def idz_frmi(m):
"""
Initialize data for :func:`idz_frm`.
:param m:
Length of vector to be transformed.
:type m: int
:return:
Greatest power-of-two integer `n` satisfying `n <= m`.
:rtype: int
:return:
Initialization array to be used by :func:`idz_frm`.
:rtype: :class:`numpy.ndarray`
"""
return _id.idz_frmi(m)
def idz_frmi(m):
"""
Initialize area_data for :func:`idz_frm`.
:param m:
Length of vector to be transformed.
:type m: int
:return:
Greatest power-of-two integer `n` satisfying `n <= m`.
:rtype: int
:return:
Initialization array to be used by :func:`idz_frm`.
:rtype: :class:`numpy.ndarray`
"""
return _id.idz_frmi(m)
def idzp_asvd(eps, A):
"""
Compute SVD of a complex matrix to a specified relative precision using
random sampling.
:param eps:
Relative precision.
:type eps: float
:param A:
Matrix.
:type A: :class:`numpy.ndarray`
:return:
Left singular vectors.
:rtype: :class:`numpy.ndarray`
:return:
Right singular vectors.
:rtype: :class:`numpy.ndarray`
:return:
Singular values.
:rtype: :class:`numpy.ndarray`
"""
A = np.asfortranarray(A)
m, n = A.shape
n2, winit = _id.idz_frmi(m)
w = np.empty(
max((min(m, n) + 1)*(3*m + 5*n + 11) + 8*min(m, n)**2,
(2*n + 1)*(n2 + 1)),
dtype=np.complex128, order='F')
k, iU, iV, iS, w, ier = _id.idzp_asvd(eps, A, winit, w)
if ier:
raise _RETCODE_ERROR
U = w[iU-1:iU+m*k-1].reshape((m, k), order='F')
V = w[iV-1:iV+n*k-1].reshape((n, k), order='F')
S = w[iS-1:iS+k-1]
return U, V, S
def idzp_asvd(eps, A):
"""
Compute SVD of a complex matrix to a specified relative precision using
random sampling.
:param eps:
Relative precision.
:type eps: float
:param A:
Matrix.
:type A: :class:`numpy.ndarray`
:return:
Left singular vectors.
:rtype: :class:`numpy.ndarray`
:return:
Right singular vectors.
:rtype: :class:`numpy.ndarray`
:return:
Singular values.
:rtype: :class:`numpy.ndarray`
"""
A = np.asfortranarray(A)
m, n = A.shape
n2, winit = _id.idz_frmi(m)
w = np.empty(
max((min(m, n) + 1)*(3*m + 5*n + 11) + 8*min(m, n)**2,
(2*n + 1)*(n2 + 1)),
dtype=np.complex128, order='F')
k, iU, iV, iS, w, ier = _id.idzp_asvd(eps, A, winit, w)
if ier:
raise _RETCODE_ERROR
U = w[iU-1:iU+m*k-1].reshape((m, k), order='F')
V = w[iV-1:iV+n*k-1].reshape((n, k), order='F')
S = w[iS-1:iS+k-1]
return U, V, S