| 1 | SUBROUTINE ZGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) |
|---|
| 2 | * .. Scalar Arguments .. |
|---|
| 3 | DOUBLE COMPLEX ALPHA,BETA |
|---|
| 4 | INTEGER K,LDA,LDB,LDC,M,N |
|---|
| 5 | CHARACTER TRANSA,TRANSB |
|---|
| 6 | * .. |
|---|
| 7 | * .. Array Arguments .. |
|---|
| 8 | DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) |
|---|
| 9 | * .. |
|---|
| 10 | * |
|---|
| 11 | * Purpose |
|---|
| 12 | * ======= |
|---|
| 13 | * |
|---|
| 14 | * ZGEMM performs one of the matrix-matrix operations |
|---|
| 15 | * |
|---|
| 16 | * C := alpha*op( A )*op( B ) + beta*C, |
|---|
| 17 | * |
|---|
| 18 | * where op( X ) is one of |
|---|
| 19 | * |
|---|
| 20 | * op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ), |
|---|
| 21 | * |
|---|
| 22 | * alpha and beta are scalars, and A, B and C are matrices, with op( A ) |
|---|
| 23 | * an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
|---|
| 24 | * |
|---|
| 25 | * Arguments |
|---|
| 26 | * ========== |
|---|
| 27 | * |
|---|
| 28 | * TRANSA - CHARACTER*1. |
|---|
| 29 | * On entry, TRANSA specifies the form of op( A ) to be used in |
|---|
| 30 | * the matrix multiplication as follows: |
|---|
| 31 | * |
|---|
| 32 | * TRANSA = 'N' or 'n', op( A ) = A. |
|---|
| 33 | * |
|---|
| 34 | * TRANSA = 'T' or 't', op( A ) = A'. |
|---|
| 35 | * |
|---|
| 36 | * TRANSA = 'C' or 'c', op( A ) = conjg( A' ). |
|---|
| 37 | * |
|---|
| 38 | * Unchanged on exit. |
|---|
| 39 | * |
|---|
| 40 | * TRANSB - CHARACTER*1. |
|---|
| 41 | * On entry, TRANSB specifies the form of op( B ) to be used in |
|---|
| 42 | * the matrix multiplication as follows: |
|---|
| 43 | * |
|---|
| 44 | * TRANSB = 'N' or 'n', op( B ) = B. |
|---|
| 45 | * |
|---|
| 46 | * TRANSB = 'T' or 't', op( B ) = B'. |
|---|
| 47 | * |
|---|
| 48 | * TRANSB = 'C' or 'c', op( B ) = conjg( B' ). |
|---|
| 49 | * |
|---|
| 50 | * Unchanged on exit. |
|---|
| 51 | * |
|---|
| 52 | * M - INTEGER. |
|---|
| 53 | * On entry, M specifies the number of rows of the matrix |
|---|
| 54 | * op( A ) and of the matrix C. M must be at least zero. |
|---|
| 55 | * Unchanged on exit. |
|---|
| 56 | * |
|---|
| 57 | * N - INTEGER. |
|---|
| 58 | * On entry, N specifies the number of columns of the matrix |
|---|
| 59 | * op( B ) and the number of columns of the matrix C. N must be |
|---|
| 60 | * at least zero. |
|---|
| 61 | * Unchanged on exit. |
|---|
| 62 | * |
|---|
| 63 | * K - INTEGER. |
|---|
| 64 | * On entry, K specifies the number of columns of the matrix |
|---|
| 65 | * op( A ) and the number of rows of the matrix op( B ). K must |
|---|
| 66 | * be at least zero. |
|---|
| 67 | * Unchanged on exit. |
|---|
| 68 | * |
|---|
| 69 | * ALPHA - COMPLEX*16 . |
|---|
| 70 | * On entry, ALPHA specifies the scalar alpha. |
|---|
| 71 | * Unchanged on exit. |
|---|
| 72 | * |
|---|
| 73 | * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is |
|---|
| 74 | * k when TRANSA = 'N' or 'n', and is m otherwise. |
|---|
| 75 | * Before entry with TRANSA = 'N' or 'n', the leading m by k |
|---|
| 76 | * part of the array A must contain the matrix A, otherwise |
|---|
| 77 | * the leading k by m part of the array A must contain the |
|---|
| 78 | * matrix A. |
|---|
| 79 | * Unchanged on exit. |
|---|
| 80 | * |
|---|
| 81 | * LDA - INTEGER. |
|---|
| 82 | * On entry, LDA specifies the first dimension of A as declared |
|---|
| 83 | * in the calling (sub) program. When TRANSA = 'N' or 'n' then |
|---|
| 84 | * LDA must be at least max( 1, m ), otherwise LDA must be at |
|---|
| 85 | * least max( 1, k ). |
|---|
| 86 | * Unchanged on exit. |
|---|
| 87 | * |
|---|
| 88 | * B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is |
|---|
| 89 | * n when TRANSB = 'N' or 'n', and is k otherwise. |
|---|
| 90 | * Before entry with TRANSB = 'N' or 'n', the leading k by n |
|---|
| 91 | * part of the array B must contain the matrix B, otherwise |
|---|
| 92 | * the leading n by k part of the array B must contain the |
|---|
| 93 | * matrix B. |
|---|
| 94 | * Unchanged on exit. |
|---|
| 95 | * |
|---|
| 96 | * LDB - INTEGER. |
|---|
| 97 | * On entry, LDB specifies the first dimension of B as declared |
|---|
| 98 | * in the calling (sub) program. When TRANSB = 'N' or 'n' then |
|---|
| 99 | * LDB must be at least max( 1, k ), otherwise LDB must be at |
|---|
| 100 | * least max( 1, n ). |
|---|
| 101 | * Unchanged on exit. |
|---|
| 102 | * |
|---|
| 103 | * BETA - COMPLEX*16 . |
|---|
| 104 | * On entry, BETA specifies the scalar beta. When BETA is |
|---|
| 105 | * supplied as zero then C need not be set on input. |
|---|
| 106 | * Unchanged on exit. |
|---|
| 107 | * |
|---|
| 108 | * C - COMPLEX*16 array of DIMENSION ( LDC, n ). |
|---|
| 109 | * Before entry, the leading m by n part of the array C must |
|---|
| 110 | * contain the matrix C, except when beta is zero, in which |
|---|
| 111 | * case C need not be set on entry. |
|---|
| 112 | * On exit, the array C is overwritten by the m by n matrix |
|---|
| 113 | * ( alpha*op( A )*op( B ) + beta*C ). |
|---|
| 114 | * |
|---|
| 115 | * LDC - INTEGER. |
|---|
| 116 | * On entry, LDC specifies the first dimension of C as declared |
|---|
| 117 | * in the calling (sub) program. LDC must be at least |
|---|
| 118 | * max( 1, m ). |
|---|
| 119 | * Unchanged on exit. |
|---|
| 120 | * |
|---|
| 121 | * |
|---|
| 122 | * Level 3 Blas routine. |
|---|
| 123 | * |
|---|
| 124 | * -- Written on 8-February-1989. |
|---|
| 125 | * Jack Dongarra, Argonne National Laboratory. |
|---|
| 126 | * Iain Duff, AERE Harwell. |
|---|
| 127 | * Jeremy Du Croz, Numerical Algorithms Group Ltd. |
|---|
| 128 | * Sven Hammarling, Numerical Algorithms Group Ltd. |
|---|
| 129 | * |
|---|
| 130 | * |
|---|
| 131 | * .. External Functions .. |
|---|
| 132 | LOGICAL LSAME |
|---|
| 133 | EXTERNAL LSAME |
|---|
| 134 | * .. |
|---|
| 135 | * .. External Subroutines .. |
|---|
| 136 | EXTERNAL XERBLA |
|---|
| 137 | * .. |
|---|
| 138 | * .. Intrinsic Functions .. |
|---|
