def test_eigh_D():
ns = 289
gA = np.random.standard_normal((ns, ns)).astype(np.float64)
gA = gA + gA.T # Make symmetric
gA = np.asfortranarray(gA)
dA = core.DistributedMatrix.from_global_array(gA, rank=0)
evalsd, dZd = rt.eigh(dA)
gZd = dZd.to_global_array(rank=0)
if rank == 0:
evalsn, gZn = la.eigh(gA)
assert allclose(evalsn, evalsd)
assert cmp_evecs(gZn, gZd)
def test_eigh_D():
ns = 289
gA = np.random.standard_normal((ns, ns)).astype(np.float64)
gA = gA + gA.T # Make symmetric
gA = np.asfortranarray(gA)
dA = core.DistributedMatrix.from_global_array(gA, rank=0)
evalsd, dZd = rt.eigh(dA)
gZd = dZd.to_global_array(rank=0)
if rank == 0:
evalsn, gZn = la.eigh(gA)
assert allclose(evalsn, evalsd)
assert cmp_evecs(gZn, gZd)
def eigh_gen(A, B, lower=True, overwrite_a=True, overwrite_b=True):
"""Solve the generalised eigenvalue problem. :math:`\mathbf{A} \mathbf{v} = \lambda \mathbf{B} \mathbf{v}` of two symmetric/hermitian matrix.
Use Scalapack to compute the eigenvalues and eigenvectors of two distributed matrix.
The returned eigenvectors is somewhate different from that returned by `scipy.linalg.eigh`. Here evecs.T.conj() corresponds to the eigenvectors returned by `scipy.linalg.eigh`, but usally they are not the same, they still may differ from a diagonal unitary matrix.
Parameters
----------
A, B : DistributedMatrix
The matrix to decompose.
lower : boolean, optional
Scalapack uses only half of the matrix, by default the lower
triangle will be used. Set to False to use the upper triangle.
overwrite_a, overwrite_b : boolean, optional
By default the input matrix is destroyed, if set to False a
copy is taken and operated on.
eigvals : tuple (lo, hi), optional
Indices of the lowest and highest eigenvalues you would like to
calculate. Indexed from zero.
Returns
-------
evals : np.ndarray
The eigenvalues of the matrix, they are returned as a global
numpy array of all values.
evecs : DistributedMatrix
The eigenvectors as a DistributedMatrix.
"""
Lambda1, R1H = rt.eigh(B, lower=lower, overwrite_a=overwrite_b)
# L1 = rt.dot(rt.dot(R1H, B, transA='C', transB='N'), R1H, transA='N', transB='N')
# L1 = L1.to_global_array(rank=0)
# if MPI.COMM_WORLD.rank == 0:
# assert np.allclose(Lambda1, np.diag(L1).real)
if not (Lambda1 > 0.0).all():
add_const = -(np.min(Lambda1) * (1.0 + 1e-12) + 1e-60)
Lambda1 += add_const
if B.context.mpi_comm.Get_rank() == 0:
print "Second matrix probably not positive definite due to numerical issues. \
Add a minimum constant %f to all of its eigenvalues to make it positive definite...." % add_const
ihalfL = np.diag(Lambda1 ** (-0.5)).astype(R1H.dtype)
# if MPI.COMM_WORLD.rank == 0:
# print np.dot(np.dot(ihalfL, np.diag(Lambda1)), ihalfL.T.conj())
ihalfL = np.asfortranarray(ihalfL)
ihalfL = core.DistributedMatrix.from_global_array(ihalfL, rank=0, block_shape=A.block_shape, context=A.context)
# R2R1 = rt.dot(ihalfL, R1H, transA='N', transB='H')
R2R1 = rt.dot(ihalfL, R1H, transA="N", transB="C")
# I = rt.dot(rt.dot(R2R1, B, transA='N', transB='N'), R2R1, transA='N', transB='C')
# I = I.to_global_array(rank=0)
# if MPI.COMM_WORLD.rank == 0:
# print 'I ='
# print I
# A1 = rt.dot(rt.dot(R2R1, A, transA='N', transB='N'), R2R1, transA='N', transB='H')
if overwrite_a:
A = rt.dot(rt.dot(R2R1, A, transA="N", transB="N"), R2R1, transA="N", transB="C")
Lambda3, R3H = rt.eigh(A, lower=lower, overwrite_a=overwrite_a)
else:
A1 = rt.dot(rt.dot(R2R1, A, transA="N", transB="N"), R2R1, transA="N", transB="C")
Lambda3, R3H = rt.eigh(A1, lower=lower, overwrite_a=True)
# R = rt.dot(R3H, R2R1, transA='H', transB='N')
R = rt.dot(R3H, R2R1, transA="C", transB="N")
return Lambda3, R
def eigh_gen(A, B, lower=True, overwrite_a=True, overwrite_b=True):
"""Solve the generalised eigenvalue problem. :math:`\mathbf{A} \mathbf{v} = \lambda \mathbf{B} \mathbf{v}` of two symmetric/hermitian matrix.
