LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlange.f
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00001 *> \brief \b DLANGE
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLANGE + 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/dlange.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlange.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          NORM
00025 *       INTEGER            LDA, M, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DLANGE  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 *> real matrix A.
00040 *> \endverbatim
00041 *>
00042 *> \return DLANGE
00043 *> \verbatim
00044 *>
00045 *>    DLANGE = ( 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 DLANGE as described
00066 *>          above.
00067 *> \endverbatim
00068 *>
00069 *> \param[in] M
00070 *> \verbatim
00071 *>          M is INTEGER
00072 *>          The number of rows of the matrix A.  M >= 0.  When M = 0,
00073 *>          DLANGE is set to zero.
00074 *> \endverbatim
00075 *>
00076 *> \param[in] N
00077 *> \verbatim
00078 *>          N is INTEGER
00079 *>          The number of columns of the matrix A.  N >= 0.  When N = 0,
00080 *>          DLANGE is set to zero.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] A
00084 *> \verbatim
00085 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00086 *>          The m by n matrix A.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] LDA
00090 *> \verbatim
00091 *>          LDA is INTEGER
00092 *>          The leading dimension of the array A.  LDA >= max(M,1).
00093 *> \endverbatim
00094 *>
00095 *> \param[out] WORK
00096 *> \verbatim
00097 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00098 *>          where LWORK >= M when NORM = 'I'; otherwise, WORK is not
00099 *>          referenced.
00100 *> \endverbatim
00101 *
00102 *  Authors:
00103 *  ========
00104 *
00105 *> \author Univ. of Tennessee 
00106 *> \author Univ. of California Berkeley 
00107 *> \author Univ. of Colorado Denver 
00108 *> \author NAG Ltd. 
00109 *
00110 *> \date November 2011
00111 *
00112 *> \ingroup doubleGEauxiliary
00113 *
00114 *  =====================================================================
00115       DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, WORK )
00116 *
00117 *  -- LAPACK auxiliary routine (version 3.4.0) --
00118 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00119 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00120 *     November 2011
00121 *
00122 *     .. Scalar Arguments ..
00123       CHARACTER          NORM
00124       INTEGER            LDA, M, N
00125 *     ..
00126 *     .. Array Arguments ..
00127       DOUBLE PRECISION   A( LDA, * ), WORK( * )
00128 *     ..
00129 *
00130 * =====================================================================
00131 *
00132 *     .. Parameters ..
00133       DOUBLE PRECISION   ONE, ZERO
00134       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00135 *     ..
00136 *     .. Local Scalars ..
00137       INTEGER            I, J
00138       DOUBLE PRECISION   SCALE, SUM, VALUE
00139 *     ..
00140 *     .. External Subroutines ..
00141       EXTERNAL           DLASSQ
00142 *     ..
00143 *     .. External Functions ..
00144       LOGICAL            LSAME
00145       EXTERNAL           LSAME
00146 *     ..
00147 *     .. Intrinsic Functions ..
00148       INTRINSIC          ABS, MAX, MIN, SQRT
00149 *     ..
00150 *     .. Executable Statements ..
00151 *
00152       IF( MIN( M, N ).EQ.0 ) THEN
00153          VALUE = ZERO
00154       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00155 *
00156 *        Find max(abs(A(i,j))).
00157 *
00158          VALUE = ZERO
00159          DO 20 J = 1, N
00160             DO 10 I = 1, M
00161                VALUE = MAX( VALUE, ABS( A( I, J ) ) )
00162    10       CONTINUE
00163    20    CONTINUE
00164       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00165 *
00166 *        Find norm1(A).
00167 *
00168          VALUE = ZERO
00169          DO 40 J = 1, N
00170             SUM = ZERO
00171             DO 30 I = 1, M
00172                SUM = SUM + ABS( A( I, J ) )
00173    30       CONTINUE
00174             VALUE = MAX( VALUE, SUM )
00175    40    CONTINUE
00176       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00177 *
00178 *        Find normI(A).
00179 *
00180          DO 50 I = 1, M
00181             WORK( I ) = ZERO
00182    50    CONTINUE
00183          DO 70 J = 1, N
00184             DO 60 I = 1, M
00185                WORK( I ) = WORK( I ) + ABS( A( I, J ) )
00186    60       CONTINUE
00187    70    CONTINUE
00188          VALUE = ZERO
00189          DO 80 I = 1, M
00190             VALUE = MAX( VALUE, WORK( I ) )
00191    80    CONTINUE
00192       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00193 *
00194 *        Find normF(A).
00195 *
00196          SCALE = ZERO
00197          SUM = ONE
00198          DO 90 J = 1, N
00199             CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM )
00200    90    CONTINUE
00201          VALUE = SCALE*SQRT( SUM )
00202       END IF
00203 *
00204       DLANGE = VALUE
00205       RETURN
00206 *
00207 *     End of DLANGE
00208 *
00209       END
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