| 139 | INTRINSIC DCONJG,MAX |
|---|
| 140 | * .. |
|---|
| 141 | * .. Local Scalars .. |
|---|
| 142 | DOUBLE COMPLEX TEMP |
|---|
| 143 | INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB |
|---|
| 144 | LOGICAL CONJA,CONJB,NOTA,NOTB |
|---|
| 145 | * .. |
|---|
| 146 | * .. Parameters .. |
|---|
| 147 | DOUBLE COMPLEX ONE |
|---|
| 148 | PARAMETER (ONE= (1.0D+0,0.0D+0)) |
|---|
| 149 | DOUBLE COMPLEX ZERO |
|---|
| 150 | PARAMETER (ZERO= (0.0D+0,0.0D+0)) |
|---|
| 151 | * .. |
|---|
| 152 | * |
|---|
| 153 | * Set NOTA and NOTB as true if A and B respectively are not |
|---|
| 154 | * conjugated or transposed, set CONJA and CONJB as true if A and |
|---|
| 155 | * B respectively are to be transposed but not conjugated and set |
|---|
| 156 | * NROWA, NCOLA and NROWB as the number of rows and columns of A |
|---|
| 157 | * and the number of rows of B respectively. |
|---|
| 158 | * |
|---|
| 159 | NOTA = LSAME(TRANSA,'N') |
|---|
| 160 | NOTB = LSAME(TRANSB,'N') |
|---|
| 161 | CONJA = LSAME(TRANSA,'C') |
|---|
| 162 | CONJB = LSAME(TRANSB,'C') |
|---|
| 163 | IF (NOTA) THEN |
|---|
| 164 | NROWA = M |
|---|
| 165 | NCOLA = K |
|---|
| 166 | ELSE |
|---|
| 167 | NROWA = K |
|---|
| 168 | NCOLA = M |
|---|
| 169 | END IF |
|---|
| 170 | IF (NOTB) THEN |
|---|
| 171 | NROWB = K |
|---|
| 172 | ELSE |
|---|
| 173 | NROWB = N |
|---|
| 174 | END IF |
|---|
| 175 | * |
|---|
| 176 | * Test the input parameters. |
|---|
| 177 | * |
|---|
| 178 | INFO = 0 |
|---|
| 179 | IF ((.NOT.NOTA) .AND. (.NOT.CONJA) .AND. |
|---|
| 180 | + (.NOT.LSAME(TRANSA,'T'))) THEN |
|---|
| 181 | INFO = 1 |
|---|
| 182 | ELSE IF ((.NOT.NOTB) .AND. (.NOT.CONJB) .AND. |
|---|
| 183 | + (.NOT.LSAME(TRANSB,'T'))) THEN |
|---|
| 184 | INFO = 2 |
|---|
| 185 | ELSE IF (M.LT.0) THEN |
|---|
| 186 | INFO = 3 |
|---|
| 187 | ELSE IF (N.LT.0) THEN |
|---|
| 188 | INFO = 4 |
|---|
| 189 | ELSE IF (K.LT.0) THEN |
|---|
| 190 | INFO = 5 |
|---|
| 191 | ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
|---|
| 192 | INFO = 8 |
|---|
| 193 | ELSE IF (LDB.LT.MAX(1,NROWB)) THEN |
|---|
| 194 | INFO = 10 |
|---|
| 195 | ELSE IF (LDC.LT.MAX(1,M)) THEN |
|---|
| 196 | INFO = 13 |
|---|
| 197 | END IF |
|---|
| 198 | IF (INFO.NE.0) THEN |
|---|
| 199 | CALL XERBLA('ZGEMM ',INFO) |
|---|
| 200 | RETURN |
|---|
| 201 | END IF |
|---|
| 202 | * |
|---|
| 203 | * Quick return if possible. |
|---|
| 204 | * |
|---|
| 205 | IF ((M.EQ.0) .OR. (N.EQ.0) .OR. |
|---|
| 206 | + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN |
|---|
| 207 | * |
|---|
| 208 | * And when alpha.eq.zero. |
|---|
| 209 | * |
|---|
| 210 | IF (ALPHA.EQ.ZERO) THEN |
|---|
| 211 | IF (BETA.EQ.ZERO) THEN |
|---|
| 212 | DO 20 J = 1,N |
|---|
| 213 | DO 10 I = 1,M |
|---|
| 214 | C(I,J) = ZERO |
|---|
| 215 | 10 CONTINUE |
|---|
| 216 | 20 CONTINUE |
|---|
| 217 | ELSE |
|---|
| 218 | DO 40 J = 1,N |
|---|
| 219 | DO 30 I = 1,M |
|---|
| 220 | C(I,J) = BETA*C(I,J) |
|---|
| 221 | 30 CONTINUE |
|---|
| 222 | 40 CONTINUE |
|---|
| 223 | END IF |
