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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A

```NAME
LAPACK-3  -  solves a system of linear equations A*X = B with a complex
Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
computed by ZHETRF

SYNOPSIS
SUBROUTINE ZHETRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, LDB, N, NRHS

INTEGER        IPIV( * )

COMPLEX*16     A( LDA, * ), B( LDB, * )

PURPOSE
ZHETRS  solves  a  system  of  linear  equations A*X = B with a complex
Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
computed by ZHETRF.

ARGUMENTS
UPLO    (input) CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= 'U':  Upper triangular, form is A = U*D*U**H;
= 'L':  Lower triangular, form is A = L*D*L**H.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

A       (input) COMPLEX*16 array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.

B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
```