zlanhe.f (3)

Functions/Subroutines

double precision function zlanhe (NORM, UPLO, N, A, LDA, WORK)

ZLANHE 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.

double precision function zlanhe (characterNORM, characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )WORK)

ZLANHE 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:

 ZLANHE  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:

ZLANHE

    ZLANHE = ( 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 ZLANHE 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

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

A

          A is COMPLEX*16 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 DOUBLE PRECISION 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 zlanhe.f.

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