LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clangb.f
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00001 *> \brief \b CLANGB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANGB + 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/clangb.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clangb.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANGB( 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 *       REAL               WORK( * )
00030 *       COMPLEX            AB( LDAB, * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> CLANGB  returns the value of the one norm,  or the Frobenius norm, or
00040 *> the  infinity norm,  or the element of  largest absolute value  of an
00041 *> n by n band matrix  A,  with kl sub-diagonals and ku super-diagonals.
00042 *> \endverbatim
00043 *>
00044 *> \return CLANGB
00045 *> \verbatim
00046 *>
00047 *>    CLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
00048 *>             (
00049 *>             ( norm1(A),         NORM = '1', 'O' or 'o'
00050 *>             (
00051 *>             ( normI(A),         NORM = 'I' or 'i'
00052 *>             (
00053 *>             ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
00054 *>
00055 *> where  norm1  denotes the  one norm of a matrix (maximum column sum),
00056 *> normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
00057 *> normF  denotes the  Frobenius norm of a matrix (square root of sum of
00058 *> squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
00059 *> \endverbatim
00060 *
00061 *  Arguments:
00062 *  ==========
00063 *
00064 *> \param[in] NORM
00065 *> \verbatim
00066 *>          NORM is CHARACTER*1
00067 *>          Specifies the value to be returned in CLANGB as described
00068 *>          above.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] N
00072 *> \verbatim
00073 *>          N is INTEGER
00074 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANGB is
00075 *>          set to zero.
00076 *> \endverbatim
00077 *>
00078 *> \param[in] KL
00079 *> \verbatim
00080 *>          KL is INTEGER
00081 *>          The number of sub-diagonals of the matrix A.  KL >= 0.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] KU
00085 *> \verbatim
00086 *>          KU is INTEGER
00087 *>          The number of super-diagonals of the matrix A.  KU >= 0.
00088 *> \endverbatim
00089 *>
00090 *> \param[in] AB
00091 *> \verbatim
00092 *>          AB is COMPLEX array, dimension (LDAB,N)
00093 *>          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
00094 *>          column of A is stored in the j-th column of the array AB as
00095 *>          follows:
00096 *>          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
00097 *> \endverbatim
00098 *>
00099 *> \param[in] LDAB
00100 *> \verbatim
00101 *>          LDAB is INTEGER
00102 *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
00103 *> \endverbatim
00104 *>
00105 *> \param[out] WORK
00106 *> \verbatim
00107 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00108 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00109 *>          referenced.
00110 *> \endverbatim
00111 *
00112 *  Authors:
00113 *  ========
00114 *
00115 *> \author Univ. of Tennessee 
00116 *> \author Univ. of California Berkeley 
00117 *> \author Univ. of Colorado Denver 
00118 *> \author NAG Ltd. 
00119 *
00120 *> \date November 2011
00121 *
00122 *> \ingroup complexGBauxiliary
00123 *
00124 *  =====================================================================
00125       REAL             FUNCTION CLANGB( NORM, N, KL, KU, AB, LDAB,
00126      $                 WORK )
00127 *
00128 *  -- LAPACK auxiliary routine (version 3.4.0) --
00129 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00130 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00131 *     November 2011
00132 *
00133 *     .. Scalar Arguments ..
00134       CHARACTER          NORM
00135       INTEGER            KL, KU, LDAB, N
00136 *     ..
00137 *     .. Array Arguments ..
00138       REAL               WORK( * )
00139       COMPLEX            AB( LDAB, * )
00140 *     ..
00141 *
00142 * =====================================================================
00143 *
00144 *     .. Parameters ..
00145       REAL               ONE, ZERO
00146       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00147 *     ..
00148 *     .. Local Scalars ..
00149       INTEGER            I, J, K, L
00150       REAL               SCALE, SUM, VALUE
00151 *     ..
00152 *     .. External Functions ..
00153       LOGICAL            LSAME
00154       EXTERNAL           LSAME
00155 *     ..
00156 *     .. External Subroutines ..
00157       EXTERNAL           CLASSQ
00158 *     ..
00159 *     .. Intrinsic Functions ..
00160       INTRINSIC          ABS, MAX, MIN, SQRT
00161 *     ..
00162 *     .. Executable Statements ..
00163 *
00164       IF( N.EQ.0 ) THEN
00165          VALUE = ZERO
00166       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00167 *
00168 *        Find max(abs(A(i,j))).
00169 *
00170          VALUE = ZERO
00171          DO 20 J = 1, N
00172             DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00173                VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00174    10       CONTINUE
00175    20    CONTINUE
00176       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00177 *
00178 *        Find norm1(A).
00179 *
00180          VALUE = ZERO
00181          DO 40 J = 1, N
00182             SUM = ZERO
00183             DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
00184                SUM = SUM + ABS( AB( I, J ) )
00185    30       CONTINUE
00186             VALUE = MAX( VALUE, SUM )
00187    40    CONTINUE
00188       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00189 *
00190 *        Find normI(A).
00191 *
00192          DO 50 I = 1, N
00193             WORK( I ) = ZERO
00194    50    CONTINUE
00195          DO 70 J = 1, N
00196             K = KU + 1 - J
00197             DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
00198                WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
00199    60       CONTINUE
00200    70    CONTINUE
00201          VALUE = ZERO
00202          DO 80 I = 1, N
00203             VALUE = MAX( VALUE, WORK( I ) )
00204    80    CONTINUE
00205       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00206 *
00207 *        Find normF(A).
00208 *
00209          SCALE = ZERO
00210          SUM = ONE
00211          DO 90 J = 1, N
00212             L = MAX( 1, J-KU )
00213             K = KU + 1 - J + L
00214             CALL CLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
00215    90    CONTINUE
00216          VALUE = SCALE*SQRT( SUM )
00217       END IF
00218 *
00219       CLANGB = VALUE
00220       RETURN
00221 *
00222 *     End of CLANGB
00223 *
00224       END
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