((value: T) => void)): Subscription;\n /** @deprecated Instead of passing separate callback arguments, use an observer argument. Signatures taking separate callback arguments will be removed in v8. Details: https://rxjs.dev/deprecations/subscribe-arguments */\n subscribe(next?: ((value: T) => void) | null, error?: ((error: any) => void) | null, complete?: (() => void) | null): Subscription;\n /**\n * Invokes an execution of an Observable and registers Observer handlers for notifications it will emit.\n *\n * Use it when you have all these Observables, but still nothing is happening.\n *\n * `subscribe` is not a regular operator, but a method that calls Observable's internal `subscribe` function. It\n * might be for example a function that you passed to Observable's constructor, but most of the time it is\n * a library implementation, which defines what will be emitted by an Observable, and when it be will emitted. This means\n * that calling `subscribe` is actually the moment when Observable starts its work, not when it is created, as it is often\n * the thought.\n *\n * Apart from starting the execution of an Observable, this method allows you to listen for values\n * that an Observable emits, as well as for when it completes or errors. You can achieve this in two\n * of the following ways.\n *\n * The first way is creating an object that implements {@link Observer} interface. It should have methods\n * defined by that interface, but note that it should be just a regular JavaScript object, which you can create\n * yourself in any way you want (ES6 class, classic function constructor, object literal etc.). In particular, do\n * not attempt to use any RxJS implementation details to create Observers - you don't need them. Remember also\n * that your object does not have to implement all methods. If you find yourself creating a method that doesn't\n * do anything, you can simply omit it. Note however, if the `error` method is not provided and an error happens,\n * it will be thrown asynchronously. Errors thrown asynchronously cannot be caught using `try`/`catch`. Instead,\n * use the {@link onUnhandledError} configuration option or use a runtime handler (like `window.onerror` or\n * `process.on('error)`) to be notified of unhandled errors. Because of this, it's recommended that you provide\n * an `error` method to avoid missing thrown errors.\n *\n * The second way is to give up on Observer object altogether and simply provide callback functions in place of its methods.\n * This means you can provide three functions as arguments to `subscribe`, where the first function is equivalent\n * of a `next` method, the second of an `error` method and the third of a `complete` method. Just as in case of an Observer,\n * if you do not need to listen for something, you can omit a function by passing `undefined` or `null`,\n * since `subscribe` recognizes these functions by where they were placed in function call. When it comes\n * to the `error` function, as with an Observer, if not provided, errors emitted by an Observable will be thrown asynchronously.\n *\n * You can, however, subscribe with no parameters at all. This may be the case where you're not interested in terminal events\n * and you also handled emissions internally by using operators (e.g. using `tap`).\n *\n * Whichever style of calling `subscribe` you use, in both cases it returns a Subscription object.\n * This object allows you to call `unsubscribe` on it, which in turn will stop the work that an Observable does and will clean\n * up all resources that an Observable used. Note that cancelling a subscription will not call `complete` callback\n * provided to `subscribe` function, which is reserved for a regular completion signal that comes from an Observable.\n *\n * Remember that callbacks provided to `subscribe` are not guaranteed to be called asynchronously.\n * It is an Observable itself that decides when these functions will be called. For example {@link of}\n * by default emits all its values synchronously. Always check documentation for how given Observable\n * will behave when subscribed and if its default behavior can be modified with a `scheduler`.\n *\n * #### Examples\n *\n * Subscribe with an {@link guide/observer Observer}\n *\n * ```ts\n * import { of } from 'rxjs';\n *\n * const sumObserver = {\n * sum: 0,\n * next(value) {\n * console.log('Adding: ' + value);\n * this.sum = this.sum + value;\n * },\n * error() {\n * // We actually could just remove this method,\n * // since we do not really care about errors right now.\n * },\n * complete() {\n * console.log('Sum equals: ' + this.sum);\n * }\n * };\n *\n * of(1, 2, 3) // Synchronously emits 1, 2, 3 and then completes.\n * .subscribe(sumObserver);\n *\n * // Logs:\n * // 'Adding: 1'\n * // 'Adding: 2'\n * // 'Adding: 3'\n * // 'Sum equals: 6'\n * ```\n *\n * Subscribe with functions ({@link deprecations/subscribe-arguments deprecated})\n *\n * ```ts\n * import { of } from 'rxjs'\n *\n * let sum = 0;\n *\n * of(1, 2, 3).subscribe(\n * value => {\n * console.log('Adding: ' + value);\n * sum = sum + value;\n * },\n * undefined,\n * () => console.log('Sum equals: ' + sum)\n * );\n *\n * // Logs:\n * // 'Adding: 1'\n * // 'Adding: 2'\n * // 'Adding: 3'\n * // 'Sum equals: 6'\n * ```\n *\n * Cancel a subscription\n *\n * ```ts\n * import { interval } from 'rxjs';\n *\n * const subscription = interval(1000).subscribe({\n * next(num) {\n * console.log(num)\n * },\n * complete() {\n * // Will not be called, even when cancelling subscription.\n * console.log('completed!');\n * }\n * });\n *\n * setTimeout(() => {\n * subscription.unsubscribe();\n * console.log('unsubscribed!');\n * }, 2500);\n *\n * // Logs:\n * // 0 after 1s\n * // 1 after 2s\n * // 'unsubscribed!' after 2.5s\n * ```\n *\n * @param {Observer|Function} observerOrNext (optional) Either an observer with methods to be called,\n * or the first of three possible handlers, which is the handler for each value emitted from the subscribed\n * Observable.\n * @param {Function} error (optional) A handler for a terminal event resulting from an error. If no error handler is provided,\n * the error will be thrown asynchronously as unhandled.\n * @param {Function} complete (optional) A handler for a terminal event resulting from successful completion.\n * @return {Subscription} a subscription reference to the registered handlers\n * @method subscribe\n */\n subscribe(\n observerOrNext?: Partial> | ((value: T) => void) | null,\n error?: ((error: any) => void) | null,\n complete?: (() => void) | null\n ): Subscription {\n const subscriber = isSubscriber(observerOrNext) ? observerOrNext : new SafeSubscriber(observerOrNext, error, complete);\n\n errorContext(() => {\n const { operator, source } = this;\n subscriber.add(\n operator\n ? // We're dealing with a subscription in the\n // operator chain to one of our lifted operators.\n operator.call(subscriber, source)\n : source\n ? // If `source` has a value, but `operator` does not, something that\n // had intimate knowledge of our API, like our `Subject`, must have\n // set it. We're going to just call `_subscribe` directly.\n this._subscribe(subscriber)\n : // In all other cases, we're likely wrapping a user-provided initializer\n // function, so we need to catch errors and handle them appropriately.\n this._trySubscribe(subscriber)\n );\n });\n\n return subscriber;\n }\n\n /** @internal */\n protected _trySubscribe(sink: Subscriber): TeardownLogic {\n try {\n return this._subscribe(sink);\n } catch (err) {\n // We don't need to return anything in this case,\n // because it's just going to try to `add()` to a subscription\n // above.