dgesv(3S)

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

SYNOPSIS
     SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )

         INTEGER       INFO, LDA, LDB, N, NRHS

         INTEGER       IPIV( * )

         DOUBLE        PRECISION A( LDA, * ), B( LDB, * )

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
     DGESV computes the solution to a real system of linear equations A * X =
     B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

     The LU decomposition with partial pivoting and row interchanges is used
     to factor A as
        A = P * L * U,
     where P is a permutation matrix, L is unit lower triangular, and U is
     upper triangular.  The factored form of A is then used to solve the
     system of equations A * X = B.


ARGUMENTS
     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) DOUBLE PRECISION array, dimension (LDA,N)
             On entry, the N-by-N coefficient matrix A.  On exit, the factors
             L and U from the factorization A = P*L*U; the unit diagonal
             elements of L are not stored.
     LDA     (input) INTEGER
             The leading dimension of the array A.  LDA >= max(1,N).

     IPIV    (output) INTEGER array, dimension (N)
             The pivot indices that define the permutation matrix P; row i of
             the matrix was interchanged with row IPIV(i).

     B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
             On entry, the N-by-NRHS matrix of 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).

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value
             > 0:  if INFO = i, U(i,i) is exactly zero.  The factorization has
             been completed, but the factor U is exactly singular, so the
             solution could not be computed.

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

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