LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clanhs.f
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00001 *> \brief \b CLANHS
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANHS + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhs.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhs.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANHS( NORM, N, A, LDA, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM
00025 *       INTEGER            LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               WORK( * )
00029 *       COMPLEX            A( LDA, * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> CLANHS  returns the value of the one norm,  or the Frobenius norm, or
00039 *> the  infinity norm,  or the  element of  largest absolute value  of a
00040 *> Hessenberg matrix A.
00041 *> \endverbatim
00042 *>
00043 *> \return CLANHS
00044 *> \verbatim
00045 *>
00046 *>    CLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00047 *>             (
00048 *>             ( norm1(A),         NORM = '1', 'O' or 'o'
00049 *>             (
00050 *>             ( normI(A),         NORM = 'I' or 'i'
00051 *>             (
00052 *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00053 *>
00054 *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
00055 *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00056 *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
00057 *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00058 *> \endverbatim
00059 *
00060 *  Arguments:
00061 *  ==========
00062 *
00063 *> \param[in] NORM
00064 *> \verbatim
00065 *>          NORM is CHARACTER*1
00066 *>          Specifies the value to be returned in CLANHS as described
00067 *>          above.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] N
00071 *> \verbatim
00072 *>          N is INTEGER
00073 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANHS is
00074 *>          set to zero.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] A
00078 *> \verbatim
00079 *>          A is COMPLEX array, dimension (LDA,N)
00080 *>          The n by n upper Hessenberg matrix A; the part of A below the
00081 *>          first sub-diagonal is not referenced.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] LDA
00085 *> \verbatim
00086 *>          LDA is INTEGER
00087 *>          The leading dimension of the array A.  LDA >= max(N,1).
00088 *> \endverbatim
00089 *>
00090 *> \param[out] WORK
00091 *> \verbatim
00092 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00093 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00094 *>          referenced.
00095 *> \endverbatim
00096 *
00097 *  Authors:
00098 *  ========
00099 *
00100 *> \author Univ. of Tennessee 
00101 *> \author Univ. of California Berkeley 
00102 *> \author Univ. of Colorado Denver 
00103 *> \author NAG Ltd. 
00104 *
00105 *> \date November 2011
00106 *
00107 *> \ingroup complexOTHERauxiliary
00108 *
00109 *  =====================================================================
00110       REAL             FUNCTION CLANHS( NORM, N, A, LDA, WORK )
00111 *
00112 *  -- LAPACK auxiliary routine (version 3.4.0) --
00113 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00114 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00115 *     November 2011
00116 *
00117 *     .. Scalar Arguments ..
00118       CHARACTER          NORM
00119       INTEGER            LDA, N
00120 *     ..
00121 *     .. Array Arguments ..
00122       REAL               WORK( * )
00123       COMPLEX            A( LDA, * )
00124 *     ..
00125 *
00126 * =====================================================================
00127 *
00128 *     .. Parameters ..
00129       REAL               ONE, ZERO
00130       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00131 *     ..
00132 *     .. Local Scalars ..
00133       INTEGER            I, J
00134       REAL               SCALE, SUM, VALUE
00135 *     ..
00136 *     .. External Functions ..
00137       LOGICAL            LSAME
00138       EXTERNAL           LSAME
00139 *     ..
00140 *     .. External Subroutines ..
00141       EXTERNAL           CLASSQ
00142 *     ..
00143 *     .. Intrinsic Functions ..
00144       INTRINSIC          ABS, MAX, MIN, SQRT
00145 *     ..
00146 *     .. Executable Statements ..
00147 *
00148       IF( N.EQ.0 ) THEN
00149          VALUE = ZERO
00150       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00151 *
00152 *        Find max(abs(A(i,j))).
00153 *
00154          VALUE = ZERO
00155          DO 20 J = 1, N
00156             DO 10 I = 1, MIN( N, J+1 )
00157                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00158    10       CONTINUE
00159    20    CONTINUE
00160       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00161 *
00162 *        Find norm1(A).
00163 *
00164          VALUE = ZERO
00165          DO 40 J = 1, N
00166             SUM = ZERO
00167             DO 30 I = 1, MIN( N, J+1 )
00168                SUM = SUM + ABS( A( I, J ) )
00169    30       CONTINUE
00170             VALUE = MAX( VALUE, SUM )
00171    40    CONTINUE
00172       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00173 *
00174 *        Find normI(A).
00175 *
00176          DO 50 I = 1, N
00177             WORK( I ) = ZERO
00178    50    CONTINUE
00179          DO 70 J = 1, N
00180             DO 60 I = 1, MIN( N, J+1 )
00181                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00182    60       CONTINUE
00183    70    CONTINUE
00184          VALUE = ZERO
00185          DO 80 I = 1, N
00186             VALUE = MAX( VALUE, WORK( I ) )
00187    80    CONTINUE
00188       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00189 *
00190 *        Find normF(A).
00191 *
00192          SCALE = ZERO
00193          SUM = ONE
00194          DO 90 J = 1, N
00195             CALL CLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
00196    90    CONTINUE
00197          VALUE = SCALE*SQRT( SUM )
00198       END IF
00199 *
00200       CLANHS = VALUE
00201       RETURN
00202 *
00203 *     End of CLANHS
00204 *
00205       END
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