LANHP - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English
template<typename T, typename Ta>
Ta lanhp(char *norm, char *uplo, integer *n, T *ap, Ta *work)#

LANHP 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:

   LANHP 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.

      CLANHP = (fla_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  fla_max(abs(A(i,j)))  is not a consistent matrix norm.
Parameters:
  • NORM[in]

    NORM is CHARACTER*1

    Specifies the value to be returned in CLANHP as described above.

  • UPLO[in]

    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[in]

    N is INTEGER

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

  • AP[in]

    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[out]

    WORK is REAL array, dimension (MAX(1,LWORK)),

    where LWORK >= N when NORM = ‘I’ or ‘1’ or ‘O’; otherwise, WORK is not referenced.

Returns:

Returns the value of norm.