scipy.linalg.solveh_banded

scipy.linalg.solveh_banded(ab, b, overwrite_ab=False, overwrite_b=False, lower=False)

Solve equation a x = b. a is Hermitian positive-definite banded 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) ab[ i - j, j] == a[i,j] (if lower 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
a00 a11 a22 a33 a44 a55

lower form:
a00 a11 a22 a33 a44 a55
a10 a21 a32 a43 a54 *
a20 a31 a42 a53 *   *

Cells marked with * are not used.

Parameters :

ab : array, shape (u + 1, M)

Banded matrix

b : array, shape (M,) or (M, K)

Right-hand side

overwrite_ab : boolean

Discard data in ab (may enhance performance)

overwrite_b : boolean

Discard data in b (may enhance performance)

lower : boolean

Is the matrix in the lower form. (Default is upper form)

Returns :

c : array, shape (u+1, M)

Cholesky factorization of a, in the same banded format as ab

x : array, shape (M,) or (M, K)

The solution to the system a x = b

Notes

The inclusion of c in the return value is deprecated. In SciPy version 0.9, the return value will be the solution x only.