def _randomized_svd(M, k, p, q, random_state):
random_state = check_random_state(random_state)
Q = randomized_range_finder(M, k + p, q, random_state)
# project M to the (k + p) dimensional space using the basis vectors
B = safe_sparse_dot(Q.T, M)
# compute the SVD on the thin matrix: (k + p) wide
Uhat_t, S, Vt = svd_ndarray(B, k)
del B
U = np.dot(Q, Uhat_t.T)
return U, S, Vt.T
def _randomized_svd(M, k, p, q, random_state):
random_state = check_random_state(random_state)
Q = randomized_range_finder(M, k+p, q, random_state)
# project M to the (k + p) dimensional space using the basis vectors
B = safe_sparse_dot(Q.T, M)
# compute the SVD on the thin matrix: (k + p) wide
Uhat_t, S, Vt = svd_ndarray(B, k)
del B
U = np.dot(Q, Uhat_t.T)
return U, S, Vt.T
def svd(matrix, k=50):
"""
Calculate the truncated singular value decomposition
:math:`A = U * Sigma * V^T` using SVDLIBC.
Returns a triple of:
- U as a dense labeled matrix
- S, a dense vector representing the diagonal of Sigma
- V as a dense labeled matrix
This matrix must not contain any empty rows or columns. If it does,
use the .squish() method first.
"""
assert matrix.ndim == 2
if isinstance(matrix, DenseMatrix):
Ut, S, Vt = svd_ndarray(matrix, k)
elif isinstance(matrix, SparseMatrix):
if matrix.nnz == 0:
# don't let svdlib touch a matrix of all zeros. It explodes and
# corrupts its state. Just return a zero result instead.
U = DenseMatrix((matrix.shape[0], k))
S = np.zeros((k,))
V = DenseMatrix((matrix.shape[1], k))
return U, S, V
if matrix.shape[1] >= matrix.shape[0] * 1.2:
# transpose the matrix for speed
V, S, U = matrix.T.svd(k)
return U, S, V
Ut, S, Vt = svd_llmat(matrix.llmatrix, k)
else:
raise TypeError("Don't know how to SVD a %r", type(matrix))
U = DenseMatrix(Ut.T, matrix.row_labels, None)
V = DenseMatrix(Vt.T, matrix.col_labels, None)
return U, S, V
def svd(matrix, k=50):
"""
Calculate the truncated singular value decomposition
:math:`A = U * Sigma * V^T` using SVDLIBC.
Returns a triple of:
- U as a dense labeled matrix
- S, a dense vector representing the diagonal of Sigma
- V as a dense labeled matrix
This matrix must not contain any empty rows or columns. If it does,
use the .squish() method first.
"""
assert matrix.ndim == 2
if isinstance(matrix, DenseMatrix):
Ut, S, Vt = svd_ndarray(matrix, k)
elif isinstance(matrix, SparseMatrix):
if matrix.nnz == 0:
# don't let svdlib touch a matrix of all zeros. It explodes and
# corrupts its state. Just return a zero result instead.
U = DenseMatrix((matrix.shape[0], k))
S = np.zeros((k, ))
V = DenseMatrix((matrix.shape[1], k))
return U, S, V
if matrix.shape[1] >= matrix.shape[0] * 1.2:
# transpose the matrix for speed
V, S, U = matrix.T.svd(k)
return U, S, V
Ut, S, Vt = svd_llmat(matrix.llmatrix, k)
else:
raise TypeError("Don't know how to SVD a %r", type(matrix))
U = DenseMatrix(Ut.T, matrix.row_labels, None)
V = DenseMatrix(Vt.T, matrix.col_labels, None)
return U, S, V