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clanhb-f(3)

clanhb.f –

Synopsis

Functions/Subroutines

REAL function clanhb (NORM, UPLO, N, K, AB, LDAB, WORK)
CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Function/Subroutine Documentation

REAL function clanhb (characterNORM, characterUPLO, integerN, integerK, complex, dimension( ldab, * )AB, integerLDAB, real, dimension( * )WORK)

CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.

Purpose:

 CLANHB 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 hermitian band matrix A, with k super-diagonals.

Returns:

CLANHB

 CLANHB = ( 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 CLANHB as described
 above.

UPLO

 UPLO is CHARACTER*1
 Specifies whether the upper or lower triangular part of the
 band matrix A is supplied.
 = 'U': Upper triangular
 = 'L': Lower triangular

N

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

K

 K is INTEGER
 The number of super-diagonals or sub-diagonals of the
 band matrix A. K >= 0.

AB

 AB is COMPLEX array, dimension (LDAB,N)
 The upper or lower triangle of the hermitian band matrix A,
 stored in the first K+1 rows of AB. The j-th column of A is
 stored in the j-th column of the array AB as follows:
 if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
 if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
 Note that the imaginary parts of the diagonal elements need
 not be set and are assumed to be zero.

LDAB

 LDAB is INTEGER
 The leading dimension of the array AB. LDAB >= K+1.

WORK

 WORK is REAL array, dimension (MAX(1,LWORK)),
 where LWORK >= N when NORM = 'I' or '1' or 'O'; 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 132 of file clanhb.f.

Author

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