zcposv (3)  Linux Manuals
NAME
zcposv.f 
SYNOPSIS
Functions/Subroutines
subroutine zcposv (UPLO, N, NRHS, A, LDA, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices
Function/Subroutine Documentation
subroutine zcposv (characterUPLO, integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, complex*16, dimension( n, * )WORK, complex, dimension( * )SWORK, double precision, dimension( * )RWORK, integerITER, integerINFO)
ZCPOSV computes the solution to system of linear equations A * X = B for PO matrices
Purpose:

ZCPOSV computes the solution to a complex system of linear equations A * X = B, where A is an NbyN Hermitian positive definite matrix and X and B are NbyNRHS 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 righthand 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 infinitynorm of the residual o XNRM is the infinitynorm of the solution o ANRM is the infinityoperatornorm 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.
NN is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
AA is COMPLEX*16 array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading NbyN 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 NbyN 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.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**H*U or A = L*L**H.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
BB is COMPLEX*16 array, dimension (LDB,NRHS) The NbyNRHS right hand side matrix B.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
XX is COMPLEX*16 array, dimension (LDX,NRHS) If INFO = 0, the NbyNRHS solution matrix X.
LDXLDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
WORKWORK is COMPLEX*16 array, dimension (N*NRHS) This array is used to hold the residual vectors.
SWORKSWORK is COMPLEX array, dimension (N*(N+NRHS)) This array is used to use the single precision matrix and the righthand sides or solutions in single precision.
RWORKRWORK is DOUBLE PRECISION array, dimension (N)
ITERITER is INTEGER < 0: iterative refinement has failed, COMPLEX*16 factorization has been performed 1 : the routine fell back to full precision for implementation or machinespecific 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 sucessfully used. Returns the number of iterations
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, the leading minor of order i of (COMPLEX*16) 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 209 of file zcposv.f.
Author
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