scipy tutorial - Baustatik-Info-Server

SciPy Reference Guide, Release 0.8.dev
Notes
This is an interface to the LAPACK routines dgeqrf, zgeqrf, dorgqr, and zungqr.
Examples
>>> from scipy import random, linalg, dot
>>> a = random.randn(9, 6)
>>> q, r = linalg.qr(a)
>>> allclose(a, dot(q, r))
True
>>> q.shape, r.shape
((9, 9), (9, 6))
>>> r2 = linalg.qr(a, mode=’r’)
>>> allclose(r, r2)
>>> q3, r3 = linalg.qr(a, econ=True)
>>> q3.shape, r3.shape
((9, 6), (6, 6))
schur(a, output=’real’, lwork=None, overwrite_a=0)
Compute Schur decomposition of a matrix.
The Schur decomposition is
A = Z T Z^H
where Z is unitary and T is either upper-triangular, or for real Schur decomposition (output=’real’), quasi-upper
triangular. In the quasi-triangular form, 2x2 blocks describing complex-valued eigenvalue pairs may extrude
from the diagonal.
See Also:
Parameters
a : array, shape (M, M)
Matrix to decompose
output : {‘real’, ‘complex’}
Construct the real or complex Schur decomposition (for real matrices).
lwork : integer
Work array size. If None or -1, it is automatically computed.
overwrite_a : boolean
Whether to overwrite data in a (may improve performance)
Returns
T : array, shape (M, M)
Schur form of A. It is real-valued for the real Schur decomposition.
Z : array, shape (M, M)
An unitary Schur transformation matrix for A. It is real-valued for the real Schur
decomposition.
rsf2csf
Convert real Schur form to complex Schur form
240 Chapter 3. Reference