# zcposv.f man page

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 (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)

**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 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.

**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 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.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.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*B*B is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N,NRHS) This array is used to hold the residual vectors.

*SWORK*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.

*RWORK*RWORK is DOUBLE PRECISION array, dimension (N)

*ITER*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

*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 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:**June 2016

Definition at line 211 of file zcposv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zcposv(3) is an alias of zcposv.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK