# p?lanhs

Returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element, of an upper Hessenberg matrix.

## Syntax

val = pslanhs(norm, n, a, ia, ja, desca, work)

val = pdlanhs(norm, n, a, ia, ja, desca, work)

val = pclanhs(norm, n, a, ia, ja, desca, work)

val = pzlanhs(norm, n, a, ia, ja, desca, work)

## Description

The routine returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an upper Hessenberg distributed matrix `sub(A) = A(ia:ia+m-1, ja:ja+n-1)`.

## Input Parameters

norm

  CHARACTER*1. Specifies the vaule to be returned by the routine:

  = 'M' or 'm': `val = max(abs(Aij))`, largest absolute value of the matrix A.

  = '1' or 'O' or 'o': `val = norm1(A)`, 1-norm of the matrix A (maximum column sum),

  = 'I' or 'i': `val = normI(A)`, infinity norm of the matrix A (maximum row sum),

  = 'F', 'f', 'E' or 'e': `val = normF(A)`, Frobenius norm of the matrix A (square root of sum of squares).

n

  (global) INTEGER.

  The number of columns to be operated on, that is, the number of columns of the distributed submatrix sub(A). When `n = 0`, p?lanhs is set to zero. n ≥ 0.

a

  (local).

  Real for pslanhs

  DOUBLE PRECISION for pdlanhs

  COMPLEX for pclanhs

  COMPLEX*16 for pzlanhs.

  Pointer into the local memory to an array of DIMENSION`(lld_a, LOCc(ja+n-1))` containing the local pieces of the distributed matrix sub(A).

ia, ja

  (global) INTEGER.

  The row and column indices in the global array A indicating the first row and the first column of the submatrix sub(A), respectively.

desca

  (global and local) INTEGER array, DIMENSION (dlen_). The array descriptor for the distributed matrix A.

work

  (local).

  Real for pslanhs

  DOUBLE PRECISION for pdlanhs

  COMPLEX for pclanhs

  COMPLEX*16 for pzlanh.

  Array, DIMENSION (lwork).

  `lwork ≥ 0` if norm = 'M' or 'm' (not referenced),

  nq0 if norm = '1', 'O' or 'o',

  mp0 if norm = 'I' or 'i',

  0 if `norm = 'F'`, 'f', 'E' or 'e' (not referenced),

  where

  iroffa = mod( ia-1, mb_a ), icoffa = mod( ja-1, nb_a ),

  iarow = indxg2p( ia, mb_a, myrow, rsrc_a, nprow ),

  iacol = indxg2p( ja, nb_a, mycol, csrc_a, npcol ),

  mp0 = numroc( m+iroffa, mb_a, myrow, iarow, nprow ),

  nq0 = numroc( n+icoffa, nb_a, mycol, iacol, npcol ),

  indxg2p and numroc are ScaLAPACK tool routines; myrow, imycol, nprow, and npcol can be determined by calling the subroutine blacs_gridinfo.

## Output Parameters

val

  The value returned by the fuction.

Parent topic: Auxiliary Routines