Scroll to navigation

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.

Author

Generated automatically by Doxygen for LAPACK from the source code.
Wed Oct 15 2014 Version 3.4.2