naginterfaces.library.lapacklin.zpttrs¶
- naginterfaces.library.lapacklin.zpttrs(uplo, d, e, b)[source]¶
zpttrs
computes the solution to a complex system of linear equations , where is an Hermitian positive definite tridiagonal matrix and and are matrices, using the factorization returned byzpttrf()
.For full information please refer to the NAG Library document for f07js
https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/f07/f07jsf.html
- Parameters
- uplostr, length 1
Specifies the form of the factorization as follows:
.
.
- dfloat, array-like, shape
Must contain the diagonal elements of the diagonal matrix from the or factorization of .
- ecomplex, array-like, shape
If , must contain the superdiagonal elements of the unit upper bidiagonal matrix from the factorization of .
If , must contain the subdiagonal elements of the unit lower bidiagonal matrix from the factorization of .
- bcomplex, array-like, shape
The matrix of right-hand sides .
- Returns
- bcomplex, ndarray, shape
The solution matrix .
- Raises
- NagValueError
- (errno )
On entry, error in parameter .
Constraint: or .
- (errno )
On entry, error in parameter .
Constraint: .
- (errno )
On entry, error in parameter .
Constraint: .
- Notes
zpttrs
should be preceded by a call tozpttrf()
, which computes a modified Cholesky factorization of the matrix aswhere is a unit lower bidiagonal matrix and is a diagonal matrix, with positive diagonal elements.
zpttrs
then utilizes the factorization to solve the required equations. Note that the factorization may also be regarded as having the form , where is a unit upper bidiagonal matrix.
- References
Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug