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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DGBMV 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00012 * 00013 * .. Scalar Arguments .. 00014 * DOUBLE PRECISION ALPHA,BETA 00015 * INTEGER INCX,INCY,KL,KU,LDA,M,N 00016 * CHARACTER TRANS 00017 * .. 00018 * .. Array Arguments .. 00019 * DOUBLE PRECISION A(LDA,*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> DGBMV performs one of the matrix-vector operations 00029 *> 00030 *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, 00031 *> 00032 *> where alpha and beta are scalars, x and y are vectors and A is an 00033 *> m by n band matrix, with kl sub-diagonals and ku super-diagonals. 00034 *> \endverbatim 00035 * 00036 * Arguments: 00037 * ========== 00038 * 00039 *> \param[in] TRANS 00040 *> \verbatim 00041 *> TRANS is CHARACTER*1 00042 *> On entry, TRANS specifies the operation to be performed as 00043 *> follows: 00044 *> 00045 *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. 00046 *> 00047 *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. 00048 *> 00049 *> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y. 00050 *> \endverbatim 00051 *> 00052 *> \param[in] M 00053 *> \verbatim 00054 *> M is INTEGER 00055 *> On entry, M specifies the number of rows of the matrix A. 00056 *> M must be at least zero. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] N 00060 *> \verbatim 00061 *> N is INTEGER 00062 *> On entry, N specifies the number of columns of the matrix A. 00063 *> N must be at least zero. 00064 *> \endverbatim 00065 *> 00066 *> \param[in] KL 00067 *> \verbatim 00068 *> KL is INTEGER 00069 *> On entry, KL specifies the number of sub-diagonals of the 00070 *> matrix A. KL must satisfy 0 .le. KL. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] KU 00074 *> \verbatim 00075 *> KU is INTEGER 00076 *> On entry, KU specifies the number of super-diagonals of the 00077 *> matrix A. KU must satisfy 0 .le. KU. 00078 *> \endverbatim 00079 *> 00080 *> \param[in] ALPHA 00081 *> \verbatim 00082 *> ALPHA is DOUBLE PRECISION. 00083 *> On entry, ALPHA specifies the scalar alpha. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] A 00087 *> \verbatim 00088 *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). 00089 *> Before entry, the leading ( kl + ku + 1 ) by n part of the 00090 *> array A must contain the matrix of coefficients, supplied 00091 *> column by column, with the leading diagonal of the matrix in 00092 *> row ( ku + 1 ) of the array, the first super-diagonal 00093 *> starting at position 2 in row ku, the first sub-diagonal 00094 *> starting at position 1 in row ( ku + 2 ), and so on. 00095 *> Elements in the array A that do not correspond to elements 00096 *> in the band matrix (such as the top left ku by ku triangle) 00097 *> are not referenced. 00098 *> The following program segment will transfer a band matrix 00099 *> from conventional full matrix storage to band storage: 00100 *> 00101 *> DO 20, J = 1, N 00102 *> K = KU + 1 - J 00103 *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) 00104 *> A( K + I, J ) = matrix( I, J ) 00105 *> 10 CONTINUE 00106 *> 20 CONTINUE 00107 *> \endverbatim 00108 *> 00109 *> \param[in] LDA 00110 *> \verbatim 00111 *> LDA is INTEGER 00112 *> On entry, LDA specifies the first dimension of A as declared 00113 *> in the calling (sub) program. LDA must be at least 00114 *> ( kl + ku + 1 ). 00115 *> \endverbatim 00116 *> 00117 *> \param[in] X 00118 *> \verbatim 00119 *> X is DOUBLE PRECISION array of DIMENSION at least 00120 *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' 00121 *> and at least 00122 *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. 00123 *> Before entry, the incremented array X must contain the 00124 *> vector x. 00125 *> \endverbatim 00126 *> 00127 *> \param[in] INCX 00128 *> \verbatim 00129 *> INCX is INTEGER 00130 *> On entry, INCX specifies the increment for the elements of 00131 *> X. INCX must not be zero. 00132 *> \endverbatim 00133 *> 00134 *> \param[in] BETA 00135 *> \verbatim 00136 *> BETA is DOUBLE PRECISION. 00137 *> On entry, BETA specifies the scalar beta. When BETA is 00138 *> supplied as zero then Y need not be set on input. 00139 *> \endverbatim 00140 *> 00141 *> \param[in,out] Y 00142 *> \verbatim 00143 *> Y is DOUBLE PRECISION array of DIMENSION at least 00144 *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' 00145 *> and at least 00146 *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. 00147 *> Before entry, the incremented array Y must contain the 00148 *> vector y. On exit, Y is overwritten by the updated vector y. 00149 *> \endverbatim 00150 *> 00151 *> \param[in] INCY 00152 *> \verbatim 00153 *> INCY is INTEGER 00154 *> On entry, INCY specifies the increment for the elements of 00155 *> Y. INCY must not be zero. 00156 *> \endverbatim 00157 * 00158 * Authors: 00159 * ======== 00160 * 00161 *> \author Univ. of Tennessee 00162 *> \author Univ. of California Berkeley 00163 *> \author Univ. of Colorado Denver 00164 *> \author NAG Ltd. 00165 * 00166 *> \date November 2011 00167 * 00168 *> \ingroup double_blas_level2 00169 * 00170 *> \par Further Details: 00171 * ===================== 00172 *> 00173 *> \verbatim 00174 *> 00175 *> Level 2 Blas routine. 00176 *> The vector and matrix arguments are not referenced when N = 0, or M = 0 00177 *> 00178 *> -- Written on 22-October-1986. 00179 *> Jack Dongarra, Argonne National Lab. 00180 *> Jeremy Du Croz, Nag Central Office. 00181 *> Sven Hammarling, Nag Central Office. 00182 *> Richard Hanson, Sandia National Labs. 00183 *> \endverbatim 00184 *> 00185 * ===================================================================== 00186 SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00187 * 00188 * -- Reference BLAS level2 routine (version 3.4.0) -- 00189 * -- Reference BLAS 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 DOUBLE PRECISION ALPHA,BETA 00195 INTEGER INCX,INCY,KL,KU,LDA,M,N 00196 CHARACTER TRANS 00197 * .. 00198 * .. Array Arguments .. 00199 DOUBLE PRECISION A(LDA,*),X(*),Y(*) 00200 * .. 00201 * 00202 * ===================================================================== 00203 * 00204 * .. Parameters .. 00205 DOUBLE PRECISION ONE,ZERO 00206 PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) 00207 * .. 00208 * .. Local Scalars .. 00209 DOUBLE PRECISION TEMP 00210 INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY 00211 * .. 00212 * .. External Functions .. 00213 LOGICAL LSAME 00214 EXTERNAL LSAME 00215 * .. 00216 * .. External Subroutines .. 00217 EXTERNAL XERBLA 00218 * .. 00219 * .. Intrinsic Functions .. 00220 INTRINSIC MAX,MIN 00221 * .. 00222 * 00223 * Test the input parameters. 00224 * 00225 INFO = 0 00226 IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00227 + .NOT.LSAME(TRANS,'C')) THEN 00228 INFO = 1 00229 ELSE IF (M.LT.0) THEN 00230 INFO = 2 00231 ELSE IF (N.LT.0) THEN 00232 INFO = 3 00233 ELSE IF (KL.LT.0) THEN 00234 INFO = 4 00235 ELSE IF (KU.LT.0) THEN 00236 INFO = 5 00237 ELSE IF (LDA.LT. (KL+KU+1)) THEN 00238 INFO = 8 00239 ELSE IF (INCX.EQ.0) THEN 00240 INFO = 10 00241 ELSE IF (INCY.EQ.0) THEN 00242 INFO = 13 00243 END IF 00244 IF (INFO.NE.0) THEN 00245 CALL XERBLA('DGBMV ',INFO) 00246 RETURN 00247 END IF 00248 * 00249 * Quick return if possible. 00250 * 00251 IF ((M.EQ.0) .OR. (N.EQ.0) .OR. 00252 + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00253 * 00254 * Set LENX and LENY, the lengths of the vectors x and y, and set 00255 * up the start points in X and Y. 00256 * 00257 IF (LSAME(TRANS,'N')) THEN 00258 LENX = N 00259 LENY = M 00260 ELSE 00261 LENX = M 00262 LENY = N 00263 END IF 00264 IF (INCX.GT.0) THEN 00265 KX = 1 00266 ELSE 00267 KX = 1 - (LENX-1)*INCX 00268 END IF 00269 IF (INCY.GT.0) THEN 00270 KY = 1 00271 ELSE 00272 KY = 1 - (LENY-1)*INCY 00273 END IF 00274 * 00275 * Start the operations. In this version the elements of A are 00276 * accessed sequentially with one pass through the band part of A. 00277 * 00278 * First form y := beta*y. 00279 * 00280 IF (BETA.NE.ONE) THEN 00281 IF (INCY.EQ.1) THEN 00282 IF (BETA.EQ.ZERO) THEN 00283 DO 10 I = 1,LENY 00284 Y(I) = ZERO 00285 10 CONTINUE 00286 ELSE 00287 DO 20 I = 1,LENY 00288 Y(I) = BETA*Y(I) 00289 20 CONTINUE 00290 END IF 00291 ELSE 00292 IY = KY 00293 IF (BETA.EQ.ZERO) THEN 00294 DO 30 I = 1,LENY 00295 Y(IY) = ZERO 00296 IY = IY + INCY 00297 30 CONTINUE 00298 ELSE 00299 DO 40 I = 1,LENY 00300 Y(IY) = BETA*Y(IY) 00301 IY = IY + INCY 00302 40 CONTINUE 00303 END IF 00304 END IF 00305 END IF 00306 IF (ALPHA.EQ.ZERO) RETURN 00307 KUP1 = KU + 1 00308 IF (LSAME(TRANS,'N')) THEN 00309 * 00310 * Form y := alpha*A*x + y. 00311 * 00312 JX = KX 00313 IF (INCY.EQ.1) THEN 00314 DO 60 J = 1,N 00315 IF (X(JX).NE.ZERO) THEN 00316 TEMP = ALPHA*X(JX) 00317 K = KUP1 - J 00318 DO 50 I = MAX(1,J-KU),MIN(M,J+KL) 00319 Y(I) = Y(I) + TEMP*A(K+I,J) 00320 50 CONTINUE 00321 END IF 00322 JX = JX + INCX 00323 60 CONTINUE 00324 ELSE 00325 DO 80 J = 1,N 00326 IF (X(JX).NE.ZERO) THEN 00327 TEMP = ALPHA*X(JX) 00328 IY = KY 00329 K = KUP1 - J 00330 DO 70 I = MAX(1,J-KU),MIN(M,J+KL) 00331 Y(IY) = Y(IY) + TEMP*A(K+I,J) 00332 IY = IY + INCY 00333 70 CONTINUE 00334 END IF 00335 JX = JX + INCX 00336 IF (J.GT.KU) KY = KY + INCY 00337 80 CONTINUE 00338 END IF 00339 ELSE 00340 * 00341 * Form y := alpha*A**T*x + y. 00342 * 00343 JY = KY 00344 IF (INCX.EQ.1) THEN 00345 DO 100 J = 1,N 00346 TEMP = ZERO 00347 K = KUP1 - J 00348 DO 90 I = MAX(1,J-KU),MIN(M,J+KL) 00349 TEMP = TEMP + A(K+I,J)*X(I) 00350 90 CONTINUE 00351 Y(JY) = Y(JY) + ALPHA*TEMP 00352 JY = JY + INCY 00353 100 CONTINUE 00354 ELSE 00355 DO 120 J = 1,N 00356 TEMP = ZERO 00357 IX = KX 00358 K = KUP1 - J 00359 DO 110 I = MAX(1,J-KU),MIN(M,J+KL) 00360 TEMP = TEMP + A(K+I,J)*X(IX) 00361 IX = IX + INCX 00362 110 CONTINUE 00363 Y(JY) = Y(JY) + ALPHA*TEMP 00364 JY = JY + INCY 00365 IF (J.GT.KU) KX = KX + INCX 00366 120 CONTINUE 00367 END IF 00368 END IF 00369 * 00370 RETURN 00371 * 00372 * End of DGBMV . 00373 * 00374 END