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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZGEMM 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 ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) 00012 * 00013 * .. Scalar Arguments .. 00014 * COMPLEX*16 ALPHA,BETA 00015 * INTEGER K,LDA,LDB,LDC,M,N 00016 * CHARACTER TRANSA,TRANSB 00017 * .. 00018 * .. Array Arguments .. 00019 * COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> ZGEMM performs one of the matrix-matrix operations 00029 *> 00030 *> C := alpha*op( A )*op( B ) + beta*C, 00031 *> 00032 *> where op( X ) is one of 00033 *> 00034 *> op( X ) = X or op( X ) = X**T or op( X ) = X**H, 00035 *> 00036 *> alpha and beta are scalars, and A, B and C are matrices, with op( A ) 00037 *> an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. 00038 *> \endverbatim 00039 * 00040 * Arguments: 00041 * ========== 00042 * 00043 *> \param[in] TRANSA 00044 *> \verbatim 00045 *> TRANSA is CHARACTER*1 00046 *> On entry, TRANSA specifies the form of op( A ) to be used in 00047 *> the matrix multiplication as follows: 00048 *> 00049 *> TRANSA = 'N' or 'n', op( A ) = A. 00050 *> 00051 *> TRANSA = 'T' or 't', op( A ) = A**T. 00052 *> 00053 *> TRANSA = 'C' or 'c', op( A ) = A**H. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] TRANSB 00057 *> \verbatim 00058 *> TRANSB is CHARACTER*1 00059 *> On entry, TRANSB specifies the form of op( B ) to be used in 00060 *> the matrix multiplication as follows: 00061 *> 00062 *> TRANSB = 'N' or 'n', op( B ) = B. 00063 *> 00064 *> TRANSB = 'T' or 't', op( B ) = B**T. 00065 *> 00066 *> TRANSB = 'C' or 'c', op( B ) = B**H. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] M 00070 *> \verbatim 00071 *> M is INTEGER 00072 *> On entry, M specifies the number of rows of the matrix 00073 *> op( A ) and of the matrix C. M must be at least zero. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] N 00077 *> \verbatim 00078 *> N is INTEGER 00079 *> On entry, N specifies the number of columns of the matrix 00080 *> op( B ) and the number of columns of the matrix C. N must be 00081 *> at least zero. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] K 00085 *> \verbatim 00086 *> K is INTEGER 00087 *> On entry, K specifies the number of columns of the matrix 00088 *> op( A ) and the number of rows of the matrix op( B ). K must 00089 *> be at least zero. 00090 *> \endverbatim 00091 *> 00092 *> \param[in] ALPHA 00093 *> \verbatim 00094 *> ALPHA is COMPLEX*16 00095 *> On entry, ALPHA specifies the scalar alpha. 00096 *> \endverbatim 00097 *> 00098 *> \param[in] A 00099 *> \verbatim 00100 *> A is COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is 00101 *> k when TRANSA = 'N' or 'n', and is m otherwise. 00102 *> Before entry with TRANSA = 'N' or 'n', the leading m by k 00103 *> part of the array A must contain the matrix A, otherwise 00104 *> the leading k by m part of the array A must contain the 00105 *> matrix A. 00106 *> \endverbatim 00107 *> 00108 *> \param[in] LDA 00109 *> \verbatim 00110 *> LDA is INTEGER 00111 *> On entry, LDA specifies the first dimension of A as declared 00112 *> in the calling (sub) program. When TRANSA = 'N' or 'n' then 00113 *> LDA must be at least max( 1, m ), otherwise LDA must be at 00114 *> least max( 1, k ). 