LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clange.f
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00001 *> \brief \b CLANGE
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANGE + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clange.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANGE( NORM, M, N, A, LDA, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM
00025 *       INTEGER            LDA, M, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               WORK( * )
00029 *       COMPLEX            A( LDA, * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> CLANGE  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 *> complex matrix A.
00041 *> \endverbatim
00042 *>
00043 *> \return CLANGE
00044 *> \verbatim
00045 *>
00046 *>    CLANGE = ( 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 CLANGE as described
00067 *>          above.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] M
00071 *> \verbatim
00072 *>          M is INTEGER
00073 *>          The number of rows of the matrix A.  M >= 0.  When M = 0,
00074 *>          CLANGE is set to zero.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] N
00078 *> \verbatim
00079 *>          N is INTEGER
00080 *>          The number of columns of the matrix A.  N >= 0.  When N = 0,
00081 *>          CLANGE is set to zero.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] A
00085 *> \verbatim
00086 *>          A is COMPLEX array, dimension (LDA,N)
00087 *>          The m by n matrix A.
00088 *> \endverbatim
00089 *>
00090 *> \param[in] LDA
00091 *> \verbatim
00092 *>          LDA is INTEGER
00093 *>          The leading dimension of the array A.  LDA >= max(M,1).
00094 *> \endverbatim
00095 *>
00096 *> \param[out] WORK
00097 *> \verbatim
00098 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00099 *>          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
00100 *>          referenced.
00101 *> \endverbatim
00102 *
00103 *  Authors:
00104 *  ========
00105 *
00106 *> \author Univ. of Tennessee 
00107 *> \author Univ. of California Berkeley 
00108 *> \author Univ. of Colorado Denver 
00109 *> \author NAG Ltd. 
00110 *
00111 *> \date November 2011
00112 *
00113 *> \ingroup complexGEauxiliary
00114 *
00115 *  =====================================================================
00116       REAL             FUNCTION CLANGE( NORM, M, N, A, LDA, WORK )
00117 *
00118 *  -- LAPACK auxiliary routine (version 3.4.0) --
00119 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00120 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00121 *     November 2011
00122 *
00123 *     .. Scalar Arguments ..
00124       CHARACTER          NORM
00125       INTEGER            LDA, M, N
00126 *     ..
00127 *     .. Array Arguments ..
00128       REAL               WORK( * )
00129       COMPLEX            A( LDA, * )
00130 *     ..
00131 *
00132 * =====================================================================
00133 *
00134 *     .. Parameters ..
00135       REAL               ONE, ZERO
00136       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00137 *     ..
00138 *     .. Local Scalars ..
00139       INTEGER            I, J
00140       REAL               SCALE, SUM, VALUE
00141 *     ..
00142 *     .. External Functions ..
00143       LOGICAL            LSAME
00144       EXTERNAL           LSAME
00145 *     ..
00146 *     .. External Subroutines ..
00147       EXTERNAL           CLASSQ
00148 *     ..
00149 *     .. Intrinsic Functions ..
00150       INTRINSIC          ABS, MAX, MIN, SQRT
00151 *     ..
00152 *     .. Executable Statements ..
00153 *
00154       IF( MIN( M, N ).EQ.0 ) THEN
00155          VALUE = ZERO
00156       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00157 *
00158 *        Find max(abs(A(i,j))).
00159 *
00160          VALUE = ZERO
00161          DO 20 J = 1, N
00162             DO 10 I = 1, M
00163                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00164    10       CONTINUE
00165    20    CONTINUE
00166       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00167 *
00168 *        Find norm1(A).
00169 *
00170          VALUE = ZERO
00171          DO 40 J = 1, N
00172             SUM = ZERO
00173             DO 30 I = 1, M
00174                SUM = SUM + ABS( A( I, J ) )
00175    30       CONTINUE
00176             VALUE = MAX( VALUE, SUM )
00177    40    CONTINUE
00178       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00179 *
00180 *        Find normI(A).
00181 *
00182          DO 50 I = 1, M
00183             WORK( I ) = ZERO
00184    50    CONTINUE
00185          DO 70 J = 1, N
00186             DO 60 I = 1, M
00187                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00188    60       CONTINUE
00189    70    CONTINUE
00190          VALUE = ZERO
00191          DO 80 I = 1, M
00192             VALUE = MAX( VALUE, WORK( I ) )
00193    80    CONTINUE
00194       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00195 *
00196 *        Find normF(A).
00197 *
00198          SCALE = ZERO
00199          SUM = ONE
00200          DO 90 J = 1, N
00201             CALL CLASSQ( M, A( 1, J ), 1, SCALE, SUM )
00202    90    CONTINUE
00203          VALUE = SCALE*SQRT( SUM )
00204       END IF
00205 *
00206       CLANGE = VALUE
00207       RETURN
00208 *
00209 *     End of CLANGE
00210 *
00211       END
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