LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
sla_gbamv.f
Go to the documentation of this file.
00001 *> \brief \b SLA_GBAMV
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download SLA_GBAMV + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_gbamv.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_gbamv.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_gbamv.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE SLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
00022 *                             INCX, BETA, Y, INCY )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       REAL               ALPHA, BETA
00026 *       INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS
00027 *       ..
00028 *       .. Array Arguments ..
00029 *       REAL               AB( LDAB, * ), X( * ), Y( * )
00030 *       ..
00031 *  
00032 *
00033 *> \par Purpose:
00034 *  =============
00035 *>
00036 *> \verbatim
00037 *>
00038 *> SLA_GBAMV  performs one of the matrix-vector operations
00039 *>
00040 *>         y := alpha*abs(A)*abs(x) + beta*abs(y),
00041 *>    or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
00042 *>
00043 *> where alpha and beta are scalars, x and y are vectors and A is an
00044 *> m by n matrix.
00045 *>
00046 *> This function is primarily used in calculating error bounds.
00047 *> To protect against underflow during evaluation, components in
00048 *> the resulting vector are perturbed away from zero by (N+1)
00049 *> times the underflow threshold.  To prevent unnecessarily large
00050 *> errors for block-structure embedded in general matrices,
00051 *> "symbolically" zero components are not perturbed.  A zero
00052 *> entry is considered "symbolic" if all multiplications involved
00053 *> in computing that entry have at least one zero multiplicand.
00054 *> \endverbatim
00055 *
00056 *  Arguments:
00057 *  ==========
00058 *
00059 *> \param[in] TRANS
00060 *> \verbatim
00061 *>          TRANS is INTEGER
00062 *>           On entry, TRANS specifies the operation to be performed as
00063 *>           follows:
00064 *>
00065 *>             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
00066 *>             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
00067 *>             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
00068 *>
00069 *>           Unchanged on exit.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] M
00073 *> \verbatim
00074 *>          M is INTEGER
00075 *>           On entry, M specifies the number of rows of the matrix A.
00076 *>           M must be at least zero.
00077 *>           Unchanged on exit.
00078 *> \endverbatim
00079 *>
00080 *> \param[in] N
00081 *> \verbatim
00082 *>          N is INTEGER
00083 *>           On entry, N specifies the number of columns of the matrix A.
00084 *>           N must be at least zero.
00085 *>           Unchanged on exit.
00086 *> \endverbatim
00087 *>
00088 *> \param[in] KL
00089 *> \verbatim
00090 *>          KL is INTEGER
00091 *>           The number of subdiagonals within the band of A.  KL >= 0.
00092 *> \endverbatim
00093 *>
00094 *> \param[in] KU
00095 *> \verbatim
00096 *>          KU is INTEGER
00097 *>           The number of superdiagonals within the band of A.  KU >= 0.
00098 *> \endverbatim
00099 *>
00100 *> \param[in] ALPHA
00101 *> \verbatim
00102 *>          ALPHA is REAL
00103 *>           On entry, ALPHA specifies the scalar alpha.
00104 *>           Unchanged on exit.
00105 *> \endverbatim
00106 *>
00107 *> \param[in] AB
00108 *> \verbatim
00109 *>          AB is REAL array of DIMENSION ( LDAB, n )
00110 *>           Before entry, the leading m by n part of the array AB must
00111 *>           contain the matrix of coefficients.
00112 *>           Unchanged on exit.
00113 *> \endverbatim
00114 *>
00115 *> \param[in] LDAB
00116 *> \verbatim
00117 *>          LDAB is INTEGER
00118 *>           On entry, LDA specifies the first dimension of AB as declared
00119 *>           in the calling (sub) program. LDAB must be at least
00120 *>           max( 1, m ).
00121 *>           Unchanged on exit.
00122 *> \endverbatim
00123 *>
00124 *> \param[in] X
00125 *> \verbatim
00126 *>          X is REAL array, dimension
00127 *>           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
00128 *>           and at least
00129 *>           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
00130 *>           Before entry, the incremented array X must contain the
00131 *>           vector x.
00132 *>           Unchanged on exit.
00133 *> \endverbatim
00134 *>
00135 *> \param[in] INCX
00136 *> \verbatim
00137 *>          INCX is INTEGER
00138 *>           On entry, INCX specifies the increment for the elements of
00139 *>           X. INCX must not be zero.
00140 *>           Unchanged on exit.
00141 *> \endverbatim
00142 *>
00143 *> \param[in] BETA
00144 *> \verbatim
00145 *>          BETA is REAL
00146 *>           On entry, BETA specifies the scalar beta. When BETA is
00147 *>           supplied as zero then Y need not be set on input.
00148 *>           Unchanged on exit.
