# 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

Univ. of Colorado Denver

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