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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZGBMV 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 ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00012 * 00013 * .. Scalar Arguments .. 00014 * COMPLEX*16 ALPHA,BETA 00015 * INTEGER INCX,INCY,KL,KU,LDA,M,N 00016 * CHARACTER TRANS 00017 * .. 00018 * .. Array Arguments .. 00019 * COMPLEX*16 A(LDA,*),X(*),Y(*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> ZGBMV performs one of the matrix-vector operations 00029 *> 00030 *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or 00031 *> 00032 *> y := alpha*A**H*x + beta*y, 00033 *> 00034 *> where alpha and beta are scalars, x and y are vectors and A is an 00035 *> m by n band matrix, with kl sub-diagonals and ku super-diagonals. 00036 *> \endverbatim 00037 * 00038 * Arguments: 00039 * ========== 00040 * 00041 *> \param[in] TRANS 00042 *> \verbatim 00043 *> TRANS is CHARACTER*1 00044 *> On entry, TRANS specifies the operation to be performed as 00045 *> follows: 00046 *> 00047 *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y. 00048 *> 00049 *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. 00050 *> 00051 *> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] M 00055 *> \verbatim 00056 *> M is INTEGER 00057 *> On entry, M specifies the number of rows of the matrix A. 00058 *> M must be at least zero. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] N 00062 *> \verbatim 00063 *> N is INTEGER 00064 *> On entry, N specifies the number of columns of the matrix A. 00065 *> N must be at least zero. 00066 *> \endverbatim 00067 *> 00068 *> \param[in] KL 00069 *> \verbatim 00070 *> KL is INTEGER 00071 *> On entry, KL specifies the number of sub-diagonals of the 00072 *> matrix A. KL must satisfy 0 .le. KL. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] KU 00076 *> \verbatim 00077 *> KU is INTEGER 00078 *> On entry, KU specifies the number of super-diagonals of the 00079 *> matrix A. KU must satisfy 0 .le. KU. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] ALPHA 00083 *> \verbatim 00084 *> ALPHA is COMPLEX*16 00085 *> On entry, ALPHA specifies the scalar alpha. 00086 *> \endverbatim 00087 *> 00088 *> \param[in] A 00089 *> \verbatim 00090 *> A is COMPLEX*16 array of DIMENSION ( LDA, n ). 00091 *> Before entry, the leading ( kl + ku + 1 ) by n part of the 00092 *> array A must contain the matrix of coefficients, supplied 00093 *> column by column, with the leading diagonal of the matrix in 00094 *> row ( ku + 1 ) of the array, the first super-diagonal 00095 *> starting at position 2 in row ku, the first sub-diagonal 00096 *> starting at position 1 in row ( ku + 2 ), and so on. 00097 *> Elements in the array A that do not correspond to elements 00098 *> in the band matrix (such as the top left ku by ku triangle) 00099 *> are not referenced. 00100 *> The following program segment will transfer a band matrix 00101 *> from conventional full matrix storage to band storage: 00102 *> 00103 *> DO 20, J = 1, N 00104 *> K = KU + 1 - J 00105 *> DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) 00106 *> A( K + I, J ) = matrix( I, J ) 00107 *> 10 CONTINUE 00108 *> 20 CONTINUE 00109 *> \endverbatim 00110 *> 00111 *> \param[in] LDA 00112 *> \verbatim 00113 *> LDA is INTEGER 00114 *> On entry, LDA specifies the first dimension of A as declared 00115 *> in the calling (sub) program. LDA must be at least 00116 *> ( kl + ku + 1 ). 00117 *> \endverbatim 00118 *> 00119 *> \param[in] X 00120 *> \verbatim 00121 *> X is COMPLEX*16 array of DIMENSION at least 00122 *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' 00123 *> and at least 00124 *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. 00125 *> Before entry, the incremented array X must contain the 00126 *> vector x. 00127 *> \endverbatim 00128 *> 00129 *> \param[in] INCX 00130 *> \verbatim 00131 *> INCX is INTEGER 00132 *> On entry, INCX specifies the increment for the elements of 00133 *> X. INCX must not be zero. 00134 *> \endverbatim 00135 *> 00136 *> \param[in] BETA 00137 *> \verbatim 00138 *> BETA is COMPLEX*16 00139 *> On entry, BETA specifies the scalar beta. When BETA is 00140 *> supplied as zero then Y need not be set on input. 00141 *> \endverbatim 00142 *> 00143 *> \param[in,out] Y 00144 *> \verbatim 00145 *> Y is COMPLEX*16 array of DIMENSION at least 00146 *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' 00147 *> and at least 00148 *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. 00149 *> Before entry, the incremented array Y must contain the 00150 *> vector y. On exit, Y is overwritten by the updated vector y. 00151 *> \endverbatim 00152 *> 00153 *> \param[in] INCY 00154 *> \verbatim 00155 *> INCY is INTEGER 00156 *> On entry, INCY specifies the increment for the elements of 00157 *> Y. INCY must not be zero. 00158 *> \endverbatim 00159 * 00160 * Authors: 00161 * ======== 00162 * 00163 *> \author Univ. of Tennessee 00164 *> \author Univ. of California Berkeley 00165 *> \author Univ. of Colorado Denver 00166 *> \author NAG Ltd. 00167 * 00168 *> \date November 2011 00169 * 00170 *> \ingroup complex16_blas_level2 00171 * 00172 *> \par Further Details: 00173 * ===================== 00174 *> 00175 *> \verbatim 00176 *> 00177 *> Level 2 Blas routine. 00178 *> The vector and matrix arguments are not referenced when N = 0, or M = 0 00179 *> 00180 *> -- Written on 22-October-1986. 00181 *> Jack Dongarra, Argonne National Lab. 00182 *> Jeremy Du Croz, Nag Central Office. 00183 *> Sven Hammarling, Nag Central Office. 00184 *> Richard Hanson, Sandia National Labs. 00185 *> \endverbatim 00186 *> 00187 * ===================================================================== 00188 SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 00189 * 00190 * -- Reference BLAS level2 routine (version 3.4.0) -- 00191 * -- Reference BLAS is a software package provided by Univ. of Tennessee, -- 00192 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00193 * November 2011 00194 * 00195 * .. Scalar Arguments .. 00196 COMPLEX*16 ALPHA,BETA 00197 INTEGER INCX,INCY,KL,KU,LDA,M,N 00198 CHARACTER TRANS 00199 * .. 00200 * .. Array Arguments .. 00201 COMPLEX*16 A(LDA,*),X(*),Y(*) 00202 * .. 00203 * 00204 * ===================================================================== 00205 * 00206 * .. Parameters .. 00207 COMPLEX*16 ONE 00208 PARAMETER (ONE= (1.0D+0,0.0D+0)) 00209 COMPLEX*16 ZERO 00210 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00211 * .. 00212 * .. Local Scalars .. 00213 COMPLEX*16 TEMP 00214 INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY 00215 LOGICAL NOCONJ 00216 * .. 00217 * .. External Functions .. 00218 LOGICAL LSAME 00219 EXTERNAL LSAME 00220 * .. 00221 * .. External Subroutines .. 00222 EXTERNAL XERBLA 00223 * .. 00224 * .. Intrinsic Functions .. 00225 INTRINSIC DCONJG,MAX,MIN 00226 * .. 00227 * 00228 * Test the input parameters. 