OpenBLAS/lapack-netlib/SRC/slanhs.f

*> \brief \b SLANHS 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 SLANHS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slanhs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slanhs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slanhs.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       REAL             FUNCTION SLANHS( NORM, N, A, LDA, WORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          NORM
*       INTEGER            LDA, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
*> \return SLANHS
*> \verbatim
*>
*>    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 consistent matrix norm.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] NORM
*> \verbatim
*>          NORM is CHARACTER*1
*>          Specifies the value to be returned in SLANHS as described
*>          above.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.  When N = 0, SLANHS is
*>          set to zero.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is 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.
*> \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 REAL 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 realOTHERauxiliary
*
*  =====================================================================
      REAL             FUNCTION SLANHS( 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
*
      IMPLICIT NONE
*     .. Scalar Arguments ..
      CHARACTER          NORM
      INTEGER            LDA, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), WORK( * )
*     ..
*
* =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J
      REAL               SUM, VALUE
*     ..
*     .. Local Arrays ..
      REAL               SSQ( 2 ), COLSSQ( 2 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME, SISNAN
      EXTERNAL           LSAME, SISNAN
*     ..
*     .. External Subroutines ..
      EXTERNAL           SLASSQ, SCOMBSSQ
*     ..
*     .. 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. SISNAN( 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. SISNAN( 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. SISNAN( 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 SLASSQ( MIN( N, J+1 ), A( 1, J ), 1,
     $                   COLSSQ( 1 ), COLSSQ( 2 ) )
            CALL SCOMBSSQ( SSQ, COLSSQ )
   90    CONTINUE
         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
      END IF
*
      SLANHS = VALUE
      RETURN
*
*     End of SLANHS
*
      END