def qr_destroy(la):
"""
Return QR decomposition of `la[0]`. Content of `la` gets destroyed in the process.
Using this function should be less memory intense than calling `scipy.linalg.qr(la[0])`,
because the memory used in `la[0]` is reclaimed earlier.
"""
a = numpy.asfortranarray(la[0])
del la[0], la # now `a` is the only reference to the input matrix
m, n = a.shape
# perform q, r = QR(a); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(a.shape))
geqrf, = get_lapack_funcs(('geqrf',), (a,))
qr, tau, work, info = geqrf(a, lwork=-1, overwrite_a=True)
qr, tau, work, info = geqrf(a, lwork=work[0], overwrite_a=True)
del a # free up mem
assert info >= 0
r = triu(qr[:n, :n])
if m < n: # rare case, #features < #topics
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr',), (qr,))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
return q, r
def qr_destroy(la):
a = numpy.asfortranarray(la[0])
del la[0], la # now `a` is the only reference to the input matrix
m, n = a.shape
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(a.shape))
geqrf, = get_lapack_funcs(('geqrf',), (a,))
qr, tau, work, info = geqrf(a, lwork = -1, overwrite_a = True)
qr, tau, work, info = geqrf(a, lwork = work[0], overwrite_a = True)
del a # free up mem
assert info >= 0
r = triu(qr[:n, :n])
if m < n: # rare case, #features < #topics
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr',), (qr,))
q, work, info = gorgqr(qr, tau, lwork = -1, overwrite_a = True)
q, work, info = gorgqr(qr, tau, lwork = work[0], overwrite_a = True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
return q, r
def qr_destroy(la):
a = numpy.asfortranarray(la[0])
del la[0], la # now `a` is the only reference to the input matrix
m, n = a.shape
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(a.shape))
geqrf, = get_lapack_funcs(('geqrf', ), (a, ))
qr, tau, work, info = geqrf(a, lwork=-1, overwrite_a=True)
qr, tau, work, info = geqrf(a, lwork=work[0], overwrite_a=True)
del a # free up mem
assert info >= 0
r = triu(qr[:n, :n])
if m < n: # rare case, #features < #topics
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr', ), (qr, ))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
return q, r
def qr_decomposition(la):
"""Reduced QR decomposition."""
print "+" * 100, "Performing reduced QR decomposition ..."
a = numpy.asfortranarray(la[0])
del la[0], la
m, n = a.shape
geqrf, = get_lapack_funcs(('geqrf', ), (a, ))
qr, tau, work, info = geqrf(a, lwork=-1, overwrite_a=True)
qr, tau, work, info = geqrf(a, lwork=work[0], overwrite_a=True)
del a
assert info >= 0
r = triu(qr[:n, :n])
if m < n:
qr = qr[:, :m]
gorgqr, = get_lapack_funcs(('orgqr', ), (qr, ))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
return q, r
def qr_decomposition(la):
"""Reduced QR decomposition."""
print "+"*100, "Performing reduced QR decomposition ..."
a = numpy.asfortranarray(la[0])
del la[0], la
m, n = a.shape
geqrf, = get_lapack_funcs(('geqrf',), (a,))
qr, tau, work, info = geqrf(a, lwork=-1, overwrite_a=True)
qr, tau, work, info = geqrf(a, lwork=work[0], overwrite_a=True)
del a
assert info >= 0
r = triu(qr[:n, :n])
if m < n:
qr = qr[:, :m]
gorgqr, = get_lapack_funcs(('orgqr',), (qr,))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
return q, r
def triu_indices(n, k=0):
m = numpy.ones((n, n), int)
a = triu(m, k)
return numpy.where(a != 0)
def merge(self, other, decay = 1.0):
"""
Merge this Projection with another.
Content of `other` is destroyed in the process, so pass this function a
copy if you need it further.
