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Single memory allocations in GPU, Move new_shift and mean_shift_vector calculations in kernel

master
Apostolos Fanakis 7 years ago
parent
commit
d29fa007d7
  1. BIN
      mean_shift_cuda/meanshift
  2. 50
      mean_shift_cuda/meanshift_kernels.cu
  3. 11
      mean_shift_cuda/meanshift_kernels.h
  4. 289
      mean_shift_cuda/meanshift_utils.cu
  5. 19
      mean_shift_cuda/meanshift_utils.h

BIN
mean_shift_cuda/meanshift

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50
mean_shift_cuda/meanshift_kernels.cu

@ -1,24 +1,8 @@
#include "meanshift_kernels.h"
#include <stdio.h>
__global__ void multiply_kernel(Matrix matrix1, Matrix matrix2, Matrix output){
// Each thread computes one element of output
// by accumulating results into cell_value
double cell_value = 0;
int row = blockIdx.x * blockDim.x + threadIdx.x;
int col = blockIdx.y * blockDim.y + threadIdx.y;
if (row + col < output.height * output.width){
for (int element_index = 0; element_index < matrix1.width; ++element_index){
cell_value += matrix1.elements[row * matrix1.width + element_index]
* matrix2.elements[element_index * matrix2.width + col];
}
output.elements[row * output.width + col] = cell_value;
}
}
__global__ void calculate_kernel_matrix_kernel(Matrix shifted_points, Matrix original_points
, double deviation, Matrix kernel_matrix){
__global__ void calculate_kernel_matrix_kernel(Matrix shifted_points, Matrix original_points,
double deviation, Matrix kernel_matrix){
// Each thread calculates one element of kernel_matrix
int row = blockIdx.x * blockDim.x + threadIdx.x;
int col = blockIdx.y * blockDim.y + threadIdx.y;
@ -48,17 +32,43 @@ __global__ void calculate_kernel_matrix_kernel(Matrix shifted_points, Matrix ori
}
}
__global__ void shift_points_kernel(Matrix original_points, Matrix kernel_matrix, Matrix shifted_points,
Matrix new_shift, Matrix denominator, Matrix mean_shift_vector){
// Each thread computes one element of new_shift
// by accumulating results into cell_value
double cell_value = 0;
int row = blockIdx.x * blockDim.x + threadIdx.x;
int col = blockIdx.y * blockDim.y + threadIdx.y;
// performs calculations only if indexes are within matrix bounds
//if (row + col < new_shift.height * new_shift.width){
if (row < new_shift.height){
// calculates new_shift
// builds nominator by multiplying kernel_matrix and original_points
for (int element_index = 0; element_index < kernel_matrix.width; ++element_index){
cell_value += kernel_matrix.elements[row * kernel_matrix.width + element_index]
* original_points.elements[element_index * original_points.width + col];
}
// new_shift elements are calculated by dividing with the denominator
new_shift.elements[row * new_shift.width + col] =
cell_value / denominator.elements[row];
// calculates mean-shift vector
mean_shift_vector.elements[row * new_shift.width + col] =
new_shift.elements[row * new_shift.width + col] -
shifted_points.elements[row * new_shift.width + col];
}
}
__global__ void denominator_kernel(Matrix denominator, Matrix kernel_matrix){
int row = blockIdx.x * blockDim.x + threadIdx.x;
int col = blockIdx.y * blockDim.y + threadIdx.y;
if (row * denominator.width + col > denominator.width * denominator.height){
return;
}
denominator.elements[col]=0;
denominator.elements[row] += kernel_matrix.elements[row*denominator.width + col];
}

11
mean_shift_cuda/meanshift_kernels.h

@ -1,17 +1,18 @@
#ifndef SERIAL_KERNELS_H /* Include guard */
#define SERIAL_KERNELS_H
typedef struct{
typedef struct {
int width;
int height;
double *elements;
} Matrix;
//Function multiply_kernel calculates the product of matrices 1 and 2 into output.
__global__ void multiply_kernel(Matrix matrix1, Matrix matrix2, Matrix output);
__global__ void calculate_kernel_matrix_kernel(Matrix shifted_points, Matrix original_points,
double deviation, Matrix kernel_matrix);
__global__ void calculate_kernel_matrix_kernel(Matrix shifted_points, Matrix original_points
, double deviation, Matrix kernel_matrix);
//Function multiply_kernel calculates the product of matrices 1 and 2 into output.
__global__ void shift_points_kernel(Matrix original_points, Matrix kernel_matrix, Matrix shifted_points,
Matrix new_shift, Matrix denominator, Matrix mean_shift_vector);
__global__ void denominator_kernel(Matrix denominator, Matrix kernel_matrix);

289
mean_shift_cuda/meanshift_utils.cu

@ -5,7 +5,6 @@
#include <string.h>
#include "meanshift_utils.h"
#include "meanshift_kernels.h"
#define OUTPUT_PREFIX "../output/output_"
@ -61,7 +60,7 @@ void get_args(int argc, char **argv, parameters *params){
void init(double ***vectors, char **labels){
int bytes_read = 0;
set_Gpu();
set_GPU();
if (params.verbose){
printf("Reading dataset and labels...\n");
@ -127,7 +126,7 @@ void init(double ***vectors, char **labels){
//Based on https://stackoverflow.com/a/28113186
//Poio psagmeno link https://www.cs.virginia.edu/~csadmin/wiki/index.php/CUDA_Support/Choosing_a_GPU
void set_Gpu(){
void set_GPU(){
int devices_count = 0, max_multiprocessors = 0, max_device = 0;
// gets devices count checking for errors like no devices or no drivers to check for
@ -162,11 +161,20 @@ void set_Gpu(){
int meanshift(double **original_points, double ***shifted_points, int deviation
, parameters *opt){
// host variables
int size = 0;
static int iteration = 0;
static double **mean_shift_vector, **kernel_matrix, *denominator;
static double **kernel_matrix, *denominator, **mean_shift_vector;
double **new_shift;
// device variables
static Matrix d_original_points, d_shifted_points, d_kernel_matrix, d_denominator,
d_mean_shift_vector;
Matrix d_new_shift;
// allocates memory and copies original points on first iteration
if (iteration == 0 || (*shifted_points) == NULL){
// allocates memory for shifted points array and copies original points into it
(*shifted_points) = alloc_2d_double(NUMBER_OF_POINTS, DIMENSIONS);
duplicate(original_points, NUMBER_OF_POINTS, DIMENSIONS, shifted_points);
@ -182,42 +190,49 @@ int meanshift(double **original_points, double ***shifted_points, int deviation
// allocates memory for other arrays needed
kernel_matrix = alloc_2d_double(NUMBER_OF_POINTS, NUMBER_OF_POINTS);
denominator = (double *)malloc(NUMBER_OF_POINTS * sizeof(double));
// allocates corresponding memory in device
init_device_memory(original_points, *shifted_points, &d_original_points, &d_shifted_points,
&d_kernel_matrix, &d_denominator, &d_mean_shift_vector);
}
// TODO move arrays to device and create global kernel for the iteration
// finds pairwise distance matrix (inside radius)
// [I, D] = rangesearch(x,y,h);
calculate_kernel_matrix((*shifted_points), original_points, deviation, &kernel_matrix);
// // calculate denominator
// for (int i=0; i<NUMBER_OF_POINTS; i++){
// double sum = 0;
// for (int j=0; j<NUMBER_OF_POINTS; j++){
// sum = sum + kernel_matrix[i][j];
// }
// denominator[i] = sum;
// }
denominator = calculate_denominator(kernel_matrix);
// creates new y vector
double **new_shift = alloc_2d_double(NUMBER_OF_POINTS, DIMENSIONS);
calculate_kernel_matrix(d_shifted_points, d_original_points, d_kernel_matrix, deviation,
&kernel_matrix);
// builds nominator
multiply(kernel_matrix, original_points, &new_shift);
// divides element-wise
// calculates denominator
for (int i=0; i<NUMBER_OF_POINTS; i++){
for (int j=0; j<DIMENSIONS; j++){
new_shift[i][j] = new_shift[i][j] / denominator[i];
// calculates mean-shift vector at the same time
mean_shift_vector[i][j] = new_shift[i][j] - (*shifted_points)[i][j];
double sum = 0;
for (int j=0; j<NUMBER_OF_POINTS; j++){
sum = sum + kernel_matrix[i][j];
}
denominator[i] = sum;
}
//calculate_denominator(kernel_matrix);
size = NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMemcpy(d_denominator.elements, &(denominator[0])
, size, cudaMemcpyHostToDevice) );
// creates new y vector
// allocates memory in every recursion
new_shift = alloc_2d_double(NUMBER_OF_POINTS, DIMENSIONS);
// allocates corresponding memory in device
d_new_shift.width = DIMENSIONS;
d_new_shift.height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMalloc(&(d_new_shift.elements), size) );
shift_points(d_kernel_matrix, d_original_points, d_shifted_points, d_new_shift, d_denominator,
d_mean_shift_vector, kernel_matrix, original_points, &new_shift, &mean_shift_vector);
// frees previously shifted points, they're now garbage
free((*shifted_points)[0]);
// updates shifted points pointer to the new array address
shifted_points = &new_shift;
d_shifted_points.elements = d_new_shift.elements;
if (params.display){
save_matrix((*shifted_points), iteration);
@ -242,12 +257,14 @@ int meanshift(double **original_points, double ***shifted_points, int deviation
free(kernel_matrix[0]);
free(kernel_matrix);
free(denominator);
free_device_memory(d_original_points, d_kernel_matrix, d_denominator, d_new_shift);
}
return iteration;
}
// TODO check why there's is a difference in the norm calculate in matlab
double norm(double **matrix, int rows, int cols){
double sum=0, temp_mul=0;
for (int i=0; i<rows; i++) {
@ -260,43 +277,57 @@ double norm(double **matrix, int rows, int cols){
return norm;
}
void calculate_kernel_matrix(double **shifted_points, double **original_points, double deviation
, double ***kernel_matrix){
static bool first_iter = true;
// allocates memory for shifted_points in GPU and copies the array
Matrix d_shifted_points;
d_shifted_points.width = DIMENSIONS;
d_shifted_points.height = NUMBER_OF_POINTS;
int size = DIMENSIONS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_shifted_points.elements, size) );
gpuErrchk( cudaMemcpy(d_shifted_points.elements, &(shifted_points[0][0])
, size, cudaMemcpyHostToDevice) );
void init_device_memory(double **original_points, double **shifted_points,
Matrix *d_original_points, Matrix *d_shifted_points, Matrix *d_kernel_matrix,
Matrix *d_denominator, Matrix *d_mean_shift_vector){
int size;
// allocates memory for original_points in GPU and copies the array
Matrix d_original_points;
d_original_points.width = DIMENSIONS;
d_original_points.height = NUMBER_OF_POINTS;
d_original_points->width = DIMENSIONS;
d_original_points->height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMalloc(&d_original_points.elements, size) );
gpuErrchk( cudaMemcpy(d_original_points.elements, &(original_points[0][0])
gpuErrchk( cudaMalloc(&(d_original_points->elements), size) );
gpuErrchk( cudaMemcpy(d_original_points->elements, &(original_points[0][0])
, size, cudaMemcpyHostToDevice) );
// allocates memory for shifted_points in GPU and copies the array
d_shifted_points->width = DIMENSIONS;
d_shifted_points->height = NUMBER_OF_POINTS;
size = DIMENSIONS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&(d_shifted_points->elements), size) );
gpuErrchk( cudaMemcpy(d_shifted_points->elements, &(shifted_points[0][0])
, size, cudaMemcpyHostToDevice) );
// allocates memory for kernel_matrix in GPU
Matrix d_kernel_matrix;
d_kernel_matrix.width = NUMBER_OF_POINTS;
d_kernel_matrix.height = NUMBER_OF_POINTS;
d_kernel_matrix->width = NUMBER_OF_POINTS;
d_kernel_matrix->height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_kernel_matrix.elements, size) );
gpuErrchk( cudaMalloc(&(d_kernel_matrix->elements), size) );
// get max sizes supported from the device
int max_block_size = (int)sqrt(device_properties.maxThreadsPerBlock);
int requested_block_size = max_block_size;
// allocates memory for denominator in GPU
d_denominator->width = 1;
d_denominator->height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&(d_denominator->elements), size) );
// allocates memory for mean_shift_vector in GPU
