dsposv()

subroutine dsposv	(	character	uplo,
		integer	n,
		integer	nrhs,
		double precision, dimension( lda, * )	a,
		integer	lda,
		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 )

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

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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

[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !>
[in,out]	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 = 0 and ITER >= 0, see description below), then A is !> unchanged, if double precision factorization has been used !> (INFO = 0 and ITER < 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. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
[in]	B	!> B is DOUBLE PRECISION array, dimension (LDB,NRHS) !> The N-by-NRHS right hand side matrix B. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	X	!> X is DOUBLE PRECISION array, dimension (LDX,NRHS) !> If INFO = 0, the N-by-NRHS solution matrix X. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension (N,NRHS) !> This array is used to hold the residual vectors. !>
[out]	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. !>
[out]	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 successfully used. !> Returns the number of iterations !>
[out]	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 principal minor of order i !> of (DOUBLE PRECISION) A is not positive, 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.