Use Scalapack to compute the eigenvalues and eigenvectors of two distributed matrix.
The returned eigenvectors is somewhate different from that returned by `scipy.linalg.eigh`. Here evecs.T.conj() corresponds to the eigenvectors returned by `scipy.linalg.eigh`, but usally they are not the same, they still may differ from a diagonal unitary matrix.
Parameters
----------
A, B : DistributedMatrix
The matrix to decompose.
lower : boolean, optional
Scalapack uses only half of the matrix, by default the lower
triangle will be used. Set to False to use the upper triangle.
overwrite_a, overwrite_b : boolean, optional
By default the input matrix is destroyed, if set to False a
copy is taken and operated on.
eigvals : tuple (lo, hi), optional
Indices of the lowest and highest eigenvalues you would like to
calculate. Indexed from zero.
Returns
-------
evals : np.ndarray
The eigenvalues of the matrix, they are returned as a global
numpy array of all values.
evecs : DistributedMatrix
The eigenvectors as a DistributedMatrix.
"""
Lambda1, R1H = rt.eigh(B, lower=lower, overwrite_a=overwrite_b)
# L1 = rt.dot(rt.dot(R1H, B, transA='C', transB='N'), R1H, transA='N', transB='N')
# L1 = L1.to_global_array(rank=0)
# if MPI.COMM_WORLD.rank == 0:
# assert np.allclose(Lambda1, np.diag(L1).real)
if not (Lambda1 > 0.0).all():
add_const = - (np.min(Lambda1) * (1.0 + 1e-12) + 1e-60)
Lambda1 += add_const
if B.context.mpi_comm.Get_rank() == 0:
print "Second matrix probably not positive definite due to numerical issues. \
Add a minimum constant %f to all of its eigenvalues to make it positive definite...." % add_const
ihalfL = np.diag(Lambda1**(-0.5)).astype(R1H.dtype)
# if MPI.COMM_WORLD.rank == 0:
# print np.dot(np.dot(ihalfL, np.diag(Lambda1)), ihalfL.T.conj())
ihalfL = np.asfortranarray(ihalfL)
ihalfL = core.DistributedMatrix.from_global_array(ihalfL, rank=0, block_shape=A.block_shape, context=A.context)
# R2R1 = rt.dot(ihalfL, R1H, transA='N', transB='H')
R2R1 = rt.dot(ihalfL, R1H, transA='N', transB='C')
# I = rt.dot(rt.dot(R2R1, B, transA='N', transB='N'), R2R1, transA='N', transB='C')
# I = I.to_global_array(rank=0)
# if MPI.COMM_WORLD.rank == 0:
# print 'I ='
# print I
# A1 = rt.dot(rt.dot(R2R1, A, transA='N', transB='N'), R2R1, transA='N', transB='H')
if overwrite_a:
A = rt.dot(rt.dot(R2R1, A, transA='N', transB='N'), R2R1, transA='N', transB='C')
Lambda3, R3H = rt.eigh(A, lower=lower, overwrite_a=overwrite_a)
else:
A1 = rt.dot(rt.dot(R2R1, A, transA='N', transB='N'), R2R1, transA='N', transB='C')
Lambda3, R3H = rt.eigh(A1, lower=lower, overwrite_a=True)
# R = rt.dot(R3H, R2R1, transA='H', transB='N')
R = rt.dot(R3H, R2R1, transA='C', transB='N')
return Lambda3, R