clanhe-f(3)

clanhe.f –

Synopsis

Functions/Subroutines

REAL function clanhe (NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.

Function/Subroutine Documentation

REAL function clanhe (characterNORM, characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )WORK)

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

Purpose:

 CLANHE returns the value of the one norm, or the Frobenius norm, or
 the infinity norm, or the element of largest absolute value of a
 complex hermitian matrix A.

Returns:

CLANHE

 CLANHE = ( 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 CLANHE as described
 above.

UPLO

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

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

 A is COMPLEX array, dimension (LDA,N)
 The hermitian matrix A. If UPLO = 'U', the leading n by n
 upper triangular part of A contains the upper triangular part
 of the matrix A, and the strictly lower triangular part of A
 is not referenced. If UPLO = 'L', the leading n by n lower
 triangular part of A contains the lower triangular part of
 the matrix A, and the strictly upper triangular part of A is
 not referenced. Note that the imaginary parts of the diagonal
 elements need not be set and are assumed to be zero.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(N,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 125 of file clanhe.f.

Author

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