zsysv(3S)

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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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 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 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 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 structure 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 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 (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 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 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.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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