LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlanhs.f
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00001 *> \brief \b DLANHS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLANHS + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanhs.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanhs.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanhs.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM
00025 *       INTEGER            LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DLANHS  returns the value of the one norm,  or the Frobenius norm, or
00038 *> the  infinity norm,  or the  element of  largest absolute value  of a
00039 *> Hessenberg matrix A.
00040 *> \endverbatim
00041 *>
00042 *> \return DLANHS
00043 *> \verbatim
00044 *>
00045 *>    DLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00046 *>             (
00047 *>             ( norm1(A),         NORM = '1', 'O' or 'o'
00048 *>             (
00049 *>             ( normI(A),         NORM = 'I' or 'i'
00050 *>             (
00051 *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00052 *>
00053 *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
00054 *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00055 *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
00056 *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00057 *> \endverbatim
00058 *
00059 *  Arguments:
00060 *  ==========
00061 *
00062 *> \param[in] NORM
00063 *> \verbatim
00064 *>          NORM is CHARACTER*1
00065 *>          Specifies the value to be returned in DLANHS as described
00066 *>          above.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] N
00070 *> \verbatim
00071 *>          N is INTEGER
00072 *>          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is
00073 *>          set to zero.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] A
00077 *> \verbatim
00078 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00079 *>          The n by n upper Hessenberg matrix A; the part of A below the
00080 *>          first sub-diagonal is not referenced.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] LDA
00084 *> \verbatim
00085 *>          LDA is INTEGER
00086 *>          The leading dimension of the array A.  LDA >= max(N,1).
00087 *> \endverbatim
00088 *>
00089 *> \param[out] WORK
00090 *> \verbatim
00091 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00092 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00093 *>          referenced.
00094 *> \endverbatim
00095 *
00096 *  Authors:
00097 *  ========
00098 *
00099 *> \author Univ. of Tennessee 
00100 *> \author Univ. of California Berkeley 
00101 *> \author Univ. of Colorado Denver 
00102 *> \author NAG Ltd. 
00103 *
00104 *> \date November 2011
00105 *
00106 *> \ingroup doubleOTHERauxiliary
00107 *
00108 *  =====================================================================
00109       DOUBLE PRECISION FUNCTION DLANHS( NORM, N, A, LDA, WORK )
00110 *
00111 *  -- LAPACK auxiliary routine (version 3.4.0) --
00112 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00113 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00114 *     November 2011
00115 *
00116 *     .. Scalar Arguments ..
00117       CHARACTER          NORM
00118       INTEGER            LDA, N
00119 *     ..
00120 *     .. Array Arguments ..
00121       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00122 *     ..
00123 *
00124 * =====================================================================
00125 *
00126 *     .. Parameters ..
00127       DOUBLE PRECISION   ONE, ZERO
00128       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00129 *     ..
00130 *     .. Local Scalars ..
00131       INTEGER            I, J
00132       DOUBLE PRECISION   SCALE, SUM, VALUE
00133 *     ..
00134 *     .. External Subroutines ..
00135       EXTERNAL           DLASSQ
00136 *     ..
00137 *     .. External Functions ..
00138       LOGICAL            LSAME
00139       EXTERNAL           LSAME
00140 *     ..
00141 *     .. Intrinsic Functions ..
00142       INTRINSIC          ABS, MAX, MIN, SQRT
00143 *     ..
00144 *     .. Executable Statements ..
00145 *
00146       IF( N.EQ.0 ) THEN
00147          VALUE = ZERO
00148       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00149 *
00150 *        Find max(abs(A(i,j))).
00151 *
00152          VALUE = ZERO
00153          DO 20 J = 1, N
00154             DO 10 I = 1, MIN( N, J+1 )
00155                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00156    10       CONTINUE
00157    20    CONTINUE
00158       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00159 *
00160 *        Find norm1(A).
00161 *
00162          VALUE = ZERO
00163          DO 40 J = 1, N
00164             SUM = ZERO
00165             DO 30 I = 1, MIN( N, J+1 )
00166                SUM = SUM + ABS( A( I, J ) )
00167    30       CONTINUE
00168             VALUE = MAX( VALUE, SUM )
00169    40    CONTINUE
00170       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00171 *
00172 *        Find normI(A).
00173 *
00174          DO 50 I = 1, N
00175             WORK( I ) = ZERO
00176    50    CONTINUE
00177          DO 70 J = 1, N
00178             DO 60 I = 1, MIN( N, J+1 )
00179                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00180    60       CONTINUE
00181    70    CONTINUE
00182          VALUE = ZERO
00183          DO 80 I = 1, N
00184             VALUE = MAX( VALUE, WORK( I ) )
00185    80    CONTINUE
00186       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00187 *
00188 *        Find normF(A).
00189 *
00190          SCALE = ZERO
00191          SUM = ONE
00192          DO 90 J = 1, N
00193             CALL DLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
00194    90    CONTINUE
00195          VALUE = SCALE*SQRT( SUM )
00196       END IF
00197 *
00198       DLANHS = VALUE
00199       RETURN
00200 *
00201 *     End of DLANHS
00202 *
00203       END
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