tbt optics correction

To do:
-apply_correction function to be replace by SC.set_magnet_setpoints
-Coupling RDTs correction to be added

pySC/correction/tbt

@@ -0,0 +1,79 @@
+import numpy as np
+import at
+
+def phase_advance_correction(ring, bpm_indices, elements_indices, dkick, cut, Px=None, Py=None, Etax=None):
+    """
+    Perform phase advance and horizontal dispersion correction on the given ring.
+
+    Parameters:
+    dkick: Change in quadrupole strength for response matrix calculation.
+    cut: number of kept singular values
+    Px, Py, Etax:  response matrices for horizontal and vertical phase advances and dispersion. 
+                   If not provided, they will be calculated.
+
+    Returns:
+    corrected ring
+    """
+    # Initial Twiss parameters 
+    _, _, twiss_err0 = at.get_optics(ring, bpm_indices)
+    elemdata0, beamdata, elemdata = at.get_optics(ring, bpm_indices)
+    mux0 = elemdata.mu[:, 0] / (2 * np.pi)
+    muy0 = elemdata.mu[:, 1] / (2 * np.pi)
+    Eta_x0 = elemdata.dispersion[:, 0]
+
+    # Calculate Response Matrix if not provided
+    if Px is None or Py is None or Etax is None:
+        Px, Py, Etax = calculate_rm(dkick, ring, elements_indices, bpm_indices, mux0, muy0, Eta_x0)
+
+    response_matrix = np.hstack((Px, Py, Etax))
+
+    elemdata0, beamdata, elemdata = at.get_optics(ring, bpm_indices)
+    mux = elemdata.mu[:, 0] / (2 * np.pi)
+    muy = elemdata.mu[:, 1] / (2 * np.pi)
+    Eta_xx = elemdata.dispersion[:, 0]
+
+    measurement = np.concatenate((mux - mux0, muy - muy0, Eta_xx - Eta_x0), axis=0)
+
+    s = np.linalg.svd(response_matrix.T, compute_uv=False)
+    system_solution = np.linalg.pinv(response_matrix.T, rcond=s[cut - 1] / s[0]) @ -measurement
+        ring = apply_correction(ring, system_solution, elements_indices)
+
+    return ring
+
+
+def calculate_rm(dkick, ring, elements_indices, bpm_indices, mux0, muy0, Eta_x0):
+    """    
+    Returns:
+    Px, Py, Etax: Response matrices for horizontal and vertical phase advances and dispersion.
+    """
+    px =[]
+    py =[] 
+    etax = []
+
+    for index in elements_indices:
+        original_setting = ring[index].PolynomB[1]
+
+        ring[index].PolynomB[1] += dkick
+        _, _, elemdata = at.get_optics(ring, bpm_indices)
+
+        mux = elemdata.mu[:, 0] / (2 * np.pi)
+        muy = elemdata.mu[:, 1] / (2 * np.pi)
+        Eta_x = elemdata.dispersion[:, 0]
+
+        px.append((mux - mux0) / dkick)
+        py.append((muy - muy0) / dkick)
+        etax.append((Eta_x - Eta_x0) / dkick)
+
+        ring[index].PolynomB[1] = original_setting
+
+    Px = np.squeeze(np.array(px))
+    Py = np.squeeze(np.array(py))
+    Etax = np.squeeze(np.array(etax))
+
+    return Px, Py, Etax
+
+
+def apply_correction(ring, corrections, elements_indices):
+    for i, index in enumerate(elements_indices):
+        ring[index].PolynomB[1] += corrections[i]
+    return ring