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venv/Lib/site-packages/sklearn/externals/_lobpcg.py
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venv/Lib/site-packages/sklearn/externals/_lobpcg.py
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"""
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scikit-learn copy of scipy/sparse/linalg/eigen/lobpcg/lobpcg.py v1.3.0
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to be deleted after scipy 1.3.0 becomes a dependency in scikit-lean
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++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG).
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References
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----------
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.. [1] A. V. Knyazev (2001),
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Toward the Optimal Preconditioned Eigensolver: Locally Optimal
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Block Preconditioned Conjugate Gradient Method.
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SIAM Journal on Scientific Computing 23, no. 2,
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pp. 517-541. http://dx.doi.org/10.1137/S1064827500366124
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.. [2] A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov (2007),
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Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX)
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in hypre and PETSc. https://arxiv.org/abs/0705.2626
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.. [3] A. V. Knyazev's C and MATLAB implementations:
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https://bitbucket.org/joseroman/blopex
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"""
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from __future__ import division, print_function, absolute_import
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import numpy as np
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from scipy.linalg import (inv, eigh, cho_factor, cho_solve, cholesky, orth,
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LinAlgError)
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from scipy.sparse.linalg import aslinearoperator
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__all__ = ['lobpcg']
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def bmat(*args, **kwargs):
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import warnings
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with warnings.catch_warnings(record=True):
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warnings.filterwarnings(
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'ignore', '.*the matrix subclass is not the recommended way.*')
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return np.bmat(*args, **kwargs)
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def _save(ar, fileName):
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# Used only when verbosity level > 10.
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np.savetxt(fileName, ar)
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def _report_nonhermitian(M, name):
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"""
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Report if `M` is not a hermitian matrix given its type.
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"""
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from scipy.linalg import norm
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md = M - M.T.conj()
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nmd = norm(md, 1)
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tol = 10 * np.finfo(M.dtype).eps
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tol = max(tol, tol * norm(M, 1))
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if nmd > tol:
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print('matrix %s of the type %s is not sufficiently Hermitian:'
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% (name, M.dtype))
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print('condition: %.e < %e' % (nmd, tol))
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def _as2d(ar):
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"""
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If the input array is 2D return it, if it is 1D, append a dimension,
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making it a column vector.
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"""
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if ar.ndim == 2:
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return ar
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else: # Assume 1!
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aux = np.array(ar, copy=False)
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aux.shape = (ar.shape[0], 1)
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return aux
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def _makeOperator(operatorInput, expectedShape):
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"""Takes a dense numpy array or a sparse matrix or
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a function and makes an operator performing matrix * blockvector
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products."""
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if operatorInput is None:
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return None
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else:
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operator = aslinearoperator(operatorInput)
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if operator.shape != expectedShape:
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raise ValueError('operator has invalid shape')
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return operator
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def _applyConstraints(blockVectorV, factYBY, blockVectorBY, blockVectorY):
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"""Changes blockVectorV in place."""
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YBV = np.dot(blockVectorBY.T.conj(), blockVectorV)
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tmp = cho_solve(factYBY, YBV)
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blockVectorV -= np.dot(blockVectorY, tmp)
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def _b_orthonormalize(B, blockVectorV, blockVectorBV=None, retInvR=False):
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"""B-orthonormalize the given block vector using Cholesky."""
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normalization = blockVectorV.max(axis=0)+np.finfo(blockVectorV.dtype).eps
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blockVectorV = blockVectorV / normalization
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if blockVectorBV is None:
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if B is not None:
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blockVectorBV = B(blockVectorV)
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else:
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blockVectorBV = blockVectorV # Shared data!!!
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else:
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blockVectorBV = blockVectorBV / normalization
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VBV = np.matmul(blockVectorV.T.conj(), blockVectorBV)
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try:
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# VBV is a Cholesky factor from now on...
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VBV = cholesky(VBV, overwrite_a=True)
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VBV = inv(VBV, overwrite_a=True)
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blockVectorV = np.matmul(blockVectorV, VBV)
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# blockVectorV = (cho_solve((VBV.T, True), blockVectorV.T)).T
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if B is not None:
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blockVectorBV = np.matmul(blockVectorBV, VBV)
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# blockVectorBV = (cho_solve((VBV.T, True), blockVectorBV.T)).T
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else:
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blockVectorBV = None
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except LinAlgError:
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# raise ValueError('Cholesky has failed')
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blockVectorV = None
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blockVectorBV = None
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VBV = None
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if retInvR:
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return blockVectorV, blockVectorBV, VBV, normalization
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else:
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return blockVectorV, blockVectorBV
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def _get_indx(_lambda, num, largest):
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"""Get `num` indices into `_lambda` depending on `largest` option."""
