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Merge pull request OpenMathLib#4338 from martin-frbg/lapack941
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Docu fix for Truncated QR With Pivoting (Reference-LAPACK PR 941)
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martin-frbg authored Nov 25, 2023
2 parents 97d3c9b + ca5a87f commit be8661b
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Showing 12 changed files with 36 additions and 36 deletions.
12 changes: 6 additions & 6 deletions lapack-netlib/SRC/cgeqp3rk.f
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*> where:
*>
*> P(K) is an N-by-N permutation matrix;
*> Q(K) is an M-by-M orthogonal matrix;
*> Q(K) is an M-by-M unitary matrix;
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
*> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal
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*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
*> e) Q(K)**H * B, the matrix B with the orthogonal
*> e) Q(K)**H * B, the matrix B with the unitary
*> transformation Q(K)**H applied on the left.
*>
*> The N-by-N permutation matrix P(K) is stored in a compact form in
*> the integer array JPIV. For 1 <= j <= N, column j
*> of the matrix A was interchanged with column JPIV(j).
*>
*> The M-by-M orthogonal matrix Q is represented as a product
*> The M-by-M unitary matrix Q is represented as a product
*> of elementary Householder reflectors
*>
*> Q(K) = H(1) * H(2) * . . . * H(K),
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*>
*> 1. The elements below the diagonal of the subarray
*> A(1:M,1:K) together with TAU(1:K) represent the
*> orthogonal matrix Q(K) as a product of K Householder
*> unitary matrix Q(K) as a product of K Householder
*> elementary reflectors.
*>
*> 2. The elements on and above the diagonal of
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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6 changes: 3 additions & 3 deletions lapack-netlib/SRC/claqp2rk.f
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*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(K) as a product of elementary
*> the unitary matrix Q(K) as a product of elementary
*> reflectors.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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6 changes: 3 additions & 3 deletions lapack-netlib/SRC/claqp3rk.f
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*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(KB) as a product of elementary
*> the unitary matrix Q(KB) as a product of elementary
*> reflectors.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/dgeqp3rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/dlaqp2rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/dlaqp3rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/sgeqp3rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/slaqp2rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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4 changes: 2 additions & 2 deletions lapack-netlib/SRC/slaqp3rk.f
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*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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12 changes: 6 additions & 6 deletions lapack-netlib/SRC/zgeqp3rk.f
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*> where:
*>
*> P(K) is an N-by-N permutation matrix;
*> Q(K) is an M-by-M orthogonal matrix;
*> Q(K) is an M-by-M unitary matrix;
*> R(K)_approx = ( R11(K), R12(K) ) is a rank K approximation of the
*> full rank factor R with K-by-K upper-triangular
*> R11(K) and K-by-N rectangular R12(K). The diagonal
Expand Down Expand Up @@ -124,14 +124,14 @@
*> d) RELMAXC2NRMK equals MAXC2NRMK divided by MAXC2NRM, the maximum
*> column 2-norm of the original matrix A, which is equal
*> to abs(R(1,1)), ( if K = min(M,N), RELMAXC2NRMK = 0.0 );
*> e) Q(K)**H * B, the matrix B with the orthogonal
*> e) Q(K)**H * B, the matrix B with the unitary
*> transformation Q(K)**H applied on the left.
*>
*> The N-by-N permutation matrix P(K) is stored in a compact form in
*> the integer array JPIV. For 1 <= j <= N, column j
*> of the matrix A was interchanged with column JPIV(j).
*>
*> The M-by-M orthogonal matrix Q is represented as a product
*> The M-by-M unitary matrix Q is represented as a product
*> of elementary Householder reflectors
*>
*> Q(K) = H(1) * H(2) * . . . * H(K),
Expand Down Expand Up @@ -300,7 +300,7 @@
*>
*> 1. The elements below the diagonal of the subarray
*> A(1:M,1:K) together with TAU(1:K) represent the
*> orthogonal matrix Q(K) as a product of K Householder
*> unitary matrix Q(K) as a product of K Householder
*> elementary reflectors.
*>
*> 2. The elements on and above the diagonal of
Expand Down Expand Up @@ -579,8 +579,8 @@
*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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6 changes: 3 additions & 3 deletions lapack-netlib/SRC/zlaqp2rk.f
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Expand Up @@ -178,7 +178,7 @@
*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:K) below
*> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(K) as a product of elementary
*> the unitary matrix Q(K) as a product of elementary
*> reflectors.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:K) is the triangular factor obtained.
Expand Down Expand Up @@ -332,8 +332,8 @@
*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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6 changes: 3 additions & 3 deletions lapack-netlib/SRC/zlaqp3rk.f
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Expand Up @@ -196,7 +196,7 @@
*> On exit:
*> 1. The elements in block A(IOFFSET+1:M,1:KB) below
*> the diagonal together with the array TAU represent
*> the orthogonal matrix Q(KB) as a product of elementary
*> the unitary matrix Q(KB) as a product of elementary
*> reflectors.
*> 2. The upper triangular block of the matrix A stored
*> in A(IOFFSET+1:M,1:KB) is the triangular factor obtained.
Expand Down Expand Up @@ -383,8 +383,8 @@
*> \verbatim
*>
*> November 2023, Igor Kozachenko, James Demmel,
*> Computer Science Division,
*> University of California, Berkeley
*> EECS Department,
*> University of California, Berkeley, USA.
*>
*> \endverbatim
*
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