d_mean_shift_vector->width = DIMENSIONS;
d_mean_shift_vector->height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMalloc(&(d_mean_shift_vector->elements), size) );
}
void calculate_kernel_matrix(Matrix d_shifted_points, Matrix d_original_points,
Matrix d_kernel_matrix, double deviation, double ***kernel_matrix){
int size;
static bool first_iter = true;
// gets max block size supported from the device
int max_block_size = device_properties.maxThreadsPerBlock;
int requested_block_size = (int)sqrt(max_block_size);
bool block_size_too_big = true;
dim3 dimBlock;
dim3 dimGrid;
do {
dimBlock.x = requested_block_size;
dimBlock.y = requested_block_size;
@ -323,65 +354,106 @@ void calculate_kernel_matrix(double **shifted_points, double **original_points,
size = NUMBER_OF_POINTS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMemcpy(&((*kernel_matrix)[0][0]), d_kernel_matrix.elements
, size, cudaMemcpyDeviceToHost) );
gpuErrchk( cudaFree(d_shifted_points.elements) );
gpuErrchk( cudaFree(d_original_points.elements) );
gpuErrchk( cudaFree(d_kernel_matrix.elements) );
}
void multiply(double **kernel_matrix, double **original_points, double ***new_shift){
double * calculate_denominator(double **kernel_matrix){
static bool first_iter = true;
// allocates memory for denominator_matrix in GPU
Matrix d_denominator_matrix;
d_denominator_matrix.width = NUMBER_OF_POINTS;
d_denominator_matrix.height = 1;
int size = NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_denominator_matrix.elements, size) );
// allocates memory for kernel_matrix in GPU and copies the array
Matrix d_kernel_matrix;
d_kernel_matrix.width = NUMBER_OF_POINTS;
d_kernel_matrix.height = NUMBER_OF_POINTS;
int size = NUMBER_OF_POINTS * NUMBER_OF_POINTS * sizeof(double);
size = NUMBER_OF_POINTS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_kernel_matrix.elements, size) );
gpuErrchk( cudaMemcpy(d_kernel_matrix.elements, &(kernel_matrix[0][0])
, size, cudaMemcpyHostToDevice) );
// allocates memory for original_points in GPU and copies the array
Matrix d_original_points;
d_original_points.width = DIMENSIONS;
d_original_points.height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMalloc(&d_original_points.elements, size) );
gpuErrchk( cudaMemcpy(d_original_points.elements, &(original_points[0][0])
, size, cudaMemcpyHostToDevice) );
// allocates memory for new_shift in GPU
Matrix d_new_shift;
d_new_shift.width = DIMENSIONS;
d_new_shift.height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMalloc(&d_new_shift.elements, size) );
, size, cudaMemcpyHostToDevice) );
// get max sizes supported from the device
int max_block_size = device_properties.maxThreadsPerBlock;
dim3 dimBlock((d_new_shift.height < sqrt(max_block_size)) ? d_new_shift.height : sqrt(max_block_size)
, (d_new_shift.width < sqrt(max_block_size)) ? d_new_shift.width : sqrt(max_block_size));
dim3 dimGrid((d_new_shift.height + dimBlock.x - 1) / dimBlock.x
, (d_new_shift.width + dimBlock.y - 1) / dimBlock.y);
dim3 dimBlock((d_denominator_matrix.height < sqrt(max_block_size)) ? d_denominator_matrix.height : sqrt(max_block_size)
, (d_denominator_matrix.width < sqrt(max_block_size)) ? d_denominator_matrix.width : sqrt(max_block_size));
dim3 dimGrid((d_denominator_matrix.height + dimBlock.x - 1) / dimBlock.x
, (d_denominator_matrix.width + dimBlock.y - 1) / dimBlock.y);
if (first_iter && params.verbose){
printf("multiply_kernel called with:\n");
printf("calculate_denominator called with:\n");
printf("dimBlock.x = %d, dimBlock.y = %d\n", dimBlock.x, dimBlock.y);
printf("dimGrid.x = %d, dimGrid.y = %d\n\n", dimGrid.x, dimGrid.y);
first_iter = false;
}
multiply_kernel<<<dimGrid, dimBlock>>>(d_kernel_matrix, d_original_points, d_new_shift);
denominator_kernel<<<dimGrid, dimBlock>>>(d_denominator_matrix, d_kernel_matrix);
gpuErrchk( cudaPeekAtLastError() );
gpuErrchk( cudaDeviceSynchronize() );
size = NUMBER_OF_POINTS * sizeof(double);
double ** denominator = (double**)malloc(size);
gpuErrchk( cudaMemcpy(&((*denominator)[0]), d_denominator_matrix.elements
,size, cudaMemcpyDeviceToHost) );