\n sink.error(err);\n }\n }\n\n /**\n * Used as a NON-CANCELLABLE means of subscribing to an observable, for use with\n * APIs that expect promises, like `async/await`. You cannot unsubscribe from this.\n *\n * **WARNING**: Only use this with observables you *know* will complete. If the source\n * observable does not complete, you will end up with a promise that is hung up, and\n * potentially all of the state of an async function hanging out in memory. To avoid\n * this situation, look into adding something like {@link timeout}, {@link take},\n * {@link takeWhile}, or {@link takeUntil} amongst others.\n *\n * #### Example\n *\n * ```ts\n * import { interval, take } from 'rxjs';\n *\n * const source$ = interval(1000).pipe(take(4));\n *\n * async function getTotal() {\n * let total = 0;\n *\n * await source$.forEach(value => {\n * total += value;\n * console.log('observable -> ' + value);\n * });\n *\n * return total;\n * }\n *\n * getTotal().then(\n * total => console.log('Total: ' + total)\n * );\n *\n * // Expected:\n * // 'observable -> 0'\n * // 'observable -> 1'\n * // 'observable -> 2'\n * // 'observable -> 3'\n * // 'Total: 6'\n * ```\n *\n * @param next a handler for each value emitted by the observable\n * @return a promise that either resolves on observable completion or\n * rejects with the handled error\n */\n forEach(next: (value: T) => void): Promise;\n\n /**\n * @param next a handler for each value emitted by the observable\n * @param promiseCtor a constructor function used to instantiate the Promise\n * @return a promise that either resolves on observable completion or\n * rejects with the handled error\n * @deprecated Passing a Promise constructor will no longer be available\n * in upcoming versions of RxJS. This is because it adds weight to the library, for very\n * little benefit. If you need this functionality, it is recommended that you either\n * polyfill Promise, or you create an adapter to convert the returned native promise\n * to whatever promise implementation you wanted. Will be removed in v8.\n */\n forEach(next: (value: T) => void, promiseCtor: PromiseConstructorLike): Promise;\n\n forEach(next: (value: T) => void, promiseCtor?: PromiseConstructorLike): Promise {\n promiseCtor = getPromiseCtor(promiseCtor);\n\n return new promiseCtor((resolve, reject) => {\n const subscriber = new SafeSubscriber({\n next: (value) => {\n try {\n next(value);\n } catch (err) {\n reject(err);\n subscriber.unsubscribe();\n }\n },\n error: reject,\n complete: resolve,\n });\n this.subscribe(subscriber);\n }) as Promise;\n }\n\n /** @internal */\n protected _subscribe(subscriber: Subscriber): TeardownLogic {\n return this.source?.subscribe(subscriber);\n }\n\n /**\n * An interop point defined by the es7-observable spec https://github.com/zenparsing/es-observable\n * @method Symbol.observable\n * @return {Observable} this instance of the observable\n */\n [Symbol_observable]() {\n return this;\n }\n\n /* tslint:disable:max-line-length */\n pipe(): Observable;\n pipe(op1: OperatorFunction): Observable;\n pipe(op1: OperatorFunction, op2: OperatorFunction): Observable;\n pipe(op1: OperatorFunction, op2: OperatorFunction, op3: OperatorFunction): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction,\n op6: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction,\n op6: OperatorFunction,\n op7: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction,\n op6: OperatorFunction,\n op7: OperatorFunction,\n op8: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction,\n op6: OperatorFunction,\n op7: OperatorFunction,\n op8: OperatorFunction,\n op9: OperatorFunction\n ): Observable;\n pipe(\n op1: OperatorFunction,\n op2: OperatorFunction,\n op3: OperatorFunction,\n op4: OperatorFunction,\n op5: OperatorFunction,\n op6: OperatorFunction,\n op7: OperatorFunction,\n op8: OperatorFunction,\n op9: OperatorFunction,\n ...operations: OperatorFunction[]\n ): Observable;\n /* tslint:enable:max-line-length */\n\n /**\n * Used to stitch together functional operators into a chain.\n * @method pipe\n * @return {Observable} the Observable result of all of the operators having\n * been called in the order they were passed in.\n *\n * ## Example\n *\n * ```ts\n * import { interval, filter, map, scan } from 'rxjs';\n *\n * interval(1000)\n * .pipe(\n * filter(x => x % 2 === 0),\n * map(x => x + x),\n * scan((acc, x) => acc + x)\n * )\n * .subscribe(x => console.log(x));\n * ```\n */\n pipe(...operations: OperatorFunction[]): Observable {\n return pipeFromArray(operations)(this);\n }\n\n /* tslint:disable:max-line-length */\n /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n toPromise(): Promise;\n /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n toPromise(PromiseCtor: typeof Promise): Promise;\n /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n toPromise(PromiseCtor: PromiseConstructorLike): Promise;\n /* tslint:enable:max-line-length */\n\n /**\n * Subscribe to this Observable and get a Promise resolving on\n * `complete` with the last emission (if any).\n *\n * **WARNING**: Only use this with observables you *know* will complete. If the source\n * observable does not complete, you will end up with a promise that is hung up, and\n * potentially all of the state of an async function hanging out in memory. To avoid\n * this situation, look into adding something like {@link timeout}, {@link take},\n * {@link takeWhile}, or {@link takeUntil} amongst others.\n *\n * @method toPromise\n * @param [promiseCtor] a constructor function used to instantiate\n * the Promise\n * @return A Promise that resolves with the last value emit, or\n * rejects on an error. If there were no emissions, Promise\n * resolves with undefined.\n * @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise\n */\n toPromise(promiseCtor?: PromiseConstructorLike): Promise {\n promiseCtor = getPromiseCtor(promiseCtor);\n\n return new promiseCtor((resolve, reject) => {\n let value: T | undefined;\n this.subscribe(\n (x: T) => (value = x),\n (err: any) => reject(err),\n () => resolve(value)\n );\n }) as Promise;\n }\n}\n\n/**\n * Decides between a passed promise constructor from consuming code,\n * A default configured promise constructor, and the native promise\n * constructor and returns it. If nothing can be found, it will throw\n * an error.\n * @param promiseCtor The optional promise constructor to passed by consuming code\n */\nfunction getPromiseCtor(promiseCtor: PromiseConstructorLike | undefined) {\n return promiseCtor ?? config.Promise ?? Promise;\n}\n\nfunction isObserver(value: any): value is Observer {\n return value && isFunction(value.next) && isFunction(value.error) && isFunction(value.complete);\n}\n\nfunction isSubscriber(value: any): value is Subscriber {\n return (value && value instanceof Subscriber) || (isObserver(value) && isSubscription(value));\n}\n", "import { Observable } from '../Observable';\nimport { Subscriber } from '../Subscriber';\nimport { OperatorFunction } from '../types';\nimport { isFunction } from './isFunction';\n\n/**\n * Used to determine if an object is an Observable with a lift function.\n */\nexport function hasLift(source: any): source is { lift: InstanceType['lift'] } {\n return isFunction(source?.lift);\n}\n\n/**\n * Creates an `OperatorFunction`. Used to define operators throughout the library in a concise way.\n * @param init The logic to connect the liftedSource to the subscriber at the moment of subscription.