Реализация параллельного алгоритма умножения матриц

Ниже приводится исходный код программы, реализующей параллельный алгоритм перемножения матриц на основе алгоритма Фокса:

#include <stdio.h>

#include <stdlib.h>

#include <time.h>

#include <math.h>

#include <mpi.h>

int ProcNum = 0; // Number of available processes

int ProcRank = 0; // Rank of current process

int GridSize; // Size of virtual processor grid

int GridCoords[2]; // Coordinates of current processor in grid

MPI_Comm GridComm; // Grid communicator

MPI_Comm ColComm; // Column communicator

MPI_Comm RowComm; // Row communicator

// Function for simple initialization of matrix elements

void DummyDataInitialization(double* pAMatrix, double* pBMatrix,int Size){

int i, j; // Loop variables

for (i=0; i<Size; i++)

for (j=0; j<Size; j++) {

pAMatrix[i*Size+j] = 1;

pBMatrix[i*Size+j] = 1;

}

}

// Function for random initialization of matrix elements

void RandomDataInitialization(double* pAMatrix, double* pBMatrix,

int Size) {

int i, j; // Loop variables

srand(unsigned(clock()));

for (i=0; i<Size; i++)

for (j=0; j<Size; j++) {

pAMatrix[i*Size+j] = rand()/double(1000);

pBMatrix[i*Size+j] = rand()/double(1000);

}

}

// Function for formatted matrix output

void PrintMatrix(double* pMatrix, int RowCount, int ColCount) {

int i, j; // Loop variables

for (i=0; i<RowCount; i++) {

for (j=0; j<ColCount; j++)

printf("%7.4f ", pMatrix[i*ColCount+j]);

printf("\n");

}

}

// Function for matrix multiplication

void SerialResultCalculation(double* pAMatrix, double* pBMatrix,

double* pCMatrix, int Size) {

int i, j, k; // Loop variables

for (i=0; i<Size; i++) {

for (j=0; j<Size; j++)

for (k=0; k<Size; k++)

pCMatrix[i*Size+j] += pAMatrix[i*Size+k]*pBMatrix[k*Size+j];

}

}

// Function for block multiplication

void BlockMultiplication(double* pAblock, double* pBblock,

double* pCblock, int Size) {

SerialResultCalculation(pAblock, pBblock, pCblock, Size);

}

// Creation of two-dimensional grid communicator

// and communicators for each row and each column of the grid

void CreateGridCommunicators() {

int DimSize[2]; // Number of processes in each dimension of the grid

int Periodic[2]; // =1, if the grid dimension should be periodic

int Subdims[2]; // =1, if the grid dimension should be fixed

DimSize[0] = GridSize;

DimSize[1] = GridSize;

Periodic[0] = 0;

Periodic[1] = 0;

// Creation of the Cartesian communicator

MPI_Cart_create(MPI_COMM_WORLD, 2, DimSize, Periodic, 1, &GridComm);

// Determination of the cartesian coordinates for every process

MPI_Cart_coords(GridComm, ProcRank, 2, GridCoords);

// Creating communicators for rows

Subdims[0] = 0; // Dimensionality fixing

Subdims[1] = 1; // The presence of the given dimension in the subgrid

MPI_Cart_sub(GridComm, Subdims, &RowComm);

// Creating communicators for columns

Subdims[0] = 1;

Subdims[1] = 0;

MPI_Cart_sub(GridComm, Subdims, &ColComm);

}

// Function for memory allocation and data initialization

void ProcessInitialization(double* &pAMatrix, double* &pBMatrix,

double* &pCMatrix, double* &pAblock, double* &pBblock, double* &pCblock,

double* &pTemporaryAblock, int &Size, int &BlockSize ) {

if (ProcRank == 0) {

do {

printf("\nEnter size of the initial objects: ");

scanf("%d", &Size);

if (Size%GridSize != 0) {

printf ("Size of matricies must be divisible by the grid size!\n");

}

}

while (Size%GridSize != 0);

}

MPI_Bcast(&Size, 1, MPI_INT, 0, MPI_COMM_WORLD);

BlockSize = Size/GridSize;

pAblock = new double [BlockSize*BlockSize];

pBblock = new double [BlockSize*BlockSize];

pCblock = new double [BlockSize*BlockSize];

pTemporaryAblock = new double [BlockSize*BlockSize];

for (int i=0; i<BlockSize*BlockSize; i++) {

pCblock[i] = 0;

}

if (ProcRank == 0) {

pAMatrix = new double [Size*Size];

pBMatrix = new double [Size*Size];

pCMatrix = new double [Size*Size];

DummyDataInitialization(pAMatrix, pBMatrix, Size);

//RandomDataInitialization(pAMatrix, pBMatrix, Size);

}

}

// Function for checkerboard matrix decomposition

void CheckerboardMatrixScatter(double* pMatrix, double* pMatrixBlock,

int Size, int BlockSize) {

double * MatrixRow = new double [BlockSize*Size];

if (GridCoords[1] == 0) {

MPI_Scatter(pMatrix, BlockSize*Size, MPI_DOUBLE, MatrixRow,

BlockSize*Size, MPI_DOUBLE, 0, ColComm);

}

for (int i=0; i<BlockSize; i++) {

MPI_Scatter(&MatrixRow[i*Size], BlockSize, MPI_DOUBLE,

&(pMatrixBlock[i*BlockSize]), BlockSize, MPI_DOUBLE, 0, RowComm);

}

delete [] MatrixRow;

}

// Data distribution among the processes

void DataDistribution(double* pAMatrix, double* pBMatrix, double*

pMatrixAblock, double* pBblock, int Size, int BlockSize) {

// Scatter the matrix among the processes of the first grid column

CheckerboardMatrixScatter(pAMatrix, pMatrixAblock, Size, BlockSize);

CheckerboardMatrixScatter(pBMatrix, pBblock, Size, BlockSize);

}

// Function for gathering the result matrix

void ResultCollection(double* pCMatrix, double* pCblock, int Size,

int BlockSize) {

double * pResultRow = new double [Size*BlockSize];

for (int i=0; i<BlockSize; i++) {

MPI_Gather( &pCblock[i*BlockSize], BlockSize, MPI_DOUBLE,

&pResultRow[i*Size], BlockSize, MPI_DOUBLE, 0, RowComm);

}

if (GridCoords[1] == 0) {

MPI_Gather(pResultRow, BlockSize*Size, MPI_DOUBLE, pCMatrix,

BlockSize*Size, MPI_DOUBLE, 0, ColComm);

}

delete [] pResultRow;

}

// Broadcasting matrix A blocks to process grid rows

void ABlockCommunication(int iter, double *pAblock, double* pMatrixAblock,

int BlockSize) {

// Defining the leading process of the process grid row

int Pivot = (GridCoords[0] + iter) % GridSize;

// Copying the transmitted block in a separate memory buffer

if (GridCoords[1] == Pivot) {

for (int i=0; i<BlockSize*BlockSize; i++)

pAblock[i] = pMatrixAblock[i];

}

// Block broadcasting

MPI_Bcast(pAblock, BlockSize*BlockSize, MPI_DOUBLE, Pivot, RowComm);

}

// Cyclic shift of matrix B blocks in the process grid columns

void BblockCommunication(double *pBblock, int BlockSize) {

MPI_Status Status;

int NextProc = GridCoords[0] + 1;

if ( GridCoords[0] == GridSize-1 ) NextProc = 0;

int PrevProc = GridCoords[0] - 1;

if ( GridCoords[0] == 0 ) PrevProc = GridSize-1;

MPI_Sendrecv_replace( pBblock, BlockSize*BlockSize, MPI_DOUBLE,

NextProc, 0, PrevProc, 0, ColComm, &Status);

}

void ParallelResultCalculation(double* pAblock, double* pMatrixAblock,

double* pBblock, double* pCblock, int BlockSize) {

for (int iter = 0; iter < GridSize; iter ++) {

// Sending blocks of matrix A to the process grid rows

ABlockCommunication (iter, pAblock, pMatrixAblock, BlockSize);

// Block multiplication

BlockMultiplication(pAblock, pBblock, pCblock, BlockSize);

// Cyclic shift of blocks of matrix B in process grid columns

BblockCommunication(pBblock, BlockSize);

}

}

// Test printing of the matrix block

void TestBlocks(double* pBlock, int BlockSize, char str[]) {

MPI_Barrier(MPI_COMM_WORLD);

if (ProcRank == 0) {

printf("%s \n", str);

}

for (int i=0; i<ProcNum; i++) {

if (ProcRank == i) {

printf ("ProcRank = %d \n", ProcRank);

PrintMatrix(pBlock, BlockSize, BlockSize);

}

MPI_Barrier(MPI_COMM_WORLD);

}

}

void TestResult(double* pAMatrix, double* pBMatrix, double* pCMatrix,

int Size) {

double* pSerialResult; // Result matrix of serial multiplication

double Accuracy = 1.e-6; // Comparison accuracy

int equal = 0; // =1, if the matrices are not equal

int i; // Loop variable

if (ProcRank == 0) {

pSerialResult = new double [Size*Size];

for (i=0; i<Size*Size; i++) {

pSerialResult[i] = 0;

}

BlockMultiplication(pAMatrix, pBMatrix, pSerialResult, Size);

for (i=0; i<Size*Size; i++) {

if (fabs(pSerialResult[i]-pCMatrix[i]) >= Accuracy)

equal = 1;

}

if (equal == 1)

printf("The results of serial and parallel algorithms are NOT "

"identical. Check your code.");

else

printf("The results of serial and parallel algorithms are "

"identical.");

}

}

// Function for computational process termination

void ProcessTermination(double* pAMatrix, double* pBMatrix,

double* pCMatrix, double* pAblock, double* pBblock, double* pCblock,

double* pMatrixAblock) {

if (ProcRank == 0) {

delete [] pAMatrix;

delete [] pBMatrix;

delete [] pCMatrix;

}

delete [] pAblock;

delete [] pBblock;

delete [] pCblock;

delete [] pMatrixAblock;

}

void main(int argc, char* argv[]) {

double* pAMatrix; // The first argument of matrix multiplication

double* pBMatrix; // The second argument of matrix multiplication

double* pCMatrix; // The result matrix

int Size; // Size of matricies

int BlockSize; // Sizes of matrix blocks on current process

double *pAblock; // Initial block of matrix A on current process

double *pBblock; // Initial block of matrix B on current process

double *pCblock; // Block of result matrix C on current process

double *pMatrixAblock;

double Start, Finish, Duration;

setvbuf(stdout, 0, _IONBF, 0);

MPI_Init(&argc, &argv);

MPI_Comm_size(MPI_COMM_WORLD, &ProcNum);

MPI_Comm_rank(MPI_COMM_WORLD, &ProcRank);

GridSize = sqrt((double)ProcNum);

if (ProcNum != GridSize*GridSize) {

if (ProcRank == 0) {

printf ("Number of processes must be a perfect square \n");

}

}

else {

if (ProcRank == 0)

printf("Parallel matrix multiplication program\n");

// Creating the cartesian grid, row and column communcators

CreateGridCommunicators();

// Memory allocation and initialization of matrix elements

ProcessInitialization ( pAMatrix, pBMatrix, pCMatrix, pAblock, pBblock,

pCblock, pMatrixAblock, Size, BlockSize );

DataDistribution(pAMatrix, pBMatrix, pMatrixAblock, pBblock, Size,

BlockSize);

// Execution of Fox method

ParallelResultCalculation(pAblock, pMatrixAblock, pBblock,

pCblock, BlockSize);

ResultCollection(pCMatrix, pCblock, Size, BlockSize);

TestResult(pAMatrix, pBMatrix, pCMatrix, Size);

// Process Termination

ProcessTermination (pAMatrix, pBMatrix, pCMatrix, pAblock, pBblock,

pCblock, pMatrixAblock);

}

MPI_Finalize();

}

В программе можно выделить несколько функциональных модулей:

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