.TH "SRC/zcposv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zcposv.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzcposv\fP (uplo, n, nrhs, a, lda, b, ldb, x, ldx, work, swork, rwork, iter, info)" .br .RI "\fB ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zcposv (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( n, * ) work, complex, dimension( * ) swork, double precision, dimension( * ) rwork, integer iter, integer info)" .PP \fB ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZCPOSV computes the solution to a complex system of linear equations !> A * X = B, !> where A is an N-by-N Hermitian positive definite matrix and X and B !> are N-by-NRHS matrices\&. !> !> ZCPOSV first attempts to factorize the matrix in COMPLEX and use this !> factorization within an iterative refinement procedure to produce a !> solution with COMPLEX*16 normwise backward error quality (see below)\&. !> If the approach fails the method switches to a COMPLEX*16 !> factorization and solve\&. !> !> The iterative refinement is not going to be a winning strategy if !> the ratio COMPLEX performance over COMPLEX*16 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of linear equations, i\&.e\&., the order of the !> matrix A\&. N >= 0\&. !> .fi .PP .br \fINRHS\fP .PP .nf !> NRHS is INTEGER !> The number of right hand sides, i\&.e\&., the number of columns !> of the matrix B\&. NRHS >= 0\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, !> dimension (LDA,N) !> On entry, the Hermitian 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\&. !> !> Note that the imaginary parts of the diagonal !> elements need not be set and are assumed to be zero\&. !> !> 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**H*U or A = L*L**H\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIB\fP .PP .nf !> B is COMPLEX*16 array, dimension (LDB,NRHS) !> The N-by-NRHS right hand side matrix B\&. !> .fi .PP .br \fILDB\fP .PP .nf !> LDB is INTEGER !> The leading dimension of the array B\&. LDB >= max(1,N)\&. !> .fi .PP .br \fIX\fP .PP .nf !> X is COMPLEX*16 array, dimension (LDX,NRHS) !> If INFO = 0, the N-by-NRHS solution matrix X\&. !> .fi .PP .br \fILDX\fP .PP .nf !> LDX is INTEGER !> The leading dimension of the array X\&. LDX >= max(1,N)\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (N,NRHS) !> This array is used to hold the residual vectors\&. !> .fi .PP .br \fISWORK\fP .PP .nf !> SWORK is COMPLEX 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\&. !> .fi .PP .br \fIRWORK\fP .PP .nf !> RWORK is DOUBLE PRECISION array, dimension (N) !> .fi .PP .br \fIITER\fP .PP .nf !> ITER is INTEGER !> < 0: iterative refinement has failed, COMPLEX*16 !> 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 CPOTRF !> -31: stop the iterative refinement after the 30th !> iterations !> > 0: iterative refinement has been successfully used\&. !> Returns the number of iterations !> .fi .PP .br \fIINFO\fP .PP .nf !> 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 (COMPLEX*16) A is not positive, so the factorization !> could not be completed, and the solution has not been !> computed\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .PP Definition at line \fB207\fP of file \fBzcposv\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.