\n */\nexport function operate(\n init: (liftedSource: Observable, subscriber: Subscriber) => (() => void) | void\n): OperatorFunction {\n return (source: Observable) => {\n if (hasLift(source)) {\n return source.lift(function (this: Subscriber, liftedSource: Observable) {\n try {\n return init(liftedSource, this);\n } catch (err) {\n this.error(err);\n }\n });\n }\n throw new TypeError('Unable to lift unknown Observable type');\n };\n}\n", "import { Subscriber } from '../Subscriber';\n\n/**\n * Creates an instance of an `OperatorSubscriber`.\n * @param destination The downstream subscriber.\n * @param onNext Handles next values, only called if this subscriber is not stopped or closed. Any\n * error that occurs in this function is caught and sent to the `error` method of this subscriber.\n * @param onError Handles errors from the subscription, any errors that occur in this handler are caught\n * and send to the `destination` error handler.\n * @param onComplete Handles completion notification from the subscription. Any errors that occur in\n * this handler are sent to the `destination` error handler.\n * @param onFinalize Additional teardown logic here. This will only be called on teardown if the\n * subscriber itself is not already closed. This is called after all other teardown logic is executed.\n */\nexport function createOperatorSubscriber(\n destination: Subscriber,\n onNext?: (value: T) => void,\n onComplete?: () => void,\n onError?: (err: any) => void,\n onFinalize?: () => void\n): Subscriber {\n return new OperatorSubscriber(destination, onNext, onComplete, onError, onFinalize);\n}\n\n/**\n * A generic helper for allowing operators to be created with a Subscriber and\n * use closures to capture necessary state from the operator function itself.\n */\nexport class OperatorSubscriber extends Subscriber {\n /**\n * Creates an instance of an `OperatorSubscriber`.\n * @param destination The downstream subscriber.\n * @param onNext Handles next values, only called if this subscriber is not stopped or closed. Any\n * error that occurs in this function is caught and sent to the `error` method of this subscriber.\n * @param onError Handles errors from the subscription, any errors that occur in this handler are caught\n * and send to the `destination` error handler.\n * @param onComplete Handles completion notification from the subscription. Any errors that occur in\n * this handler are sent to the `destination` error handler.\n * @param onFinalize Additional finalization logic here. This will only be called on finalization if the\n * subscriber itself is not already closed. This is called after all other finalization logic is executed.\n * @param shouldUnsubscribe An optional check to see if an unsubscribe call should truly unsubscribe.\n * NOTE: This currently **ONLY** exists to support the strange behavior of {@link groupBy}, where unsubscription\n * to the resulting observable does not actually disconnect from the source if there are active subscriptions\n * to any grouped observable. (DO NOT EXPOSE OR USE EXTERNALLY!!!)\n */\n constructor(\n destination: Subscriber,\n onNext?: (value: T) => void,\n onComplete?: () => void,\n onError?: (err: any) => void,\n private onFinalize?: () => void,\n private shouldUnsubscribe?: () => boolean\n ) {\n // It's important - for performance reasons - that all of this class's\n // members are initialized and that they are always initialized in the same\n // order. This will ensure that all OperatorSubscriber instances have the\n // same hidden class in V8. This, in turn, will help keep the number of\n // hidden classes involved in property accesses within the base class as\n // low as possible. If the number of hidden classes involved exceeds four,\n // the property accesses will become megamorphic and performance penalties\n // will be incurred - i.e. inline caches won't be used.\n //\n // The reasons for ensuring all instances have the same hidden class are\n // further discussed in this blog post from Benedikt Meurer:\n // https://benediktmeurer.de/2018/03/23/impact-of-polymorphism-on-component-based-frameworks-like-react/\n super(destination);\n this._next = onNext\n ? function (this: OperatorSubscriber, value: T) {\n try {\n onNext(value);\n } catch (err) {\n destination.error(err);\n }\n }\n : super._next;\n this._error = onError\n ? function (this: OperatorSubscriber, err: any) {\n try {\n onError(err);\n } catch (err) {\n // Send any errors that occur down stream.\n destination.error(err);\n } finally {\n // Ensure finalization.\n this.unsubscribe();\n }\n }\n : super._error;\n this._complete = onComplete\n ? function (this: OperatorSubscriber) {\n try {\n onComplete();\n } catch (err) {\n // Send any errors that occur down stream.\n destination.error(err);\n } finally {\n // Ensure finalization.\n this.unsubscribe();\n }\n }\n : super._complete;\n }\n\n unsubscribe() {\n if (!this.shouldUnsubscribe || this.shouldUnsubscribe()) {\n const { closed } = this;\n super.unsubscribe();\n // Execute additional teardown if we have any and we didn't already do so.\n !closed && this.onFinalize?.();\n }\n }\n}\n", "import { Subscription } from '../Subscription';\n\ninterface AnimationFrameProvider {\n schedule(callback: FrameRequestCallback): Subscription;\n requestAnimationFrame: typeof requestAnimationFrame;\n cancelAnimationFrame: typeof cancelAnimationFrame;\n delegate:\n | {\n requestAnimationFrame: typeof requestAnimationFrame;\n cancelAnimationFrame: typeof cancelAnimationFrame;\n }\n | undefined;\n}\n\nexport const animationFrameProvider: AnimationFrameProvider = {\n // When accessing the delegate, use the variable rather than `this` so that\n // the functions can be called without being bound to the provider.\n schedule(callback) {\n let request = requestAnimationFrame;\n let cancel: typeof cancelAnimationFrame | undefined = cancelAnimationFrame;\n const { delegate } = animationFrameProvider;\n if (delegate) {\n request = delegate.requestAnimationFrame;\n cancel = delegate.cancelAnimationFrame;\n }\n const handle = request((timestamp) => {\n // Clear the cancel function. The request has been fulfilled, so\n // attempting to cancel the request upon unsubscription would be\n // pointless.\n cancel = undefined;\n callback(timestamp);\n });\n return new Subscription(() => cancel?.(handle));\n },\n requestAnimationFrame(...args) {\n const { delegate } = animationFrameProvider;\n return (delegate?.requestAnimationFrame || requestAnimationFrame)(...args);\n },\n cancelAnimationFrame(...args) {\n const { delegate } = animationFrameProvider;\n return (delegate?.cancelAnimationFrame || cancelAnimationFrame)(...args);\n },\n delegate: undefined,\n};\n", "import { createErrorClass } from './createErrorClass';\n\nexport interface ObjectUnsubscribedError extends Error {}\n\nexport interface ObjectUnsubscribedErrorCtor {\n /**\n * @deprecated Internal implementation detail. Do not construct error instances.\n * Cannot be tagged as internal: https://github.com/ReactiveX/rxjs/issues/6269\n */\n new (): ObjectUnsubscribedError;\n}\n\n/**\n * An error thrown when an action is invalid because the object has been\n * unsubscribed.\n *\n * @see {@link Subject}\n * @see {@link BehaviorSubject}\n *\n * @class ObjectUnsubscribedError\n */\nexport const ObjectUnsubscribedError: ObjectUnsubscribedErrorCtor = createErrorClass(\n (_super) =>\n function ObjectUnsubscribedErrorImpl(this: any) {\n _super(this);\n this.name = 'ObjectUnsubscribedError';\n this.message = 'object unsubscribed';\n }\n);\n", "import { Operator } from './Operator';\nimport { Observable } from './Observable';\nimport { Subscriber } from './Subscriber';\nimport { Subscription, EMPTY_SUBSCRIPTION } from './Subscription';\nimport { Observer, SubscriptionLike, TeardownLogic } from './types';\nimport { ObjectUnsubscribedError } from './util/ObjectUnsubscribedError';\nimport { arrRemove } from './util/arrRemove';\nimport { errorContext } from './util/errorContext';\n\n/**\n * A Subject is a special type of Observable that allows values to be\n * multicasted to many Observers. Subjects are like EventEmitters.\n *\n * Every Subject is an Observable and an Observer. You can subscribe to a\n * Subject, and you can call next to feed values as well as error and complete.\n */\nexport class Subject extends Observable implements SubscriptionLike {\n closed = false;\n\n private currentObservers: Observer[] | null = null;\n\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n observers: Observer[] = [];\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n isStopped = false;\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n hasError = false;\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n thrownError: any = null;\n\n /**\n * Creates a \"subject\" by basically gluing an observer to an observable.\n *\n * @nocollapse\n * @deprecated Recommended you do not use. Will be removed at some point in the future. Plans for replacement still under discussion.\n */\n static create: (...args: any[]) => any = (destination: Observer, source: Observable): AnonymousSubject => {\n return new AnonymousSubject(destination, source);\n };\n\n constructor() {\n // NOTE: This must be here to obscure Observable's constructor.\n super();\n }\n\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n lift(operator: Operator): Observable {\n const subject = new AnonymousSubject(this, this);\n subject.operator = operator as any;\n return subject as any;\n }\n\n /** @internal */\n protected _throwIfClosed() {\n if (this.closed) {\n throw new ObjectUnsubscribedError();\n }\n }\n\n next(value: T) {\n errorContext(() => {\n this._throwIfClosed();\n if (!this.isStopped) {\n if (!this.currentObservers) {\n this.currentObservers = Array.from(this.observers);\n }\n for (const observer of this.currentObservers) {\n observer.next(value);\n }\n }\n });\n }\n\n error(err: any) {\n errorContext(() => {\n this._throwIfClosed();\n if (!this.isStopped) {\n this.hasError = this.isStopped = true;\n this.thrownError = err;\n const { observers } = this;\n while (observers.length) {\n observers.shift()!.error(err);\n }\n }\n });\n }\n\n complete() {\n errorContext(() => {\n this._throwIfClosed();\n if (!this.isStopped) {\n this.isStopped = true;\n const { observers } = this;\n while (observers.length) {\n observers.shift()!.complete();\n }\n }\n });\n }\n\n unsubscribe() {\n this.isStopped = this.closed = true;\n this.observers = this.currentObservers = null!;\n }\n\n get observed() {\n return this.observers?.length > 0;\n }\n\n /** @internal */\n protected _trySubscribe(subscriber: Subscriber): TeardownLogic {\n this._throwIfClosed();\n return super._trySubscribe(subscriber);\n }\n\n /** @internal */\n protected _subscribe(subscriber: Subscriber): Subscription {\n this._throwIfClosed();\n this._checkFinalizedStatuses(subscriber);\n return this._innerSubscribe(subscriber);\n }\n\n /** @internal */\n protected _innerSubscribe(subscriber: Subscriber) {\n const { hasError, isStopped, observers } = this;\n if (hasError || isStopped) {\n return EMPTY_SUBSCRIPTION;\n }\n this.currentObservers = null;\n observers.push(subscriber);\n return new Subscription(() => {\n this.currentObservers = null;\n arrRemove(observers, subscriber);\n });\n }\n\n /** @internal */\n protected _checkFinalizedStatuses(subscriber: Subscriber) {\n const { hasError, thrownError, isStopped } = this;\n if (hasError) {\n subscriber.error(thrownError);\n } else if (isStopped) {\n subscriber.complete();\n }\n }\n\n /**\n * Creates a new Observable with this Subject as the source. You can do this\n * to create custom Observer-side logic of the Subject and conceal it from\n * code that uses the Observable.\n * @return {Observable} Observable that the Subject casts to\n */\n asObservable(): Observable {\n const observable: any = new Observable();\n observable.source = this;\n return observable;\n }\n}\n\n/**\n * @class AnonymousSubject\n */\nexport class AnonymousSubject extends Subject {\n constructor(\n /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n public destination?: Observer,\n source?: Observable\n ) {\n super();\n this.source = source;\n }\n\n next(value: T) {\n this.destination?.next?.(value);\n }\n\n error(err: any) {\n this.destination?.error?.(err);\n }\n\n complete() {\n this.destination?.complete?.();\n }\n\n /** @internal */\n protected _subscribe(subscriber: Subscriber): Subscription {\n return this.source?.subscribe(subscriber) ?? EMPTY_SUBSCRIPTION;\n }\n}\n", "import { Subject } from './Subject';\nimport { Subscriber } from './Subscriber';\nimport { Subscription } from './Subscription';\n\n/**\n * A variant of Subject that requires an initial value and emits its current\n * value whenever it is subscribed to.\n *\n * @class BehaviorSubject\n */\nexport class BehaviorSubject extends Subject {\n constructor(private _value: T) {\n super();\n }\n\n get value(): T {\n return this.getValue();\n }\n\n /** @internal */\n protected _subscribe(subscriber: Subscriber): Subscription {\n const subscription = super._subscribe(subscriber);\n !subscription.closed && subscriber.next(this._value);\n return subscription;\n }\n\n getValue(): T {\n const { hasError, thrownError, _value } = this;\n if (hasError) {\n throw thrownError;\n }\n this._throwIfClosed();\n return _value;\n }\n\n next(value: T): void {\n super.next((this._value = value));\n }\n}\n", "import { TimestampProvider } from '../types';\n\ninterface DateTimestampProvider extends TimestampProvider {\n delegate: TimestampProvider | undefined;\n}\n\nexport const dateTimestampProvider: DateTimestampProvider = {\n now() {\n // Use the variable rather than `this` so that the function can be called\n // without being bound to the provider.\n return (dateTimestampProvider.delegate || Date).now();\n },\n delegate: undefined,\n};\n", "import { Subject } from './Subject';\nimport { TimestampProvider } from './types';\nimport { Subscriber } from './Subscriber';\nimport { Subscription } from './Subscription';\nimport { dateTimestampProvider } from './scheduler/dateTimestampProvider';\n\n/**\n * A variant of {@link Subject} that \"replays\" old values to new subscribers by emitting them when they first subscribe.\n *\n * `ReplaySubject` has an internal buffer that will store a specified number of values that it has observed. Like `Subject`,\n * `ReplaySubject` \"observes\" values by having them passed to its `next` method. When it observes a value, it will store that\n * value for a time determined by the configuration of the `ReplaySubject`, as passed to its constructor.\n *\n * When a new subscriber subscribes to the `ReplaySubject` instance, it will synchronously emit all values in its buffer in\n * a First-In-First-Out (FIFO) manner. The `ReplaySubject` will also complete, if it has observed completion; and it will\n * error if it has observed an error.\n *\n * There are two main configuration items to be concerned with:\n *\n * 1. `bufferSize` - This will determine how many items are stored in the buffer, defaults to infinite.\n * 2. `windowTime` - The amount of time to hold a value in the buffer before removing it from the buffer.\n *\n * Both configurations may exist simultaneously. So if you would like to buffer a maximum of 3 values, as long as the values\n * are less than 2 seconds old, you could do so with a `new ReplaySubject(3, 2000)`.\n *\n * ### Differences with BehaviorSubject\n *\n * `BehaviorSubject` is similar to `new ReplaySubject(1)`, with a couple of exceptions:\n *\n * 1. `BehaviorSubject` comes \"primed\" with a single value upon construction.\n * 2. `ReplaySubject` will replay values, even after observing an error, where `BehaviorSubject` will not.\n *\n * @see {@link Subject}\n * @see {@link BehaviorSubject}\n * @see {@link shareReplay}\n */\nexport class ReplaySubject extends Subject {\n private _buffer: (T | number)[] = [];\n private _infiniteTimeWindow = true;\n\n /**\n * @param bufferSize The size of the buffer to replay on subscription\n * @param windowTime The amount of time the buffered items will stay buffered\n * @param timestampProvider An object with a `now()` method that provides the current timestamp. This is used to\n * calculate the amount of time something has been buffered.\n */\n constructor(\n private _bufferSize = Infinity,\n private _windowTime = Infinity,\n private _timestampProvider: TimestampProvider = dateTimestampProvider\n ) {\n super();\n this._infiniteTimeWindow = _windowTime === Infinity;\n this._bufferSize = Math.max(1, _bufferSize);\n this._windowTime = Math.max(1, _windowTime);\n }\n\n next(value: T): void {\n const { isStopped, _buffer, _infiniteTimeWindow, _timestampProvider, _windowTime } = this;\n if (!isStopped) {\n _buffer.push(value);\n !_infiniteTimeWindow && _buffer.push(_timestampProvider.now() + _windowTime);\n }\n this._trimBuffer();\n super.next(value);\n }\n\n /** @internal */\n protected _subscribe(subscriber: Subscriber): Subscription {\n this._throwIfClosed();\n this._trimBuffer();\n\n const subscription = this._innerSubscribe(subscriber);\n\n const { _infiniteTimeWindow, _buffer } = this;\n // We use a copy here, so reentrant code does not mutate our array while we're\n // emitting it to a new subscriber.\n const copy = _buffer.slice();\n for (let i = 0; i < copy.length && !subscriber.closed; i += _infiniteTimeWindow ? 1 : 2) {\n subscriber.next(copy[i] as T);\n }\n\n this._checkFinalizedStatuses(subscriber);\n\n return subscription;\n }\n\n private _trimBuffer() {\n const { _bufferSize, _timestampProvider, _buffer, _infiniteTimeWindow } = this;\n // If we don't have an infinite buffer size, and we're over the length,\n // use splice to truncate the old buffer values off. Note that we have to\n // double the size for instances where we're not using an infinite time window\n // because we're storing the values and the timestamps in the same array.\n const adjustedBufferSize = (_infiniteTimeWindow ? 1 : 2) * _bufferSize;\n _bufferSize < Infinity && adjustedBufferSize < _buffer.length && _buffer.splice(0, _buffer.length - adjustedBufferSize);\n\n // Now, if we're not in an infinite time window, remove all values where the time is\n // older than what is allowed.\n if (!_infiniteTimeWindow) {\n const now = _timestampProvider.now();\n let last = 0;\n // Search the array for the first timestamp that isn't expired and\n // truncate the buffer up to that point.\n for (let i = 1; i < _buffer.length && (_buffer[i] as number) <= now; i += 2) {\n last = i;\n }\n last && _buffer.splice(0, last + 1);\n }\n }\n}\n", "import { Scheduler } from '../Scheduler';\nimport { Subscription } from '../Subscription';\nimport { SchedulerAction } from '../types';\n\n/**\n * A unit of work to be executed in a `scheduler`. An action is typically\n * created from within a {@link SchedulerLike} and an RxJS user does not need to concern\n * themselves about creating and manipulating an Action.\n *\n * ```ts\n * class Action extends Subscription {\n * new (scheduler: Scheduler, work: (state?: T) => void);\n * schedule(state?: T, delay: number = 0): Subscription;\n * }\n * ```\n *\n * @class Action\n */\nexport class Action extends Subscription {\n constructor(scheduler: Scheduler, work: (this: SchedulerAction, state?: T) => void) {\n super();\n }\n /**\n * Schedules this action on its parent {@link SchedulerLike} for execution. May be passed\n * some context object, `state`. May happen at some point in the future,\n * according to the `delay` parameter, if specified.\n * @param {T} [state] Some contextual data that the `work` function uses when\n * called by the Scheduler.\n * @param {number} [delay] Time to wait before executing the work, where the\n * time unit is implicit and defined by the Scheduler.\n * @return {void}\n */\n public schedule(state?: T, delay: number = 0): Subscription {\n return this;\n }\n}\n", "import type { TimerHandle } from './timerHandle';\ntype SetIntervalFunction = (handler: () => void, timeout?: number, ...args: any[]) => TimerHandle;\ntype ClearIntervalFunction = (handle: TimerHandle) => void;\n\ninterface IntervalProvider {\n setInterval: SetIntervalFunction;\n clearInterval: ClearIntervalFunction;\n delegate:\n | {\n setInterval: SetIntervalFunction;\n clearInterval: ClearIntervalFunction;\n }\n | undefined;\n}\n\nexport const intervalProvider: IntervalProvider = {\n // When accessing the delegate, use the variable rather than `this` so that\n // the functions can be called without being bound to the provider.\n setInterval(handler: () => void, timeout?: number, ...args) {\n const { delegate } = intervalProvider;\n if (delegate?.setInterval) {\n return delegate.setInterval(handler, timeout, ...args);\n }\n return setInterval(handler, timeout, ...args);\n },\n clearInterval(handle) {\n const { delegate } = intervalProvider;\n return (delegate?.clearInterval || clearInterval)(handle as any);\n },\n delegate: undefined,\n};\n", "import { Action } from './Action';\nimport { SchedulerAction } from '../types';\nimport { Subscription } from '../Subscription';\nimport { AsyncScheduler } from './AsyncScheduler';\nimport { intervalProvider } from './intervalProvider';\nimport { arrRemove } from '../util/arrRemove';\nimport { TimerHandle } from './timerHandle';\n\nexport class AsyncAction extends Action {\n public id: TimerHandle | undefined;\n public state?: T;\n // @ts-ignore: Property has no initializer and is not definitely assigned\n public delay: number;\n protected pending: boolean = false;\n\n constructor(protected scheduler: AsyncScheduler, protected work: (this: SchedulerAction, state?: T) => void) {\n super(scheduler, work);\n }\n\n public schedule(state?: T, delay: number = 0): Subscription {\n if (this.closed) {\n return this;\n }\n\n // Always replace the current state with the new state.\n this.state = state;\n\n const id = this.id;\n const scheduler = this.scheduler;\n\n //\n // Important implementation note:\n //\n // Actions only execute once by default, unless rescheduled from within the\n // scheduled callback. This allows us to implement single and repeat\n // actions via the same code path, without adding API surface area, as well\n // as mimic traditional recursion but across asynchronous boundaries.\n //\n // However, JS runtimes and timers distinguish between intervals achieved by\n // serial `setTimeout` calls vs. a single `setInterval` call. An interval of\n // serial `setTimeout` calls can be individually delayed, which delays\n // scheduling the next `setTimeout`, and so on. `setInterval` attempts to\n // guarantee the interval callback will be invoked more precisely to the\n // interval period, regardless of load.\n //\n // Therefore, we use `setInterval` to schedule single and repeat actions.\n // If the action reschedules itself with the same delay, the interval is not\n // canceled. If the action doesn't reschedule, or reschedules with a\n // different delay, the interval will be canceled after scheduled callback\n // execution.