LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
clantb.f
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00001 *> \brief \b CLANTB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download CLANTB + 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/clantb.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clantb.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB,
00022 *                        LDAB, WORK )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          DIAG, NORM, UPLO
00026 *       INTEGER            K, 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 *> CLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
00042 *> \endverbatim
00043 *>
00044 *> \return CLANTB
00045 *> \verbatim
00046 *>
00047 *>    CLANTB = ( 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 CLANTB as described
00068 *>          above.
00069 *> \endverbatim
00070 *>
00071 *> \param[in] UPLO
00072 *> \verbatim
00073 *>          UPLO is CHARACTER*1
00074 *>          Specifies whether the matrix A is upper or lower triangular.
00075 *>          = 'U':  Upper triangular
00076 *>          = 'L':  Lower triangular
00077 *> \endverbatim
00078 *>
00079 *> \param[in] DIAG
00080 *> \verbatim
00081 *>          DIAG is CHARACTER*1
00082 *>          Specifies whether or not the matrix A is unit triangular.
00083 *>          = 'N':  Non-unit triangular
00084 *>          = 'U':  Unit triangular
00085 *> \endverbatim
00086 *>
00087 *> \param[in] N
00088 *> \verbatim
00089 *>          N is INTEGER
00090 *>          The order of the matrix A.  N >= 0.  When N = 0, CLANTB is
00091 *>          set to zero.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] K
00095 *> \verbatim
00096 *>          K is INTEGER
00097 *>          The number of super-diagonals of the matrix A if UPLO = 'U',
00098 *>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
00099 *>          K >= 0.
00100 *> \endverbatim
00101 *>
00102 *> \param[in] AB
00103 *> \verbatim
00104 *>          AB is COMPLEX array, dimension (LDAB,N)
00105 *>          The upper or lower triangular band matrix A, stored in the
00106 *>          first k+1 rows of AB.  The j-th column of A is stored
00107 *>          in the j-th column of the array AB as follows:
00108 *>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
00109 *>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
00110 *>          Note that when DIAG = 'U', the elements of the array AB
00111 *>          corresponding to the diagonal elements of the matrix A are
00112 *>          not referenced, but are assumed to be one.
00113 *> \endverbatim
00114 *>
00115 *> \param[in] LDAB
00116 *> \verbatim
00117 *>          LDAB is INTEGER
00118 *>          The leading dimension of the array AB.  LDAB >= K+1.
00119 *> \endverbatim
00120 *>
00121 *> \param[out] WORK
00122 *> \verbatim
00123 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00124 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00125 *>          referenced.
00126 *> \endverbatim
00127 *
00128 *  Authors:
00129 *  ========
00130 *
00131 *> \author Univ. of Tennessee 
00132 *> \author Univ. of California Berkeley 
00133 *> \author Univ. of Colorado Denver 
00134 *> \author NAG Ltd. 
00135 *
00136 *> \date November 2011
00137 *
00138 *> \ingroup complexOTHERauxiliary
00139 *
00140 *  =====================================================================
00141       REAL             FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB,
00142      $                 LDAB, WORK )
00143 *
00144 *  -- LAPACK auxiliary routine (version 3.4.0) --
00145 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00146 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00147 *     November 2011
00148 *
00149 *     .. Scalar Arguments ..
00150       CHARACTER          DIAG, NORM, UPLO
00151       INTEGER            K, LDAB, N
00152 *     ..
00153 *     .. Array Arguments ..
00154       REAL               WORK( * )
00155       COMPLEX            AB( LDAB, * )
00156 *     ..
00157 *
00158 * =====================================================================
00159 *
00160 *     .. Parameters ..
00161       REAL               ONE, ZERO
00162       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00163 *     ..
00164 *     .. Local Scalars ..
00165       LOGICAL            UDIAG
00166       INTEGER            I, J, L
00167       REAL               SCALE, SUM, VALUE
00168 *     ..
00169 *     .. External Functions ..
00170       LOGICAL            LSAME
00171       EXTERNAL           LSAME
00172 *     ..
00173 *     .. External Subroutines ..
00174       EXTERNAL           CLASSQ
00175 *     ..
00176 *     .. Intrinsic Functions ..
00177       INTRINSIC          ABS, MAX, MIN, SQRT
00178 *     ..
00179 *     .. Executable Statements ..
00180 *
00181       IF( N.EQ.0 ) THEN
00182          VALUE = ZERO
00183       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00184 *
00185 *        Find max(abs(A(i,j))).
00186 *
00187          IF( LSAME( DIAG, 'U' ) ) THEN
00188             VALUE = ONE
00189             IF( LSAME( UPLO, 'U' ) ) THEN
00190                DO 20 J = 1, N
00191                   DO 10 I = MAX( K+2-J, 1 ), K
00192                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00193    10             CONTINUE
00194    20          CONTINUE
00195             ELSE
00196                DO 40 J = 1, N
00197                   DO 30 I = 2, MIN( N+1-J, K+1 )
00198                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00199    30             CONTINUE
00200    40          CONTINUE
00201             END IF
00202          ELSE
00203             VALUE = ZERO
00204             IF( LSAME( UPLO, 'U' ) ) THEN
00205                DO 60 J = 1, N
00206                   DO 50 I = MAX( K+2-J, 1 ), K + 1
00207                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00208    50             CONTINUE
00209    60          CONTINUE
00210             ELSE
00211                DO 80 J = 1, N
00212                   DO 70 I = 1, MIN( N+1-J, K+1 )
00213                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00214    70             CONTINUE
00215    80          CONTINUE
00216             END IF
00217          END IF
00218       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00219 *
00220 *        Find norm1(A).
00221 *
00222          VALUE = ZERO
00223          UDIAG = LSAME( DIAG, 'U' )
00224          IF( LSAME( UPLO, 'U' ) ) THEN
00225             DO 110 J = 1, N
00226                IF( UDIAG ) THEN
00227                   SUM = ONE
00228                   DO 90 I = MAX( K+2-J, 1 ), K
00229                      SUM = SUM + ABS( AB( I, J ) )
00230    90             CONTINUE
00231                ELSE
00232                   SUM = ZERO
00233                   DO 100 I = MAX( K+2-J, 1 ), K + 1
00234                      SUM = SUM + ABS( AB( I, J ) )
00235   100             CONTINUE
00236                END IF
00237                VALUE = MAX( VALUE, SUM )
00238   110       CONTINUE
00239          ELSE
00240             DO 140 J = 1, N
00241                IF( UDIAG ) THEN
00242                   SUM = ONE
00243                   DO 120 I = 2, MIN( N+1-J, K+1 )
00244                      SUM = SUM + ABS( AB( I, J ) )
00245   120             CONTINUE
00246                ELSE
00247                   SUM = ZERO
00248                   DO 130 I = 1, MIN( N+1-J, K+1 )
00249                      SUM = SUM + ABS( AB( I, J ) )
00250   130             CONTINUE
00251                END IF
00252                VALUE = MAX( VALUE, SUM )
00253   140       CONTINUE
00254          END IF
00255       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00256 *
00257 *        Find normI(A).
00258 *
00259          VALUE = ZERO
00260          IF( LSAME( UPLO, 'U' ) ) THEN
00261             IF( LSAME( DIAG, 'U' ) ) THEN
00262                DO 150 I = 1, N
00263                   WORK( I ) = ONE
00264   150          CONTINUE
00265                DO 170 J = 1, N
00266                   L = K + 1 - J
00267                   DO 160 I = MAX( 1, J-K ), J - 1
00268                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00269   160             CONTINUE
00270   170          CONTINUE
00271             ELSE
00272                DO 180 I = 1, N
00273                   WORK( I ) = ZERO
00274   180          CONTINUE
00275                DO 200 J = 1, N
00276                   L = K + 1 - J
00277                   DO 190 I = MAX( 1, J-K ), J
00278                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00279   190             CONTINUE
00280   200          CONTINUE
00281             END IF
00282          ELSE
00283             IF( LSAME( DIAG, 'U' ) ) THEN
00284                DO 210 I = 1, N
00285                   WORK( I ) = ONE
00286   210          CONTINUE
00287                DO 230 J = 1, N
00288                   L = 1 - J
00289                   DO 220 I = J + 1, MIN( N, J+K )
00290                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00291   220             CONTINUE
00292   230          CONTINUE
00293             ELSE
00294                DO 240 I = 1, N
00295                   WORK( I ) = ZERO
00296   240          CONTINUE
00297                DO 260 J = 1, N
00298                   L = 1 - J
00299                   DO 250 I = J, MIN( N, J+K )
00300                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00301   250             CONTINUE
00302   260          CONTINUE
00303             END IF
00304          END IF
00305          DO 270 I = 1, N
00306             VALUE = MAX( VALUE, WORK( I ) )
00307   270    CONTINUE
00308       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00309 *
00310 *        Find normF(A).
00311 *
00312          IF( LSAME( UPLO, 'U' ) ) THEN
00313             IF( LSAME( DIAG, 'U' ) ) THEN
00314                SCALE = ONE
00315                SUM = N
00316                IF( K.GT.0 ) THEN
00317                   DO 280 J = 2, N
00318                      CALL CLASSQ( MIN( J-1, K ),
00319      $                            AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
00320      $                            SUM )
00321   280             CONTINUE
00322                END IF
00323             ELSE
00324                SCALE = ZERO
00325                SUM = ONE
00326                DO 290 J = 1, N
00327                   CALL CLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
00328      $                         1, SCALE, SUM )
00329   290          CONTINUE
00330             END IF
00331          ELSE
00332             IF( LSAME( DIAG, 'U' ) ) THEN
00333                SCALE = ONE
00334                SUM = N
00335                IF( K.GT.0 ) THEN
00336                   DO 300 J = 1, N - 1
00337                      CALL CLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
00338      $                            SUM )
00339   300             CONTINUE
00340                END IF
00341             ELSE
00342                SCALE = ZERO
00343                SUM = ONE
00344                DO 310 J = 1, N
00345                   CALL CLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
00346      $                         SUM )
00347   310          CONTINUE
00348             END IF
00349          END IF
00350          VALUE = SCALE*SQRT( SUM )
00351       END IF
00352 *
00353       CLANTB = VALUE
00354       RETURN
00355 *
00356 *     End of CLANTB
00357 *
00358       END
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