# sla_gercond.f man page

sla_gercond.f —

## Synopsis

### Functions/Subroutines

REAL functionsla_gercond(TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)SLA_GERCONDestimates the Skeel condition number for a general matrix.

## Function/Subroutine Documentation

### REAL function sla_gercond (characterTRANS, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( ldaf, * )AF, integerLDAF, integer, dimension( * )IPIV, integerCMODE, real, dimension( * )C, integerINFO, real, dimension( * )WORK, integer, dimension( * )IWORK)

**SLA_GERCOND** estimates the Skeel condition number for a general matrix.

**Purpose:**

```
SLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.
```

**Parameters:**

*TRANS*

```
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate Transpose = Transpose)
```

*N*

```
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
```

*A*

```
A is REAL array, dimension (LDA,N)
On entry, the N-by-N matrix A.
```

*LDA*

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

*AF*

```
AF is REAL array, dimension (LDAF,N)
The factors L and U from the factorization
A = P*L*U as computed by SGETRF.
```

*LDAF*

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

*IPIV*

```
IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by SGETRF; row i of the matrix was interchanged
with row IPIV(i).
```

*CMODE*

```
CMODE is INTEGER
Determines op2(C) in the formula op(A) * op2(C) as follows:
CMODE = 1 op2(C) = C
CMODE = 0 op2(C) = I
CMODE = -1 op2(C) = inv(C)
```

*C*

```
C is REAL array, dimension (N)
The vector C in the formula op(A) * op2(C).
```

*INFO*

```
INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.
```

*WORK*

```
WORK is REAL array, dimension (3*N).
Workspace.
```

*IWORK*

```
IWORK is INTEGER array, dimension (N).
Workspace.2
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 150 of file sla_gercond.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK