# ?la_gbrcond_c

Computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

## Syntax

call cla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork )

call zla_gbrcond_c( trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork )

• mkl.fi

## Description

The function computes the infinity norm condition number of

op(A) * inv(diag(c))

where the c is a REAL vector for cla_gbrcond_c and a DOUBLE PRECISION vector for zla_gbrcond_c.

## Input Parameters

trans

CHARACTER*1. Must be 'N' or 'T' or 'C'.

Specifies the form of the system of equations:

If trans = 'N', the system has the form A*X = B (No transpose)

If trans = 'T', the system has the form AT*X = B (Transpose)

If trans = 'C', the system has the form AH*X = B (Conjugate Transpose = Transpose)

n

INTEGER. The number of linear equations, that is, the order of the matrix A; n 0.

kl

INTEGER. The number of subdiagonals within the band of A; kl 0.

ku

INTEGER. The number of superdiagonals within the band of A; ku 0.

ab, afb, work

COMPLEX for cla_gbrcond_c

DOUBLE COMPLEX for zla_gbrcond_c

Arrays:

ab(ldab,*) contains the original band matrix A stored in rows from 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)

afb(ldafb,*) contains details of the LU factorization of the band matrix A, as returned by ?gbtrf. 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.

work is a workspace array of DIMENSION (5*n).

The second dimension of ab and afb must be at least max(1, n).

ldab

INTEGER. The leading dimension of the array ab. ldabkl+ku+1.

ldafb

INTEGER. The leading dimension of afb. ldafb2*kl+ku+1.

ipiv

INTEGER.

Array with DIMENSIONn. The pivot indices from the factorization A = P*L*U as computed by ?gbtrf. Row i of the matrix was interchanged with row ipiv(i).

c, rwork

REAL for cla_gbrcond_c

DOUBLE PRECISION for zla_gbrcond_c

Array c with DIMENSIONn. The vector c in the formula

op(A) * inv(diag(c)).

Array rwork with DIMENSIONn is a workspace.

capply

LOGICAL. If .TRUE., then the function uses the vector c from the formula

op(A) * inv(diag(c)).

## Output Parameters

info

INTEGER.

If info = 0, the execution is successful.

If i > 0, the i-th parameter is invalid.