# -*- coding: utf-8 -*-
#
# This file is subject to the terms and conditions defined in
# file 'LICENSE', which is part of this source code package.
#
#
import os
try:
from mpi4py import MPI
except ImportError:#pragma: no cover
print("MPI capabilities not available")
import numpy as np
from scipy import sparse
[docs]
def ComputeReducedOrderBasisFromCollectionProblemData(
collectionProblemData, solutionName, tolerance, snapshotCorrelationOperator = None
):
"""
Computes a reducedOrderBasis using the SnapshotPOD algorithm, from the
snapshots contained in the solutions of name "solutionName" from all
problemDatas in collectionProblemData, with tolerance as target accuracy of
the data compression
Parameters
----------
collectionProblemData : CollectionProblemData
input collectionProblemData containing the data
solutionName : str
name of the solutions from which snapshots are taken
tolerance : float
target accuracy of the data compression
snapshotCorrelationOperator : scipy.sparse.csr_matrix, optional
correlation operator between the snapshots
Returns
-------
np.ndarray
of size (numberOfModes, numberOfDOFs)
"""
assert isinstance(solutionName, str)
snapshotsIterator = collectionProblemData.SnapshotsIterator(solutionName)
if snapshotCorrelationOperator is None:
snapshotCorrelationOperator = sparse.eye(collectionProblemData.GetSolutionsNumberOfDofs(solutionName))
return ComputeReducedOrderBasis(snapshotsIterator, snapshotCorrelationOperator, tolerance)
[docs]
def ComputeReducedOrderBasis(snapshotsIterator, snapshotCorrelationOperator, tolerance):
"""
Computes a reducedOrderBasis using the SnapshotPOD algorithm, from the
snapshots contained in the iterator snapshotsIterator, which a correlation
operator between the snapshots defined by the matrix
snapshotCorrelationOperator, with tolerance as target accuracy of the data
compression
Parameters
----------
snapshotsIterator : iterator
iterator over the snapshots on which we want to compute a reducedOrderBasis
snapshotCorrelationOperator : scipy.sparse.csr
correlation operator between the snapshots
tolerance : float
target accuracy of the data compression
Returns
-------
np.ndarray
of size (numberOfModes, numberOfDOFs)
"""
snapshots = []
for s in snapshotsIterator:
snapshots.append(s)
snapshots = np.array(snapshots)
numberOfSnapshots = snapshots.shape[0]
correlationMatrix = np.zeros((numberOfSnapshots, numberOfSnapshots))
for i, snapshot1 in enumerate(snapshots):
matVecProduct = snapshotCorrelationOperator.dot(snapshot1)
for j, snapshot2 in enumerate(snapshots):
if i >= j:
correlationMatrix[i, j] = np.dot(matVecProduct, snapshot2)
mpiReducedCorrelationMatrix = np.zeros((numberOfSnapshots, numberOfSnapshots))
MPI.COMM_WORLD.Allreduce([correlationMatrix, MPI.DOUBLE], [mpiReducedCorrelationMatrix, MPI.DOUBLE])
from Mordicus.BasicAlgorithms import SVD as SVD
eigenValuesRed, eigenVectorsRed = SVD.TruncatedSVDSymLower(mpiReducedCorrelationMatrix, tolerance)
nbePODModes = eigenValuesRed.shape[0]
print("nbePODModes =", nbePODModes)
changeOfBasisMatrix = np.zeros((nbePODModes,numberOfSnapshots))
for j in range(nbePODModes):
changeOfBasisMatrix[j,:] = eigenVectorsRed[:,j]/np.sqrt(eigenValuesRed[j])
reducedOrderBasis = np.dot(changeOfBasisMatrix,snapshots)
return reducedOrderBasis
if __name__ == "__main__":# pragma: no cover
from Mordicus import RunTestFile
RunTestFile(__file__)