benchmarks/cg.cpp
/*******************************************************
* Copyright (c) 2014, ArrayFire
* All rights reserved.
*
* This file is distributed under 3-clause BSD license.
* The complete license agreement can be obtained at:
* http://arrayfire.com/licenses/BSD-3-Clause
********************************************************/
#include <arrayfire.h>
#include <iostream>
using namespace af;
static size_t dimension = 4 * 1024;
static const int maxIter = 10;
static const int sparsityFactor = 7;
static array A;
static array spA; // Sparse A
static array x0;
static array b;
void setupInputs()
{
// Generate a random input: A
array T = randu(dimension, dimension, f32);
// Create 0s in input.
// Anything that is no divisible by sparsityFactor will become 0.
A = floor(T * 1000);
A = A * ((A % sparsityFactor) == 0) / 1000;
// Make it positive definite
A = transpose(A) + A + A. dims(0)*identity(A.dims(0), A.dims(0), f32);
// Make A sparse as spA
spA = sparse(A);
// Generate x0: Random guess
x0 = randu(A.dims(0), f32);
//Generate b
b = matmul(A, x0);
std::cout << "Sparsity of A = "
<< 100.f * (float)sparseGetNNZ(spA) / (float)spA.elements()
<< "%" << std::endl;
std::cout << "Memory Usage of A = "
<< A. bytes() / (1024.f * 1024.f)
<< " MB" << std::endl;
std::cout << "Memory Usage of spA = "
<<(sparseGetValues(spA).bytes()
+ sparseGetRowIdx(spA).bytes()
+ sparseGetColIdx(spA).bytes()) / (1024.f * 1024.f)
<< " MB" << std::endl;
}
void sparseConjugateGradient(void)
{
array x = constant(0, b.dims(), f32);
array r = b - matmul(spA, x);
array p = r;
for (int i = 0; i < maxIter; ++i) {
array Ap = matmul(spA, p);
array alpha_num = dot(r, r);
array alpha_den = dot(p, Ap);
array alpha = alpha_num/alpha_den;
r -= tile(alpha, Ap.dims())*Ap;
x += tile(alpha, Ap.dims())*p;
array beta_num = dot(r, r);
array beta = beta_num/alpha_num;
p = r + tile(beta, p.dims()) * p;
}
}
void denseConjugateGradient(void)
{
array x = constant(0, b.dims(), f32);
array r = b - matmul(A, x);
array p = r;
for (int i = 0; i < maxIter; ++i) {
array Ap = matmul(A, p);
array alpha_num = dot(r, r);
array alpha_den = dot(p, Ap);
array alpha = alpha_num/alpha_den;
r -= tile(alpha, Ap.dims())*Ap;
x += tile(alpha, Ap.dims())*p;
array beta_num = dot(r, r);
array beta = beta_num/alpha_num;
p = r + tile(beta, p.dims()) * p;
}
}
void checkConjugateGradient(const af::array in)
{
array x = constant(0, b.dims(), f32);
array r = b - matmul(in, x);
array p = r;
for (int i = 0; i < maxIter; ++i) {
array Ap = matmul(in, p);
array alpha_num = dot(r, r);
array alpha_den = dot(p, Ap);
array alpha = alpha_num/alpha_den;
r -= tile(alpha, Ap.dims())*Ap;
x += tile(alpha, Ap.dims())*p;
array beta_num = dot(r, r);
array beta = beta_num/alpha_num;
p = r + tile(beta, p.dims()) * p;
}
array res = x0 - x;
std::cout<<"Final difference in solutions:\n";
af_print(dot(res, res));
}
int main(int argc, char *argv[])
{
af::info();
setupInputs();
std::cout << "Verifying Dense Conjugate Gradient:" << std::endl;
checkConjugateGradient(A);
std::cout << "Verifying Sparse Conjugate Gradient:" << std::endl;
checkConjugateGradient(spA);
af::sync();
std::cout << "Dense Conjugate Gradient Time: "
<< timeit(denseConjugateGradient) * 1000
<< "ms" << std::endl;
std::cout << "Sparse Conjugate Gradient Time: "
<< timeit(sparseConjugateGradient) * 1000
<< "ms" << std::endl;
return 0;
}