|---|
| 224 | RETURN |
|---|
| 225 | END IF |
|---|
| 226 | * |
|---|
| 227 | * Start the operations. |
|---|
| 228 | * |
|---|
| 229 | IF (NOTB) THEN |
|---|
| 230 | IF (NOTA) THEN |
|---|
| 231 | * |
|---|
| 232 | * Form C := alpha*A*B + beta*C. |
|---|
| 233 | * |
|---|
| 234 | DO 90 J = 1,N |
|---|
| 235 | IF (BETA.EQ.ZERO) THEN |
|---|
| 236 | DO 50 I = 1,M |
|---|
| 237 | C(I,J) = ZERO |
|---|
| 238 | 50 CONTINUE |
|---|
| 239 | ELSE IF (BETA.NE.ONE) THEN |
|---|
| 240 | DO 60 I = 1,M |
|---|
| 241 | C(I,J) = BETA*C(I,J) |
|---|
| 242 | 60 CONTINUE |
|---|
| 243 | END IF |
|---|
| 244 | DO 80 L = 1,K |
|---|
| 245 | IF (B(L,J).NE.ZERO) THEN |
|---|
| 246 | TEMP = ALPHA*B(L,J) |
|---|
| 247 | DO 70 I = 1,M |
|---|
| 248 | C(I,J) = C(I,J) + TEMP*A(I,L) |
|---|
| 249 | 70 CONTINUE |
|---|
| 250 | END IF |
|---|
| 251 | 80 CONTINUE |
|---|
| 252 | 90 CONTINUE |
|---|
| 253 | ELSE IF (CONJA) THEN |
|---|
| 254 | * |
|---|
| 255 | * Form C := alpha*conjg( A' )*B + beta*C. |
|---|
| 256 | * |
|---|
| 257 | DO 120 J = 1,N |
|---|
| 258 | DO 110 I = 1,M |
|---|
| 259 | TEMP = ZERO |
|---|
| 260 | DO 100 L = 1,K |
|---|
| 261 | TEMP = TEMP + DCONJG(A(L,I))*B(L,J) |
|---|
| 262 | 100 CONTINUE |
|---|
| 263 | IF (BETA.EQ.ZERO) THEN |
|---|
| 264 | C(I,J) = ALPHA*TEMP |
|---|
| 265 | ELSE |
|---|
| 266 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 267 | END IF |
|---|
| 268 | 110 CONTINUE |
|---|
| 269 | 120 CONTINUE |
|---|
| 270 | ELSE |
|---|
| 271 | * |
|---|
| 272 | * Form C := alpha*A'*B + beta*C |
|---|
| 273 | * |
|---|
| 274 | DO 150 J = 1,N |
|---|
| 275 | DO 140 I = 1,M |
|---|
| 276 | TEMP = ZERO |
|---|
| 277 | DO 130 L = 1,K |
|---|
| 278 | TEMP = TEMP + A(L,I)*B(L,J) |
|---|
| 279 | 130 CONTINUE |
|---|
| 280 | IF (BETA.EQ.ZERO) THEN |
|---|
| 281 | C(I,J) = ALPHA*TEMP |
|---|
| 282 | ELSE |
|---|
| 283 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 284 | END IF |
|---|
| 285 | 140 CONTINUE |
|---|
| 286 | 150 CONTINUE |
|---|
| 287 | END IF |
|---|
| 288 | ELSE IF (NOTA) THEN |
|---|
| 289 | IF (CONJB) THEN |
|---|
| 290 | * |
|---|
| 291 | * Form C := alpha*A*conjg( B' ) + beta*C. |
|---|
| 292 | * |
|---|
| 293 | DO 200 J = 1,N |
|---|
| 294 | IF (BETA.EQ.ZERO) THEN |
|---|
| 295 | DO 160 I = 1,M |
|---|
| 296 | C(I,J) = ZERO |
|---|
| 297 | 160 CONTINUE |
|---|
| 298 | ELSE IF (BETA.NE.ONE) THEN |
|---|
| 299 | DO 170 I = 1,M |
|---|
| 300 | C(I,J) = BETA*C(I,J) |
|---|
| 301 | 170 CONTINUE |
|---|
| 302 | END IF |
|---|
| 303 | DO 190 L = 1,K |
|---|
| 304 | IF (B(J,L).NE.ZERO) THEN |
|---|
| 305 | TEMP = ALPHA*DCONJG(B(J,L)) |
|---|
| 306 | DO 180 I = 1,M |
|---|
| 307 | C(I,J) = C(I,J) + TEMP*A(I,L) |
|---|
| 308 | 180 CONTINUE |
|---|
| 309 | END IF |
|---|
| 310 | 190 CONTINUE |
|---|
| 311 | 200 CONTINUE |
|---|
| 312 | ELSE |
|---|
| 313 | * |
|---|
| 314 | * Form C := alpha*A*B' + beta*C |
|---|
| 315 | * |
|---|
| 316 | DO 250 J = 1,N |
|---|
| 317 | IF (BETA.EQ.ZERO) THEN |
|---|
| 318 | DO 210 I = 1,M |
|---|