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ii = np.argsort(_lambda)
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if largest:
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ii = ii[:-num-1:-1]
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else:
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ii = ii[:num]
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return ii
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def lobpcg(A, X,
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B=None, M=None, Y=None,
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tol=None, maxiter=20,
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largest=True, verbosityLevel=0,
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retLambdaHistory=False, retResidualNormsHistory=False):
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"""Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG)
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LOBPCG is a preconditioned eigensolver for large symmetric positive
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definite (SPD) generalized eigenproblems.
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Parameters
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----------
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A : {sparse matrix, dense matrix, LinearOperator}
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The symmetric linear operator of the problem, usually a
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sparse matrix. Often called the "stiffness matrix".
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X : ndarray, float32 or float64
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Initial approximation to the ``k`` eigenvectors (non-sparse). If `A`
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has ``shape=(n,n)`` then `X` should have shape ``shape=(n,k)``.
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B : {dense matrix, sparse matrix, LinearOperator}, optional
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The right hand side operator in a generalized eigenproblem.
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By default, ``B = Identity``. Often called the "mass matrix".
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M : {dense matrix, sparse matrix, LinearOperator}, optional
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Preconditioner to `A`; by default ``M = Identity``.
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`M` should approximate the inverse of `A`.
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Y : ndarray, float32 or float64, optional
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n-by-sizeY matrix of constraints (non-sparse), sizeY < n
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The iterations will be performed in the B-orthogonal complement
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of the column-space of Y. Y must be full rank.
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tol : scalar, optional
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Solver tolerance (stopping criterion).
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The default is ``tol=n*sqrt(eps)``.
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maxiter : int, optional
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Maximum number of iterations. The default is ``maxiter=min(n, 20)``.
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largest : bool, optional
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When True, solve for the largest eigenvalues, otherwise the smallest.
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verbosityLevel : int, optional
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Controls solver output. The default is ``verbosityLevel=0``.
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retLambdaHistory : bool, optional
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Whether to return eigenvalue history. Default is False.
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retResidualNormsHistory : bool, optional
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Whether to return history of residual norms. Default is False.
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Returns
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-------
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w : ndarray
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Array of ``k`` eigenvalues
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v : ndarray
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An array of ``k`` eigenvectors. `v` has the same shape as `X`.
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lambdas : list of ndarray, optional
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The eigenvalue history, if `retLambdaHistory` is True.
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rnorms : list of ndarray, optional
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The history of residual norms, if `retResidualNormsHistory` is True.
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Notes
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-----
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If both ``retLambdaHistory`` and ``retResidualNormsHistory`` are True,
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the return tuple has the following format
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``(lambda, V, lambda history, residual norms history)``.
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In the following ``n`` denotes the matrix size and ``m`` the number
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of required eigenvalues (smallest or largest).
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The LOBPCG code internally solves eigenproblems of the size ``3m`` on every
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iteration by calling the "standard" dense eigensolver, so if ``m`` is not
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small enough compared to ``n``, it does not make sense to call the LOBPCG
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code, but rather one should use the "standard" eigensolver, e.g. numpy or
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scipy function in this case.
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If one calls the LOBPCG algorithm for ``5m > n``, it will most likely break
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internally, so the code tries to call the standard function instead.
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It is not that ``n`` should be large for the LOBPCG to work, but rather the
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ratio ``n / m`` should be large. It you call LOBPCG with ``m=1``
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and ``n=10``, it works though ``n`` is small. The method is intended
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for extremely large ``n / m``, see e.g., reference [28] in
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https://arxiv.org/abs/0705.2626
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The convergence speed depends basically on two factors:
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1. How well relatively separated the seeking eigenvalues are from the rest
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of the eigenvalues. One can try to vary ``m`` to make this better.
