RayBNN_DiffEq

Differential Equation Solver using GPUs, CPUs, and FPGAs via CUDA, OpenCL, and oneAPI

Requires Arrayfire and Arrayfire Rust

Supports f16, f32, f64, Complexf16, Complexf32, Complexf64

Also supports Matrix Differential Equations and Sparse Matrix Differential Equations

Matrix Sizes upto 100000x100000

Install Arrayfire

Install the Arrayfire 3.9.0 binaries at https://arrayfire.com/binaries/

or build from source https://github.com/arrayfire/arrayfire/wiki/Getting-ArrayFire

Add to your Cargo.toml

arrayfire = { version = "3.8.1", package = "arrayfire_fork" } num = "0.4.1" num-traits = "0.2.16" half = { version = "2.3.1" , features = ["num-traits"] } raybnn_diffeq = "0.1.3"

List of Examples

Linear ODE with CUDA f64
3x3 Linear Matrix ODE with CUDA f64
1000x1000 Linear Matrix ODE with CUDA f64
Linear ODE with CUDA f32
Selecting between CPU, OpenCL, and CUDA

Solving a Simple Linear ODE on CUDA with Float 64 bit precision

Equation 1

``` //cargo run --example Linear_ODE --release

use arrayfire; use RayBNN_DiffEq;

//Select CUDA and GPU Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CUDA; const DEVICE: i32 = 0;

fn main() {

arrayfire::set_backend(BACK_END);
arrayfire::set_device(DEVICE);

// Set the Linear Differentail Equation
// dy/dt = sin(t)
let diffeq = |t: &arrayfire::Array<f64>, y: &arrayfire::Array<f64>| -> arrayfire::Array<f64> {
    arrayfire::sin(&t) 
};

//Start at t=0 and end at t=1000
//Step size of 0.001
//Relative error of 1E-9
//Absolute error of 1E-9
//Error Type compute the total error of every element in y
let options: RayBNN_DiffEq::ODE::ODE45::ODE45_Options<f64> = RayBNN_DiffEq::ODE::ODE45::ODE45_Options {
    tstart: 0.0f64,
    tend: 1000.0f64,
    tstep: 0.001f64,
    rtol: 1.0E-9f64,
    atol: 1.0E-9f64,
    error_select: RayBNN_DiffEq::ODE::ODE45::error_type::TOTAL_ERROR
};

let t_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut t = arrayfire::constant::<f64>(0.0,t_dims);

let y0_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut y = arrayfire::constant::<f64>(0.0,y0_dims);
let mut dydt = arrayfire::constant::<f64>(0.0,y0_dims);

//Initial Point of Differential Equation
//Set y(t=0) = 1.0
let y0 = arrayfire::constant::<f64>(1.0,y0_dims);

println!("Running");

arrayfire::sync(DEVICE);
let starttime = std::time::Instant::now();

//Run Solver
RayBNN_DiffEq::ODE::ODE45::solve(
    &y0
    ,diffeq
    ,&options
    ,&mut t
    ,&mut y
    ,&mut dydt
);

arrayfire::sync(DEVICE);

let elapsedtime = starttime.elapsed();

arrayfire::sync(DEVICE);

arrayfire::print_gen("y".to_string(), &y,Some(6));
arrayfire::print_gen("t".to_string(), &t,Some(6));

println!("Computed {} Steps In: {:.6?}", y.dims()[1],elapsedtime);


//Error Analysis
let actualy = 2.0f64 - arrayfire::cos(&t);
let error = y - actualy;
//arrayfire::print_gen("error".to_string(), &error,Some(6));

} ```

Computed 11704 Steps In: 5.444366s

Solving a 3x3 Matrix Linear ODE on CUDA with Float 64 bit precision

Equation 2

``` //cargo run --example LinearMatrixODE --release

use arrayfire; use RayBNN_DiffEq;

//Select CUDA and GPU Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CUDA; const DEVICE: i32 = 0;

fn main() {

arrayfire::set_backend(BACK_END);
arrayfire::set_device(DEVICE);


//Create A matrix
let A_vec:Vec<f64> = vec![1.0, 1.2, 1.1,    0.8, -1.0, 0.0,    0.0, 0.0, -1.2];
let mut A = arrayfire::Array::new(&A_vec, arrayfire::Dim4::new(&[3, 3, 1, 1]));
arrayfire::print_gen("A".to_string(), &A,Some(6));

//A
//1.000000     0.800000     0.000000 
//1.200000    -1.000000     0.000000 
//1.100000     0.000000    -1.200000 

// Set the Linear Matrix Differentail Equation
// dy1/dt = 1.0y1 + 0.8y2  + 0.0y3
// dy2/dt = 1.2y1 + -1.0y2 + 0.0y3
// dy3/dt = 1.1y1 + 0.0y2  + -1.2y3 
let diffeq = |t: &arrayfire::Array<f64>, y: &arrayfire::Array<f64>| -> arrayfire::Array<f64> {
    arrayfire::matmul(&A, y, arrayfire::MatProp::NONE, arrayfire::MatProp::NONE)
};

//Start at t=0 and end at t=10
//Step size of 0.001
//Relative error of 1E-9
//Absolute error of 1E-9
//Error Type compute the total error of every element in y
let options: RayBNN_DiffEq::ODE::ODE45::ODE45_Options<f64> = RayBNN_DiffEq::ODE::ODE45::ODE45_Options {
    tstart: 0.0f64,
    tend: 10.0f64,
    tstep: 0.001f64,
    rtol: 1.0E-9f64,
    atol: 1.0E-9f64,
    error_select: RayBNN_DiffEq::ODE::ODE45::error_type::TOTAL_ERROR
};

let t_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut t = arrayfire::constant::<f64>(0.0,t_dims);

let y0_dims = arrayfire::Dim4::new(&[3,1,1,1]);
let mut y = arrayfire::constant::<f64>(0.0,y0_dims);
let mut dydt = arrayfire::constant::<f64>(0.0,y0_dims);

//Initial Point of Differential Equation
//Set y1(0) = 0.1
//Set y2(0) = 0.2
//Set y3(0) = -0.3
let y0_vec:Vec<f64> = vec![0.1, 0.2, -0.3];
let y0 = arrayfire::Array::new(&y0_vec, y0_dims);


println!("Running");

arrayfire::sync(DEVICE);
let starttime = std::time::Instant::now();

//Run Solver
RayBNN_DiffEq::ODE::ODE45::solve(
    &y0
    ,diffeq
    ,&options
    ,&mut t
    ,&mut y
    ,&mut dydt
);

arrayfire::sync(DEVICE);

let elapsedtime = starttime.elapsed();

arrayfire::sync(DEVICE);

arrayfire::print_gen("y".to_string(), &y,Some(6));
arrayfire::print_gen("t".to_string(), &t,Some(6));

println!("Computed {} Steps In: {:.6?}", y.dims()[1],elapsedtime);

} Computed 983 Steps In: 391.827121ms ```

Solving a 1000x1000 Matrix Linear ODE on CUDA with Float 64 bit precision

``` //cargo run --example LinearMatrixODE --release

use arrayfire; use RayBNN_DiffEq;

//Select CUDA and GPU Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CUDA; const DEVICE: i32 = 0;

fn main() {

arrayfire::set_backend(BACK_END);
arrayfire::set_device(DEVICE);


//Create A matrix from random normal numbers
let A_dims = arrayfire::Dim4::new(&[1000,1000,1,1]);
let A = arrayfire::randn::<f64>(A_dims)/100.0f64;

// Set the Linear Matrix Differentail Equation
// dy/dt = A*y
let diffeq = |t: &arrayfire::Array<f64>, y: &arrayfire::Array<f64>| -> arrayfire::Array<f64> {
    arrayfire::matmul(&A, y, arrayfire::MatProp::NONE, arrayfire::MatProp::NONE)
};

//Start at t=0 and end at t=50
//Step size of 0.001
//Relative error of 1E-9
//Absolute error of 1E-9
//Error Type compute the individual error of every element in y
let options: RayBNN_DiffEq::ODE::ODE45::ODE45_Options<f64> = RayBNN_DiffEq::ODE::ODE45::ODE45_Options {
    tstart: 0.0f64,
    tend: 50.0f64,
    tstep: 0.001f64,
    rtol: 1.0E-9f64,
    atol: 1.0E-9f64,
    error_select: RayBNN_DiffEq::ODE::ODE45::error_type::INDIVIDUAL_ERROR
};

let t_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut t = arrayfire::constant::<f64>(0.0,t_dims);

let y0_dims = arrayfire::Dim4::new(&[1000,1,1,1]);
let mut y = arrayfire::constant::<f64>(0.0,y0_dims);
let mut dydt = arrayfire::constant::<f64>(0.0,y0_dims);

//Initial Point of Differential Equation
let y0 = arrayfire::randn::<f64>(y0_dims)/100.0f64;


println!("Running");

arrayfire::sync(DEVICE);
let starttime = std::time::Instant::now();

//Run Solver
RayBNN_DiffEq::ODE::ODE45::solve(
    &y0
    ,diffeq
    ,&options
    ,&mut t
    ,&mut y
    ,&mut dydt
);

arrayfire::sync(DEVICE);

let elapsedtime = starttime.elapsed();

arrayfire::sync(DEVICE);

//let lasty = arrayfire::col(&y, y.dims()[1] as i64);
//arrayfire::print_gen("lasty".to_string(), &lasty,Some(6));
//arrayfire::print_gen("t".to_string(), &t,Some(6));

println!("Computed {} Steps In: {:.6?}", y.dims()[1],elapsedtime);

} ```

Computed 3366 Steps In: 4.635253s

Solving a Simple Linear ODE on CUDA with Float 32 bit precision

Equation 1

