clangb-f(3)

clangb.f –

Synopsis

Functions/Subroutines

REAL function clangb (NORM, N, KL, KU, AB, LDAB, WORK)
CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Function/Subroutine Documentation

REAL function clangb (characterNORM, integerN, integerKL, integerKU, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)

CLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:

 CLANGB returns the value of the one norm, or the Frobenius norm, or
 the infinity norm, or the element of largest absolute value of an
 n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns:

CLANGB

 CLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
 (
 ( norm1(A), NORM = '1', 'O' or 'o'
 (
 ( normI(A), NORM = 'I' or 'i'
 (
 ( normF(A), NORM = 'F', 'f', 'E' or 'e'
 where norm1 denotes the one norm of a matrix (maximum column sum),
 normI denotes the infinity norm of a matrix (maximum row sum) and
 normF denotes the Frobenius norm of a matrix (square root of sum of
 squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters:

NORM

 NORM is CHARACTER*1
 Specifies the value to be returned in CLANGB as described
 above.

 N is INTEGER
 The order of the matrix A. N >= 0. When N = 0, CLANGB is
 set to zero.

 KL is INTEGER
 The number of sub-diagonals of the matrix A. KL >= 0.

 KU is INTEGER
 The number of super-diagonals of the matrix A. KU >= 0.

 AB is COMPLEX array, dimension (LDAB,N)
 The band matrix A, stored 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.

WORK

 WORK is REAL array, dimension (MAX(1,LWORK)),
 where LWORK >= N when NORM = 'I'; otherwise, WORK is not
 referenced.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 125 of file clangb.f.

Author

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