clanhp: Clanhp.f -

Function/Subroutine Documentation

real function clanhp (characterNORM, characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )WORK)

CLANHP 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 supplied in packed form.

Purpose:

 CLANHP  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,  supplied in packed form.

Returns:

CLANHP

    CLANHP = ( 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 CLANHP as described
          above.

UPLO

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

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

          AP is COMPLEX array, dimension (N*(N+1)/2)
          The upper or lower triangle of the hermitian matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
          Note that the  imaginary parts of the diagonal elements need
          not be set and are assumed to be zero.

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 118 of file clanhp.f.

clanhp (3)

SYNOPSIS

Functions/Subroutines

Function/Subroutine Documentation

real function clanhp (characterNORM, characterUPLO, integerN, complex, dimension( * )AP, real, dimension( * )WORK)

Author