``` //cargo run --example LinearODEf32 --release

use arrayfire; use RayBNN_DiffEq;

//Select CUDA and GPU Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CUDA; const DEVICE: i32 = 0;

fn main() {

arrayfire::set_backend(BACK_END);
arrayfire::set_device(DEVICE);

// Set the Linear Differentail Equation
// dy/dt = sin(t)
let diffeq = |t: &arrayfire::Array<f32>, y: &arrayfire::Array<f32>| -> arrayfire::Array<f32> {
    arrayfire::sin(&t) 
};

//Start at t=0 and end at t=1000
//Step size of 0.0001
//Relative error of 1E-4
//Absolute error of 1E-4
//Error Type compute the total error of every element in y
let options: RayBNN_DiffEq::ODE::ODE45::ODE45_Options<f32> = RayBNN_DiffEq::ODE::ODE45::ODE45_Options {
    tstart: 0.0f32,
    tend: 1000.0f32,
    tstep: 0.0001f32,
    rtol: 1.0E-4f32,
    atol: 1.0E-4f32,
    error_select: RayBNN_DiffEq::ODE::ODE45::error_type::TOTAL_ERROR
};

let t_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut t = arrayfire::constant::<f32>(0.0,t_dims);

let y0_dims = arrayfire::Dim4::new(&[1,1,1,1]);
let mut y = arrayfire::constant::<f32>(0.0,y0_dims);
let mut dydt = arrayfire::constant::<f32>(0.0,y0_dims);

//Initial Point of Differential Equation
//Set y(t=0) = 1.0
let y0 = arrayfire::constant::<f32>(1.0,y0_dims);

println!("Running");

arrayfire::sync(DEVICE);
let starttime = std::time::Instant::now();

//Run Solver
RayBNN_DiffEq::ODE::ODE45::solve(
    &y0
    ,diffeq
    ,&options
    ,&mut t
    ,&mut y
    ,&mut dydt
);

arrayfire::sync(DEVICE);

let elapsedtime = starttime.elapsed();

arrayfire::sync(DEVICE);

arrayfire::print_gen("y".to_string(), &y,Some(6));
arrayfire::print_gen("t".to_string(), &t,Some(6));

println!("Computed {} Steps In: {:.6?}", y.dims()[1],elapsedtime);


//Error Analysis
let actualy = 2.0f32 - arrayfire::cos(&t);
let error = y - actualy;
//arrayfire::print_gen("error".to_string(), &error,Some(6));

} ```

Computed 712 Steps In: 450.653767ms

Selecting between CPU, OpenCL, and CUDA

``` //Select CPU Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CPU; const DEVICE: i32 = 0;

//Select OpenCL Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::OpenCL; const DEVICE: i32 = 0;

//Select CUDA Device 0 const BACK_END: arrayfire::Backend = arrayfire::Backend::CUDA; const DEVICE: i32 = 0; ```