00149 *> \endverbatim
00150 *>
00151 *> \param[in,out] Y
00152 *> \verbatim
00153 *>          Y is REAL array, dimension
00154 *>           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
00155 *>           and at least
00156 *>           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
00157 *>           Before entry with BETA non-zero, the incremented array Y
00158 *>           must contain the vector y. On exit, Y is overwritten by the
00159 *>           updated vector y.
00160 *> \endverbatim
00161 *>
00162 *> \param[in] INCY
00163 *> \verbatim
00164 *>          INCY is INTEGER
00165 *>           On entry, INCY specifies the increment for the elements of
00166 *>           Y. INCY must not be zero.
00167 *>           Unchanged on exit.
00168 *>
00169 *>  Level 2 Blas routine.
00170 *> \endverbatim
00171 *
00172 *  Authors:
00173 *  ========
00174 *
00175 *> \author Univ. of Tennessee 
00176 *> \author Univ. of California Berkeley 
00177 *> \author Univ. of Colorado Denver 
00178 *> \author NAG Ltd. 
00179 *
00180 *> \date November 2011
00181 *
00182 *> \ingroup realGBcomputational
00183 *
00184 *  =====================================================================
00185       SUBROUTINE SLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB, LDAB, X,
00186      $                      INCX, BETA, Y, INCY )
00187 *
00188 *  -- LAPACK computational routine (version 3.4.0) --
00189 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00190 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00191 *     November 2011
00192 *
00193 *     .. Scalar Arguments ..
00194       REAL               ALPHA, BETA
00195       INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS
00196 *     ..
00197 *     .. Array Arguments ..
00198       REAL               AB( LDAB, * ), X( * ), Y( * )
00199 *     ..
00200 *
00201 *  =====================================================================
00202 *     .. Parameters ..
00203       REAL               ONE, ZERO
00204       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00205 *     ..
00206 *     .. Local Scalars ..
00207       LOGICAL            SYMB_ZERO
00208       REAL               TEMP, SAFE1
00209       INTEGER            I, INFO, IY, J, JX, KX, KY, LENX, LENY, KD, KE
00210 *     ..
00211 *     .. External Subroutines ..
00212       EXTERNAL           XERBLA, SLAMCH
00213       REAL               SLAMCH
00214 *     ..
00215 *     .. External Functions ..
00216       EXTERNAL           ILATRANS
00217       INTEGER            ILATRANS
00218 *     ..
00219 *     .. Intrinsic Functions ..
00220       INTRINSIC          MAX, ABS, SIGN
00221 *     ..
00222 *     .. Executable Statements ..
00223 *
00224 *     Test the input parameters.
00225 *
00226       INFO = 0
00227       IF     ( .NOT.( ( TRANS.EQ.ILATRANS( 'N' ) )
00228      $           .OR. ( TRANS.EQ.ILATRANS( 'T' ) )
00229      $           .OR. ( TRANS.EQ.ILATRANS( 'C' ) ) ) ) THEN
00230          INFO = 1
00231       ELSE IF( M.LT.0 )THEN
00232          INFO = 2
00233       ELSE IF( N.LT.0 )THEN
00234          INFO = 3
00235       ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
00236          INFO = 4
00237       ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
00238          INFO = 5
00239       ELSE IF( LDAB.LT.KL+KU+1 )THEN
00240          INFO = 6
00241       ELSE IF( INCX.EQ.0 )THEN
00242          INFO = 8
00243       ELSE IF( INCY.EQ.0 )THEN
00244          INFO = 11
00245       END IF
00246       IF( INFO.NE.0 )THEN
00247          CALL XERBLA( 'SLA_GBAMV ', INFO )
00248          RETURN
00249       END IF
00250 *
00251 *     Quick return if possible.
00252 *
00253       IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
00254      $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
00255      $   RETURN
00256 *
00257 *     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
00258 *     up the start points in  X  and  Y.
00259 *
00260       IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
00261          LENX = N
00262          LENY = M
00263       ELSE
00264          LENX = M
00265          LENY = N
00266       END IF
00267       IF( INCX.GT.0 )THEN
00268          KX = 1
00269       ELSE
00270          KX = 1 - ( LENX - 1 )*INCX
00271       END IF
00272       IF( INCY.GT.0 )THEN
00273          KY = 1
00274       ELSE
00275          KY = 1 - ( LENY - 1 )*INCY
00276       END IF
00277 *
00278 *     Set SAFE1 essentially to be the underflow threshold times the
00279 *     number of additions in each row.
00280 *
00281       SAFE1 = SLAMCH( 'Safe minimum' )
00282       SAFE1 = (N+1)*SAFE1
00283 *
00284 *     Form  y := alpha*abs(A)*abs(x) + beta*abs(y).