00115 *> \endverbatim 00116 *> 00117 *> \param[in] B 00118 *> \verbatim 00119 *> B is COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is 00120 *> n when TRANSB = 'N' or 'n', and is k otherwise. 00121 *> Before entry with TRANSB = 'N' or 'n', the leading k by n 00122 *> part of the array B must contain the matrix B, otherwise 00123 *> the leading n by k part of the array B must contain the 00124 *> matrix B. 00125 *> \endverbatim 00126 *> 00127 *> \param[in] LDB 00128 *> \verbatim 00129 *> LDB is INTEGER 00130 *> On entry, LDB specifies the first dimension of B as declared 00131 *> in the calling (sub) program. When TRANSB = 'N' or 'n' then 00132 *> LDB must be at least max( 1, k ), otherwise LDB must be at 00133 *> least max( 1, n ). 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 C need not be set on input. 00141 *> \endverbatim 00142 *> 00143 *> \param[in,out] C 00144 *> \verbatim 00145 *> C is COMPLEX*16 array of DIMENSION ( LDC, n ). 00146 *> Before entry, the leading m by n part of the array C must 00147 *> contain the matrix C, except when beta is zero, in which 00148 *> case C need not be set on entry. 00149 *> On exit, the array C is overwritten by the m by n matrix 00150 *> ( alpha*op( A )*op( B ) + beta*C ). 00151 *> \endverbatim 00152 *> 00153 *> \param[in] LDC 00154 *> \verbatim 00155 *> LDC is INTEGER 00156 *> On entry, LDC specifies the first dimension of C as declared 00157 *> in the calling (sub) program. LDC must be at least 00158 *> max( 1, m ). 00159 *> \endverbatim 00160 * 00161 * Authors: 00162 * ======== 00163 * 00164 *> \author Univ. of Tennessee 00165 *> \author Univ. of California Berkeley 00166 *> \author Univ. of Colorado Denver 00167 *> \author NAG Ltd. 00168 * 00169 *> \date November 2011 00170 * 00171 *> \ingroup complex16_blas_level3 00172 * 00173 *> \par Further Details: 00174 * ===================== 00175 *> 00176 *> \verbatim 00177 *> 00178 *> Level 3 Blas routine. 00179 *> 00180 *> -- Written on 8-February-1989. 00181 *> Jack Dongarra, Argonne National Laboratory. 00182 *> Iain Duff, AERE Harwell. 00183 *> Jeremy Du Croz, Numerical Algorithms Group Ltd. 00184 *> Sven Hammarling, Numerical Algorithms Group Ltd. 00185 *> \endverbatim 00186 *> 00187 * ===================================================================== 00188 SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) 00189 * 00190 * -- Reference BLAS level3 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 K,LDA,LDB,LDC,M,N 00198 CHARACTER TRANSA,TRANSB 00199 * .. 00200 * .. Array Arguments .. 00201 COMPLEX*16 A(LDA,*),B(LDB,*),C(LDC,*) 00202 * .. 00203 * 00204 * ===================================================================== 00205 * 00206 * .. External Functions .. 00207 LOGICAL LSAME 00208 EXTERNAL LSAME 00209 * .. 00210 * .. External Subroutines .. 00211 EXTERNAL XERBLA 00212 * .. 00213 * .. Intrinsic Functions .. 00214 INTRINSIC DCONJG,MAX 00215 * .. 00216 * .. Local Scalars .. 