dsposv.f man page

dsposv.f —

Synopsis

Functions/Subroutines

subroutine dsposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Function/Subroutine Documentation

subroutine dsposv (characterUPLO, integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( n, * )WORK, real, dimension( * )SWORK, integerITER, integerINFO)

DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

Purpose:

DSPOSV computes the solution to a real system of linear equations
   A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.

DSPOSV 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:

UPLO

UPLO is CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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 symmetric matrix A.  If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced.  If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
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 factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.

LDA

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

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 SPOTRF
     -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, the leading minor of order i of (DOUBLE
      PRECISION) A is not positive definite, so the
      factorization could not be completed, and the solution
      has not been computed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 199 of file dsposv.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK