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dsposv.f(3) LAPACK dsposv.f(3)

NAME

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

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