\n //\n if (id != null) {\n this.id = this.recycleAsyncId(scheduler, id, delay);\n }\n\n // Set the pending flag indicating that this action has been scheduled, or\n // has recursively rescheduled itself.\n this.pending = true;\n\n this.delay = delay;\n // If this action has already an async Id, don't request a new one.\n this.id = this.id ?? this.requestAsyncId(scheduler, this.id, delay);\n\n return this;\n }\n\n protected requestAsyncId(scheduler: AsyncScheduler, _id?: TimerHandle, delay: number = 0): TimerHandle {\n return intervalProvider.setInterval(scheduler.flush.bind(scheduler, this), delay);\n }\n\n protected recycleAsyncId(_scheduler: AsyncScheduler, id?: TimerHandle, delay: number | null = 0): TimerHandle | undefined {\n // If this action is rescheduled with the same delay time, don't clear the interval id.\n if (delay != null && this.delay === delay && this.pending === false) {\n return id;\n }\n // Otherwise, if the action's delay time is different from the current delay,\n // or the action has been rescheduled before it's executed, clear the interval id\n if (id != null) {\n intervalProvider.clearInterval(id);\n }\n\n return undefined;\n }\n\n /**\n * Immediately executes this action and the `work` it contains.\n * @return {any}\n */\n public execute(state: T, delay: number): any {\n if (this.closed) {\n return new Error('executing a cancelled action');\n }\n\n this.pending = false;\n const error = this._execute(state, delay);\n if (error) {\n return error;\n } else if (this.pending === false && this.id != null) {\n // Dequeue if the action didn't reschedule itself. Don't call\n // unsubscribe(), because the action could reschedule later.\n // For example:\n // ```\n // scheduler.schedule(function doWork(counter) {\n // /* ... I'm a busy worker bee ... */\n // var originalAction = this;\n // /* wait 100ms before rescheduling the action */\n // setTimeout(function () {\n // originalAction.schedule(counter + 1);\n // }, 100);\n // }, 1000);\n // ```\n this.id = this.recycleAsyncId(this.scheduler, this.id, null);\n }\n }\n\n protected _execute(state: T, _delay: number): any {\n let errored: boolean = false;\n let errorValue: any;\n try {\n this.work(state);\n } catch (e) {\n errored = true;\n // HACK: Since code elsewhere is relying on the \"truthiness\" of the\n // return here, we can't have it return \"\" or 0 or false.\n // TODO: Clean this up when we refactor schedulers mid-version-8 or so.\n errorValue = e ? e : new Error('Scheduled action threw falsy error');\n }\n if (errored) {\n this.unsubscribe();\n return errorValue;\n }\n }\n\n unsubscribe() {\n if (!this.closed) {\n const { id, scheduler } = this;\n const { actions } = scheduler;\n\n this.work = this.state = this.scheduler = null!;\n this.pending = false;\n\n arrRemove(actions, this);\n if (id != null) {\n this.id = this.recycleAsyncId(scheduler, id, null);\n }\n\n this.delay = null!;\n super.unsubscribe();\n }\n }\n}\n", "import { Action } from './scheduler/Action';\nimport { Subscription } from './Subscription';\nimport { SchedulerLike, SchedulerAction } from './types';\nimport { dateTimestampProvider } from './scheduler/dateTimestampProvider';\n\n/**\n * An execution context and a data structure to order tasks and schedule their\n * execution. Provides a notion of (potentially virtual) time, through the\n * `now()` getter method.\n *\n * Each unit of work in a Scheduler is called an `Action`.\n *\n * ```ts\n * class Scheduler {\n * now(): number;\n * schedule(work, delay?, state?): Subscription;\n * }\n * ```\n *\n * @class Scheduler\n * @deprecated Scheduler is an internal implementation detail of RxJS, and\n * should not be used directly. Rather, create your own class and implement\n * {@link SchedulerLike}. Will be made internal in v8.\n */\nexport class Scheduler implements SchedulerLike {\n public static now: () => number = dateTimestampProvider.now;\n\n constructor(private schedulerActionCtor: typeof Action, now: () => number = Scheduler.now) {\n this.now = now;\n }\n\n /**\n * A getter method that returns a number representing the current time\n * (at the time this function was called) according to the scheduler's own\n * internal clock.\n * @return {number} A number that represents the current time. May or may not\n * have a relation to wall-clock time. May or may not refer to a time unit\n * (e.g. milliseconds).\n */\n public now: () => number;\n\n /**\n * Schedules a function, `work`, for execution. May happen at some point in\n * the future, according to the `delay` parameter, if specified. May be passed\n * some context object, `state`, which will be passed to the `work` function.\n *\n * The given arguments will be processed an stored as an Action object in a\n * queue of actions.\n *\n * @param {function(state: ?T): ?Subscription} work A function representing a\n * task, or some unit of work to be executed by the Scheduler.\n * @param {number} [delay] Time to wait before executing the work, where the\n * time unit is implicit and defined by the Scheduler itself.\n * @param {T} [state] Some contextual data that the `work` function uses when\n * called by the Scheduler.\n * @return {Subscription} A subscription in order to be able to unsubscribe\n * the scheduled work.\n */\n public schedule(work: (this: SchedulerAction, state?: T) => void, delay: number = 0, state?: T): Subscription {\n return new this.schedulerActionCtor(this, work).schedule(state, delay);\n }\n}\n", "import { Scheduler } from '../Scheduler';\nimport { Action } from './Action';\nimport { AsyncAction } from './AsyncAction';\nimport { TimerHandle } from './timerHandle';\n\nexport class AsyncScheduler extends Scheduler {\n public actions: Array> = [];\n /**\n * A flag to indicate whether the Scheduler is currently executing a batch of\n * queued actions.\n * @type {boolean}\n * @internal\n */\n public _active: boolean = false;\n /**\n * An internal ID used to track the latest asynchronous task such as those\n * coming from `setTimeout`, `setInterval`, `requestAnimationFrame`, and\n * others.\n * @type {any}\n * @internal\n */\n public _scheduled: TimerHandle | undefined;\n\n constructor(SchedulerAction: typeof Action, now: () => number = Scheduler.now) {\n super(SchedulerAction, now);\n }\n\n public flush(action: AsyncAction): void {\n const { actions } = this;\n\n if (this._active) {\n actions.push(action);\n return;\n }\n\n let error: any;\n this._active = true;\n\n do {\n if ((error = action.execute(action.state, action.delay))) {\n break;\n }\n } while ((action = actions.shift()!)); // exhaust the scheduler queue\n\n this._active = false;\n\n if (error) {\n while ((action = actions.shift()!)) {\n action.unsubscribe();\n }\n throw error;\n }\n }\n}\n", "import { AsyncAction } from './AsyncAction';\nimport { AsyncScheduler } from './AsyncScheduler';\n\n/**\n *\n * Async Scheduler\n *\n * Schedule task as if you used setTimeout(task, duration)\n *\n * `async` scheduler schedules tasks asynchronously, by putting them on the JavaScript\n * event loop queue. It is best used to delay tasks in time or to schedule tasks repeating\n * in intervals.\n *\n * If you just want to \"defer\" task, that is to perform it right after currently\n * executing synchronous code ends (commonly achieved by `setTimeout(deferredTask, 0)`),\n * better choice will be the {@link asapScheduler} scheduler.\n *\n * ## Examples\n * Use async scheduler to delay task\n * ```ts\n * import { asyncScheduler } from 'rxjs';\n *\n * const task = () => console.log('it works!');\n *\n * asyncScheduler.schedule(task, 2000);\n *\n * // After 2 seconds logs:\n * // \"it works!\"\n * ```\n *\n * Use async scheduler to repeat task in intervals\n * ```ts\n * import { asyncScheduler } from 'rxjs';\n *\n * function task(state) {\n * console.log(state);\n * this.schedule(state + 1, 1000); // `this` references currently executing Action,\n * // which we reschedule with new state and delay\n * }\n *\n * asyncScheduler.schedule(task, 3000, 0);\n *\n * // Logs:\n * // 0 after 3s\n * // 1 after 4s\n * // 2 after 5s\n * // 3 after 6s\n * ```\n */\n\nexport const asyncScheduler = new AsyncScheduler(AsyncAction);\n\n/**\n * @deprecated Renamed to {@link asyncScheduler}. Will be removed in v8.\n */\nexport const async = asyncScheduler;\n", "import { AsyncAction } from './AsyncAction';\nimport { Subscription } from '../Subscription';\nimport { QueueScheduler } from './QueueScheduler';\nimport { SchedulerAction } from '../types';\nimport { TimerHandle } from './timerHandle';\n\nexport class QueueAction extends AsyncAction {\n constructor(protected scheduler: QueueScheduler, protected work: (this: SchedulerAction, state?: T) => void) {\n super(scheduler, work);\n }\n\n public schedule(state?: T, delay: number = 0): Subscription {\n if (delay > 0) {\n return super.schedule(state, delay);\n }\n this.delay = delay;\n this.state = state;\n this.scheduler.flush(this);\n return this;\n }\n\n public execute(state: T, delay: number): any {\n return delay > 0 || this.closed ? super.execute(state, delay) : this._execute(state, delay);\n }\n\n protected requestAsyncId(scheduler: QueueScheduler, id?: TimerHandle, delay: number = 0): TimerHandle {\n // If delay exists and is greater than 0, or if the delay is null (the\n // action wasn't rescheduled) but was originally scheduled as an async\n // action, then recycle as an async action.\n\n if ((delay != null && delay > 0) || (delay == null && this.delay > 0)) {\n return super.requestAsyncId(scheduler, id, delay);\n }\n\n // Otherwise flush the scheduler starting with this action.\n scheduler.flush(this);\n\n // HACK: In the past, this was returning `void`. However, `void` isn't a valid\n // `TimerHandle`, and generally the return value here isn't really used. So the\n // compromise is to return `0` which is both \"falsy\" and a valid `TimerHandle`,\n // as opposed to refactoring every other instanceo of `requestAsyncId`.\n return 0;\n }\n}\n", "import { AsyncScheduler } from './AsyncScheduler';\n\nexport class QueueScheduler extends AsyncScheduler {\n}\n", "import { QueueAction } from './QueueAction';\nimport { QueueScheduler } from './QueueScheduler';\n\n/**\n *\n * Queue Scheduler\n *\n * Put every next task on a queue, instead of executing it immediately\n *\n * `queue` scheduler, when used with delay, behaves the same as {@link asyncScheduler} scheduler.\n *\n * When used without delay, it schedules given task synchronously - executes it right when\n * it is scheduled. However when called recursively, that is when inside the scheduled task,\n * another task is scheduled with queue scheduler, instead of executing immediately as well,\n * that task will be put on a queue and wait for current one to finish.\n *\n * This means that when you execute task with `queue` scheduler, you are sure it will end\n * before any other task scheduled with that scheduler will start.\n *\n * ## Examples\n * Schedule recursively first, then do something\n * ```ts\n * import { queueScheduler } from 'rxjs';\n *\n * queueScheduler.schedule(() => {\n * queueScheduler.schedule(() => console.log('second')); // will not happen now, but will be put on a queue\n *\n * console.log('first');\n * });\n *\n * // Logs:\n * // \"first\"\n * // \"second\"\n * ```\n *\n * Reschedule itself recursively\n * ```ts\n * import { queueScheduler } from 'rxjs';\n *\n * queueScheduler.schedule(function(state) {\n * if (state !== 0) {\n * console.log('before', state);\n * this.schedule(state - 1); // `this` references currently executing Action,\n * // which we reschedule with new state\n * console.log('after', state);\n * }\n * }, 0, 3);\n *\n * // In scheduler that runs recursively, you would expect:\n * // \"before\", 3\n * // \"before\", 2\n * // \"before\", 1\n * // \"after\", 1\n * // \"after\", 2\n * // \"after\", 3\n *\n * // But with queue it logs:\n * // \"before\", 3\n * // \"after\", 3\n * // \"before\", 2\n * // \"after\", 2\n * // \"before\", 1\n * // \"after\", 1\n * ```\n */\n\nexport const queueScheduler = new QueueScheduler(QueueAction);\n\n/**\n * @deprecated Renamed to {@link queueScheduler}. Will be removed in v8.\n */\nexport const queue = queueScheduler;\n", "import { AsyncAction } from './AsyncAction';\nimport { AnimationFrameScheduler } from './AnimationFrameScheduler';\nimport { SchedulerAction } from '../types';\nimport { animationFrameProvider } from './animationFrameProvider';\nimport { TimerHandle } from './timerHandle';\n\nexport class AnimationFrameAction extends AsyncAction {\n constructor(protected scheduler: AnimationFrameScheduler, protected work: (this: SchedulerAction, state?: T) => void) {\n super(scheduler, work);\n }\n\n protected requestAsyncId(scheduler: AnimationFrameScheduler, id?: TimerHandle, delay: number = 0): TimerHandle {\n // If delay is greater than 0, request as an async action.\n if (delay !== null && delay > 0) {\n return super.requestAsyncId(scheduler, id, delay);\n }\n // Push the action to the end of the scheduler queue.\n scheduler.actions.push(this);\n // If an animation frame has already been requested, don't request another\n // one. If an animation frame hasn't been requested yet, request one. Return\n // the current animation frame request id.\n return scheduler._scheduled || (scheduler._scheduled = animationFrameProvider.requestAnimationFrame(() => scheduler.flush(undefined)));\n }\n\n protected recycleAsyncId(scheduler: AnimationFrameScheduler, id?: TimerHandle, delay: number = 0): TimerHandle | undefined {\n // If delay exists and is greater than 0, or if the delay is null (the\n // action wasn't rescheduled) but was originally scheduled as an async\n // action, then recycle as an async action.\n if (delay != null ? delay > 0 : this.delay > 0) {\n return super.recycleAsyncId(scheduler, id, delay);\n }\n // If the scheduler queue has no remaining actions with the same async id,\n // cancel the requested animation frame and set the scheduled flag to\n // undefined so the next AnimationFrameAction will request its own.\n const { actions } = scheduler;\n if (id != null && actions[actions.length - 1]?.id !== id) {\n animationFrameProvider.cancelAnimationFrame(id as number);\n scheduler._scheduled = undefined;\n }\n // Return undefined so the action knows to request a new async id if it's rescheduled.\n return undefined;\n }\n}\n", "import { AsyncAction } from './AsyncAction';\nimport { AsyncScheduler } from './AsyncScheduler';\n\nexport class AnimationFrameScheduler extends AsyncScheduler {\n public flush(action?: AsyncAction): void {\n this._active = true;\n // The async id that effects a call to flush is stored in _scheduled.\n // Before executing an action, it's necessary to check the action's async\n // id to determine whether it's supposed to be executed in the current\n // flush.\n // Previous implementations of this method used a count to determine this,\n // but that was unsound, as actions that are unsubscribed - i.e. cancelled -\n // are removed from the actions array and that can shift actions that are\n // scheduled to be executed in a subsequent flush into positions at which\n // they are executed within the current flush.