dsgesv.f man page

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.

Referenced By

dsgesv(3) is an alias of dsgesv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK