dsgesv.f(3)

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 (integer N, integer NRHS, double precision, dimension( lda, * ) A, integer LDA, integer, dimension( * ) IPIV, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( n, * ) WORK, real, dimension( * ) SWORK, integer ITER, integer INFO)

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 successfully 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:
    June 2016

Definition at line 197 of file dsgesv.f.

Author

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