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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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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
Download DSPOSV + dependencies [TGZ] [ZIP] [TXT]
!> !> 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. !>
[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. !> |
Definition at line 195 of file dsposv.f.