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2. How well conditioned the problem is. This can be changed by using proper
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preconditioning. For example, a rod vibration test problem (under tests
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directory) is ill-conditioned for large ``n``, so convergence will be
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slow, unless efficient preconditioning is used. For this specific
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problem, a good simple preconditioner function would be a linear solve
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for `A`, which is easy to code since A is tridiagonal.
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References
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----------
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.. [1] A. V. Knyazev (2001),
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Toward the Optimal Preconditioned Eigensolver: Locally Optimal
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Block Preconditioned Conjugate Gradient Method.
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SIAM Journal on Scientific Computing 23, no. 2,
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pp. 517-541. http://dx.doi.org/10.1137/S1064827500366124
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.. [2] A. V. Knyazev, I. Lashuk, M. E. Argentati, and E. Ovchinnikov
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(2007), Block Locally Optimal Preconditioned Eigenvalue Xolvers
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(BLOPEX) in hypre and PETSc. https://arxiv.org/abs/0705.2626
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.. [3] A. V. Knyazev's C and MATLAB implementations:
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https://bitbucket.org/joseroman/blopex
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Examples
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--------
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Solve ``A x = lambda x`` with constraints and preconditioning.
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>>> import numpy as np
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>>> from scipy.sparse import spdiags, issparse
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>>> from scipy.sparse.linalg import lobpcg, LinearOperator
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>>> n = 100
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>>> vals = np.arange(1, n + 1)
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>>> A = spdiags(vals, 0, n, n)
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>>> A.toarray()
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array([[ 1., 0., 0., ..., 0., 0., 0.],
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[ 0., 2., 0., ..., 0., 0., 0.],
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[ 0., 0., 3., ..., 0., 0., 0.],
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...,
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[ 0., 0., 0., ..., 98., 0., 0.],
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[ 0., 0., 0., ..., 0., 99., 0.],
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[ 0., 0., 0., ..., 0., 0., 100.]])
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Constraints:
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>>> Y = np.eye(n, 3)
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Initial guess for eigenvectors, should have linearly independent
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columns. Column dimension = number of requested eigenvalues.
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>>> X = np.random.rand(n, 3)
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Preconditioner in the inverse of A in this example:
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>>> invA = spdiags([1./vals], 0, n, n)
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The preconditiner must be defined by a function:
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>>> def precond( x ):
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... return invA @ x
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The argument x of the preconditioner function is a matrix inside `lobpcg`,
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thus the use of matrix-matrix product ``@``.
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The preconditioner function is passed to lobpcg as a `LinearOperator`:
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>>> M = LinearOperator(matvec=precond, matmat=precond,
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... shape=(n, n), dtype=float)
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Let us now solve the eigenvalue problem for the matrix A:
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>>> eigenvalues, _ = lobpcg(A, X, Y=Y, M=M, largest=False)
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>>> eigenvalues
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array([4., 5., 6.])
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Note that the vectors passed in Y are the eigenvectors of the 3 smallest
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eigenvalues. The results returned are orthogonal to those.
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"""
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blockVectorX = X
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blockVectorY = Y
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residualTolerance = tol
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maxIterations = maxiter
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if blockVectorY is not None:
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sizeY = blockVectorY.shape[1]
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else:
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sizeY = 0
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# Block size.
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if len(blockVectorX.shape) != 2:
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raise ValueError('expected rank-2 array for argument X')
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n, sizeX = blockVectorX.shape
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if verbosityLevel:
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aux = "Solving "
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if B is None:
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aux += "standard"
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else:
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aux += "generalized"
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aux += " eigenvalue problem with"
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if M is None:
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aux += "out"
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aux += " preconditioning\n\n"
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aux += "matrix size %d\n" % n
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aux += "block size %d\n\n" % sizeX
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if blockVectorY is None:
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aux += "No constraints\n\n"
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else:
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if sizeY > 1:
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aux += "%d constraints\n\n" % sizeY
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else:
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aux += "%d constraint\n\n" % sizeY
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print(aux)
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A = _makeOperator(A, (n, n))
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B = _makeOperator(B, (n, n))
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M = _makeOperator(M, (n, n))
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if (n - sizeY) < (5 * sizeX):
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# warn('The problem size is small compared to the block size.' \
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# ' Using dense eigensolver instead of LOBPCG.')
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sizeX = min(sizeX, n)
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if blockVectorY is not None:
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raise NotImplementedError('The dense eigensolver '
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'does not support constraints.')
