Gram-Schmidt process on GPU

This repository contains an implementation of the Gram-Schmidt process written on C++ with Vulkan API.

Requirements

To run this code, you'll need to have:

• C++11-compatible compiler;
• Vulkan SDK with API version 1.2 (provided by LunarG, for example);
• A GPU capable of compute operations in double precision and having at least one partition of device memory that is both host visible and host coherent.

Usage

Steps are as follows:

1. Include file vulkan-gram-schmidt/vulkan-gram-schmidt.hpp into your program.
2. Write your code.
3. During compilation, add the path to the Include folder of your Vulkan SDK to the include path.
4. During linking, link the static library vulkan-1.lib from the Lib folder of your Vulkan SDK.
5. Run.

If you do not need benchmarking data or a tool for benchmarking, you may delete the benchmark folder.

Example

// Let's find an orthonormal basis in 2D
// with initial vectors (1, 2) and (3, 4)
#include <iostream>
#include "vulkan-gram-schmidt/vulkan-gram-schmidt.hpp"

int main(void)
{
    // Before we can use the solver, we need to specify the path to
    // the vulkan-gram-schmidt.spv file - the binary SPIR-V shader
    // that computes Gram-Schmidt. You may find an equivalent shader
    // vulkan-gram-schmidt.comp written in GLSL in the vulkan-gram-schmidt
    // folder.
    GPUGramSchmidt::shader_folder = "./vulkan-gram-schmidt";
    // Next, we create the solver itself.
    GPUGramSchmidt solver;
    
    // Imagine that you are a mathematician and you only store vector
    // coordinates as columns.
    // Matrix type here is just std::vector<std::vector<double>>
    GPUGramSchmidt::Matrix vectors{{1, 3},
                                   {2, 4}};
    
    // Run the solver
    solver.run(vectors, /*vectors_as_columns = */ true);
    
    // Print the answer!
    for (auto &row : vectors)
    {
        for (auto &elem : row)
            std::cout << elem << '\t';
        std::cout << '\n';
    }
    
    return 0;
}

The output will be:

0.447214        0.894427
0.894427        -0.447214

Thus, the resulting ortonormal basis is the first column (0.447214, 0.894427) and the second column (0.894427, -0.447214). If we set vectors_as_columns to false, then the rows of the matrix will be interpreted as the initial vectors and the resulting vectors will be written in rows as well.

Further details

Documentation can be found in the vulkan-gram-schmidt folder.