NAME

       dsgesv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dsgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
            DSGESV computes the solution to system of linear equations A * X = B for GE matrices
           (mixed precision with iterative refinement)

Function/Subroutine Documentation

   subroutine dsgesv (integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA,
       integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, double
       precision, dimension( ldx, * )X, integerLDX, double precision, dimension( n, * )WORK,
       real, dimension( * )SWORK, integerITER, integerINFO)
        DSGESV computes the solution to system of linear equations A * X = B for GE matrices
       (mixed precision with iterative refinement)

       Purpose:

            DSGESV 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.

            DSGESV first attempts to factorize the matrix in SINGLE PRECISION
            and use this factorization within an iterative refinement procedure
            to produce a solution with DOUBLE PRECISION normwise backward error
            quality (see below). If the approach fails the method switches to a
            DOUBLE PRECISION factorization and solve.

            The iterative refinement is not going to be a winning strategy if
            the ratio SINGLE PRECISION performance over DOUBLE PRECISION
            performance is too small. A reasonable strategy should take the
            number of right-hand sides and the size of the matrix into account.
            This might be done with a call to ILAENV in the future. Up to now, we
            always try iterative refinement.

            The iterative refinement process is stopped if
                ITER > ITERMAX
            or for all the RHS we have:
                RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
            where
                o ITER is the number of the current iteration in the iterative
                  refinement process
                o RNRM is the infinity-norm of the residual
                o XNRM is the infinity-norm of the solution
                o ANRM is the infinity-operator-norm of the matrix A
                o EPS is the machine epsilon returned by DLAMCH('Epsilon')
            The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
            respectively.

       Parameters:
           N

                     N is INTEGER
                     The number of linear equations, i.e., the order of the
                     matrix A.  N >= 0.

           NRHS

                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           A

                     A is DOUBLE PRECISION array,
                     dimension (LDA,N)
                     On entry, the N-by-N coefficient matrix A.
                     On exit, if iterative refinement has been successfully used
                     (INFO.EQ.0 and ITER.GE.0, see description below), then A is
                     unchanged, if double precision factorization has been used
                     (INFO.EQ.0 and ITER.LT.0, see description below), then the
                     array A contains the factors L and U from the factorization
                     A = P*L*U; the unit diagonal elements of L are not stored.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     The pivot indices that define the permutation matrix P;
                     row i of the matrix was interchanged with row IPIV(i).
                     Corresponds either to the single precision factorization
                     (if INFO.EQ.0 and ITER.GE.0) or the double precision
                     factorization (if INFO.EQ.0 and ITER.LT.0).

           B

                     B is DOUBLE PRECISION array, dimension (LDB,NRHS)
                     The N-by-NRHS right hand side matrix B.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           X

                     X is DOUBLE PRECISION array, dimension (LDX,NRHS)
                     If INFO = 0, the N-by-NRHS solution matrix X.

           LDX

                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           WORK

                     WORK is DOUBLE PRECISION array, dimension (N,NRHS)
                     This array is used to hold the residual vectors.

           SWORK

                     SWORK is REAL array, dimension (N*(N+NRHS))
                     This array is used to use the single precision matrix and the
                     right-hand sides or solutions in single precision.

           ITER

                     ITER is INTEGER
                     < 0: iterative refinement has failed, double precision
                          factorization has been performed
                          -1 : the routine fell back to full precision for
                               implementation- or machine-specific reasons
                          -2 : narrowing the precision induced an overflow,
                               the routine fell back to full precision
                          -3 : failure of SGETRF
                          -31: stop the iterative refinement after the 30th
                               iterations
                     > 0: iterative refinement has been sucessfully used.
                          Returns the number of iterations

           INFO

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 195 of file dsgesv.f.

Author

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