NAME

zhesv - compute the solution to a complex system of linear equations A * X = B,

SYNOPSIS

  SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, 
 *      LDWORK, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
  INTEGER N, NRHS, LDA, LDB, LDWORK, INFO
  INTEGER IPIVOT(*)

  SUBROUTINE ZHESV_64( UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, 
 *      LDWORK, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
  INTEGER*8 N, NRHS, LDA, LDB, LDWORK, INFO
  INTEGER*8 IPIVOT(*)

F95 INTERFACE

  SUBROUTINE HESV( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER :: N, NRHS, LDA, LDB, LDWORK, INFO
  INTEGER, DIMENSION(:) :: IPIVOT

  SUBROUTINE HESV_64( UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], 
 *       [WORK], [LDWORK], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER(8) :: N, NRHS, LDA, LDB, LDWORK, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT

C INTERFACE

#include <sunperf.h>

void zhesv(char uplo, int n, int nrhs, doublecomplex *a, int lda, int *ipivot, doublecomplex *b, int ldb, int *info);

void zhesv_64(char uplo, long n, long nrhs, doublecomplex *a, long lda, long *ipivot, doublecomplex *b, long ldb, long *info);

PURPOSE

zhesv computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as

   A = U * D * U**H,  if UPLO = 'U', or

   A = L * D * L**H,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B.

ARGUMENTS

UPLO (input)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The number of linear equations, i.e., the order of the matrix A. N > = 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns of the matrix B. NRHS > = 0.
A (input/output)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF.
LDA (input)
The leading dimension of the array A. LDA > = max(1,N).
IPIVOT (output)
Details of the interchanges and the block structure of D, as determined by CHETRF. If IPIVOT(k) > 0, then rows and columns k and IPIVOT(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) = IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
B (input/output)
On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.
LDB (input)
The leading dimension of the array B. LDB > = max(1,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The length of WORK. LDWORK > = 1, and for best performance LDWORK > = N*NB, where NB is the optimal blocksize for CHETRF.
If LDWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LDWORK is issued by XERBLA.

INFO (output)

 = 0: successful exit

 < 0: if INFO  = -i, the i-th argument had an illegal value

 > 0: if INFO  = i, D(i,i) is exactly zero.  The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be computed.