This is the optimized merge described in algorithm 5.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError("vector space mismatch: update has %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" % (str(self.u.shape), str(other.u.shape)))
# diff = numpy.dot(self.u.T, self.u) - numpy.eye(self.u.shape[1])
# logger.info('orth error after=%f' % numpy.sum(diff * diff))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with gorgqr.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in numpy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm, = get_blas_funcs(('gemm',), (self.u,))
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a = True)
gemm(-1.0, self.u, c, beta = 1.0, c = other.u, overwrite_c = True)
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(other.u.shape))
geqrf, = get_lapack_funcs(('geqrf',), (other.u,))
qr, tau, work, info = geqrf(other.u, lwork = -1, overwrite_a = True) # sometimes segfaults with overwrite_a=True...
qr, tau, work, info = geqrf(other.u, lwork = work[0], overwrite_a = True) # sometimes segfaults with overwrite_a=True...
del other.u
assert info >= 0
r = triu(qr[:n2, :n2])
if m < n2: # rare case...
qr = qr[:,:m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr',), (qr,))
q, work, info = gorgqr(qr, tau, lwork = -1, overwrite_a = True)
q, work, info = gorgqr(qr, tau, lwork = work[0], overwrite_a = True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
# find rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), c * other.s], [matutils.pad(numpy.matrix([]).reshape(0, 0), n2, n1), r * other.s]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
u_k, s_k, _ = numpy.linalg.svd(k, full_matrices = False) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
k = clipSpectrum(s_k, self.k)
u_k, s_k = u_k[:, :k], s_k[:k]
# update & rotate current basis U
logger.debug("updating orthonormal basis U")
self.u = gemm(1.0, self.u, u_k[:n1]) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u_k[n1:], beta = 1.0, c = self.u, overwrite_c = True) # u = [u,u']*u_k
self.s = s_k
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
Content of `other` is destroyed in the process, so pass this function a
copy if you need it further.
This is the optimized merge described in algorithm 5.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
if other.s is None:
# other.u contains a direct document chunk, not svd => perform svd
docs = other.u
assert scipy.sparse.issparse(docs)
if self.m * self.k < 10000:
# SVDLIBC gives spurious results for small matrices.. run full
# LAPACK on them instead
logger.info("computing dense SVD of %s matrix" %
str(docs.shape))
u, s, vt = numpy.linalg.svd(docs.todense(),
full_matrices=False)
else:
try:
import sparsesvd
except ImportError:
raise ImportError(
"for LSA, the `sparsesvd` module is needed but not found; run `easy_install sparsesvd`"
)
logger.info("computing sparse SVD of %s matrix" %
str(docs.shape))
ut, s, vt = sparsesvd.sparsesvd(
docs, self.k + 30
) # ask for a few extra factors, because for some reason SVDLIBC sometimes returns fewer factors than requested
u = ut.T
del ut
del vt
k = clipSpectrum(s, self.k)
self.u = u[:, :k].copy('F')
self.s = s[:k]
else:
self.u = other.u.copy('F')
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update has %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" %
(str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
if other.s is None:
other.u = other.u.todense()
other.s = 1.0 # broadcasting will promote this to eye(n2) where needed
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with gorgqr.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in numpy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(
self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm, = get_blas_funcs(('gemm', ), (self.u, ))
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a=True)
gemm(-1.0, self.u, c, beta=1.0, c=other.u, overwrite_c=True)
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(other.u.shape))
geqrf, = get_lapack_funcs(('geqrf', ), (other.u, ))
qr, tau, work, info = geqrf(
other.u, lwork=-1,
overwrite_a=True) # sometimes segfaults with overwrite_a=True...?
qr, tau, work, info = geqrf(
other.u, lwork=work[0],
overwrite_a=True) # sometimes segfaults with overwrite_a=True...?
del other.u
assert info >= 0
r = triu(qr[:n2, :n2])
if m < n2: # rare case, #features < #topics
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr', ), (qr, ))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
# find rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), c * other.s],
[
matutils.pad(
numpy.matrix([]).reshape(0, 0), min(m, n2),
n1), r * other.s
]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
u_k, s_k, _ = numpy.linalg.svd(
k, full_matrices=False
) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
k = clipSpectrum(s_k, self.k)
u_k, s_k = u_k[:, :k], s_k[:k]
# update & rotate current basis U
logger.debug("updating orthonormal basis U")
self.u = gemm(
1.0, self.u, u_k[:n1]
) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u_k[n1:], beta=1.0, c=self.u,
overwrite_c=True) # u = [u,u']*u_k
self.s = s_k
def merge(self, other, decay=1.0):
"""
Merge this Projection with another.