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# Define the closed range of indices of eigenvalues to return.
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if largest:
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eigvals = (n - sizeX, n-1)
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else:
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eigvals = (0, sizeX-1)
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A_dense = A(np.eye(n, dtype=A.dtype))
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B_dense = None if B is None else B(np.eye(n, dtype=B.dtype))
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vals, vecs = eigh(A_dense, B_dense, eigvals=eigvals,
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check_finite=False)
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if largest:
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# Reverse order to be compatible with eigs() in 'LM' mode.
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vals = vals[::-1]
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vecs = vecs[:, ::-1]
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return vals, vecs
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if (residualTolerance is None) or (residualTolerance <= 0.0):
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residualTolerance = np.sqrt(1e-15) * n
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# Apply constraints to X.
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if blockVectorY is not None:
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if B is not None:
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blockVectorBY = B(blockVectorY)
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else:
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blockVectorBY = blockVectorY
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# gramYBY is a dense array.
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gramYBY = np.dot(blockVectorY.T.conj(), blockVectorBY)
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try:
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# gramYBY is a Cholesky factor from now on...
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gramYBY = cho_factor(gramYBY)
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except LinAlgError:
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raise ValueError('cannot handle linearly dependent constraints')
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_applyConstraints(blockVectorX, gramYBY, blockVectorBY, blockVectorY)
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##
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# B-orthonormalize X.
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blockVectorX, blockVectorBX = _b_orthonormalize(B, blockVectorX)
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##
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# Compute the initial Ritz vectors: solve the eigenproblem.
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blockVectorAX = A(blockVectorX)
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gramXAX = np.dot(blockVectorX.T.conj(), blockVectorAX)
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_lambda, eigBlockVector = eigh(gramXAX, check_finite=False)
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ii = _get_indx(_lambda, sizeX, largest)
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_lambda = _lambda[ii]
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eigBlockVector = np.asarray(eigBlockVector[:, ii])
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blockVectorX = np.dot(blockVectorX, eigBlockVector)
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blockVectorAX = np.dot(blockVectorAX, eigBlockVector)
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if B is not None:
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blockVectorBX = np.dot(blockVectorBX, eigBlockVector)
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##
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# Active index set.
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activeMask = np.ones((sizeX,), dtype=bool)
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lambdaHistory = [_lambda]
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residualNormsHistory = []
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previousBlockSize = sizeX
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ident = np.eye(sizeX, dtype=A.dtype)
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ident0 = np.eye(sizeX, dtype=A.dtype)
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##
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# Main iteration loop.
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blockVectorP = None # set during iteration
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blockVectorAP = None
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blockVectorBP = None
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iterationNumber = -1
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restart = True
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explicitGramFlag = False
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while iterationNumber < maxIterations:
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iterationNumber += 1
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if verbosityLevel > 0:
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print('iteration %d' % iterationNumber)
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if B is not None:
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aux = blockVectorBX * _lambda[np.newaxis, :]
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else:
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aux = blockVectorX * _lambda[np.newaxis, :]
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blockVectorR = blockVectorAX - aux
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aux = np.sum(blockVectorR.conj() * blockVectorR, 0)
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residualNorms = np.sqrt(aux)
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residualNormsHistory.append(residualNorms)
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ii = np.where(residualNorms > residualTolerance, True, False)
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activeMask = activeMask & ii
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if verbosityLevel > 2:
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print(activeMask)
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currentBlockSize = activeMask.sum()
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if currentBlockSize != previousBlockSize:
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previousBlockSize = currentBlockSize
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ident = np.eye(currentBlockSize, dtype=A.dtype)
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if currentBlockSize == 0:
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break
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if verbosityLevel > 0:
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print('current block size:', currentBlockSize)
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print('eigenvalue:', _lambda)
|
||||
print('residual norms:', residualNorms)
|
||||
if verbosityLevel > 10:
|
||||
print(eigBlockVector)
|
||||
|
||||
activeBlockVectorR = _as2d(blockVectorR[:, activeMask])
|
||||
|
||||
if iterationNumber > 0:
|
||||
activeBlockVectorP = _as2d(blockVectorP[:, activeMask])
|
||||
activeBlockVectorAP = _as2d(blockVectorAP[:, activeMask])
|
||||
if B is not None:
|
||||
activeBlockVectorBP = _as2d(blockVectorBP[:, activeMask])
|
||||
|
||||
if M is not None:
|
||||
# Apply preconditioner T to the active residuals.
|
||||
activeBlockVectorR = M(activeBlockVectorR)
|
||||
|
||||
##
|
||||
# Apply constraints to the preconditioned residuals.
|
||||
if blockVectorY is not None:
|
||||
_applyConstraints(activeBlockVectorR,
|
||||
gramYBY, blockVectorBY, blockVectorY)
|
||||
|
||||
##
|
||||
# B-orthogonalize the preconditioned residuals to X.
|
||||
if B is not None:
|
||||
activeBlockVectorR = activeBlockVectorR - \
|
||||
np.matmul(blockVectorX,
|
||||
np.matmul(blockVectorBX.T.conj(),
|
||||
activeBlockVectorR))
|
||||
else:
|
||||
activeBlockVectorR = activeBlockVectorR - \
|
||||
np.matmul(blockVectorX,
|
||||
np.matmul(blockVectorX.T.conj(),
|
||||
activeBlockVectorR))
|
||||
|
||||
##
|
||||
# B-orthonormalize the preconditioned residuals.
|
||||
aux = _b_orthonormalize(B, activeBlockVectorR)
|
||||
activeBlockVectorR, activeBlockVectorBR = aux
|
||||
|
||||
activeBlockVectorAR = A(activeBlockVectorR)
|
||||
|
||||
if iterationNumber > 0:
|
||||
if B is not None:
|
||||
aux = _b_orthonormalize(B, activeBlockVectorP,
|
||||
activeBlockVectorBP, retInvR=True)
|
||||
activeBlockVectorP, activeBlockVectorBP, invR, normal = aux
|
||||
else:
|
||||
aux = _b_orthonormalize(B, activeBlockVectorP, retInvR=True)
|
||||
activeBlockVectorP, _, invR, normal = aux
|
||||
# Function _b_orthonormalize returns None if Cholesky fails
|
||||
if activeBlockVectorP is not None:
|
||||
activeBlockVectorAP = activeBlockVectorAP / normal
|
||||
activeBlockVectorAP = np.dot(activeBlockVectorAP, invR)
|
||||
restart = False
|
||||
else:
|
||||
restart = True
|
||||
|
||||
##
|
||||
# Perform the Rayleigh Ritz Procedure:
|
||||
# Compute symmetric Gram matrices:
|
||||
|
||||
if activeBlockVectorAR.dtype == 'float32':
|
||||
myeps = 1
|
||||
elif activeBlockVectorR.dtype == 'float32':
|
||||
myeps = 1e-4
|
||||
else:
|
||||
myeps = 1e-8
|
||||
|
||||
if residualNorms.max() > myeps and not explicitGramFlag:
|
||||
explicitGramFlag = False
|
||||
else:
|
||||
# Once explicitGramFlag, forever explicitGramFlag.
|
||||
explicitGramFlag = True
|
||||
|
||||
# Shared memory assingments to simplify the code
|
||||
if B is None:
|
||||
blockVectorBX = blockVectorX
|
||||
activeBlockVectorBR = activeBlockVectorR
|
||||
if not restart:
|
||||
activeBlockVectorBP = activeBlockVectorP
|
||||
|
||||
# Common submatrices:
|
||||
gramXAR = np.dot(blockVectorX.T.conj(), activeBlockVectorAR)
|
||||
gramRAR = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorAR)
|
||||
|
||||
if explicitGramFlag:
|
||||
gramRAR = (gramRAR + gramRAR.T.conj())/2
|
||||
gramXAX = np.dot(blockVectorX.T.conj(), blockVectorAX)
|
||||
gramXAX = (gramXAX + gramXAX.T.conj())/2
|
||||
gramXBX = np.dot(blockVectorX.T.conj(), blockVectorBX)
|
||||
gramRBR = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorBR)
