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dlanhs
C DLANHS    SOURCE    FANDEUR   22/05/02    21:15:08     11359          *> \brief \b 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.**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download DLANHS + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanhs.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanhs.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanhs.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       REAL*8 FUNCTION DLANHS( NORM, N, A, LDA, WORK )**       .. Scalar Arguments ..*       CHARACTER          NORM*       INTEGER            LDA, N*       ..*       .. Array Arguments ..*       REAL*8   A( LDA, * ), WORK( * )*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> 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.*> \endverbatim*>*> \return DLANHS*> \verbatim*>*>    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.*> \endverbatim**  Arguments:*  ==========**> \param[in] NORM*> \verbatim*>          NORM is CHARACTER*1*>          Specifies the value to be returned in DLANHS as described*>          above.*> \endverbatim*>*> \param[in] N*> \verbatim*>          N is INTEGER*>          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is*>          set to zero.*> \endverbatim*>*> \param[in] A*> \verbatim*>          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.*> \endverbatim*>*> \param[in] LDA*> \verbatim*>          LDA is INTEGER*>          The leading dimension of the array A.  LDA >= max(N,1).*> \endverbatim*>*> \param[out] WORK*> \verbatim*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),*>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not*>          referenced.*> \endverbatim**  Authors:*  ========**> \author Univ. of Tennessee*> \author Univ. of California Berkeley*> \author Univ. of Colorado Denver*> \author NAG Ltd.**> \date December 2016**> \ingroup doubleOTHERauxiliary**  =====================================================================      FUNCTION DLANHS( NORM, N, A, LDA, WORK )**  -- 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**     .. Scalar Arguments ..      REAL*8             DLANHS      CHARACTER          NORM      INTEGER            LDA, N*     ..*     .. Array Arguments ..      REAL*8   A( LDA, * ), WORK( * )*     ..** =====================================================================**     .. Parameters ..      REAL*8   ONE, ZERO      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )*     ..*     .. Local Scalars ..      INTEGER            I, J      REAL*8   SCALE, SUM, VALUE*     ..*     .. External Subroutines ..      EXTERNAL           DLASSQ*     ..*     .. External Functions ..      LOGICAL            LSAME, DISNAN      EXTERNAL           LSAME, DISNAN*     ..**     .. 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).*         SCALE = ZERO         SUM = ONE         DO 90 J = 1, N            CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )   90    CONTINUE         VALUE = SCALE*SQRT( SUM )      END IF*      DLANHS = VALUE      RETURN**     End of DLANHS*      END    

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