CLANHE (3lapack)

return 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

SYNOPSIS

  REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )

      CHARACTER NORM, UPLO

      INTEGER   LDA, N

      REAL      WORK( * )

      COMPLEX   A( LDA, * )

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.

DESCRIPTION

  CLANHE returns the value

     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  matrix norm.

ARGUMENTS

  NORM    (input) CHARACTER*1
          Specifies the value to be returned in CLANHE as described above.

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

  A       (input) 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     (input) INTEGER
          The leading dimension of the array A.  LDA >= max(N,1).

  WORK    (workspace) REAL array, dimension (LWORK),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is
          not referenced.