|
||||
gramXBR = np.dot(blockVectorX.T.conj(), activeBlockVectorBR)
|
||||
else:
|
||||
gramXAX = np.diag(_lambda)
|
||||
gramXBX = ident0
|
||||
gramRBR = ident
|
||||
gramXBR = np.zeros((sizeX, currentBlockSize), dtype=A.dtype)
|
||||
|
||||
def _handle_gramA_gramB_verbosity(gramA, gramB):
|
||||
if verbosityLevel > 0:
|
||||
_report_nonhermitian(gramA, 'gramA')
|
||||
_report_nonhermitian(gramB, 'gramB')
|
||||
if verbosityLevel > 10:
|
||||
# Note: not documented, but leave it in here for now
|
||||
np.savetxt('gramA.txt', gramA)
|
||||
np.savetxt('gramB.txt', gramB)
|
||||
|
||||
if not restart:
|
||||
gramXAP = np.dot(blockVectorX.T.conj(), activeBlockVectorAP)
|
||||
gramRAP = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorAP)
|
||||
gramPAP = np.dot(activeBlockVectorP.T.conj(), activeBlockVectorAP)
|
||||
gramXBP = np.dot(blockVectorX.T.conj(), activeBlockVectorBP)
|
||||
gramRBP = np.dot(activeBlockVectorR.T.conj(), activeBlockVectorBP)
|
||||
if explicitGramFlag:
|
||||
gramPAP = (gramPAP + gramPAP.T.conj())/2
|
||||
gramPBP = np.dot(activeBlockVectorP.T.conj(),
|
||||
activeBlockVectorBP)
|
||||
else:
|
||||
gramPBP = ident
|
||||
|
||||
gramA = bmat([[gramXAX, gramXAR, gramXAP],
|
||||
[gramXAR.T.conj(), gramRAR, gramRAP],
|
||||
[gramXAP.T.conj(), gramRAP.T.conj(), gramPAP]])
|
||||
gramB = bmat([[gramXBX, gramXBR, gramXBP],
|
||||
[gramXBR.T.conj(), gramRBR, gramRBP],
|
||||
[gramXBP.T.conj(), gramRBP.T.conj(), gramPBP]])
|
||||
|
||||
_handle_gramA_gramB_verbosity(gramA, gramB)
|
||||
|
||||
try:
|
||||
_lambda, eigBlockVector = eigh(gramA, gramB,
|
||||
check_finite=False)
|
||||
except LinAlgError:
|
||||
# try again after dropping the direction vectors P from RR
|
||||
restart = True
|
||||
|
||||
if restart:
|
||||
gramA = bmat([[gramXAX, gramXAR],
|
||||
[gramXAR.T.conj(), gramRAR]])
|
||||
gramB = bmat([[gramXBX, gramXBR],
|
||||
[gramXBR.T.conj(), gramRBR]])
|
||||
|
||||
_handle_gramA_gramB_verbosity(gramA, gramB)
|
||||
|
||||
try:
|
||||
_lambda, eigBlockVector = eigh(gramA, gramB,
|
||||
check_finite=False)
|
||||
except LinAlgError:
|
||||
raise ValueError('eigh has failed in lobpcg iterations')
|
||||
|
||||
ii = _get_indx(_lambda, sizeX, largest)
|
||||
if verbosityLevel > 10:
|
||||
print(ii)
|
||||
print(_lambda)
|
||||
|
||||
_lambda = _lambda[ii]
|
||||
eigBlockVector = eigBlockVector[:, ii]
|
||||
|
||||
lambdaHistory.append(_lambda)
|
||||
|
||||
if verbosityLevel > 10:
|
||||
print('lambda:', _lambda)
|
||||
# # Normalize eigenvectors!
|
||||
# aux = np.sum( eigBlockVector.conj() * eigBlockVector, 0 )
|
||||
# eigVecNorms = np.sqrt( aux )
|
||||
# eigBlockVector = eigBlockVector / eigVecNorms[np.newaxis, :]
|
||||
# eigBlockVector, aux = _b_orthonormalize( B, eigBlockVector )
|
||||
|
||||
if verbosityLevel > 10:
|
||||
print(eigBlockVector)
