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# sla_gercond.f - Man Page

SRC/sla_gercond.f

## Synopsis

### Functions/Subroutines

real function sla_gercond (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
SLA_GERCOND estimates the Skeel condition number for a general matrix.

## Function/Subroutine Documentation

### real function sla_gercond (character trans, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

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

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

NAG Ltd.

Definition at line 148 of file sla_gercond.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK