LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
slantb.f
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00001 *> \brief \b SLANTB
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLANTB + 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/slantb.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantb.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       REAL             FUNCTION SLANTB( 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               AB( LDAB, * ), WORK( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> SLANTB  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 triangular band matrix A,  with ( k + 1 ) diagonals.
00041 *> \endverbatim
00042 *>
00043 *> \return SLANTB
00044 *> \verbatim
00045 *>
00046 *>    SLANTB = ( 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 SLANTB as described
00067 *>          above.
00068 *> \endverbatim
00069 *>
00070 *> \param[in] UPLO
00071 *> \verbatim
00072 *>          UPLO is CHARACTER*1
00073 *>          Specifies whether the matrix A is upper or lower triangular.
00074 *>          = 'U':  Upper triangular
00075 *>          = 'L':  Lower triangular
00076 *> \endverbatim
00077 *>
00078 *> \param[in] DIAG
00079 *> \verbatim
00080 *>          DIAG is CHARACTER*1
00081 *>          Specifies whether or not the matrix A is unit triangular.
00082 *>          = 'N':  Non-unit triangular
00083 *>          = 'U':  Unit triangular
00084 *> \endverbatim
00085 *>
00086 *> \param[in] N
00087 *> \verbatim
00088 *>          N is INTEGER
00089 *>          The order of the matrix A.  N >= 0.  When N = 0, SLANTB is
00090 *>          set to zero.
00091 *> \endverbatim
00092 *>
00093 *> \param[in] K
00094 *> \verbatim
00095 *>          K is INTEGER
00096 *>          The number of super-diagonals of the matrix A if UPLO = 'U',
00097 *>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
00098 *>          K >= 0.
00099 *> \endverbatim
00100 *>
00101 *> \param[in] AB
00102 *> \verbatim
00103 *>          AB is REAL array, dimension (LDAB,N)
00104 *>          The upper or lower triangular band matrix A, stored in the
00105 *>          first k+1 rows of AB.  The j-th column of A is stored
00106 *>          in the j-th column of the array AB as follows:
00107 *>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
00108 *>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
00109 *>          Note that when DIAG = 'U', the elements of the array AB
00110 *>          corresponding to the diagonal elements of the matrix A are
00111 *>          not referenced, but are assumed to be one.
00112 *> \endverbatim
00113 *>
00114 *> \param[in] LDAB
00115 *> \verbatim
00116 *>          LDAB is INTEGER
00117 *>          The leading dimension of the array AB.  LDAB >= K+1.
00118 *> \endverbatim
00119 *>
00120 *> \param[out] WORK
00121 *> \verbatim
00122 *>          WORK is REAL array, dimension (MAX(1,LWORK)),
00123 *>          where LWORK >= N when NORM = 'I'; otherwise, WORK is not
00124 *>          referenced.
00125 *> \endverbatim
00126 *
00127 *  Authors:
00128 *  ========
00129 *
00130 *> \author Univ. of Tennessee 
00131 *> \author Univ. of California Berkeley 
00132 *> \author Univ. of Colorado Denver 
00133 *> \author NAG Ltd. 
00134 *
00135 *> \date November 2011
00136 *
00137 *> \ingroup realOTHERauxiliary
00138 *
00139 *  =====================================================================
00140       REAL             FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB,
00141      $                 LDAB, WORK )
00142 *
00143 *  -- LAPACK auxiliary routine (version 3.4.0) --
00144 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00145 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00146 *     November 2011
00147 *
00148 *     .. Scalar Arguments ..
00149       CHARACTER          DIAG, NORM, UPLO
00150       INTEGER            K, LDAB, N
00151 *     ..
00152 *     .. Array Arguments ..
00153       REAL               AB( LDAB, * ), WORK( * )
00154 *     ..
00155 *
00156 * =====================================================================
00157 *
00158 *     .. Parameters ..
00159       REAL               ONE, ZERO
00160       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00161 *     ..
00162 *     .. Local Scalars ..
00163       LOGICAL            UDIAG
00164       INTEGER            I, J, L
00165       REAL               SCALE, SUM, VALUE
00166 *     ..
00167 *     .. External Subroutines ..
00168       EXTERNAL           SLASSQ
00169 *     ..
00170 *     .. External Functions ..
00171       LOGICAL            LSAME
00172       EXTERNAL           LSAME
00173 *     ..
00174 *     .. Intrinsic Functions ..
00175       INTRINSIC          ABS, MAX, MIN, SQRT
00176 *     ..
00177 *     .. Executable Statements ..
00178 *
00179       IF( N.EQ.0 ) THEN
00180          VALUE = ZERO
00181       ELSE IF( LSAME( NORM, 'M' ) ) THEN
00182 *
00183 *        Find max(abs(A(i,j))).
00184 *
00185          IF( LSAME( DIAG, 'U' ) ) THEN
00186             VALUE = ONE
00187             IF( LSAME( UPLO, 'U' ) ) THEN
00188                DO 20 J = 1, N
00189                   DO 10 I = MAX( K+2-J, 1 ), K
00190                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00191    10             CONTINUE
00192    20          CONTINUE
00193             ELSE
00194                DO 40 J = 1, N
00195                   DO 30 I = 2, MIN( N+1-J, K+1 )
00196                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00197    30             CONTINUE
00198    40          CONTINUE
00199             END IF
00200          ELSE
00201             VALUE = ZERO
00202             IF( LSAME( UPLO, 'U' ) ) THEN
00203                DO 60 J = 1, N
00204                   DO 50 I = MAX( K+2-J, 1 ), K + 1
00205                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00206    50             CONTINUE
00207    60          CONTINUE
00208             ELSE
00209                DO 80 J = 1, N
00210                   DO 70 I = 1, MIN( N+1-J, K+1 )
00211                      VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
00212    70             CONTINUE
00213    80          CONTINUE
00214             END IF
00215          END IF
00216       ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
00217 *
00218 *        Find norm1(A).
00219 *
00220          VALUE = ZERO
00221          UDIAG = LSAME( DIAG, 'U' )
00222          IF( LSAME( UPLO, 'U' ) ) THEN
00223             DO 110 J = 1, N
00224                IF( UDIAG ) THEN
00225                   SUM = ONE
00226                   DO 90 I = MAX( K+2-J, 1 ), K
00227                      SUM = SUM + ABS( AB( I, J ) )
00228    90             CONTINUE
00229                ELSE
00230                   SUM = ZERO
00231                   DO 100 I = MAX( K+2-J, 1 ), K + 1
00232                      SUM = SUM + ABS( AB( I, J ) )
00233   100             CONTINUE
00234                END IF
00235                VALUE = MAX( VALUE, SUM )
00236   110       CONTINUE
00237          ELSE
00238             DO 140 J = 1, N
00239                IF( UDIAG ) THEN
00240                   SUM = ONE
00241                   DO 120 I = 2, MIN( N+1-J, K+1 )
00242                      SUM = SUM + ABS( AB( I, J ) )
00243   120             CONTINUE
00244                ELSE
00245                   SUM = ZERO
00246                   DO 130 I = 1, MIN( N+1-J, K+1 )
00247                      SUM = SUM + ABS( AB( I, J ) )
00248   130             CONTINUE
00249                END IF
00250                VALUE = MAX( VALUE, SUM )
00251   140       CONTINUE
00252          END IF
00253       ELSE IF( LSAME( NORM, 'I' ) ) THEN
00254 *
00255 *        Find normI(A).
00256 *
00257          VALUE = ZERO
00258          IF( LSAME( UPLO, 'U' ) ) THEN
00259             IF( LSAME( DIAG, 'U' ) ) THEN
00260                DO 150 I = 1, N
00261                   WORK( I ) = ONE
00262   150          CONTINUE
00263                DO 170 J = 1, N
00264                   L = K + 1 - J
00265                   DO 160 I = MAX( 1, J-K ), J - 1
00266                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00267   160             CONTINUE
00268   170          CONTINUE
00269             ELSE
00270                DO 180 I = 1, N
00271                   WORK( I ) = ZERO
00272   180          CONTINUE
00273                DO 200 J = 1, N
00274                   L = K + 1 - J
00275                   DO 190 I = MAX( 1, J-K ), J
00276                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00277   190             CONTINUE
00278   200          CONTINUE
00279             END IF
00280          ELSE
00281             IF( LSAME( DIAG, 'U' ) ) THEN
00282                DO 210 I = 1, N
00283                   WORK( I ) = ONE
00284   210          CONTINUE
00285                DO 230 J = 1, N
00286                   L = 1 - J
00287                   DO 220 I = J + 1, MIN( N, J+K )
00288                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00289   220             CONTINUE
00290   230          CONTINUE
00291             ELSE
00292                DO 240 I = 1, N
00293                   WORK( I ) = ZERO
00294   240          CONTINUE
00295                DO 260 J = 1, N
00296                   L = 1 - J
00297                   DO 250 I = J, MIN( N, J+K )
00298                      WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
00299   250             CONTINUE
00300   260          CONTINUE
00301             END IF
00302          END IF
00303          DO 270 I = 1, N
00304             VALUE = MAX( VALUE, WORK( I ) )
00305   270    CONTINUE
00306       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
00307 *
00308 *        Find normF(A).
00309 *
00310          IF( LSAME( UPLO, 'U' ) ) THEN
00311             IF( LSAME( DIAG, 'U' ) ) THEN
00312                SCALE = ONE
00313                SUM = N
00314                IF( K.GT.0 ) THEN
00315                   DO 280 J = 2, N
00316                      CALL SLASSQ( MIN( J-1, K ),
00317      $                            AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
00318      $                            SUM )
00319   280             CONTINUE
00320                END IF
00321             ELSE
00322                SCALE = ZERO
00323                SUM = ONE
00324                DO 290 J = 1, N
00325                   CALL SLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
00326      $                         1, SCALE, SUM )
00327   290          CONTINUE
00328             END IF
00329          ELSE
00330             IF( LSAME( DIAG, 'U' ) ) THEN
00331                SCALE = ONE
00332                SUM = N
00333                IF( K.GT.0 ) THEN
00334                   DO 300 J = 1, N - 1
00335                      CALL SLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
00336      $                            SUM )
00337   300             CONTINUE
00338                END IF
00339             ELSE
00340                SCALE = ZERO
00341                SUM = ONE
00342                DO 310 J = 1, N
00343                   CALL SLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
00344      $                         SUM )
00345   310          CONTINUE
00346             END IF
00347          END IF
00348          VALUE = SCALE*SQRT( SUM )
00349       END IF
00350 *
00351       SLANTB = VALUE
00352       RETURN
00353 *
00354 *     End of SLANTB
00355 *
00356       END
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