# zcgesv.f man page

zcgesv.f —

## Synopsis

### Functions/Subroutines

subroutinezcgesv(N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)ZCGESV computes the solution to system of linear equations A * X = B for GE matrices(mixed precision with iterative refinement)

## Function/Subroutine Documentation

### subroutine zcgesv (integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, 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)

**ZCGESV computes the solution to system of linear equations A * X = B for GE matrices** (mixed precision with iterative refinement)

**Purpose:**

```
ZCGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
ZCGESV 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:**

*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 N-by-N coefficient matrix A.
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 factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
```

*LDA*

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

*IPIV*

```
IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO.EQ.0 and ITER.GE.0) or the double precision
factorization (if INFO.EQ.0 and ITER.LT.0).
```

*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 CGETRF
-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, U(i,i) computed in COMPLEX*16 is exactly
zero. The factorization has been completed, but the
factor U is exactly singular, so the solution
could not be computed.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 201 of file zcgesv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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