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dgesv examples
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Man Page Details
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NAME
       DGESV - 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, * )

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 fac-
               tors L and U from the factorization A = P*L*U; the unit  diago-
               nal 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.