\n const flushId = this._scheduled;\n this._scheduled = undefined;\n\n const { actions } = this;\n let error: any;\n action = action || actions.shift()!;\n\n do {\n if ((error = action.execute(action.state, action.delay))) {\n break;\n }\n } while ((action = actions[0]) && action.id === flushId && actions.shift());\n\n this._active = false;\n\n if (error) {\n while ((action = actions[0]) && action.id === flushId && actions.shift()) {\n action.unsubscribe();\n }\n throw error;\n }\n }\n}\n", "import { AnimationFrameAction } from './AnimationFrameAction';\nimport { AnimationFrameScheduler } from './AnimationFrameScheduler';\n\n/**\n *\n * Animation Frame Scheduler\n *\n * Perform task when `window.requestAnimationFrame` would fire\n *\n * When `animationFrame` scheduler is used with delay, it will fall back to {@link asyncScheduler} scheduler\n * behaviour.\n *\n * Without delay, `animationFrame` scheduler can be used to create smooth browser animations.\n * It makes sure scheduled task will happen just before next browser content repaint,\n * thus performing animations as efficiently as possible.\n *\n * ## Example\n * Schedule div height animation\n * ```ts\n * // html:
\n * import { animationFrameScheduler } from 'rxjs';\n *\n * const div = document.querySelector('div');\n *\n * animationFrameScheduler.schedule(function(height) {\n * div.style.height = height + \"px\";\n *\n * this.schedule(height + 1); // `this` references currently executing Action,\n * // which we reschedule with new state\n * }, 0, 0);\n *\n * // You will see a div element growing in height\n * ```\n */\n\nexport const animationFrameScheduler = new AnimationFrameScheduler(AnimationFrameAction);\n\n/**\n * @deprecated Renamed to {@link animationFrameScheduler}. Will be removed in v8.\n */\nexport const animationFrame = animationFrameScheduler;\n", "import { Observable } from '../Observable';\nimport { SchedulerLike } from '../types';\n\n/**\n * A simple Observable that emits no items to the Observer and immediately\n * emits a complete notification.\n *\n * Just emits 'complete', and nothing else.\n *\n * ![](empty.png)\n *\n * A simple Observable that only emits the complete notification. It can be used\n * for composing with other Observables, such as in a {@link mergeMap}.\n *\n * ## Examples\n *\n * Log complete notification\n *\n * ```ts\n * import { EMPTY } from 'rxjs';\n *\n * EMPTY.subscribe({\n * next: () => console.log('Next'),\n * complete: () => console.log('Complete!')\n * });\n *\n * // Outputs\n * // Complete!\n * ```\n *\n * Emit the number 7, then complete\n *\n * ```ts\n * import { EMPTY, startWith } from 'rxjs';\n *\n * const result = EMPTY.pipe(startWith(7));\n * result.subscribe(x => console.log(x));\n *\n * // Outputs\n * // 7\n * ```\n *\n * Map and flatten only odd numbers to the sequence `'a'`, `'b'`, `'c'`\n *\n * ```ts\n * import { interval, mergeMap, of, EMPTY } from 'rxjs';\n *\n * const interval$ = interval(1000);\n * const result = interval$.pipe(\n * mergeMap(x => x % 2 === 1 ? of('a', 'b', 'c') : EMPTY),\n * );\n * result.subscribe(x => console.log(x));\n *\n * // Results in the following to the console:\n * // x is equal to the count on the interval, e.g. (0, 1, 2, 3, ...)\n * // x will occur every 1000ms\n * // if x % 2 is equal to 1, print a, b, c (each on its own)\n * // if x % 2 is not equal to 1, nothing will be output\n * ```\n *\n * @see {@link Observable}\n * @see {@link NEVER}\n * @see {@link of}\n * @see {@link throwError}\n */\nexport const EMPTY = new Observable((subscriber) => subscriber.complete());\n\n/**\n * @param scheduler A {@link SchedulerLike} to use for scheduling\n * the emission of the complete notification.\n * @deprecated Replaced with the {@link EMPTY} constant or {@link scheduled} (e.g. `scheduled([], scheduler)`). Will be removed in v8.\n */\nexport function empty(scheduler?: SchedulerLike) {\n return scheduler ? emptyScheduled(scheduler) : EMPTY;\n}\n\nfunction emptyScheduled(scheduler: SchedulerLike) {\n return new Observable((subscriber) => scheduler.schedule(() => subscriber.complete()));\n}\n", "import { SchedulerLike } from '../types';\nimport { isFunction } from './isFunction';\n\nexport function isScheduler(value: any): value is SchedulerLike {\n return value && isFunction(value.schedule);\n}\n", "import { SchedulerLike } from '../types';\nimport { isFunction } from './isFunction';\nimport { isScheduler } from './isScheduler';\n\nfunction last(arr: T[]): T | undefined {\n return arr[arr.length - 1];\n}\n\nexport function popResultSelector(args: any[]): ((...args: unknown[]) => unknown) | undefined {\n return isFunction(last(args)) ? args.pop() : undefined;\n}\n\nexport function popScheduler(args: any[]): SchedulerLike | undefined {\n return isScheduler(last(args)) ? args.pop() : undefined;\n}\n\nexport function popNumber(args: any[], defaultValue: number): number {\n return typeof last(args) === 'number' ? args.pop()! : defaultValue;\n}\n", "export const isArrayLike = ((x: any): x is ArrayLike => x && typeof x.length === 'number' && typeof x !== 'function');", "import { isFunction } from \"./isFunction\";\n\n/**\n * Tests to see if the object is \"thennable\".\n * @param value the object to test\n */\nexport function isPromise(value: any): value is PromiseLike {\n return isFunction(value?.then);\n}\n", "import { InteropObservable } from '../types';\nimport { observable as Symbol_observable } from '../symbol/observable';\nimport { isFunction } from './isFunction';\n\n/** Identifies an input as being Observable (but not necessary an Rx Observable) */\nexport function isInteropObservable(input: any): input is InteropObservable {\n return isFunction(input[Symbol_observable]);\n}\n", "import { isFunction } from './isFunction';\n\nexport function isAsyncIterable(obj: any): obj is AsyncIterable {\n return Symbol.asyncIterator && isFunction(obj?.[Symbol.asyncIterator]);\n}\n", "/**\n * Creates the TypeError to throw if an invalid object is passed to `from` or `scheduled`.\n * @param input The object that was passed.\n */\nexport function createInvalidObservableTypeError(input: any) {\n // TODO: We should create error codes that can be looked up, so this can be less verbose.\n return new TypeError(\n `You provided ${\n input !== null && typeof input === 'object' ? 'an invalid object' : `'${input}'`\n } where a stream was expected. You can provide an Observable, Promise, ReadableStream, Array, AsyncIterable, or Iterable.`\n );\n}\n", "export function getSymbolIterator(): symbol {\n if (typeof Symbol !== 'function' || !Symbol.iterator) {\n return '@@iterator' as any;\n }\n\n return Symbol.iterator;\n}\n\nexport const iterator = getSymbolIterator();\n", "import { iterator as Symbol_iterator } from '../symbol/iterator';\nimport { isFunction } from './isFunction';\n\n/** Identifies an input as being an Iterable */\nexport function isIterable(input: any): input is Iterable {\n return isFunction(input?.[Symbol_iterator]);\n}\n", "import { ReadableStreamLike } from '../types';\nimport { isFunction } from './isFunction';\n\nexport async function* readableStreamLikeToAsyncGenerator(readableStream: ReadableStreamLike): AsyncGenerator {\n const reader = readableStream.getReader();\n try {\n while (true) {\n const { value, done } = await reader.read();\n if (done) {\n return;\n }\n yield value!;\n }\n } finally {\n reader.releaseLock();\n }\n}\n\nexport function isReadableStreamLike(obj: any): obj is ReadableStreamLike {\n // We don't want to use instanceof checks because they would return\n // false for instances from another Realm, like an