| 319 | C(I,J) = ZERO |
|---|
| 320 | 210 CONTINUE |
|---|
| 321 | ELSE IF (BETA.NE.ONE) THEN |
|---|
| 322 | DO 220 I = 1,M |
|---|
| 323 | C(I,J) = BETA*C(I,J) |
|---|
| 324 | 220 CONTINUE |
|---|
| 325 | END IF |
|---|
| 326 | DO 240 L = 1,K |
|---|
| 327 | IF (B(J,L).NE.ZERO) THEN |
|---|
| 328 | TEMP = ALPHA*B(J,L) |
|---|
| 329 | DO 230 I = 1,M |
|---|
| 330 | C(I,J) = C(I,J) + TEMP*A(I,L) |
|---|
| 331 | 230 CONTINUE |
|---|
| 332 | END IF |
|---|
| 333 | 240 CONTINUE |
|---|
| 334 | 250 CONTINUE |
|---|
| 335 | END IF |
|---|
| 336 | ELSE IF (CONJA) THEN |
|---|
| 337 | IF (CONJB) THEN |
|---|
| 338 | * |
|---|
| 339 | * Form C := alpha*conjg( A' )*conjg( B' ) + beta*C. |
|---|
| 340 | * |
|---|
| 341 | DO 280 J = 1,N |
|---|
| 342 | DO 270 I = 1,M |
|---|
| 343 | TEMP = ZERO |
|---|
| 344 | DO 260 L = 1,K |
|---|
| 345 | TEMP = TEMP + DCONJG(A(L,I))*DCONJG(B(J,L)) |
|---|
| 346 | 260 CONTINUE |
|---|
| 347 | IF (BETA.EQ.ZERO) THEN |
|---|
| 348 | C(I,J) = ALPHA*TEMP |
|---|
| 349 | ELSE |
|---|
| 350 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 351 | END IF |
|---|
| 352 | 270 CONTINUE |
|---|
| 353 | 280 CONTINUE |
|---|
| 354 | ELSE |
|---|
| 355 | * |
|---|
| 356 | * Form C := alpha*conjg( A' )*B' + beta*C |
|---|
| 357 | * |
|---|
| 358 | DO 310 J = 1,N |
|---|
| 359 | DO 300 I = 1,M |
|---|
| 360 | TEMP = ZERO |
|---|
| 361 | DO 290 L = 1,K |
|---|
| 362 | TEMP = TEMP + DCONJG(A(L,I))*B(J,L) |
|---|
| 363 | 290 CONTINUE |
|---|
| 364 | IF (BETA.EQ.ZERO) THEN |
|---|
| 365 | C(I,J) = ALPHA*TEMP |
|---|
| 366 | ELSE |
|---|
| 367 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 368 | END IF |
|---|
| 369 | 300 CONTINUE |
|---|
| 370 | 310 CONTINUE |
|---|
| 371 | END IF |
|---|
| 372 | ELSE |
|---|
| 373 | IF (CONJB) THEN |
|---|
| 374 | * |
|---|
| 375 | * Form C := alpha*A'*conjg( B' ) + beta*C |
|---|
| 376 | * |
|---|
| 377 | DO 340 J = 1,N |
|---|
| 378 | DO 330 I = 1,M |
|---|
| 379 | TEMP = ZERO |
|---|
| 380 | DO 320 L = 1,K |
|---|
| 381 | TEMP = TEMP + A(L,I)*DCONJG(B(J,L)) |
|---|
| 382 | 320 CONTINUE |
|---|
| 383 | IF (BETA.EQ.ZERO) THEN |
|---|
| 384 | C(I,J) = ALPHA*TEMP |
|---|
| 385 | ELSE |
|---|
| 386 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 387 | END IF |
|---|
| 388 | 330 CONTINUE |
|---|
| 389 | 340 CONTINUE |
|---|
| 390 | ELSE |
|---|
| 391 | * |
|---|
| 392 | * Form C := alpha*A'*B' + beta*C |
|---|
| 393 | * |
|---|
| 394 | DO 370 J = 1,N |
|---|
| 395 | DO 360 I = 1,M |
|---|
| 396 | TEMP = ZERO |
|---|
| 397 | DO 350 L = 1,K |
|---|
| 398 | TEMP = TEMP + A(L,I)*B(J,L) |
|---|
| 399 | 350 CONTINUE |
|---|
| 400 | IF (BETA.EQ.ZERO) THEN |
|---|
| 401 | C(I,J) = ALPHA*TEMP |
|---|
| 402 | ELSE |
|---|
| 403 | C(I,J) = ALPHA*TEMP + BETA*C(I,J) |
|---|
| 404 | END IF |
|---|
| 405 | 360 CONTINUE |
|---|
| 406 | 370 CONTINUE |
|---|
| 407 | END IF |
|---|
| 408 | END IF |
|---|
| 409 | * |
|---|
| 410 | RETURN |
|---|
| 411 | * |
|---|
| 412 | * End of ZGEMM . |
|---|
| 413 | * |
|---|
| 414 | END |
|---|
