LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dlangb.f
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00001 *> \brief \b DLANGB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DLANGB + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangb.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangb.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
00022 *                        WORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          NORM
00026 *       INTEGER            KL, KU, LDAB, N
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> DLANGB  returns the value of the one norm,  or the Frobenius norm, or
00039 *> the  infinity norm,  or the element of  largest absolute value  of an
00040 *> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
00041 *> \endverbatim
00042 *>
00043 *> \return DLANGB
00044 *> \verbatim
00045 *>
00046 *>    DLANGB = ( 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 DLANGB 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, DLANGB is
00074 *>          set to zero.
00075 *> \endverbatim
00076 *>
00077 *> \param[in] KL
00078 *> \verbatim
00079 *>          KL is INTEGER
00080 *>          The number of sub-diagonals of the matrix A.  KL >= 0.
00081 *> \endverbatim
00082 *>
00083 *> \param[in] KU
00084 *> \verbatim
00085 *>          KU is INTEGER
00086 *>          The number of super-diagonals of the matrix A.  KU >= 0.
00087 *> \endverbatim
00088 *>
00089 *> \param[in] AB
00090 *> \verbatim
00091 *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
00092 *>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
00093 *>          column of A is stored in the j-th column of the array AB as
00094 *>          follows:
00095 *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
00096 *> \endverbatim
00097 *>
00098 *> \param[in] LDAB
00099 *> \verbatim
00100 *>          LDAB is INTEGER
00101 *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
00102 *> \endverbatim
00103 *>
00104 *> \param[out] WORK
00105 *> \verbatim
00106 *>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
00107 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00108 *>          referenced.
00109 *> \endverbatim
00110 *
00111 *  Authors:
00112 *  ========
00113 *
00114 *> \author Univ. of Tennessee 
00115 *> \author Univ. of California Berkeley 
00116 *> \author Univ. of Colorado Denver 
00117 *> \author NAG Ltd. 
00118 *
00119 *> \date November 2011
00120 *
00121 *> \ingroup doubleGBauxiliary
00122 *
00123 *  =====================================================================
00124       DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
00125      $                 WORK )
00126 *
00127 *  -- LAPACK auxiliary routine (version 3.4.0) --
00128 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00129 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00130 *     November 2011
00131 *
00132 *     .. Scalar Arguments ..
00133       CHARACTER          NORM
00134       INTEGER            KL, KU, LDAB, N
00135 *     ..
00136 *     .. Array Arguments ..
00137       DOUBLE PRECISION   AB( LDAB, * ), WORK( * )
00138 *     ..
00139 *
00140 * =====================================================================
00141 *
00142 *
00143 *     .. Parameters ..
00144       DOUBLE PRECISION   ONE, ZERO
00145       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00146 *     ..
00147 *     .. Local Scalars ..
00148       INTEGER            I, J, K, L
00149       DOUBLE PRECISION   SCALE, SUM, VALUE
00150 *     ..
00151 *     .. External Subroutines ..
00152       EXTERNAL           DLASSQ
00153 *     ..
00154 *     .. External Functions ..
00155       LOGICAL            LSAME
00156       EXTERNAL           LSAME
00157 *     ..
00158 *     .. Intrinsic Functions ..
00159       INTRINSIC          ABS, MAX, MIN, SQRT
00160 *     ..
00161 *     .. Executable Statements ..
00162 *
00163       IF( N.EQ.0 ) THEN
00164          VALUE = ZERO
00165       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00166 *
00167 *        Find max(abs(A(i,j))).
00168 *
00169          VALUE = ZERO
00170          DO 20 J = 1, N
00171             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00172                VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00173    10       CONTINUE
00174    20    CONTINUE
00175       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00176 *
00177 *        Find norm1(A).
00178 *
00179          VALUE = ZERO
00180          DO 40 J = 1, N
00181             SUM = ZERO
00182             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00183                SUM = SUM + ABS( AB( I, J ) )
00184    30       CONTINUE
00185             VALUE = MAX( VALUE, SUM )
00186    40    CONTINUE
00187       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00188 *
00189 *        Find normI(A).
00190 *
00191          DO 50 I = 1, N
00192             WORK( I ) = ZERO
00193    50    CONTINUE
00194          DO 70 J = 1, N
00195             K = KU + 1 - J
00196             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
00197                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
00198    60       CONTINUE
00199    70    CONTINUE
00200          VALUE = ZERO
00201          DO 80 I = 1, N
00202             VALUE = MAX( VALUE, WORK( I ) )
00203    80    CONTINUE
00204       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00205 *
00206 *        Find normF(A).
00207 *
00208          SCALE = ZERO
00209          SUM = ONE
00210          DO 90 J = 1, N
00211             L = MAX( 1, J-KU )
00212             K = KU + 1 - J + L
00213             CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
00214    90    CONTINUE
00215          VALUE = SCALE*SQRT( SUM )
00216       END IF
00217 *
00218       DLANGB = VALUE
00219       RETURN
00220 *
00221 *     End of DLANGB
00222 *
00223       END
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