dlanhs()

double precision function dlanhs	(	character	NORM,
		integer	N,
		double precision, dimension( lda, * )	A,
		integer	LDA,
		double precision, dimension( * )	WORK
	)

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

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Purpose:

 DLANHS  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.

Returns

DLANHS

    DLANHS = ( 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

[in]	NORM	NORM is CHARACTER*1 Specifies the value to be returned in DLANHS as described above.
[in]	N	N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANHS is set to zero.
[in]	A	A is DOUBLE PRECISION array, dimension (LDA,N) The n by n upper Hessenberg matrix A; the part of A below the first sub-diagonal is not referenced.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 110 of file dlanhs.f.

*
*  -- LAPACK auxiliary routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
      IMPLICIT NONE
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            LDA, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      DOUBLE PRECISION   SUM, VALUE
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   SSQ( 2 ), COLSSQ( 2 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, DISNAN
      EXTERNAL           lsame, disnan
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlassq, dcombssq
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, min, sqrt
*     ..
*     .. Executable Statements ..
*
      IF( n.EQ.0 ) THEN
         VALUE = zero
      ELSE IF( lsame( norm, 'M' ) ) THEN
*
*        Find max(abs(A(i,j))).
*
         VALUE = zero
         DO 20 j = 1, n
            DO 10 i = 1, min( n, j+1 )
               sum = abs( a( i, j ) )
               IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   10       CONTINUE
   20    CONTINUE
      ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
*
*        Find norm1(A).
*
         VALUE = zero
         DO 40 j = 1, n
            sum = zero
            DO 30 i = 1, min( n, j+1 )
               sum = sum + abs( a( i, j ) )
   30       CONTINUE
            IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   40    CONTINUE
      ELSE IF( lsame( norm, 'I' ) ) THEN
*
*        Find normI(A).
*
         DO 50 i = 1, n
            work( i ) = zero
   50    CONTINUE
         DO 70 j = 1, n
            DO 60 i = 1, min( n, j+1 )
               work( i ) = work( i ) + abs( a( i, j ) )
   60       CONTINUE
   70    CONTINUE
         VALUE = zero
         DO 80 i = 1, n
            sum = work( i )
            IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
   80    CONTINUE
      ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
*
*        Find normF(A).
*        SSQ(1) is scale
*        SSQ(2) is sum-of-squares
*        For better accuracy, sum each column separately.
*
         ssq( 1 ) = zero
         ssq( 2 ) = one
         DO 90 j = 1, n
            colssq( 1 ) = zero
            colssq( 2 ) = one
            CALL dlassq( min( n, j+1 ), a( 1, j ), 1,
     $                   colssq( 1 ), colssq( 2 ) )
            CALL dcombssq( ssq, colssq )
   90    CONTINUE
         VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
      END IF
*
      dlanhs = VALUE
      RETURN
*
*     End of DLANHS
*

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