稀疏矩阵 part 5
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? 目前为止能跑的所有代码及其结果（2019年2月24日），之后添加：DIA 乘法 GPU 版；其他维度的乘法（矩阵乘矩阵）；其他稀疏矩阵格式之间的相互转化
1 #include <stdio.h> 2 #include <stdlib.h> 3 #include <memory.h> 4 #include <malloc.h> 5 #include <math.h> 6 #include <time.h> 7 #include "cuda_runtime.h" 8 #include "device_launch_parameters.h" 9 10 #define ROW (8192) 11 #define COL (8192) 12 #define RATIO 0.1 // 系数矩阵非零元素占比 13 #define EPSILON 0.0001 // 浮点数比较 14 #define THREAD_SIZE 256 15 #define SEED 1 // (unsigned int)time(NULL) 16 #define MAX(x,y) (((x)>(y))?(x):(y)) 17 #define CEIL(x,y) (int)(( x - 1 ) / y + 1) 18 #define INT // 数字格式用 int 还是 float 19 20 #ifdef INT 21 typedef int format; 22 #else 23 typedef float format; 24 #endif 25 26 // 矩阵存储格式 27 typedef struct // 顺序格式 28 { 29 int row; // 行数 30 int col; // 列数 31 int count; // 非零元个数（用于转换，不用于计算） 32 format *data; // 元素的值 33 } 34 MAT; 35 36 typedef struct // Compressed Sparse Row 格式 37 { 38 int row; // 行数 39 int col; // 列数 40 format *data; // 元素的值 41 int *index; // 元素的列号 42 int *ptr; // 每行首元在 index 中的下标，最后一个元素的值等于矩阵非零元个数 43 } 44 CSR; 45 46 typedef struct // Compressed Sparse Row 格式 47 { 48 int row; // 行数 49 int col; // 列数 50 format *data; // 元素的值 51 int *index; // 元素的行号 52 int *ptr; // 每列首元在 index 中的下标，最后一个元素的值等于矩阵非零元个数 53 } 54 CSC; 55 56 57 typedef struct // ELLPACK 格式 58 { 59 int row; // 行数 60 int col; // 列数，相当于MAT格式的行数 61 int colOrigin; // 原列数，相当于MAT格式的列数 62 format *data; // 元素的值 63 int *index; // 元素在MAT格式中的列号 64 } 65 ELL; 66 67 typedef struct // Coordinate 格式 68 { 69 int row; // 行数 70 int col; // 列数 71 int count; // 非零元个数 72 int *rowIndex; // 行向量 73 int *colIndex; // 列向量 74 format *data; // 元素的值 75 } 76 COO; 77 78 typedef struct // Diagonal 格式 79 { 80 int row; // 行数 81 int col; // 列数 82 int colOrigin; // 原列数 83 format *data; // 元素的值 84 int *index; // 原矩阵各对角线是否非零 85 } 86 DIA; 87 88 // 全局指针 89 __managed__ MAT *aMAT, *xMAT, *yMATRef, *yMATCal; 90 __managed__ CSR *aCSR; 91 __managed__ ELL *aELL; 92 __managed__ COO *aCOO; 93 94 // 通用函数 95 __host__ __device__ inline void checkNULL(const void *input) // 有点问题，设备函数无法使用 exit(1) 来推出 96 { 97 if (input == NULL) 98 printf(" find a NULL!"); 99 return; 100 } 101 102 __host__ inline void checkCudaError(cudaError input) 103 { 104 if (input != cudaSuccess) 105 { 106 printf(" find a cudaError!"); 107 exit(1); 108 } 109 return; 110 } 111 112 int checkEqual(const format * in1, const format * in2, const int length)// 注意两向量相等时返 0，否则返回“值不等的元素下标加一” 113 { 114 int i; 115 for (i = 0; i < length; i++) 116 { 117 #ifdef INT 118 if (in1[i] != in2[i]) 119 #else 120 if (fabs(in1[i] - in2[i]) > EPSILON) 121 #endif 122 { 123 printf(" Error at i = %d in1[i] = %10f, in2[i] = %10f ", i, (float)in1[i], (float)in2[i]); 124 return i + 1; 125 } 126 } 127 printf(" Check output, passed. "); 128 return 0; 129 } 130 131 // 打印矩阵 132 void print(const char* info, const MAT *in)// 打印MAT格式的矩阵 133 { 134 printf("%s MAT, row = %d, col = %d, count = %d", info, in->row, in->col, in->count); 135 printf(" data = "); 136 for (int i = 0; i < in->row * in->col; i++) 137 { 138 #ifdef INT 139 printf("%d ", in->data[i]); 140 #else 141 printf("%.2f ", in->data[i]); 142 #endif 143 if ((i + 1) % in->col == 0) 144 printf(" "); 145 } 146 printf(" "); 147 return; 148 } 149 150 void print(const char* info, const CSR *in)// 打印CSR格式的矩阵 151 { 152 printf("%s CSR, row = %d, col = %d", info, in->row, in->col); 153 printf(" data = "); 154 for (int i = 0; i < in->ptr[in->row]; i++) 155 #ifdef INT 156 printf("%d ", in->data[i]); 157 #else 158 printf("%.2f ", in->data[i]); 159 #endif 160 printf(" index = "); 161 for (int i = 0; i < in->ptr[in->row]; i++) 162 printf("%d ", in->index[i]); 163 printf(" ptr = "); 164 for (int i = 0; i < in->row + 1; i++) 165 printf("%d ", in->ptr[i]); 166 printf(" "); 167 return; 168 } 169 170 void print(const char* info, const ELL *in)// 打印ELL格式的矩阵 171 { 172 int i; 173 printf("%s ELL, row = %d, col = %d, colOrigin = %d", info, in->row, in->col, in->colOrigin); 174 printf(" data = "); 175 for (i = 0; i < in->row * in->col; i++) 176 { 177 #ifdef INT 178 printf("%d ", in->data[i]); 179 #else 180 printf("%.2f ", in->data[i]); 181 #endif 182 if ((i + 1) % in->col == 0) 183 printf(" "); 184 } 185 printf("index = "); 186 for (i = 0; i < in->row * in->col; i++) 187 { 188 printf("%d ", in->index[i]); 189 if ((i + 1) % in->col == 0) 190 printf(" "); 191 } 192 printf(" "); 193 return; 194 } 195 196 void print(const char* info, const COO *in)// 打印COO格式的矩阵 197 { 198 int i; 199 printf("%s COO, row = %d, col = %d, count = %d", info, in->row, in->col, in->count); 200 printf(" (rowIndex, colIndex, data) = "); 201 for (i = 0; i < in->count; i++) 202 { 203 #ifdef INT 204 printf("(%d,%d,%d) ", in->rowIndex[i], in->colIndex[i], in->data[i]); 205 #else 206 printf("(%d,%d,%.2f) ", in->rowIndex[i], in->colIndex[i], in->data[i]); 207 #endif 208 } 209 printf(" "); 210 return; 211 } 212 213 void print(const char* info, const DIA *in)// 打印DIA格式的矩阵 214 { 215 int i; 216 printf("%s DIA, row = %d, col = %d, colOrigin = %d", info, in->row, in->col, in->colOrigin,in->colOrigin); 217 printf(" data = "); 218 int * inverseIndex = (int *)malloc(sizeof(int) * in->col); 219 for (int i = 0, j = 0; i < in->row + in->col - 1; i++) 220 { 221 if (in->index[i] == 1) 222 { 223 inverseIndex[j] = i; 224 j++; 225 } 226 } 227 for (i = 0; i < in->row * in->col; i++) 228 { 229 if (i / in->col < in->row - 1 - inverseIndex[i % in->col] || i / in->col > inverseIndex[in->col - 1] - inverseIndex[i % in->col]) 230 printf("* "); 231 else 232 #ifdef INT 233 printf("%d ", in->data[i]); 234 #else 235 printf("%.2f ", in->data[i]); 236 #endif 237 if ((i + 1) % in->col == 0) 238 printf(" "); 239 } 240 printf("index = "); 241 for (i = 0; i < in->row + in->col - 1; i++) 242 printf("%d ", in->index[i]); 243 printf(" "); 244 free(inverseIndex); 245 return; 246 } 247 248 // 矩阵初始化与清理 249 MAT *initializeMAT(const int row, const int col, const int count = 0)// 初始化MAT，注意非零元默认为 0 250 { 251 MAT *temp; 252 checkCudaError(cudaMallocManaged((void **)&temp, sizeof(MAT))); 253 temp->row = row; 254 temp->col = col; 255 temp->count = count; 256 checkCudaError(cudaMallocManaged((void **)&temp->data, sizeof(format) * row * col)); 257 return temp; 258 } 259 260 // 统计MAT形式的矩阵中的非零元素个数 261 #define COUNT_MAT(in) 262 { 263 checkNULL(in); 264 int i, zero; 265 for (i = zero = 0; i < in->row * in->col; i++) 266 zero += !in->data[i]; 267 in->count = in->row * in->col - zero; 268 } 269 270 int freeMatrix(MAT *in)// 释放MAT 271 { 272 checkNULL(in); 273 cudaFree(in->data); 274 cudaFree(in); 275 return 0; 276 } 277 278 CSR * initializeCSR(const int row, const int col, const int count)// 初始化CSR，要求给出 count 279 { 280 CSR *temp; 281 checkCudaError(cudaMallocManaged((void **)&temp, sizeof(CSR))); 282 temp->row = row; 283 temp->col = col; 284 checkCudaError(cudaMallocManaged((void **)&temp->data, sizeof(format) * count)); 285 checkCudaError(cudaMallocManaged((void **)&temp->index, sizeof(int) * count)); 286 checkCudaError(cudaMallocManaged((void **)&temp->ptr, sizeof(int) * (row + 1))); 287 return temp; 288 } 289 290 int freeMatrix(CSR *in)// 释放CSR 291 { 292 checkNULL(in); 293 cudaFree(in->data); 294 cudaFree(in->index); 295 cudaFree(in->ptr); 296 cudaFree(in); 297 return 0; 298 } 299 300 ELL * initializeELL(const int row, const int col, const int colOrigin)// 初始化ELL，要求给出原列数 301 { 302 ELL *temp; 303 checkCudaError(cudaMallocManaged((void **)&temp, sizeof(ELL))); 304 temp->row = row; 305 temp->col = col; 306 temp->colOrigin = colOrigin; 307 checkCudaError(cudaMallocManaged((void **)&temp->data, sizeof(format) * row * col)); 308 checkCudaError(cudaMallocManaged((void **)&temp->index, sizeof(int) * row * col)); 309 return temp; 310 } 311 312 int freeMatrix(ELL *in)// 释放ELL 313 { 314 cudaFree(in->data); 315 cudaFree(in->index); 316 cudaFree(in); 317 return 0; 318 } 319 320 COO * initializeCOO(const int row, const int col, const int count)// 初始化COO，要求给出 count 321 { 322 COO * temp; 323 checkCudaError(cudaMallocManaged((void **)&temp, sizeof(COO))); 324 temp->row = row; 325 temp->col = col; 326 temp->count = count; 327 checkCudaError(cudaMallocManaged((void **)&temp->data, sizeof(format) * count)); 328 checkCudaError(cudaMallocManaged((void **)&temp->rowIndex, sizeof(int) * count)); 329 checkCudaError(cudaMallocManaged((void **)&temp->colIndex, sizeof(int) * count)); 330 return temp; 331 } 332 333 int freeMatrix(COO *in)// 释放COO 334 { 335 checkNULL(in); 336 cudaFree(in->data); 337 cudaFree(in->rowIndex); 338 cudaFree(in->colIndex); 339 cudaFree(in); 340 return 0; 341 } 342 343 DIA * initializeDIA(const int row, const int col, const int colOrigin)// 初始化DIA，要求给出原行数、原列数 344 { 345 DIA * temp; 346 checkCudaError(cudaMallocManaged((void **)&temp, sizeof(DIA))); 347 temp->row = row; 348 temp->col = col; 349 temp->colOrigin = colOrigin; 350 checkCudaError(cudaMallocManaged((void **)&temp->data, sizeof(format) * row * col)); 351 checkCudaError(cudaMallocManaged((void **)&temp->index, sizeof(format) * (row + col - 1))); 352 return temp; 353 } 354 355 int freeMatrix(DIA *in)// 释放DIA 356 { 357 checkNULL(in); 358 cudaFree(in->data); 359 cudaFree(in->index); 360 cudaFree(in); 361 return 0; 362 } 363 364 // 矩阵格式的相互转化 365 CSR * MATToCSR(const MAT *in) // MAT 转 CSR 366 { 367 checkNULL(in); 368 CSR * out = initializeCSR(in->row, in->col, in->count); 369 checkNULL(out); 370 371 out->ptr[0] = 0; 372 for (int i = 0, j = 0, k = 1; i < in->row * in->col; i++) // i 遍历 in->data 373 { 374 if (in->data[i] != 0) // 找到非零元 375 { 376 if (j == in->count) // 在 out->data 已经填满了的基础上又发现了非零元，错误 377 return NULL; 378 out->data[j] = in->data[i]; // 填充非零元素 379 out->index[j] = i % in->col; // 填充列号 380 j++; 381 } 382 if ((i + 1) % in->col == 0) // 到了最后一列，写入行指针号 383 out->ptr[k++] = j; 384 } 385 return out; 386 } 387 388 MAT * CSRToMAT(const CSR *in) // CSR转MAT 389 { 390 checkNULL(in); 391 MAT *out = initializeMAT(in->row, in->col, in->ptr[in->row]); 392 checkNULL(out); 393 394 memset(out->data, 0, sizeof(format) * in->row * in->col); 395 for (int i = 0; i < in->row; i++) // i 遍历行 396 { 397 for (int j = in->ptr[i]; j < in->ptr[i + 1]; j++) // j 遍历列 398 out->data[i * in->col + in->index[j]] = in->data[j]; 399 } 400 return out; 401 } 402 403 ELL * MATToELL(const MAT *in)// MAT转ELL 404 { 405 checkNULL(in); 406 407 int i, j, maxElement; 408 for (i = j = maxElement = 0; i < in->row * in->col; i++) // i 遍历 in->data，j 记录该行非零元素数，maxElement 记录一行非零元素最大值 409 { 410 if (in->data[i] != 0) // 找到非零元 411 j++; 412 if ((i + 1) % in->col == 0) // 行末，更新 maxElement 413 { 414 maxElement = MAX(j, maxElement); 415 j = 0; // 开始下一行之前清空 j 416 } 417 } 418 format* temp_data=(format *)malloc(sizeof(format) * in->row * maxElement); // 临时数组，将列数压缩到 maxElement 419 checkNULL(temp_data); 420 int* temp_index = (int *)malloc(sizeof(int) * in->row * maxElement); 421 checkNULL(temp_index); 422 memset(temp_data, 0, sizeof(format) * in->row * maxElement); 423 memset(temp_index, 0, sizeof(int) * in->row * maxElement); 424 for (i = j = 0; i < in->row * in->col; i++) // i 遍历 in->data，j 记录该行非零元素数，把 in 中每行的元素往左边推 425 { 426 if (in->data[i] != 0) // 找到非零元 427 { 428 temp_data[i / in->col * maxElement + j] = in->data[i]; // 存放元素 429 temp_index[i / in->col * maxElement + j] = i % in->col; // 记录所在的列号 430 j++; 431 } 432 if ((i + 1) % in->col == 0) // 行末，将剩余位置的下标记作 -1，即无效元素 433 { 434 for (j += i / in->col * in->col; j < maxElement * (i / in->col + 1); j++) // 使得 j 指向本行最后一个非零元素之后的元素，再开始填充 435 temp_index[j] = -1; 436 j = 0; // 开始下一行之前清空 j 437 } 438 } 439 ELL *out = initializeELL(maxElement, in->row, in->col); // 最终输出，如果不转置的话不要这部分 440 checkNULL(out); 441 for (i = 0; i < out->row * out->col; i++) // 将 temp_data 和 temp_index 转置以提高缓存利用 442 { 443 out->data[i] = temp_data[i % out->col * out->row + i / out->col]; 444 out->index[i] = temp_index[i % out->col * out->row + i / out->col]; 445 } 446 free(temp_data); 447 free(temp_index); 448 return out; 449 } 450 451 MAT * ELLToMAT(const ELL *in) // ELL转MAT 452 { 453 checkNULL(in); 454 MAT *out = initializeMAT(in->col, in->colOrigin); 455 checkNULL(out); 456 457 for (int i = 0; i < in->row * in->col; i++) // i 遍历 out->data 458 { 459 if (in->index[i] < 0) // 注意跳过无效元素 460 continue; 461 out->data[i % in->col * in->colOrigin + in->index[i]] = in->data[i]; 462 } 463 COUNT_MAT(out); 464 return out; 465 } 466 467 COO * MATToCOO(const MAT *in) // MAT转COO 468 { 469 checkNULL(in); 470 COO *out = initializeCOO(in->row, in->col, in->count); 471 472 for (int i=0, j = 0; i < in->row * in->col; i++) 473 { 474 #ifdef INT 475 if (in->data[i] != 0) 476 #else 477 if (fabs(in->data[i]) > EPSILON) 478 #endif 479 { 480 out->data[j] = in->data[i]; 481 out->rowIndex[j] = i / in->col; 482 out->colIndex[j] = i % in->col; 483 j++; 484 } 485 } 486 return out; 487 } 488 489 MAT * COOToMAT(const COO *in) // COO转MAT 490 { 491 checkNULL(in); 492 MAT *out = initializeMAT(in->row, in->col, in->count); 493 checkNULL(out); 494 495 for (int i = 0; i < in->row * in->col; i++) 496 out->data[i] = 0; 497 for (int i = 0; i < in->count; i++) 498 out->data[in->rowIndex[i] * in->col + in->colIndex[i]] = in->data[i]; 499 return out; 500 } 501 502 DIA * MATToDIA(const MAT *in) // MAT转DIA 503 { 504 checkNULL(in); 505 506 int *index = (int *)malloc(sizeof(int)*(in->row + in->col - 1)); 507 for (int diff = in->row - 1; diff > 0; diff--) // 左侧零对角线情况 508 { 509 int flagNonZero = 0; 510 for (int i = 0; i < in->col && i + diff < in->row; i++) // i 沿着对角线方向遍历 in->data，flagNonZero 记录该对角线是否全部为零元 511 { 512 #ifdef INT 513 if (in->data[(i + diff) * in->col + i] != 0) 514 #else 515 if (fabs(in->data[(i + diff) * in->col + i]) > EPSILON) 516 #endif 517 flagNonZero = 1; 518 } 519 index[in->row - 1 - diff] = flagNonZero; // 标记该对角线上有非零元 520 } 521 for (int diff = in->col - 1; diff >= 0; diff--) // 右侧零对角线情况 522 { 523 int flagNonZero = 0; 524 for (int j = 0; j < in->row && j + diff < in->col; j++) 