ssysv(3F)

NAME
     SSYSV - compute the solution to a real system of linear equations  A * X
     = B,

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

         CHARACTER     UPLO

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

         INTEGER       IPIV( * )

         REAL          A( LDA, * ), B( LDB, * ), WORK( LWORK )

PURPOSE
     SSYSV computes the solution to a real 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) REAL 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 SSYTRF.

     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 SSYTRF.  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) REAL 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) REAL 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 SSYTRF.

     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.