
ZHESV(l) ) ZHESV(l)
NAME
ZHESV  compute the solution to a complex system of linear equations A * X = B,
SYNOPSIS
SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
INTEGER IPIV( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
ZHESV computes the solution to a complex system of linear equations A * X = B, where A is
an NbyN Hermitian matrix and X and B are NbyNRHS 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 1by1 and 2by2 diagonal blocks. The factored
form of A is then used to solve the system of equations A * X = B.
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The number of linear equations, i.e., 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/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading NbyN upper trian
gular 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
NbyN 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 ZHETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as determined by ZHETRF.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k)
is a 1by1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0, then rows
and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2
diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns
k+1 and IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2by2 diagonal block.
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the NbyNRHS right hand side matrix B. On exit, if INFO = 0, the Nby
NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of WORK. LWORK >= 1, and for best performance LWORK >= N*NB, where NB
is the optimal blocksize for ZHETRF.
If LWORK = 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 LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith 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.
LAPACK version 3.0 15 June 2000 ZHESV(l) 
