الگوریتم ضرب ماتریسی به صورت موازی

[monirprogram]

سلام دوستان عزیز. استاد من، یکسری از الگوریتمهای ضرب موازی ماتریس ها را برای ما توضیح داده، مثل تقسیم ماتریس به 8 پردازنده ثابت، n*n مستقیم(n* پردازنده)، بلوکی s*s(s تعداد پردازنده)،Recursive، cannon n*n، کانون بلوکی، fox n*n و فاکس بلوکی.
حالا سوال، ازمون خواسته یکی دیگه از الگوریتمهای ضرب موازی را تحلیل کنیم. کسی میتونه الگوریتمی معرفی کنه برای این مسئله. با تعداد n پردازنده

[MIDOSE]

به (https://docs.google.com/viewer?a=v&q=cache:UmPtD1J0diAJ:citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.120.4575%26rep%3Drep1%26ty pe%3Dpdf+&hl=en&pid=bl&srcid=ADGEESjH5P6BmnEOOa7UhP3Mj-7F3lM1qJvMJopDMKe39uUSIfpvxMe4NW-OA4Ukz2joEnG57VMKfR67O-LPRvfakS2EWj_YNzGpQqZEkAqK70Ah559lqdTlhX1O3rM8rtpu cHRO-Amb&sig=AHIEtbSJxbd7If1NBkUx1q-hx6dJspMJoA)این (https://docs.google.com/viewer?a=v&q=cache:UmPtD1J0diAJ:citeseerx.ist.psu.edu/viewdoc/download%3Fdoi%3D10.1.1.120.4575%26rep%3Drep1%26ty pe%3Dpdf+&hl=en&pid=bl&srcid=ADGEESjH5P6BmnEOOa7UhP3Mj-7F3lM1qJvMJopDMKe39uUSIfpvxMe4NW-OA4Ukz2joEnG57VMKfR67O-LPRvfakS2EWj_YNzGpQqZEkAqK70Ah559lqdTlhX1O3rM8rtpu cHRO-Amb&sig=AHIEtbSJxbd7If1NBkUx1q-hx6dJspMJoA) و این (http://www.academia.edu/1078766/New_Parallel_Matrix_Multiplication_Algorithms_for_ Wormhole-Routed_All-Port_2D_3D_Torus_Networks) یکی سر بزن!کتابی به نام معماری و طراحی سیستم های پیشرفته کامپیوتری و پردازش موازی چاپ دانشگاه علم و صنعت ایران سال 1378(البته مطمئن نیستم که که مطلبی در این مورد داشته باشه چون محتوای کاملش الان دقیق یادم نمیاد)؛ و گوگل (https://www.google.com/)!

[مصطفی ساتکی]

به طور مثال این کد تو زبان cuda دو تا ماتریس رو به صورت موازی ضرب می کنه.

// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.stride + col)
typedef struct {
int width;
int height;
int stride;
float* elements;
} Matrix;
// Get a matrix element
__device__ float GetElement(const Matrix A, int row, int col)
{
return A.elements[row * A.stride + col];
}
// Set a matrix element
__device__ void SetElement(Matrix A, int row, int col,
float value)
{
A.elements[row * A.stride + col] = value;
}
// Get the BLOCK_SIZExBLOCK_SIZE sub-matrix Asub of A that is
// located col sub-matrices to the right and row sub-matrices down
// from the upper-left corner of A
__device__ Matrix GetSubMatrix(Matrix A, int row, int col)
{
Matrix Asub;
Asub.width = BLOCK_SIZE;
Asub.height = BLOCK_SIZE;
Asub.stride = A.stride;
Asub.elements = &A.elements[A.stride * BLOCK_SIZE * row
+ BLOCK_SIZE * col];
return Asub;
}
// Thread block size
#define BLOCK_SIZE 16
// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);
// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix N, Matrix C)
{
// Load A and
d_A.width = d_A.stride = A.width; d_A.height = A.height;
size_t size = A.width * A.height * sizeof(float);
cudaMalloc((void**)&d_A.elements, size);
cudaMemcpy(d_A.elements, A.elements, size,
cudaMemcpyHostToDevice);
Matrix d_B;
d_B.width = d_B.stride = B.width; d_B.height = B.height;
size = B.width * B.height * sizeof(float);
cudaMalloc((void**)&d_B.elements, size);
cudaMemcpy(d_B.elements, B.elements, size,
cudaMemcpyHostToDevice);
// Allocate C in device memory
Matrix d_C;
d_C.width = d_C.stride = C.width; d_C.height = C.height;
size = C.width * C.height * sizeof(float);
cudaMalloc((void**)&d_C.elements, size);
// Invoke kernel
dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);
// Read C from device memory
cudaMemcpy(C.elements, d_C.elements, size,
cudaMemcpyDeviceToHost);
// Free device memory
cudaFree(d_A.elements);
cudaFree(d_B.elements);
cudaFree(d_C.elements);
}
// Matrix multiplication kernel called by MatrixMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
// Block row and column
int blockRow = blockIdx.y;
int blockCol = blockIdx.x;
// Each thread block computes one sub-matrix Csub of C
Matrix Csub = GetSubMatrix(C, blockRow, blockCol);
// Each thread computes one element of Csub
// by accumulating results into Cvalue
float Cvalue = 0;
// Thread row and column within Csub
int row = threadIdx.y;
int col = threadIdx.x;
// Loop over all the sub-matrices of A and B that are
// required to compute Csub
// Multiply each pair of sub-matrices together
// and accumulate the results
for (int m = 0; m < (A.width / BLOCK_SIZE); ++m) {// Get sub-matrix Asub of A
Matrix Asub = GetSubMatrix(A, blockRow, m);
// Get sub-matrix Bsub of B
Matrix Bsub = GetSubMatrix(B, m, blockCol);
// Shared memory used to store Asub and Bsub respectively
__shared__ float As[BLOCK_SIZE][BLOCK_SIZE];
__shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];
// Load Asub and Bsub from device memory to shared memory
// Each thread loads one element of each sub-matrix
As[row][col] = GetElement(Asub, row, col);
Bs[row][col] = GetElement(Bsub, row, col);
// Synchronize to make sure the sub-matrices are loaded
// before starting the computation
__syncthreads();
// Multiply Asub and Bsub together
for (int e = 0; e < BLOCK_SIZE; ++e)
Cvalue += As[row][e] * Bs[e][col];
// Synchronize to make sure that the preceding
// computation is done before loading two new
// sub-matrices of A and B in the next iteration
__syncthreads();
}
// Write Csub to device memory
// Each thread writes one element
SetElement(Csub, row, col, Cvalue);
}

[monirprogram]

به طور مثال این کد تو زبان cuda دو تا ماتریس رو به صورت موازی ضرب می کنه.

// Matrices are stored in row-major order:
// M(row, col) = *(M.elements + row * M.stride + col)
typedef struct {
int width;
int height;
int stride;
float* elements;
} Matrix;
// Get a matrix element
__device__ float GetElement(const Matrix A, int row, int col)
{
return A.elements[row * A.stride + col];
}
// Set a matrix element
__device__ void SetElement(Matrix A, int row, int col,
float value)
{
A.elements[row * A.stride + col] = value;
}
// Get the BLOCK_SIZExBLOCK_SIZE sub-matrix Asub of A that is
// located col sub-matrices to the right and row sub-matrices down
// from the upper-left corner of A
__device__ Matrix GetSubMatrix(Matrix A, int row, int col)
{
Matrix Asub;
Asub.width = BLOCK_SIZE;
Asub.height = BLOCK_SIZE;
Asub.stride = A.stride;
Asub.elements = &A.elements[A.stride * BLOCK_SIZE * row
+ BLOCK_SIZE * col];
return Asub;
}
// Thread block size
#define BLOCK_SIZE 16
// Forward declaration of the matrix multiplication kernel
__global__ void MatMulKernel(const Matrix, const Matrix, Matrix);
// Matrix multiplication - Host code
// Matrix dimensions are assumed to be multiples of BLOCK_SIZE
void MatMul(const Matrix A, const Matrix N, Matrix C)
{
// Load A and
d_A.width = d_A.stride = A.width; d_A.height = A.height;
size_t size = A.width * A.height * sizeof(float);
cudaMalloc((void**)&d_A.elements, size);
cudaMemcpy(d_A.elements, A.elements, size,
cudaMemcpyHostToDevice);
Matrix d_B;
d_B.width = d_B.stride = B.width; d_B.height = B.height;
size = B.width * B.height * sizeof(float);
cudaMalloc((void**)&d_B.elements, size);
cudaMemcpy(d_B.elements, B.elements, size,
cudaMemcpyHostToDevice);
// Allocate C in device memory
Matrix d_C;
d_C.width = d_C.stride = C.width; d_C.height = C.height;
size = C.width * C.height * sizeof(float);
cudaMalloc((void**)&d_C.elements, size);
// Invoke kernel
dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);
dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);
MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);
// Read C from device memory
cudaMemcpy(C.elements, d_C.elements, size,
cudaMemcpyDeviceToHost);
// Free device memory
cudaFree(d_A.elements);
cudaFree(d_B.elements);
cudaFree(d_C.elements);
}
// Matrix multiplication kernel called by MatrixMul()
__global__ void MatMulKernel(Matrix A, Matrix B, Matrix C)
{
// Block row and column
int blockRow = blockIdx.y;
int blockCol = blockIdx.x;
// Each thread block computes one sub-matrix Csub of C
Matrix Csub = GetSubMatrix(C, blockRow, blockCol);
// Each thread computes one element of Csub
// by accumulating results into Cvalue
float Cvalue = 0;
// Thread row and column within Csub
int row = threadIdx.y;
int col = threadIdx.x;
// Loop over all the sub-matrices of A and B that are
// required to compute Csub
// Multiply each pair of sub-matrices together
// and accumulate the results
for (int m = 0; m < (A.width / BLOCK_SIZE); ++m) {// Get sub-matrix Asub of A
Matrix Asub = GetSubMatrix(A, blockRow, m);
// Get sub-matrix Bsub of B
Matrix Bsub = GetSubMatrix(B, m, blockCol);
// Shared memory used to store Asub and Bsub respectively
__shared__ float As[BLOCK_SIZE][BLOCK_SIZE];
__shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];
// Load Asub and Bsub from device memory to shared memory
// Each thread loads one element of each sub-matrix
As[row][col] = GetElement(Asub, row, col);
Bs[row][col] = GetElement(Bsub, row, col);
// Synchronize to make sure the sub-matrices are loaded
// before starting the computation
__syncthreads();
// Multiply Asub and Bsub together
for (int e = 0; e < BLOCK_SIZE; ++e)
Cvalue += As[row][e] * Bs[e][col];
// Synchronize to make sure that the preceding
// computation is done before loading two new
// sub-matrices of A and B in the next iteration
__syncthreads();
}
// Write Csub to device memory
// Each thread writes one element
SetElement(Csub, row, col, Cvalue);
}

بابتشون ممنون. ولی من کوبول بلدد نیستم. ولی باز هم ممنون

[صبا زرباف]

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