SLANHS (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 Hessenberg matrix A

SYNOPSIS

  REAL FUNCTION SLANHS( NORM, N, A, LDA, WORK )

      CHARACTER NORM

      INTEGER   LDA, N

      REAL      A( LDA, * ), WORK( * )

PURPOSE

  SLANHS  returns the value of the one norm,  or the Frobenius norm, or the
  infinity norm,  or the  element of  largest absolute value  of a Hessenberg
  matrix A.

DESCRIPTION

  SLANHS returns the value

     SLANHS = ( 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 SLANHS as described above.

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

  A       (input) REAL array, dimension (LDA,N)
          The n by n upper Hessenberg matrix A; the part of A below the first
          sub-diagonal is not referenced.

  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'; otherwise, WORK is not
          referenced.