Content of `other` is destroyed in the process, so pass this function a
copy if you need it further.
This is the optimized merge described in algorithm 5.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
self.u = other.u.copy()
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError(
"vector space mismatch: update has %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" %
(str(self.u.shape), str(other.u.shape)))
# diff = numpy.dot(self.u.T, self.u) - numpy.eye(self.u.shape[1])
# logger.info('orth error after=%f' % numpy.sum(diff * diff))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with gorgqr.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in numpy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(
self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm, = get_blas_funcs(('gemm', ), (self.u, ))
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a=True)
gemm(-1.0, self.u, c, beta=1.0, c=other.u, overwrite_c=True)
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(other.u.shape))
geqrf, = get_lapack_funcs(('geqrf', ), (other.u, ))
qr, tau, work, info = geqrf(
other.u, lwork=-1,
overwrite_a=True) # sometimes segfaults with overwrite_a=True...
qr, tau, work, info = geqrf(
other.u, lwork=work[0],
overwrite_a=True) # sometimes segfaults with overwrite_a=True...
del other.u
assert info >= 0
r = triu(qr[:n2, :n2])
if m < n2: # rare case...
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr', ), (qr, ))
q, work, info = gorgqr(qr, tau, lwork=-1, overwrite_a=True)
q, work, info = gorgqr(qr, tau, lwork=work[0], overwrite_a=True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
# find rotation that diagonalizes r
k = numpy.bmat([[
numpy.diag(decay * self.s), c * other.s
], [matutils.pad(numpy.matrix([]).reshape(0, 0), n2, n1),
r * other.s]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
u_k, s_k, _ = numpy.linalg.svd(
k, full_matrices=False
) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
k = clipSpectrum(s_k, self.k)
u_k, s_k = u_k[:, :k], s_k[:k]
# update & rotate current basis U
logger.debug("updating orthonormal basis U")
self.u = gemm(
1.0, self.u, u_k[:n1]
) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u_k[n1:], beta=1.0, c=self.u,
overwrite_c=True) # u = [u,u']*u_k
self.s = s_k
def merge(self, other, decay = 1.0):
"""
Merge this Projection with another.
Content of `other` is destroyed in the process, so pass this function a
copy if you need it further.
This is the optimized merge described in algorithm 5.
"""
if other.u is None:
# the other projection is empty => do nothing
return
if self.u is None:
# we are empty => result of merge is the other projection, whatever it is
if other.s is None:
# other.u contains a direct document chunk, not svd => perform svd
docs = other.u
assert scipy.sparse.issparse(docs)
if self.m * self.k < 10000:
# SVDLIBC gives spurious results for small matrices.. run full
# LAPACK on them instead
logger.info("computing dense SVD of %s matrix" % str(docs.shape))
u, s, vt = numpy.linalg.svd(docs.todense(), full_matrices = False)
else:
try:
import sparsesvd
except ImportError:
raise ImportError("for LSA, the `sparsesvd` module is needed but not found; run `easy_install sparsesvd`")
logger.info("computing sparse SVD of %s matrix" % str(docs.shape))
ut, s, vt = sparsesvd.sparsesvd(docs, self.k + 30) # ask for a few extra factors, because for some reason SVDLIBC sometimes returns fewer factors than requested
u = ut.T
del ut
del vt
k = clipSpectrum(s, self.k)
self.u = u[:, :k].copy('F')
self.s = s[:k]
else:
self.u = other.u.copy('F')
self.s = other.s.copy()
return
if self.m != other.m:
raise ValueError("vector space mismatch: update has %s features, expected %s" %
(other.m, self.m))
logger.info("merging projections: %s + %s" % (str(self.u.shape), str(other.u.shape)))
m, n1, n2 = self.u.shape[0], self.u.shape[1], other.u.shape[1]
if other.s is None:
other.u = other.u.todense()
other.s = 1.0 # broadcasting will promote this to eye(n2) where needed
# TODO Maybe keep the bases as elementary reflectors, without
# forming explicit matrices with gorgqr.
# The only operation we ever need is basis^T*basis ond basis*component.
# But how to do that in numpy? And is it fast(er)?
# find component of u2 orthogonal to u1
# IMPORTANT: keep matrices in suitable order for matrix products; failing to do so gives 8x lower performance :(
self.u = numpy.asfortranarray(self.u) # does nothing if input already fortran-order array
other.u = numpy.asfortranarray(other.u)
gemm, = get_blas_funcs(('gemm',), (self.u,))
logger.debug("constructing orthogonal component")
c = gemm(1.0, self.u, other.u, trans_a = True)
gemm(-1.0, self.u, c, beta = 1.0, c = other.u, overwrite_c = True)
# perform q, r = QR(component); code hacked out of scipy.linalg.qr
logger.debug("computing QR of %s dense matrix" % str(other.u.shape))
geqrf, = get_lapack_funcs(('geqrf',), (other.u,))
qr, tau, work, info = geqrf(other.u, lwork = -1, overwrite_a = True) # sometimes segfaults with overwrite_a=True...?
qr, tau, work, info = geqrf(other.u, lwork = work[0], overwrite_a = True) # sometimes segfaults with overwrite_a=True...?
del other.u
assert info >= 0
r = triu(qr[:n2, :n2])
if m < n2: # rare case, #features < #topics
qr = qr[:, :m] # retains fortran order
gorgqr, = get_lapack_funcs(('orgqr',), (qr,))
q, work, info = gorgqr(qr, tau, lwork = -1, overwrite_a = True)
q, work, info = gorgqr(qr, tau, lwork = work[0], overwrite_a = True)
assert info >= 0, "qr failed"
assert q.flags.f_contiguous
# find rotation that diagonalizes r
k = numpy.bmat([[numpy.diag(decay * self.s), c * other.s], [matutils.pad(numpy.matrix([]).reshape(0, 0), min(m, n2), n1), r * other.s]])
logger.debug("computing SVD of %s dense matrix" % str(k.shape))
try:
# in numpy < 1.1.0, running SVD sometimes results in "LinAlgError: SVD did not converge'.
# for these early versions of numpy, catch the error and try to compute
# SVD again, but over k*k^T.
# see http://www.mail-archive.com/[email protected]/msg07224.html and
# bug ticket http://projects.scipy.org/numpy/ticket/706
u_k, s_k, _ = numpy.linalg.svd(k, full_matrices = False) # TODO *ugly overkill*!! only need first self.k SVD factors... but there is no LAPACK wrapper for partial svd/eigendecomp in numpy :(
except numpy.linalg.LinAlgError:
logging.error("SVD(A) failed; trying SVD(A * A^T)")
u_k, s_k, _ = numpy.linalg.svd(numpy.dot(k, k.T), full_matrices = False) # if this fails too, give up
s_k = numpy.sqrt(s_k)
k = clipSpectrum(s_k, self.k)
u_k, s_k = u_k[:, :k], s_k[:k]
# update & rotate current basis U
logger.debug("updating orthonormal basis U")
self.u = gemm(1.0, self.u, u_k[:n1]) # TODO temporarily creates an extra (m,k) dense array in memory. find a way to avoid this!
gemm(1.0, q, u_k[n1:], beta = 1.0, c = self.u, overwrite_c = True) # u = [u,u']*u_k
self.s = s_k