00217 COMPLEX*16 TEMP 00218 INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB 00219 LOGICAL CONJA,CONJB,NOTA,NOTB 00220 * .. 00221 * .. Parameters .. 00222 COMPLEX*16 ONE 00223 PARAMETER (ONE= (1.0D+0,0.0D+0)) 00224 COMPLEX*16 ZERO 00225 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 00226 * .. 00227 * 00228 * Set NOTA and NOTB as true if A and B respectively are not 00229 * conjugated or transposed, set CONJA and CONJB as true if A and 00230 * B respectively are to be transposed but not conjugated and set 00231 * NROWA, NCOLA and NROWB as the number of rows and columns of A 00232 * and the number of rows of B respectively. 00233 * 00234 NOTA = LSAME(TRANSA,'N') 00235 NOTB = LSAME(TRANSB,'N') 00236 CONJA = LSAME(TRANSA,'C') 00237 CONJB = LSAME(TRANSB,'C') 00238 IF (NOTA) THEN 00239 NROWA = M 00240 NCOLA = K 00241 ELSE 00242 NROWA = K 00243 NCOLA = M 00244 END IF 00245 IF (NOTB) THEN 00246 NROWB = K 00247 ELSE 00248 NROWB = N 00249 END IF 00250 * 00251 * Test the input parameters. 00252 * 00253 INFO = 0 00254 IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND. 00255 + (.NOT.LSAME(TRANSA,'T'))) THEN 00256 INFO = 1 00257 ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND. 00258 + (.NOT.LSAME(TRANSB,'T'))) THEN 00259 INFO = 2 00260 ELSE IF (M.LT.0) THEN 00261 INFO = 3 00262 ELSE IF (N.LT.0) THEN 00263 INFO = 4 00264 ELSE IF (K.LT.0) THEN 00265 INFO = 5 00266 ELSE IF (LDA.LT.MAX(1,NROWA)) THEN 00267 INFO = 8 00268 ELSE IF (LDB.LT.MAX(1,NROWB)) THEN 00269 INFO = 10 00270 ELSE IF (LDC.LT.MAX(1,M)) THEN 00271 INFO = 13 00272 END IF 00273 IF (INFO.NE.0) THEN 00274 CALL XERBLA('ZGEMM ',INFO) 00275 RETURN 00276 END IF 00277 * 00278 * Quick return if possible. 00279 * 00280 IF ((M.EQ.0) .OR. (N.EQ.0) .OR. 00281 + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN 00282 * 00283 * And when alpha.eq.zero. 00284 * 00285 IF (ALPHA.EQ.ZERO) THEN 00286 IF (BETA.EQ.ZERO) THEN 00287 DO 20 J = 1,N 00288 DO 10 I = 1,M 00289 C(I,J) = ZERO 00290 10 CONTINUE 00291 20 CONTINUE 00292 ELSE 00293 DO 40 J = 1,N 00294 DO 30 I = 1,M 00295 C(I,J) = BETA*C(I,J) 00296 30 CONTINUE 00297 40 CONTINUE 00298 END IF 00299 RETURN 00300 END IF 00301 * 00302 * Start the operations. 00303 * 00304 IF (NOTB) THEN 00305 IF (NOTA) THEN 00306 * 00307 * Form C := alpha*A*B + beta*C. 00308 * 00309 DO 90 J = 1,N 00310 IF (BETA.EQ.ZERO) THEN 00311 DO 50 I = 1,M 00312 C(I,J) = ZERO 00313 50 CONTINUE 00314 ELSE IF (BETA.NE.ONE) THEN 00315 DO 60 I = 1,M 00316 C(I,J) = BETA*C(I,J) 00317 60 CONTINUE 00318 END IF 00319 DO 80 L = 1,K 00320 IF (B(L,J).NE.ZERO) THEN 00321 TEMP = ALPHA*B(L,J) 00322 DO 70 I = 1,M 00323 C(I,J) = C(I,J) + TEMP*A(I,L) 00324 70 CONTINUE 00325 END IF 00326 80 CONTINUE 00327 90 CONTINUE 00328 ELSE IF (CONJA) THEN 00329 * 00330 * Form C := alpha*A**H*B + beta*C. 00331 * 00332 DO 120 J = 1,N 00333 DO 110 I = 1,M 00334 TEMP = ZERO 00335 DO 100 L = 1,K 00336 TEMP = TEMP + DCONJG(A(L,I))*B(L,J) 00337 100 CONTINUE 00338 IF (BETA.EQ.ZERO) THEN 00339 C(I,J) = ALPHA*TEMP 00340 ELSE 00341 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00342 END IF 00343 110 CONTINUE 00344 120 CONTINUE 00345 ELSE 00346 * 