# sla_gbrcond.f - Man Page

SRC/sla_gbrcond.f

## Synopsis

### Functions/Subroutines

real function **sla_gbrcond** (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)**SLA_GBRCOND** estimates the Skeel condition number for a general banded matrix.

## Function/Subroutine Documentation

### real function sla_gbrcond (character trans, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork)

**SLA_GBRCOND** estimates the Skeel condition number for a general banded matrix.

**Purpose:**

SLA_GBRCOND 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.

*KL*KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

*KU*KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

*AB*AB is REAL array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)

*LDAB*LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.

*AFB*AFB is REAL array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.

*LDAFB*LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

*IPIV*IPIV is INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by SGBTRF; 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 (5*N). Workspace.

*IWORK*IWORK is INTEGER array, dimension (N). Workspace.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **166** of file **sla_gbrcond.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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