scipy tutorial - Baustatik-Info-Server

See Also:
svd
Returns
Q : array, shape (M, K)
SciPy Reference Guide, Release 0.8.dev
Orthonormal basis for the range of A. K = effective rank of A, as determined by
automatic cutoff
Singular value decomposition of a matrix
cholesky(a, lower=0, overwrite_a=0)
Compute the Cholesky decomposition of a matrix.
Returns the Cholesky decomposition, :lm:‘A = L L^*‘ or :lm:‘A = U^* U‘ of a Hermitian positive-definite
matrix :lm:‘A‘.
Examples
Parameters
a : array, shape (M, M)
Matrix to be decomposed
lower : boolean
Whether to compute the upper or lower triangular Cholesky factorization (Default:
upper-triangular)
overwrite_a : boolean
Whether to overwrite data in a (may improve performance)
Returns
B : array, shape (M, M)
Upper- or lower-triangular Cholesky factor of A
Raises LinAlgError if decomposition fails :
>>> from scipy import array, linalg, dot
>>> a = array([[1,-2j],[2j,5]])
>>> L = linalg.cholesky(a, lower=True)
>>> L
array([[ 1.+0.j, 0.+0.j],
[ 0.+2.j, 1.+0.j]])
>>> dot(L, L.T.conj())
array([[ 1.+0.j, 0.-2.j],
[ 0.+2.j, 5.+0.j]])
cholesky_banded(ab, overwrite_ab=0, lower=0)
Cholesky decompose a banded Hermitian positive-definite matrix
The matrix a is stored in ab either in lower diagonal or upper diagonal ordered form:
ab[u + i - j, j] == a[i,j] (if upper form; i = j)
Example of ab (shape of a is (6,6), u=2):
upper form:
* * a02 a13 a24 a35
* a01 a12 a23 a34 a45
3.7. Linear algebra (scipy.linalg) 237