00347 * Form C := alpha*A**T*B + beta*C 00348 * 00349 DO 150 J = 1,N 00350 DO 140 I = 1,M 00351 TEMP = ZERO 00352 DO 130 L = 1,K 00353 TEMP = TEMP + A(L,I)*B(L,J) 00354 130 CONTINUE 00355 IF (BETA.EQ.ZERO) THEN 00356 C(I,J) = ALPHA*TEMP 00357 ELSE 00358 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00359 END IF 00360 140 CONTINUE 00361 150 CONTINUE 00362 END IF 00363 ELSE IF (NOTA) THEN 00364 IF (CONJB) THEN 00365 * 00366 * Form C := alpha*A*B**H + beta*C. 00367 * 00368 DO 200 J = 1,N 00369 IF (BETA.EQ.ZERO) THEN 00370 DO 160 I = 1,M 00371 C(I,J) = ZERO 00372 160 CONTINUE 00373 ELSE IF (BETA.NE.ONE) THEN 00374 DO 170 I = 1,M 00375 C(I,J) = BETA*C(I,J) 00376 170 CONTINUE 00377 END IF 00378 DO 190 L = 1,K 00379 IF (B(J,L).NE.ZERO) THEN 00380 TEMP = ALPHA*DCONJG(B(J,L)) 00381 DO 180 I = 1,M 00382 C(I,J) = C(I,J) + TEMP*A(I,L) 00383 180 CONTINUE 00384 END IF 00385 190 CONTINUE 00386 200 CONTINUE 00387 ELSE 00388 * 00389 * Form C := alpha*A*B**T + beta*C 00390 * 00391 DO 250 J = 1,N 00392 IF (BETA.EQ.ZERO) THEN 00393 DO 210 I = 1,M 00394 C(I,J) = ZERO 00395 210 CONTINUE 00396 ELSE IF (BETA.NE.ONE) THEN 00397 DO 220 I = 1,M 00398 C(I,J) = BETA*C(I,J) 00399 220 CONTINUE 00400 END IF 00401 DO 240 L = 1,K 00402 IF (B(J,L).NE.ZERO) THEN 00403 TEMP = ALPHA*B(J,L) 00404 DO 230 I = 1,M 00405 C(I,J) = C(I,J) + TEMP*A(I,L) 00406 230 CONTINUE 00407 END IF 00408 240 CONTINUE 00409 250 CONTINUE 00410 END IF 00411 ELSE IF (CONJA) THEN 00412 IF (CONJB) THEN 00413 * 00414 * Form C := alpha*A**H*B**H + beta*C. 00415 * 00416 DO 280 J = 1,N 00417 DO 270 I = 1,M 00418 TEMP = ZERO 00419 DO 260 L = 1,K 00420 TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L)) 00421 260 CONTINUE 00422 IF (BETA.EQ.ZERO) THEN 00423 C(I,J) = ALPHA*TEMP 00424 ELSE 00425 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00426 END IF 00427 270 CONTINUE 00428 280 CONTINUE 00429 ELSE 00430 * 00431 * Form C := alpha*A**H*B**T + beta*C 00432 * 00433 DO 310 J = 1,N 00434 DO 300 I = 1,M 00435 TEMP = ZERO 00436 DO 290 L = 1,K 00437 TEMP = TEMP + DCONJG(A(L,I))*B(J,L) 00438 290 CONTINUE 00439 IF (BETA.EQ.ZERO) THEN 00440 C(I,J) = ALPHA*TEMP 00441 ELSE 00442 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00443 END IF 00444 300 CONTINUE 00445 310 CONTINUE 00446 END IF 00447 ELSE 00448 IF (CONJB) THEN 00449 * 00450 * Form C := alpha*A**T*B**H + beta*C 00451 * 00452 DO 340 J = 1,N 00453 DO 330 I = 1,M 00454 TEMP = ZERO 00455 DO 320 L = 1,K 00456 TEMP = TEMP + A(L,I)*DCONJG(B(J,L)) 00457 320 CONTINUE 00458 IF (BETA.EQ.ZERO) THEN 00459 C(I,J) = ALPHA*TEMP 00460 ELSE 00461 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00462 END IF 00463 330 CONTINUE 00464 340 CONTINUE 00465 ELSE 00466 * 00467 * Form C := alpha*A**T*B**T + beta*C 00468 * 00469 DO 370 J = 1,N 00470 DO 360 I = 1,M 00471 TEMP = ZERO 00472 DO 350 L = 1,K 00473 TEMP = TEMP + A(L,I)*B(J,L) 00474 350 CONTINUE 00475 IF (BETA.EQ.ZERO) THEN 00476 C(I,J) = ALPHA*TEMP 00477 ELSE 00478 C(I,J) = ALPHA*TEMP + BETA*C(I,J) 00479 END IF 00480 360 CONTINUE 00481 370 CONTINUE 00482 END IF 00483 END IF 00484 * 00485 RETURN 00486 * 00487 * End of ZGEMM . 00488 * 00489 END