# clanhb.f(3) [centos man page]

clanhb.f(3) LAPACK clanhb.f(3)NAME

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.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 clanhb.f(3)

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CLANHB(l)) CLANHB(l)NAME

CLANHB - return 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-diagonalsSYNOPSIS

REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB, WORK ) CHARACTER NORM, UPLO INTEGER K, LDAB, N REAL WORK( * ) COMPLEX AB( LDAB, * )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.DESCRIPTION

CLANHB returns the value 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 matrix norm.ARGUMENTS

NORM (input) CHARACTER*1 Specifies the value to be returned in CLANHB as described above. UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHB is set to zero. K (input) INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB (input) 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 (input) INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK (workspace) REAL array, dimension (LWORK), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.LAPACK version 3.015 June 2000 CLANHB(l)