SRC/dsposv.f(3) Library Functions Manual SRC/dsposv.f(3) NAME SRC/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 (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 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 = 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. 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 successfully 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 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. Definition at line 197 of file dsposv.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 SRC/dsposv.f(3)