zhesv (l)  Linux Manuals
zhesv: computes the solution to a complex system of linear equations A * X = B,
NAME
ZHESV  computes 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 equationsA
The diagonal pivoting method is used to factor A as
A
A
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

= aqUaq: Upper triangle of A is stored;
= aqLaq: 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 = aqUaq, the leading NbyN 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 = aqLaq, 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 = aqUaq 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 = aqLaq 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 NbyNRHS solution matrix X.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,N).
 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,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 >= max(1,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.