naginterfaces.library.lapacklin.zhetrs

naginterfaces.library.lapacklin.zhetrs(uplo, a, ipiv, b)

zhetrs solves a complex Hermitian indefinite system of linear equations with multiple right-hand sides,

$$AX=B\text{,}$$

where $A$ has been factorized by zhetrf().

For full information please refer to the NAG Library document for f07ms

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/f07/f07msf.html

Parameters

uplostr, length 1

Specifies how $A$ has been factorized.

$uplo=\text{'U'}$

$A=PUD{U}^H{P}^T$, where $U$ is upper triangular.

$uplo=\text{'L'}$

$A=PLD{L}^H{P}^T$, where $L$ is lower triangular.

acomplex, array-like, shape $(n,n)$

Details of the factorization of $A$, as returned by zhetrf().

ipivint, array-like, shape $\left(n\right)$

Details of the interchanges and the block structure of $D$, as returned by zhetrf().

bcomplex, array-like, shape $(n,\text{nrhs})$

The $n\times r$ right-hand side matrix $B$.

Returns

bcomplex, ndarray, shape $(n,\text{nrhs})$

The $n\times r$ solution matrix $X$.

Raises

NagValueError

(errno $-1$)

On entry, error in parameter $uplo$.

Constraint: $uplo=\text{'U'}$ or $\text{'L'}$.

(errno $-2$)

On entry, error in parameter $\text{n}$.

Constraint: $n\ge 0$.

(errno $-3$)

On entry, error in parameter $\text{nrhs}$.

Constraint: $\text{nrhs}\ge 0$.

Notes

zhetrs is used to solve a complex Hermitian indefinite system of linear equations $AX=B$, this function must be preceded by a call to zhetrf() which computes the Bunch–Kaufman factorization of $A$.

If $uplo=\text{'U'}$, $A=PUD{U}^H{P}^T$, where $P$ is a permutation matrix, $U$ is an upper triangular matrix and $D$ is an Hermitian block diagonal matrix with $1\times 1$ and $2\times 2$ blocks; the solution $X$ is computed by solving $PUDY=B$ and then $U^H{P}^{T}X=Y$.

If $uplo=\text{'L'}$, $A=PLD{L}^H{P}^T$, where $L$ is a lower triangular matrix; the solution $X$ is computed by solving $PLDY=B$ and then $L^H{P}^{T}X=Y$.

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore