# zcposv.f man page

zcposv.f —

## Synopsis

### Functions/Subroutines

subroutinezcposv(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 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 sucessfully 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:**

November 2011

Definition at line 209 of file zcposv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zcposv(3) is an alias of zcposv.f(3).