NAME

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

SYNOPSIS

SUBROUTINE CSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )

CHARACTER UPLO

INTEGER INFO, LDA, LDB, LWORK, N, NRHS

INTEGER IPIV( ∗ )

COMPLEX A( LDA, ∗ ), B( LDB, ∗ ), WORK( LWORK )

#include <sunperf.h>

void csysv(char uplo, int n, int nrhs, complex ∗ca, int lda, int ∗ipivot, complex ∗cb, int ldb, int ∗info);

PURPOSE

CSYSV 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 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 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 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∗∗T or A = L∗D∗L∗∗T as computed by CSYTRF.

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 CSYTRF.  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 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 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 CSYTRF.

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.

SunOS 5.0  —  Last change: 10 Dec 1998