00285 *
00286 *     The O(M*N) SYMB_ZERO tests could be replaced by O(N) queries to
00287 *     the inexact flag.  Still doesn't help change the iteration order
00288 *     to per-column.
00289 *
00290       KD = KU + 1
00291       KE = KL + 1
00292       IY = KY
00293       IF ( INCX.EQ.1 ) THEN
00294          IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
00295             DO I = 1, LENY
00296                IF ( BETA .EQ. ZERO ) THEN
00297                   SYMB_ZERO = .TRUE.
00298                   Y( IY ) = 0.0
00299                ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
00300                   SYMB_ZERO = .TRUE.
00301                ELSE
00302                   SYMB_ZERO = .FALSE.
00303                   Y( IY ) = BETA * ABS( Y( IY ) )
00304                END IF
00305                IF ( ALPHA .NE. ZERO ) THEN
00306                   DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
00307                      TEMP = ABS( AB( KD+I-J, J ) )
00308                      SYMB_ZERO = SYMB_ZERO .AND.
00309      $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
00310 
00311                      Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
00312                   END DO
00313                END IF
00314 
00315                IF ( .NOT.SYMB_ZERO )
00316      $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
00317                IY = IY + INCY
00318             END DO
00319          ELSE
00320             DO I = 1, LENY
00321                IF ( BETA .EQ. ZERO ) THEN
00322                   SYMB_ZERO = .TRUE.
00323                   Y( IY ) = 0.0
00324                ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
00325                   SYMB_ZERO = .TRUE.
00326                ELSE
00327                   SYMB_ZERO = .FALSE.
00328                   Y( IY ) = BETA * ABS( Y( IY ) )
00329                END IF
00330                IF ( ALPHA .NE. ZERO ) THEN
00331                   DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
00332                      TEMP = ABS( AB( KE-I+J, I ) )
00333                      SYMB_ZERO = SYMB_ZERO .AND.
00334      $                    ( X( J ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
00335 
00336                      Y( IY ) = Y( IY ) + ALPHA*ABS( X( J ) )*TEMP
00337                   END DO
00338                END IF
00339 
00340                IF ( .NOT.SYMB_ZERO )
00341      $              Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
00342                IY = IY + INCY
00343             END DO
00344          END IF
00345       ELSE
00346          IF( TRANS.EQ.ILATRANS( 'N' ) )THEN
00347             DO I = 1, LENY
00348                IF ( BETA .EQ. ZERO ) THEN
00349                   SYMB_ZERO = .TRUE.
00350                   Y( IY ) = 0.0
00351                ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
00352                   SYMB_ZERO = .TRUE.
00353                ELSE
00354                   SYMB_ZERO = .FALSE.
00355                   Y( IY ) = BETA * ABS( Y( IY ) )
00356                END IF
00357                IF ( ALPHA .NE. ZERO ) THEN
00358                   JX = KX
00359                   DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
00360                      TEMP = ABS( AB( KD+I-J, J ) )
00361                      SYMB_ZERO = SYMB_ZERO .AND.
00362      $                    ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
00363 
00364                      Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
00365                      JX = JX + INCX
00366                   END DO
00367                END IF
00368 
00369                IF ( .NOT.SYMB_ZERO )
00370      $           Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
00371 
00372                IY = IY + INCY
00373             END DO
00374          ELSE
00375             DO I = 1, LENY
00376                IF ( BETA .EQ. ZERO ) THEN
00377                   SYMB_ZERO = .TRUE.
00378                   Y( IY ) = 0.0
00379                ELSE IF ( Y( IY ) .EQ. ZERO ) THEN
00380                   SYMB_ZERO = .TRUE.
00381                ELSE
00382                   SYMB_ZERO = .FALSE.
00383                   Y( IY ) = BETA * ABS( Y( IY ) )
00384                END IF
00385                IF ( ALPHA .NE. ZERO ) THEN
00386                   JX = KX
00387                   DO J = MAX( I-KL, 1 ), MIN( I+KU, LENX )
00388                      TEMP = ABS( AB( KE-I+J, I ) )
00389                      SYMB_ZERO = SYMB_ZERO .AND.
00390      $                    ( X( JX ) .EQ. ZERO .OR. TEMP .EQ. ZERO )
00391 
00392                      Y( IY ) = Y( IY ) + ALPHA*ABS( X( JX ) )*TEMP
00393                      JX = JX + INCX
00394                   END DO
00395                END IF
00396 
00397                IF ( .NOT.SYMB_ZERO )
00398      $           Y( IY ) = Y( IY ) + SIGN( SAFE1, Y( IY ) )
00399 
00400                IY = IY + INCY
00401             END DO
00402          END IF
00403 
00404       END IF
00405 *
00406       RETURN
00407 *
00408 *     End of SLA_GBAMV
00409 *
00410       END
 All Files Functions