zsysv(3)

NAME

ZSYSV - compute the solution to a complex system of linear

equations A * X = B,

SYNOPSIS

SUBROUTINE  ZSYSV(  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

ZSYSV computes the solution to a complex system of linear

equations A * X = B, where A is an N-by-N symmetric matrix and X

and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as

A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',

where U (or L) is a product of permutation and unit upper

(lower) triangular matrices, and D is symmetric and block diago

nal 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 symmetric 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 triangu

lar 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**T or A = L*D*L**T as computed by ZSYTRF.

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 struc

ture of D, as determined by ZSYTRF. 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 IP

IV(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

(LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The length of WORK. LWORK >= 1, and for best per

formance LWORK >= N*NB, where NB is the optimal blocksize for

ZSYTRF.

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 ille

gal 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

ZSYSV(3)