dsgesv.f(3)							      LAPACK							       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 (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
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dsgesv.f(3)