525 { 526 #ifdef INT 527 if (in->data[j * in->col + j + diff] != 0) 528 #else 529 if (fabs(in->data[j * in->col + j + diff]) > EPSILON) 530 #endif 531 flagNonZero = 1; 532 } 533 index[in->row - 1 + diff] = flagNonZero; // 标记该对角线上有非零元 534 } 535 int *prefixSumIndex = (int *)malloc(sizeof(int)*(in->row + in->col - 1)); 536 prefixSumIndex[0] = index[0]; 537 for (int i = 1; i < in->row + in->col - 1; i++) // 闭前缀和，prefixSumIndex[i] 表示原矩阵第 0 ~ i 条对角线中共有多少条非零对角线（含） 538 prefixSumIndex[i] = prefixSumIndex[i-1] + index[i]; // index[in->row + in->col -2] 表示原矩阵非零对角线条数，等于 DIA 矩阵列数 539 DIA *out = initializeDIA(in->row, prefixSumIndex[in->row + in->col - 2], in->col); 540 checkNULL(out); 541 542 memset(out->data, 0, sizeof(int)*out->row * out->col); 543 for (int i = 0; i < in->row + in->col - 1; i++) 544 out->index[i] = index[i]; // index 搬进 out 545 for (int i = 0; i < in->row; i++) // i，j 遍历原矩阵，将元素搬进 out 546 { 547 for (int j = 0; j < in->col; j++) 548 { 549 int temp = j - i + in->row - 1; 550 if (index[temp] == 0) 551 continue; 552 out->data[i * out->col + (temp > 0 ? prefixSumIndex[temp - 1] : 0)] = in->data[i * in->col + j]; // 第 row - 1 行第 0 列元素 temp == 0，单独处理 553 } 554 } 555 free(index); 556 free(prefixSumIndex); 557 return out; 558 } 559 560 MAT * DIAToMAT(const DIA *in) // DIA转MAT 561 { 562 checkNULL(in); 563 MAT *out = initializeMAT(in->row, in->colOrigin); 564 checkNULL(out); 565 566 int * inverseIndex = (int *)malloc(sizeof(int) * in->col); 567 for (int i = 0, j = 0; i < in->row + in->col - 1; i++) // 求一个 index 的逆，即 DIA 中第 i 列对应原矩阵第 inverseIndex[i] 对角线 568 { // 原矩阵对角线编号 (row-1, 0) 为第 0 条，(0, 0) 为第 row - 1 条，(col-1, 0) 为第 row + col - 2 条 569 if (in->index[i] == 1) 570 { 571 inverseIndex[j] = i; 572 j++; 573 } 574 } 575 for (int i = 0; i < in->row; i++) // i 遍历 in->data 行，j 遍历 in->data 列 576 { 577 for (int j = 0; j < in->col; j++) 578 { 579 if (i < in->row - 1 - inverseIndex[j] || i > inverseIndex[in->col - 1] - inverseIndex[j]) // 跳过两边呈三角形的无效元素 580 continue; 581 out->data[i * in->col + inverseIndex[j] - in->row + 1] = in->data[i * in->col + j]; // 利用 inverseIndex 来找钙元素在原距震中的位置 582 } 583 } 584 free(inverseIndex); 585 return out; 586 } 587 588 // 各种形式的矩阵和一个向量的乘法 589 int dotCPU(const MAT *a, const MAT *x, MAT *y) // CPU MAT 乘法 590 { 591 checkNULL(a); checkNULL(x); checkNULL(y); 592 if (a->col != x->row) 593 { 594 printf("dotMATCPU dimension mismatch! "); 595 return 1; 596 } 597 598 y->row = a->row; 599 y->col = x->col; 600 for (int i = 0; i < a->row; i++) 601 { 602 format sum = 0; 603 for (int j = 0; j < a->col; j++) 604 sum += a->data[i * a->col + j] * x->data[j]; 605 y->data[i] = sum; 606 } 607 COUNT_MAT(y); 608 return 0; 609 } 610 611 int dotCPU(const CSR *a, const MAT *x, MAT *y) // CPU CSR 乘法 612 { 613 checkNULL(a); checkNULL(x); checkNULL(y); 614 if (a->col != x->row) 615 { 616 printf("dotCSRCPU dimension mismatch! "); 617 return 1; 618 } 619 620 y->row = a->row; 621 y->col = x->col; 622 for (int i = 0; i < a->row; i++) // i 遍历 ptr，j 遍历行内数据，A 中为 0 的元素不参加乘法 623 { 624 format sum = 0; 625 for (int j = a->ptr[i]; j < a->ptr[i + 1]; j++) 626 sum += a->data[j] * x->data[a->index[j]]; 627 y->data[i] = sum; 628 } 629 COUNT_MAT(y); 630 return 0; 631 } 632 633 int dotCPU(const ELL *a, const MAT *x, MAT *y) // CPU ELL乘法 634 { 635 checkNULL(a); checkNULL(x); checkNULL(y); 636 if (a->colOrigin != x->row) 637 { 638 printf("dotELLCPU dimension mismatch! "); 639 return 1; 640 } 641 642 y->row = a->col; 643 y->col = x->col; 644 for (int i = 0; i<a->col; i++) 645 { 646 format sum = 0; 647 for (int j = 0; j < a->row; j++) 648 { 649 int temp = a->index[j * a->col + i]; 650 if (temp < 0) // 跳过无效元素 651 continue; 652 sum += a->data[j * a->col + i] * x->data[temp]; 653 } 654 y->data[i] = sum; 655 } 656 COUNT_MAT(y); 657 return 0; 658 } 659 660 int dotCPU(const COO *a, const MAT *x, MAT *y)// CPU COO乘法 661 { 662 checkNULL(a); checkNULL(x); checkNULL(y); 663 if (a->col != x->row) 664 { 665 printf("dotCOOCPU null! "); 666 return 1; 667 } 668 669 y->row = a->row; 670 y->col = x->col; 671 for (int i = 0; i<a->count; i++) 672 y->data[a->rowIndex[i]] += a->data[i] * x->data[a->colIndex[i]]; 673 COUNT_MAT(y); 674 return 0; 675 } 676 677 int dotCPU(const DIA *a, const MAT *x, MAT *y)// CPU DIA乘法 678 { 679 checkNULL(a); checkNULL(x); checkNULL(y); 680 if (a->colOrigin != x->row) 681 { 682 printf("dotDIACPU null! "); 683 return 1; 684 } 685 y->row = a->row; 686 y->col = x->col; 687 int * inverseIndex = (int *)malloc(sizeof(int) * a->col); 688 for (int i = 0, j = 0; i < a->row + a->col - 1; i++) 689 { 690 if (a->index[i] == 1) 691 { 692 inverseIndex[j] = i; 693 j++; 694 } 695 } 696 for (int i = 0; i < a->row; i++) 697 { 698 format sum = 0; 699 for (int j = 0; j < a->col; j++) 700 { 701 if (i < a->row - 1 - inverseIndex[j] || i > inverseIndex[a->col - 1] - inverseIndex[j]) 702 continue; 703 sum += a->data[i * a->col + j] * x->data[i + inverseIndex[j] - a->row + 1]; 704 } 705 y->data[i] = sum; 706 } 707 COUNT_MAT(y); 708 free(inverseIndex); 709 return 0; 710 } 711 712 __global__ void dotGPU(const MAT *a, const MAT *x, MAT *y)// GPU MAT乘法 713 { 714 int id = blockIdx.x * blockDim.x + threadIdx.x; 715 if (id < a->row) 716 { 717 format sum = 0; 718 for (int i = 0; i < a->col; i++) 719 sum += a->data[id * a->col + i] * x->data[i]; 720 y->data[id] = sum; 721 } 722 if (id == 0) 723 { 724 y->row = a->row; 725 y->col = x->col; 726 COUNT_MAT(y); 727 } 728 return; 729 } 730 731 __global__ void dotGPU(const CSR *a, const MAT *x, MAT *y)// GPU CSR乘法 732 { 733 int id = blockIdx.x * blockDim.x + threadIdx.x; 734 if (id < a->row) 735 { 736 format sum = 0; 737 for (int j = a->ptr[id]; j < a->ptr[id + 1]; j++) 738 sum += a->data[j] * x->data[a->index[j]]; 739 y->data[id] = sum; 740 } 741 if (id == 0) 742 { 743 y->row = a->row; 744 y->col = x->col; 745 COUNT_MAT(y); 746 } 747 return; 748 } 749 750 __global__ void dotGPU(const ELL *a, const MAT *x, MAT *y)// GPU ELL乘法 751 { 752 int id = blockIdx.x * blockDim.x + threadIdx.x; 753 if (id < a->col) 754 { 755 format sum = 0; 756 for (int j = 0; j < a->row; j++) 757 sum += a->data[id + j * a->col] * (a->index[id + j * a->col] < 0 ? 0 : x->data[a->index[id + j * a->col]]); 758 y->data[id] = sum; 759 } 760 if (id == 0) 761 { 762 y->row = a->col; 763 y->col = x->col; 764 COUNT_MAT(y); 765 } 766 return; 767 } 768 769 __global__ void dotGPU(const COO *a, const MAT *x, MAT *y)// GPU COO乘法 770 { 771 int id = blockIdx.x * blockDim.x + threadIdx.x; 772 if (id < a->count) 773 atomicAdd(&(y->data[a->rowIndex[id]]), a->data[id] * x->data[a->colIndex[id]]); 774 if (id == 0) 775 { 776 y->row = a->row; 777 y->col = x->col; 778 COUNT_MAT(y); 779 } 780 return; 781 } 782 783 int test()// 测试矩阵打印和CPU计算的函数 784 { 785 const int row = 4, col = 5; 786 787 MAT* a = initializeMAT(row, col); 788 a->data[0] = 3, a->data[2] = 1, a->data[4] = 5, a->data[11] = 2; 789 a->data[12] = 4, a->data[13] = 1, a->data[15] = 1, a->data[18] = 1; 790 COUNT_MAT(a); 791 792 MAT* x = initializeMAT(col, 1); 793 for (int i = 0; i < x->row; i++) 794 x->data[i] = i + 1; 795 COUNT_MAT(x); 796 797 MAT* y = initializeMAT(row, 1); 798 COUNT_MAT(y); 799 800 print("MAT a =", a); 801 print("MAT x =", x); 802 dotCPU(a, x, y); 803 print("MAT y = a * x = ", y); 804 805 CSR* b = MATToCSR(a); 806 print("CSR b = a = ", b); 807 memset(y->data, 0, sizeof(format) * y->row * y->col); 808 dotCPU(b, x, y); 809 print("MAT y = b * x = ", y); 810 MAT* c = CSRToMAT(b); 811 print("MAT c = b =", c); 812 freeMatrix(b); 813 814 ELL* d = MATToELL(a); 815 print("ELL d = a =", d); 816 memset(y->data, 0, sizeof(format) * y->row * y->col); 817 dotCPU(d, x, y); 818 print("MAT y = d * x =", y); 819 c = ELLToMAT(d); 820 print("MAT c = d =", c); 821 freeMatrix(d); 822 823 COO* e = MATToCOO(a); 824 print("ELL e = a = ", e); 825 memset(y->data, 0, sizeof(format) * y->row * y->col); 826 dotCPU(e, x, y); 827 print("MAT y = e * x = ", y); 828 c = COOToMAT(e); 829 print("MAT c = e =", c); 830 freeMatrix(e); 831 832 DIA* f = MATToDIA(a); 833 print("DIA f = a = ", f); 834 memset(y->data, 0, sizeof(format) * y->row * y->col); 835 dotCPU(f, x, y); 836 print("MAT y = f * x = ", y); 837 c = DIAToMAT(f); 838 print("MAT c = f =", c); 839 freeMatrix(f); 840 841 freeMatrix(a); 842 freeMatrix(x); 843 freeMatrix(y); 844 freeMatrix(c); 845 return 0; 846 } 847 848 int main() 849 { 850 test(); 851 852 clock_t timeCPU; 853 cudaEvent_t startGPU, stopGPU; 854 float timeGPU; 855 cudaEventCreate(&startGPU); 856 cudaEventCreate(&stopGPU); 857 858 printf(" Start. Matrix dimension: %d × %d", ROW, COL); 859 860 // 初始化 861 timeCPU = clock(); 862 aMAT = initializeMAT(ROW, COL); 863 xMAT = initializeMAT(COL, 1); 864 yMATRef = initializeMAT(ROW, 1); 865 yMATCal = initializeMAT(ROW, 1); 866 867 srand(SEED); 868 #ifdef INT 869 for (int i = 0; i < COL * ROW; i++) 870 aMAT->data[i] = ((float)rand() < RAND_MAX * RATIO) ? (rand() - RAND_MAX / 2) % 32 : 0; 871 COUNT_MAT(aMAT); 872 int count = aMAT->count; 873 for (int i = 0; i < COL; i++) 874 xMAT->data[i] = i % 32; 875 COUNT_MAT(xMAT); 876 #else 877 for (int i = 0; i < COL * ROW; i++) 878 aMAT->data[i] = ((float)rand() < RAND_MAX * RATIO) ? ((float)rand() / RAND_MAX) : 0; 879 aMAT->count = countMAT(aMAT); 880 for (int i = 0; i < COL; i++) 881 xMAT->data[i] = ((float)rand() / RAND_MAX); 882 xMAT->count = countMAT(xMAT); 883 #endif 884 printf(" Initialized. Time: %d ms ", clock() - timeCPU); 885 886 //CPU计算部分 887 //MAT 格式 888 timeCPU = clock(); 889 dotCPU(aMAT, xMAT, yMATRef); 890 timeCPU = clock() - timeCPU; 891 printf(" dotMATCPU time: %8.3f ms ", (float)timeCPU); 892 893 // CSR格式 894 aCSR = MATToCSR(aMAT); 895 timeCPU = clock(); 896 dotCPU(aCSR, xMAT, yMATCal); 897 timeCPU = clock() - timeCPU; 898 printf(" dotCSRCPU time: %8.3f ms ", (float)timeCPU); 899 checkEqual(yMATRef->data, yMATCal->data, ROW); 900 901 // ELL格式 902 aELL = MATToELL(aMAT); 903 timeCPU = clock(); 904 dotCPU(aELL, xMAT, yMATCal); 905 timeCPU = clock() - timeCPU; 906 printf(" dotELLCPU time: %8.3f ms ", (float)timeCPU); 907 checkEqual(yMATRef->data, yMATCal->data, ROW); 908 909 // COO格式 910 aCOO = MATToCOO(aMAT); 911 timeCPU = clock(); 912 dotCPU(aCOO, xMAT, yMATCal); 913 timeCPU = clock() - timeCPU; 914 printf(" dotCOOCPU time: %8.3f ms ", (float)timeCPU); 915 checkEqual(yMATRef->data, yMATCal->data, ROW); 916 917 // GPU计算部分 918 // MAT格式 919 cudaMemset(yMATCal->data, 0, sizeof(format) * yMATCal->row * yMATCal->col); 