316 lines
11 KiB
Python
316 lines
11 KiB
Python
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"""
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Python wrapper for PROPACK
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--------------------------
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PROPACK is a collection of Fortran routines for iterative computation
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of partial SVDs of large matrices or linear operators.
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Based on BSD licensed pypropack project:
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http://github.com/jakevdp/pypropack
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Author: Jake Vanderplas <vanderplas@astro.washington.edu>
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PROPACK source is BSD licensed, and available at
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http://soi.stanford.edu/~rmunk/PROPACK/
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"""
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__all__ = ['_svdp']
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import numpy as np
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from scipy._lib._util import check_random_state
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from scipy.sparse.linalg import aslinearoperator
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from scipy.linalg import LinAlgError
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from ._propack import _spropack # type: ignore[attr-defined]
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from ._propack import _dpropack # type: ignore[attr-defined]
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from ._propack import _cpropack # type: ignore[attr-defined]
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from ._propack import _zpropack # type: ignore[attr-defined]
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_lansvd_dict = {
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'f': _spropack.slansvd,
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'd': _dpropack.dlansvd,
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'F': _cpropack.clansvd,
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'D': _zpropack.zlansvd,
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}
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_lansvd_irl_dict = {
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'f': _spropack.slansvd_irl,
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'd': _dpropack.dlansvd_irl,
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'F': _cpropack.clansvd_irl,
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'D': _zpropack.zlansvd_irl,
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}
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_which_converter = {
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'LM': 'L',
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'SM': 'S',
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}
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class _AProd:
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"""
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Wrapper class for linear operator
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The call signature of the __call__ method matches the callback of
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the PROPACK routines.
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"""
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def __init__(self, A):
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try:
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self.A = aslinearoperator(A)
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except TypeError:
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self.A = aslinearoperator(np.asarray(A))
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def __call__(self, transa, m, n, x, y, sparm, iparm):
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if transa == 'n':
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y[:] = self.A.matvec(x)
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else:
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y[:] = self.A.rmatvec(x)
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@property
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def shape(self):
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return self.A.shape
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@property
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def dtype(self):
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try:
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return self.A.dtype
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except AttributeError:
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return self.A.matvec(np.zeros(self.A.shape[1])).dtype
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def _svdp(A, k, which='LM', irl_mode=True, kmax=None,
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compute_u=True, compute_v=True, v0=None, full_output=False, tol=0,
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delta=None, eta=None, anorm=0, cgs=False, elr=True,
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min_relgap=0.002, shifts=None, maxiter=None, random_state=None):
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"""
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Compute the singular value decomposition of a linear operator using PROPACK
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Parameters
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----------
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A : array_like, sparse matrix, or LinearOperator
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Operator for which SVD will be computed. If `A` is a LinearOperator
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object, it must define both ``matvec`` and ``rmatvec`` methods.
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k : int
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Number of singular values/vectors to compute
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which : {"LM", "SM"}
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Which singular triplets to compute:
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- 'LM': compute triplets corresponding to the `k` largest singular
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values
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- 'SM': compute triplets corresponding to the `k` smallest singular
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values
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`which='SM'` requires `irl_mode=True`. Computes largest singular
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values by default.
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irl_mode : bool, optional
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If `True`, then compute SVD using IRL (implicitly restarted Lanczos)
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mode. Default is `True`.
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kmax : int, optional
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Maximal number of iterations / maximal dimension of the Krylov
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subspace. Default is ``10 * k``.
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compute_u : bool, optional
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If `True` (default) then compute left singular vectors, `u`.
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compute_v : bool, optional
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If `True` (default) then compute right singular vectors, `v`.
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tol : float, optional
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The desired relative accuracy for computed singular values.
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If not specified, it will be set based on machine precision.
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v0 : array_like, optional
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Starting vector for iterations: must be of length ``A.shape[0]``.
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If not specified, PROPACK will generate a starting vector.
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full_output : bool, optional
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If `True`, then return sigma_bound. Default is `False`.
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delta : float, optional
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Level of orthogonality to maintain between Lanczos vectors.
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Default is set based on machine precision.
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eta : float, optional
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Orthogonality cutoff. During reorthogonalization, vectors with
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component larger than `eta` along the Lanczos vector will be purged.
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Default is set based on machine precision.
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anorm : float, optional
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Estimate of ``||A||``. Default is `0`.
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cgs : bool, optional
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If `True`, reorthogonalization is done using classical Gram-Schmidt.
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If `False` (default), it is done using modified Gram-Schmidt.
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elr : bool, optional
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If `True` (default), then extended local orthogonality is enforced
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when obtaining singular vectors.
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min_relgap : float, optional
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The smallest relative gap allowed between any shift in IRL mode.
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Default is `0.001`. Accessed only if ``irl_mode=True``.
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shifts : int, optional
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Number of shifts per restart in IRL mode. Default is determined
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to satisfy ``k <= min(kmax-shifts, m, n)``. Must be
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>= 0, but choosing 0 might lead to performance degradation.
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Accessed only if ``irl_mode=True``.
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maxiter : int, optional
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Maximum number of restarts in IRL mode. Default is `1000`.
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Accessed only if ``irl_mode=True``.
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random_state : {None, int, `numpy.random.Generator`,
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`numpy.random.RandomState`}, optional
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Pseudorandom number generator state used to generate resamples.
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If `random_state` is ``None`` (or `np.random`), the
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`numpy.random.RandomState` singleton is used.
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If `random_state` is an int, a new ``RandomState`` instance is used,
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seeded with `random_state`.
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If `random_state` is already a ``Generator`` or ``RandomState``
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instance then that instance is used.
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Returns
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-------
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u : ndarray
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The `k` largest (``which="LM"``) or smallest (``which="SM"``) left
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singular vectors, ``shape == (A.shape[0], 3)``, returned only if
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``compute_u=True``.
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sigma : ndarray
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The top `k` singular values, ``shape == (k,)``
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vt : ndarray
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The `k` largest (``which="LM"``) or smallest (``which="SM"``) right
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singular vectors, ``shape == (3, A.shape[1])``, returned only if
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``compute_v=True``.
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sigma_bound : ndarray
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the error bounds on the singular values sigma, returned only if
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``full_output=True``.
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"""
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random_state = check_random_state(random_state)
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which = which.upper()
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if which not in {'LM', 'SM'}:
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raise ValueError("`which` must be either 'LM' or 'SM'")
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if not irl_mode and which == 'SM':
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raise ValueError("`which`='SM' requires irl_mode=True")
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aprod = _AProd(A)
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typ = aprod.dtype.char
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try:
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lansvd_irl = _lansvd_irl_dict[typ]
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lansvd = _lansvd_dict[typ]
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except KeyError:
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# work with non-supported types using native system precision
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if np.iscomplexobj(np.empty(0, dtype=typ)):
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typ = np.dtype(complex).char
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else:
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typ = np.dtype(float).char
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lansvd_irl = _lansvd_irl_dict[typ]
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lansvd = _lansvd_dict[typ]
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m, n = aprod.shape
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if (k < 1) or (k > min(m, n)):
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raise ValueError("k must be positive and not greater than m or n")
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if kmax is None:
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kmax = 10*k
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if maxiter is None:
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maxiter = 1000
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# guard against unnecessarily large kmax
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kmax = min(m + 1, n + 1, kmax)
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if kmax < k:
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raise ValueError(
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"kmax must be greater than or equal to k, "
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f"but kmax ({kmax}) < k ({k})")
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# convert python args to fortran args
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jobu = 'y' if compute_u else 'n'
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jobv = 'y' if compute_v else 'n'
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# these will be the output arrays
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u = np.zeros((m, kmax + 1), order='F', dtype=typ)
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v = np.zeros((n, kmax), order='F', dtype=typ)
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# Specify the starting vector. if v0 is all zero, PROPACK will generate
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# a random starting vector: the random seed cannot be controlled in that
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# case, so we'll instead use numpy to generate a random vector
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if v0 is None:
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u[:, 0] = random_state.uniform(size=m)
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if np.iscomplexobj(np.empty(0, dtype=typ)): # complex type
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u[:, 0] += 1j * random_state.uniform(size=m)
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else:
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try:
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u[:, 0] = v0
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except ValueError:
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raise ValueError(f"v0 must be of length {m}")
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# process options for the fit
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if delta is None:
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delta = np.sqrt(np.finfo(typ).eps)
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if eta is None:
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eta = np.finfo(typ).eps ** 0.75
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if irl_mode:
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doption = np.array((delta, eta, anorm, min_relgap), dtype=typ.lower())
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# validate or find default shifts
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if shifts is None:
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shifts = kmax - k
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if k > min(kmax - shifts, m, n):
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raise ValueError('shifts must satisfy '
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'k <= min(kmax-shifts, m, n)!')
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elif shifts < 0:
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raise ValueError('shifts must be >= 0!')
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else:
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doption = np.array((delta, eta, anorm), dtype=typ.lower())
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ioption = np.array((int(bool(cgs)), int(bool(elr))), dtype='i')
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# If computing `u` or `v` (left and right singular vectors,
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# respectively), `blocksize` controls how large a fraction of the
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# work is done via fast BLAS level 3 operations. A larger blocksize
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# may lead to faster computation at the expense of greater memory
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# consumption. `blocksize` must be ``>= 1``. Choosing blocksize
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# of 16, but docs don't specify; it's almost surely a
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# power of 2.
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blocksize = 16
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# Determine lwork & liwork:
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# the required lengths are specified in the PROPACK documentation
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if compute_u or compute_v:
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lwork = m + n + 9*kmax + 5*kmax*kmax + 4 + max(
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3*kmax*kmax + 4*kmax + 4,
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blocksize*max(m, n))
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liwork = 8*kmax
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else:
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lwork = m + n + 9*kmax + 2*kmax*kmax + 4 + max(m + n, 4*kmax + 4)
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liwork = 2*kmax + 1
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work = np.empty(lwork, dtype=typ.lower())
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iwork = np.empty(liwork, dtype=np.int32)
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# dummy arguments: these are passed to aprod, and not used in this wrapper
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dparm = np.empty(1, dtype=typ.lower())
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iparm = np.empty(1, dtype=np.int32)
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if typ.isupper():
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# PROPACK documentation is unclear on the required length of zwork.
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# Use the same length Julia's wrapper uses
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# see https://github.com/JuliaSmoothOptimizers/PROPACK.jl/
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zwork = np.empty(m + n + 32*m, dtype=typ)
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works = work, zwork, iwork
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else:
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works = work, iwork
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if irl_mode:
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u, sigma, bnd, v, info = lansvd_irl(_which_converter[which], jobu,
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jobv, m, n, shifts, k, maxiter,
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aprod, u, v, tol, *works, doption,
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ioption, dparm, iparm)
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else:
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u, sigma, bnd, v, info = lansvd(jobu, jobv, m, n, k, aprod, u, v, tol,
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*works, doption, ioption, dparm, iparm)
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if info > 0:
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raise LinAlgError(
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f"An invariant subspace of dimension {info} was found.")
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elif info < 0:
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raise LinAlgError(
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f"k={k} singular triplets did not converge within "
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f"kmax={kmax} iterations")
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# info == 0: The K largest (or smallest) singular triplets were computed
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# successfully!
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return u[:, :k], sigma, v[:, :k].conj().T, bnd
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