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sparse_mult.cpp
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/**
* @file sparse_mult.cpp
* @brief This file contains the implementation of a function that performs multiplication between a sparse matrix and a dense matrix of rank r.
*
* The function is designed to be compiled into a MEX file for use with MATLAB. It utilizes OpenMP for parallel computation to improve performance for large datasets.
*
* To compile this file into a MEX file, use the following commands in the MATLAB terminal:
*
* ```matlab
* mex -setup C++
* mex sparse_mult.cpp
* ```
*
* The main function `mexFunction` handles the input and output arguments from MATLAB, and performs the matrix multiplication based on the value of `r`.
* For values of `r` from 1 to 10, specialized loops are used for optimization. For other values of `r`, a general case function is called.
*
* The function uses atomic operations to ensure thread safety when updating the result matrix in parallel.
*
* @param nlhs Number of left-hand side (output) arguments
* @param plhs Array of pointers to the left-hand side (output) arguments
* @param nrhs Number of right-hand side (input) arguments
* @param prhs Array of pointers to the right-hand side (input) arguments
*/
#include "mex.h"
#include <omp.h>
// Function for handling general cases of `r`
inline void performGeneralCase(const double* Y_vec, const double* omega_row, const double* omega_col,
const double* R, double* res, int n1, int n2, int r, int pn) {
#pragma omp parallel for if(pn > 1000) // Perform parallel computation only when `pn` is large
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
for (int j = 0; j < r; j++) {
int res_index = row + j * n1; // Precompute result index
int R_index = col + j * n2; // Precompute R matrix index
#pragma omp atomic // Atomic to ensure thread safety
res[res_index] += Y_vec[i] * R[R_index];
}
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
// Check the number of input arguments
if (nrhs != 7) {
mexErrMsgIdAndTxt("MATLAB:mm_mex:nrhs", "Seven inputs required.");
}
// Check the number of output arguments
if (nlhs != 1) {
mexErrMsgIdAndTxt("MATLAB:mm_mex:nlhs", "One output required.");
}
// Get input arguments
const double *Y_vec = mxGetPr(prhs[0]);
const double *omega_row = mxGetPr(prhs[1]);
const double *omega_col = mxGetPr(prhs[2]);
const double *R = mxGetPr(prhs[3]);
int n1 = static_cast<int>(mxGetScalar(prhs[4]));
int n2 = static_cast<int>(mxGetScalar(prhs[5]));
int r = static_cast<int>(mxGetScalar(prhs[6]));
// Get the length of Y_vec
int pn = static_cast<int>(mxGetNumberOfElements(prhs[0]));
// Create output matrix
plhs[0] = mxCreateDoubleMatrix(n1, r, mxREAL);
double *res = mxGetPr(plhs[0]);
// Choose the ideal loop strategy based on the value of r
switch (r) {
case 1: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
}
break;
}
case 2: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
}
break;
}
case 3: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
}
break;
}
case 4: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
}
break;
}
case 5: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
}
break;
}
case 6: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
#pragma omp atomic
res[row + 5 * n1] += Y_vec[i] * R[col + 5 * n2];
}
break;
}
case 7: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
#pragma omp atomic
res[row + 5 * n1] += Y_vec[i] * R[col + 5 * n2];
#pragma omp atomic
res[row + 6 * n1] += Y_vec[i] * R[col + 6 * n2];
}
break;
}
case 8: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
#pragma omp atomic
res[row + 5 * n1] += Y_vec[i] * R[col + 5 * n2];
#pragma omp atomic
res[row + 6 * n1] += Y_vec[i] * R[col + 6 * n2];
#pragma omp atomic
res[row + 7 * n1] += Y_vec[i] * R[col + 7 * n2];
}
break;
}
case 9: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
#pragma omp atomic
res[row + 5 * n1] += Y_vec[i] * R[col + 5 * n2];
#pragma omp atomic
res[row + 6 * n1] += Y_vec[i] * R[col + 6 * n2];
#pragma omp atomic
res[row + 7 * n1] += Y_vec[i] * R[col + 7 * n2];
#pragma omp atomic
res[row + 8 * n1] += Y_vec[i] * R[col + 8 * n2];
}
break;
}
case 10: {
#pragma omp parallel for if(pn > 1000)
for (int i = 0; i < pn; i++) {
int row = static_cast<int>(omega_row[i]) - 1;
int col = static_cast<int>(omega_col[i]) - 1;
#pragma omp atomic
res[row] += Y_vec[i] * R[col];
#pragma omp atomic
res[row + n1] += Y_vec[i] * R[col + n2];
#pragma omp atomic
res[row + 2 * n1] += Y_vec[i] * R[col + 2 * n2];
#pragma omp atomic
res[row + 3 * n1] += Y_vec[i] * R[col + 3 * n2];
#pragma omp atomic
res[row + 4 * n1] += Y_vec[i] * R[col + 4 * n2];
#pragma omp atomic
res[row + 5 * n1] += Y_vec[i] * R[col + 5 * n2];
#pragma omp atomic
res[row + 6 * n1] += Y_vec[i] * R[col + 6 * n2];
#pragma omp atomic
res[row + 7 * n1] += Y_vec[i] * R[col + 7 * n2];
#pragma omp atomic
res[row + 8 * n1] += Y_vec[i] * R[col + 8 * n2];
#pragma omp atomic
res[row + 9 * n1] += Y_vec[i] * R[col + 9 * n2];
}
break;
}
default: {
performGeneralCase(Y_vec, omega_row, omega_col, R, res, n1, n2, r, pn);
break;
}
}
}