00229 * 00230 INFO = 0 00231 IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 00232 + .NOT.LSAME(TRANS,'C')) THEN 00233 INFO = 1 00234 ELSE IF (M.LT.0) THEN 00235 INFO = 2 00236 ELSE IF (N.LT.0) THEN 00237 INFO = 3 00238 ELSE IF (KL.LT.0) THEN 00239 INFO = 4 00240 ELSE IF (KU.LT.0) THEN 00241 INFO = 5 00242 ELSE IF (LDA.LT. (KL+KU+1)) THEN 00243 INFO = 8 00244 ELSE IF (INCX.EQ.0) THEN 00245 INFO = 10 00246 ELSE IF (INCY.EQ.0) THEN 00247 INFO = 13 00248 END IF 00249 IF (INFO.NE.0) THEN 00250 CALL XERBLA('ZGBMV ',INFO) 00251 RETURN 00252 END IF 00253 * 00254 * Quick return if possible. 00255 * 00256 IF ((M.EQ.0) .OR. (N.EQ.0) .OR. 00257 + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 00258 * 00259 NOCONJ = LSAME(TRANS,'T') 00260 * 00261 * Set LENX and LENY, the lengths of the vectors x and y, and set 00262 * up the start points in X and Y. 00263 * 00264 IF (LSAME(TRANS,'N')) THEN 00265 LENX = N 00266 LENY = M 00267 ELSE 00268 LENX = M 00269 LENY = N 00270 END IF 00271 IF (INCX.GT.0) THEN 00272 KX = 1 00273 ELSE 00274 KX = 1 - (LENX-1)*INCX 00275 END IF 00276 IF (INCY.GT.0) THEN 00277 KY = 1 00278 ELSE 00279 KY = 1 - (LENY-1)*INCY 00280 END IF 00281 * 00282 * Start the operations. In this version the elements of A are 00283 * accessed sequentially with one pass through the band part of A. 00284 * 00285 * First form y := beta*y. 00286 * 00287 IF (BETA.NE.ONE) THEN 00288 IF (INCY.EQ.1) THEN 00289 IF (BETA.EQ.ZERO) THEN 00290 DO 10 I = 1,LENY 00291 Y(I) = ZERO 00292 10 CONTINUE 00293 ELSE 00294 DO 20 I = 1,LENY 00295 Y(I) = BETA*Y(I) 00296 20 CONTINUE 00297 END IF 00298 ELSE 00299 IY = KY 00300 IF (BETA.EQ.ZERO) THEN 00301 DO 30 I = 1,LENY 00302 Y(IY) = ZERO 00303 IY = IY + INCY 00304 30 CONTINUE 00305 ELSE 00306 DO 40 I = 1,LENY 00307 Y(IY) = BETA*Y(IY) 00308 IY = IY + INCY 00309 40 CONTINUE 00310 END IF 00311 END IF 00312 END IF 00313 IF (ALPHA.EQ.ZERO) RETURN 00314 KUP1 = KU + 1 00315 IF (LSAME(TRANS,'N')) THEN 00316 * 00317 * Form y := alpha*A*x + y. 00318 * 00319 JX = KX 00320 IF (INCY.EQ.1) THEN 00321 DO 60 J = 1,N 00322 IF (X(JX).NE.ZERO) THEN 00323 TEMP = ALPHA*X(JX) 00324 K = KUP1 - J 00325 DO 50 I = MAX(1,J-KU),MIN(M,J+KL) 00326 Y(I) = Y(I) + TEMP*A(K+I,J) 00327 50 CONTINUE 00328 END IF 00329 JX = JX + INCX 00330 60 CONTINUE 00331 ELSE 00332 DO 80 J = 1,N 00333 IF (X(JX).NE.ZERO) THEN 00334 TEMP = ALPHA*X(JX) 00335 IY = KY 00336 K = KUP1 - J 00337 DO 70 I = MAX(1,J-KU),MIN(M,J+KL) 00338 Y(IY) = Y(IY) + TEMP*A(K+I,J) 00339 IY = IY + INCY 00340 70 CONTINUE 00341 END IF 00342 JX = JX + INCX 00343 IF (J.GT.KU) KY = KY + INCY 00344 80 CONTINUE 00345 END IF 00346 ELSE 00347 * 00348 * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y. 00349 * 00350 JY = KY 00351 IF (INCX.EQ.1) THEN 00352 DO 110 J = 1,N 00353 TEMP = ZERO 00354 K = KUP1 - J 00355 IF (NOCONJ) THEN 00356 DO 90 I = MAX(1,J-KU),MIN(M,J+KL) 00357 TEMP = TEMP + A(K+I,J)*X(I) 00358 90 CONTINUE 00359 ELSE 00360 DO 100 I = MAX(1,J-KU),MIN(M,J+KL) 00361 TEMP = TEMP + DCONJG(A(K+I,J))*X(I) 00362 100 CONTINUE 00363 END IF 00364 Y(JY) = Y(JY) + ALPHA*TEMP 00365 JY = JY + INCY 00366 110 CONTINUE 00367 ELSE 00368 DO 140 J = 1,N 00369 TEMP = ZERO 00370 IX = KX 00371 K = KUP1 - J 00372 IF (NOCONJ) THEN 00373 DO 120 I = MAX(1,J-KU),MIN(M,J+KL) 00374 TEMP = TEMP + A(K+I,J)*X(IX) 00375 IX = IX + INCX 00376 120 CONTINUE 00377 ELSE 00378 DO 130 I = MAX(1,J-KU),MIN(M,J+KL) 00379 TEMP = TEMP + DCONJG(A(K+I,J))*X(IX) 00380 IX = IX + INCX 00381 130 CONTINUE 00382 END IF 00383 Y(JY) = Y(JY) + ALPHA*TEMP 00384 JY = JY + INCY 00385 IF (J.GT.KU) KX = KX + INCX 00386 140 CONTINUE 00387 END IF 00388 END IF 00389 * 00390 RETURN 00391 * 00392 * End of ZGBMV . 00393 * 00394 END