From d09eff990f9160e70bc837174990305a7be791db Mon Sep 17 00:00:00 2001
From: jan <jan@mpxd.net>
Date: Sun, 17 Dec 2017 20:51:34 -0800
Subject: [PATCH] Update Rayleigh quotient iteration to allow arbitrary linear
 operators

---
 fdfd_tools/eigensolvers.py | 26 ++++++++++++++++++++++----
 1 file changed, 22 insertions(+), 4 deletions(-)

diff --git a/fdfd_tools/eigensolvers.py b/fdfd_tools/eigensolvers.py
index 24d7339..e348cd7 100644
--- a/fdfd_tools/eigensolvers.py
+++ b/fdfd_tools/eigensolvers.py
@@ -33,10 +33,11 @@ def power_iteration(operator: sparse.spmatrix,
     return lm_eigval, v
 
 
-def rayleigh_quotient_iteration(operator: sparse.spmatrix,
+def rayleigh_quotient_iteration(operator: sparse.spmatrix or spalg.LinearOperator,
                                 guess_vector: numpy.ndarray,
                                 iterations: int = 40,
                                 tolerance: float = 1e-13,
+                                solver=None,
                                 ) -> Tuple[complex, numpy.ndarray]:
     """
     Use Rayleigh quotient iteration to refine an eigenvector guess.
@@ -46,16 +47,33 @@ def rayleigh_quotient_iteration(operator: sparse.spmatrix,
     :param iterations: Maximum number of iterations to perform. Default 40.
     :param tolerance: Stop iteration if (A - I*eigenvalue) @ v < tolerance.
         Default 1e-13.
+    :param solver: Solver function of the form x = solver(A, b).
+        By default, use scipy.sparse.spsolve for sparse matrices and
+        scipy.sparse.bicgstab for general LinearOperator instances.
     :return: (eigenvalue, eigenvector)
     """
+    try:
+        _test = operator - sparse.eye(operator.shape)
+        shift = lambda eigval: eigval * sparse.eye(operator.shape[0])
+        if solver is None:
+            solver = spalg.spsolve
+    except TypeError:
+        shift = lambda eigval: spalg.LinearOperator(shape=operator.shape,
+                                                    dtype=operator.dtype,
+                                                    matvec=lambda v: eigval * v)
+        if solver is None:
+            solver = lambda A, b: spalg.bicgstab(A, b)[0]
+
     v = guess_vector
+    v /= norm(v)
     for _ in range(iterations):
-        eigval = v.conj() @ operator @ v
+        eigval = v.conj() @ (operator @ v)
         if norm(operator @ v - eigval * v) < tolerance:
             break
-        v = spalg.spsolve(operator - eigval * sparse.eye(operator.shape[0]), v)
-        v /= norm(v)
 
+        shifted_operator = operator - shift(eigval)
+        v = solver(shifted_operator, v)
+        v /= norm(v)
     return eigval, v