gpuErrchk( cudaFree(d_kernel_matrix.elements) );
gpuErrchk( cudaFree(d_denominator_matrix.elements) );
return (*denominator);
}
void shift_points(Matrix d_kernel_matrix, Matrix d_original_points, Matrix d_shifted_points,
Matrix d_new_shift, Matrix d_denominator, Matrix d_mean_shift_vector, double **kernel_matrix,
double **original_points, double ***new_shift, double ***mean_shift_vector){
int size;
static bool first_iter = true;
// gets max block size supported from the device
int max_block_size = device_properties.maxThreadsPerBlock;
int requested_block_size = (int)sqrt(max_block_size);
bool block_size_too_big = true;
dim3 dimBlock;
dim3 dimGrid;
do {
dimBlock.x = requested_block_size;
dimBlock.y = 2;
dimGrid.x = (d_kernel_matrix.height + dimBlock.x - 1) / dimBlock.x;
dimGrid.y = 1;
shift_points_kernel<<<dimGrid, dimBlock>>>(d_original_points, d_kernel_matrix, d_shifted_points,
d_new_shift, d_denominator, d_mean_shift_vector);
if (cudaGetLastError() != cudaSuccess){
--requested_block_size;
} else {
block_size_too_big = false;
gpuErrchk( cudaDeviceSynchronize() );
}
} while(block_size_too_big);
if (first_iter && params.verbose){
printf("shift_points_kernel called with:\n");
printf("dimBlock.x = %d, dimBlock.y = %d\n", dimBlock.x, dimBlock.y);
printf("dimGrid.x = %d, dimGrid.y = %d\n\n", dimGrid.x, dimGrid.y);
first_iter = false;
}
size = NUMBER_OF_POINTS * DIMENSIONS * sizeof(double);
gpuErrchk( cudaMemcpy(&((*new_shift)[0][0]), d_new_shift.elements
, size, cudaMemcpyDeviceToHost) );
gpuErrchk( cudaMemcpy(&((*mean_shift_vector)[0][0]), d_mean_shift_vector.elements
, size, cudaMemcpyDeviceToHost) );
}
gpuErrchk( cudaFree(d_kernel_matrix.elements) );
void free_device_memory(Matrix d_original_points, Matrix d_kernel_matrix, Matrix d_denominator,
Matrix d_new_shift){
// frees all memory previously allocated in device
gpuErrchk( cudaFree(d_original_points.elements) );
gpuErrchk( cudaFree(d_kernel_matrix.elements) );
//gpuErrchk( cudaFree(d_shifted_points.elements) );
gpuErrchk( cudaFree(d_denominator.elements) );
gpuErrchk( cudaFree(d_new_shift.elements) );
}
@ -434,53 +506,4 @@ void save_matrix(double **matrix, int iteration){
}
fprintf(file, "\n");
}
}
double * calculate_denominator(double **kernel_matrix){
static bool first_iter = true;
// allocates memory for denominator_matrix in GPU
Matrix d_denominator_matrix;
d_denominator_matrix.width = NUMBER_OF_POINTS;
d_denominator_matrix.height = 1;
int size = NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_denominator_matrix.elements, size) );
// allocates memory for kernel_matrix in GPU and copies the array
Matrix d_kernel_matrix;
d_kernel_matrix.width = NUMBER_OF_POINTS;
d_kernel_matrix.height = NUMBER_OF_POINTS;
size = NUMBER_OF_POINTS * NUMBER_OF_POINTS * sizeof(double);
gpuErrchk( cudaMalloc(&d_kernel_matrix.elements, size) );
gpuErrchk( cudaMemcpy(d_kernel_matrix.elements, &(kernel_matrix[0][0])
, size, cudaMemcpyHostToDevice) );
// get max sizes supported from the device
int max_block_size = device_properties.maxThreadsPerBlock;
dim3 dimBlock((d_denominator_matrix.height < sqrt(max_block_size)) ? d_denominator_matrix.height : sqrt(max_block_size)
, (d_denominator_matrix.width < sqrt(max_block_size)) ? d_denominator_matrix.width : sqrt(max_block_size));
dim3 dimGrid((d_denominator_matrix.height + dimBlock.x - 1) / dimBlock.x
, (d_denominator_matrix.width + dimBlock.y - 1) / dimBlock.y);
if (first_iter && params.verbose){
printf("calculate_denominator called with:\n");
printf("dimBlock.x = %d, dimBlock.y = %d\n", dimBlock.x, dimBlock.y);
printf("dimGrid.x = %d, dimGrid.y = %d\n\n", dimGrid.x, dimGrid.y);
first_iter = false;
}
denominator_kernel<<<dimGrid, dimBlock>>>(d_denominator_matrix, d_kernel_matrix);
gpuErrchk( cudaPeekAtLastError() );
gpuErrchk( cudaDeviceSynchronize() );
size = NUMBER_OF_POINTS * sizeof(double);
double ** denominator = (double**)malloc(size);
gpuErrchk( cudaMemcpy(&((*denominator)[0]), d_denominator_matrix.elements
,size, cudaMemcpyDeviceToHost) );
gpuErrchk( cudaFree(d_kernel_matrix.elements) );
gpuErrchk( cudaFree(d_denominator_matrix.elements) );
return (*denominator);
}

19
mean_shift_cuda/meanshift_utils.h

@ -2,6 +2,7 @@
#define SERIAL_UTILS_H
#include <stdbool.h>
#include "meanshift_kernels.h"
//GPU error check snippet taken from:
//https://stackoverflow.com/a/14038590
@ -35,7 +36,7 @@ void get_args(int argc, char **argv, parameters *params);
//Function init reads the dataset and label arrays from the corresponding files.
void init(double ***vectors, char **labels);
void set_Gpu();
void set_GPU();
//Function meanshift recursively shifts original points according to th
//mean-shift algorithm saving the result to shiftedPoints. Struct opt has user
@ -43,16 +44,24 @@ void set_Gpu();
int meanshift(double **original_points, double ***shifted_points, int h
, parameters *opt);
void init_device_memory(double **original_points, double **shifted_points,
Matrix *d_original_points, Matrix *d_shifted_points,
Matrix *d_kernel_matrix, Matrix *d_denominator, Matrix *d_new_shift);
//Function norm returns the second norm of matrix of dimensions rowsXcols.
double norm(double **matrix, int rows, int cols);
void calculate_kernel_matrix(double **shifted_points, double **original_points, double deviation
, double ***kernel_matrix);
void calculate_kernel_matrix(Matrix d_shifted_points, Matrix d_original_points,
Matrix d_kernel_matrix, double deviation, double ***kernel_matrix);
//Function multiply allocates memory in GPU, sends the data and calls the
//multiply kernel function.
void multiply(double **kernel_matrix, double **original_points
, double ***new_shift);
void shift_points(Matrix d_kernel_matrix, Matrix d_original_points, Matrix d_shifted_points,
Matrix d_new_shift, Matrix d_denominator, Matrix d_mean_shift_vector, double **kernel_matrix,
double **original_points, double ***new_shift, double ***mean_shift_vector);
void free_device_memory(Matrix d_original_points, Matrix d_kernel_matrix, Matrix d_denominator,
Matrix d_new_shift);
//Function calculateDistance returns the distance between x and y vectors.
double calculateDistance(double *y, double *x);

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