ZHESV(3) LAPACK driver routine (version 3.1) ZHESV(3)
NAME
ZHESV - 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 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) tri-
angular 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) 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
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 mul-
tipliers used to obtain the factor U or L from the factoriza-
tion 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 1-by-1 diagonal
block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows
and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 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 2-by-2 diagonal
block.
B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
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) 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 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.
LAPACK driver routine (version 3.N1o)vember 2006 ZHESV(3)