920 yMATCal->count = 0; 921 cudaEventRecord(startGPU, 0); 922 dotGPU << <CEIL(ROW, THREAD_SIZE), THREAD_SIZE >> > (aMAT, xMAT, yMATCal); 923 cudaDeviceSynchronize(); 924 cudaEventRecord(stopGPU, 0); 925 cudaEventSynchronize(stopGPU); 926 cudaEventElapsedTime(&timeGPU, startGPU, stopGPU); 927 printf(" dotMATGPU time: %8.3f ms ", timeGPU); 928 checkEqual(yMATRef->data, yMATCal->data, ROW); 929 freeMatrix(aMAT); 930 931 // CSR格式 932 cudaMemset(yMATCal->data, 0, sizeof(format) * yMATCal->row * yMATCal->col); 933 yMATCal->count = 0; 934 cudaEventRecord(startGPU, 0); 935 dotGPU << <CEIL(ROW, THREAD_SIZE), THREAD_SIZE >> > (aCSR, xMAT, yMATCal); 936 cudaDeviceSynchronize(); 937 cudaEventRecord(stopGPU, 0); 938 cudaEventSynchronize(stopGPU); 939 cudaEventElapsedTime(&timeGPU, startGPU, stopGPU); 940 printf(" dotCSRGPU time: %8.3f ms ", timeGPU); 941 checkEqual(yMATRef->data, yMATCal->data, ROW); 942 freeMatrix(aCSR); 943 944 // ELL格式 945 cudaMemset(yMATCal->data, 0, sizeof(format) * yMATCal->row * yMATCal->col); 946 yMATCal->count = 0; 947 cudaEventRecord(startGPU, 0); 948 dotGPU << <CEIL(ROW, THREAD_SIZE), THREAD_SIZE >> > (aELL, xMAT, yMATCal); 949 cudaDeviceSynchronize(); 950 cudaEventRecord(stopGPU, 0); 951 cudaEventSynchronize(stopGPU); 952 cudaEventElapsedTime(&timeGPU, startGPU, stopGPU); 953 printf(" dotELLGPU time: %8.3f ms ", timeGPU); 954 checkEqual(yMATRef->data, yMATCal->data, ROW); 955 freeMatrix(aELL); 956 957 // COO格式 958 cudaMemset(yMATCal->data, 0, sizeof(format) * yMATCal->row * yMATCal->col); 959 yMATCal->count = 0; 960 cudaEventRecord(startGPU, 0); 961 dotGPU << <CEIL(count, THREAD_SIZE), THREAD_SIZE >> > (aCOO, xMAT, yMATCal); 962 cudaDeviceSynchronize(); 963 cudaEventRecord(stopGPU, 0); 964 cudaEventSynchronize(stopGPU); 965 cudaEventElapsedTime(&timeGPU, startGPU, stopGPU); 966 printf(" dotCOOGPU time: %8.3f ms ", timeGPU); 967 checkEqual(yMATRef->data, yMATCal->data, ROW); 968 freeMatrix(aCOO); 969 970 // 清理内存 971 freeMatrix(xMAT); 972 freeMatrix(yMATRef); 973 freeMatrix(yMATCal); 974 975 getchar(); 976 return 0; 977 }
● 输出结果
MAT a = MAT, row = 4, col = 5, count = 8 3 0 1 0 5 0 0 0 0 0 0 2 4 1 0 1 0 0 1 0 MAT x = MAT, row = 5, col = 1, count = 5 1 2 3 4 5 MAT y = a * x = MAT, row = 4, col = 1, count = 3 31 0 20 5 CSR b = a = CSR, row = 4, col = 5 3 1 5 2 4 1 1 1 0 2 4 1 2 3 0 3 0 3 3 6 8 MAT y = b * x = MAT, row = 4, col = 1, count = 3 31 0 20 5 MAT c = b = MAT, row = 4, col = 5, count = 8 3 0 1 0 5 0 0 0 0 0 0 2 4 1 0 1 0 0 1 0 ELL d = a = ELL, row = 3, col = 4, colOrigin = 5 3 0 2 1 1 0 4 1 5 0 1 0 0 0 1 0 2 0 2 3 4 -1 3 0 MAT y = d * x = MAT, row = 4, col = 1, count = 3 31 0 20 5 MAT c = d = MAT, row = 4, col = 5, count = 7 3 0 1 0 5 0 0 0 0 0 0 2 4 1 0 0 0 0 1 0 ELL e = a = COO, row = 4, col = 5, count = 8 (0,0,3) (0,2,1) (0,4,5) (2,1,2) (2,2,4) (2,3,1) (3,0,1) (3,3,1) MAT y = e * x MAT, row = 4, col = 1, count = 3 31 0 20 5 MAT c = e = MAT, row = 4, col = 5, count = 8 3 0 1 0 5 0 0 0 0 0 0 2 4 1 0 1 0 0 1 0 Start. Matrix dimension: 8192 × 8192 Initialized. Time: 0.000 ms dotMATCPU time: 304.000 ms dotCSRCPU time: 3.000 ms Check output, passed. dotCELLPU time: 103.000 ms Check output, passed. dotCOOCPU time: 11.000 ms Check output, passed. dotMATGPU time: 5.133 ms Check output, passed. dotCSRGPU time: 2.263 ms Check output, passed. dotELLGPU time: 1.253 ms Check output, passed. dotCOOGPU time: 4.754 ms Check output, passed.
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