|
||||
|
||||
# Compute Ritz vectors.
|
||||
if B is not None:
|
||||
if not restart:
|
||||
eigBlockVectorX = eigBlockVector[:sizeX]
|
||||
eigBlockVectorR = eigBlockVector[sizeX:sizeX+currentBlockSize]
|
||||
eigBlockVectorP = eigBlockVector[sizeX+currentBlockSize:]
|
||||
|
||||
pp = np.dot(activeBlockVectorR, eigBlockVectorR)
|
||||
pp += np.dot(activeBlockVectorP, eigBlockVectorP)
|
||||
|
||||
app = np.dot(activeBlockVectorAR, eigBlockVectorR)
|
||||
app += np.dot(activeBlockVectorAP, eigBlockVectorP)
|
||||
|
||||
bpp = np.dot(activeBlockVectorBR, eigBlockVectorR)
|
||||
bpp += np.dot(activeBlockVectorBP, eigBlockVectorP)
|
||||
else:
|
||||
eigBlockVectorX = eigBlockVector[:sizeX]
|
||||
eigBlockVectorR = eigBlockVector[sizeX:]
|
||||
|
||||
pp = np.dot(activeBlockVectorR, eigBlockVectorR)
|
||||
app = np.dot(activeBlockVectorAR, eigBlockVectorR)
|
||||
bpp = np.dot(activeBlockVectorBR, eigBlockVectorR)
|
||||
|
||||
if verbosityLevel > 10:
|
||||
print(pp)
|
||||
print(app)
|
||||
print(bpp)
|
||||
|
||||
blockVectorX = np.dot(blockVectorX, eigBlockVectorX) + pp
|
||||
blockVectorAX = np.dot(blockVectorAX, eigBlockVectorX) + app
|
||||
blockVectorBX = np.dot(blockVectorBX, eigBlockVectorX) + bpp
|
||||
|
||||
blockVectorP, blockVectorAP, blockVectorBP = pp, app, bpp
|
||||
|
||||
else:
|
||||
if not restart:
|
||||
eigBlockVectorX = eigBlockVector[:sizeX]
|
||||
eigBlockVectorR = eigBlockVector[sizeX:sizeX+currentBlockSize]
|
||||
eigBlockVectorP = eigBlockVector[sizeX+currentBlockSize:]
|
||||
|
||||
pp = np.dot(activeBlockVectorR, eigBlockVectorR)
|
||||
pp += np.dot(activeBlockVectorP, eigBlockVectorP)
|
||||
|
||||
app = np.dot(activeBlockVectorAR, eigBlockVectorR)
|
||||
app += np.dot(activeBlockVectorAP, eigBlockVectorP)
|
||||
else:
|
||||
eigBlockVectorX = eigBlockVector[:sizeX]
|
||||
eigBlockVectorR = eigBlockVector[sizeX:]
|
||||
|
||||
pp = np.dot(activeBlockVectorR, eigBlockVectorR)
|
||||
app = np.dot(activeBlockVectorAR, eigBlockVectorR)
|
||||
|
||||
if verbosityLevel > 10:
|
||||
print(pp)
|
||||
print(app)
|
||||
|
||||
blockVectorX = np.dot(blockVectorX, eigBlockVectorX) + pp
|
||||
blockVectorAX = np.dot(blockVectorAX, eigBlockVectorX) + app
|
||||
|
||||
blockVectorP, blockVectorAP = pp, app
|
||||
|
||||
if B is not None:
|
||||
aux = blockVectorBX * _lambda[np.newaxis, :]
|
||||
|
||||
else:
|
||||
aux = blockVectorX * _lambda[np.newaxis, :]
|
||||
|
||||
blockVectorR = blockVectorAX - aux
|
||||
|
||||
aux = np.sum(blockVectorR.conj() * blockVectorR, 0)
|
||||
residualNorms = np.sqrt(aux)
|
||||
|
||||
# Future work: Need to add Postprocessing here:
|
||||
# Making sure eigenvectors "exactly" satisfy the blockVectorY constrains?
|
||||
# Making sure eigenvecotrs are "exactly" othonormalized by final "exact" RR
|
||||
# Computing the actual true residuals
|
||||
|
||||
if verbosityLevel > 0:
|
||||
print('final eigenvalue:', _lambda)
|
||||
print('final residual norms:', residualNorms)
|
||||
|
||||
if retLambdaHistory:
|
||||
if retResidualNormsHistory:
|
||||
return _lambda, blockVectorX, lambdaHistory, residualNormsHistory
|
||||
else:
|
||||
return _lambda, blockVectorX, lambdaHistory
|
||||
else:
|
||||
if retResidualNormsHistory:
|
||||
return _lambda, blockVectorX, residualNormsHistory
|
||||
else:
|
||||
return _lambda, blockVectorX
|
||||
Loading…
Add table
Add a link
Reference in a new issue