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// sir_ddft - A Rust implementation of the SIR-DDFT model
// Copyright (C) 2021 Julian Jeggle, Raphael Wittkowski
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as
// published by the Free Software Foundation, either version 3 of the
// License, or (at your option) any later version.
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Affero General Public License for more details.
// You should have received a copy of the GNU Affero General Public License
// along with this program. If not, see <https://www.gnu.org/licenses/>.
//! Solver for the SZ-DDFT model under periodic boundary conditions in
//! two spatial dimensions
use std::sync::Arc;
use rustfft::{FftPlanner, Fft, FftDirection};
use num_complex::Complex64;
use itertools::izip;
use crate::{
Grid1D, Grid2D,
helpers::*,
ode::{ODEIVP, StopCondition},
SZDDFTParameters, SZDiffusionParameters, SZParameters, SZStateSpatial2D, SZStateSpatial2DBorrowed
};
/// Initial value problem for the SZ-DDFT model in two spatial dimensions
///
/// Note: The model is technically a PDE, but is transformed to a high-dimensional
/// ODE via the finite difference method.
pub struct SZDDFT2DIVP {
/// Flattened SIRStateSpatial2D (during integration ownership is passed to the
/// integrator so state is None then!)
state: Option<Vec<f64>>,
/// x distance between grid points
/// (currently only equidistant grids are supported!)
dx: f64,
/// y distance between grid points
/// (currently only equidistant grids are supported!)
dy: f64,
/// Number of grid points in x
nx: usize,
/// Number of grid points in y
ny: usize,
/// Originally passed grid
grid: Grid2D,
/// Model parameters for all SIR models
sz_params: SZParameters,
/// Model parameters for diffusion
diff_params: SZDiffusionParameters,
/// Model parameters specific to the SIR DDFT model
ddft_params: SZDDFTParameters,
/// Current time of integration
time: f64,
/// Total duration of integration
duration: f64,
/// Precalculated social distancing kernel
kernel_sz_fft: Vec<Complex64>,
/// Precalculated self isolation kernel
kernel_zs_fft: Vec<Complex64>,
/// Fourier transform
fft: Arc<dyn Fft<f64>>,
/// Inverse fourier transform
ifft: Arc<dyn Fft<f64>>,
/// Scratch space for 2D FFT
scratch: Vec<Complex64>,
/// Convolution buffer for convolution of Z with the SZ kernel
conv_sz: Vec<Complex64>,
/// Convolution buffer for convolution of S with the ZS kernel
conv_zs: Vec<Complex64>,
/// Thread pool for parallel convolution
#[cfg(not(target_arch = "wasm32"))]
thread_pool: scoped_threadpool::Pool
}
impl<S> ODEIVP<S,f64> for SZDDFT2DIVP {
#[allow(non_snake_case)]
fn rhs(&mut self, _ : f64, y: &[f64], rhs: &mut[f64]) {
// Number of gridpoints
let n = y.len() / 2;
// Split state vector into S,I,R
let (S,Z) = y.split_at(n);
// Split RHS vector
let (dS,dZ) = rhs.split_at_mut(n);
// Shorthands for parameters
let bite_param = self.sz_params.bite_parameter;
let kill_param = self.sz_params.kill_parameter;
let diff_S = self.diff_params.diffusivity_S;
let diff_Z = self.diff_params.diffusivity_Z;
let mob_S = self.ddft_params.mobility_S;
let mob_Z = self.ddft_params.mobility_Z;
let dx = self.dx;
let dy = self.dy;
let nx = self.nx;
let ny = self.ny;
let kernel_sz_fft = self.kernel_sz_fft.as_slice();
let kernel_zs_fft = self.kernel_zs_fft.as_slice();
let fft = self.fft.clone();
let ifft = self.ifft.clone();
let scratch = self.scratch.as_mut_slice();
// Platform dependant parts:
#[allow(unused_variables)]
let (thread_pool, num_threads);
#[cfg(not(target_arch = "wasm32"))]
{
thread_pool = &mut self.thread_pool;
num_threads = thread_pool.thread_count();
}
// Stubs for WASM
#[cfg(target_arch = "wasm32")]
#[allow(unused_assignments)]
{
thread_pool = ();
num_threads = 1;
}
// -- Calculate RHS --
// Convolutions for S and R:
let conv_sz = self.conv_sz.as_mut_slice();
let conv_zs = self.conv_zs.as_mut_slice(); // "Borrow" conv_i as temp storage
for (conv_sz, conv_zs, S, Z) in izip!(conv_sz.iter_mut(), conv_zs.iter_mut(), S, Z) {
*conv_sz = Complex64::new(*Z, 0.0);
*conv_zs = Complex64::new(*S, 0.0);
}
convolve_2d_parallel(conv_sz, kernel_sz_fft, fft.clone(), ifft.clone(), scratch, thread_pool);
convolve_2d_parallel(conv_zs, kernel_zs_fft, fft.clone(), ifft.clone(), scratch, thread_pool);
// Calculate RHS fields
macro_rules! idx2 {
($ix: expr, $iy: expr) => {
($ix) + ($iy)*nx
}
}
// Calculate contributions for a single row
let add_contrib = |iy: usize, offset: usize, dS: &mut[f64], dZ: &mut[f64]| {
let [prevprev_y,prev_y,next_y,nextnext_y] = calc_indices(iy as i32, ny as i32);
for ix in 0..nx {
let [prevprev_x,prev_x,next_x,nextnext_x] = calc_indices(ix as i32, nx as i32);
let curr = idx2!(ix,iy);
// Discretized form of model equations
macro_rules! ddft_term {
($field:expr, $conv:expr) => {
(
grad_1d_val(
$field[idx2!(next_x,iy)] * grad_1d_val(
$conv[idx2!(nextnext_x, iy)].re,
$conv[curr].re, dx),
$field[idx2!(prev_x,iy)] * grad_1d_val(
$conv[curr].re,
$conv[idx2!(prevprev_x, iy)].re, dx), dx) +
grad_1d_val(
$field[idx2!(ix,next_y)] * grad_1d_val(
$conv[idx2!(ix,nextnext_y)].re,
$conv[curr].re, dy),
$field[idx2!(ix,prev_y)] * grad_1d_val(
$conv[curr].re,
$conv[idx2!(ix,prevprev_y)].re, dy), dy)
)
}
}
dS[curr-offset] = diff_S * laplace_2d9(S,
prev_x, ix, next_x, prev_y, iy, next_y, nx, dx, dy)
- bite_param * S[curr] * Z[curr]
- mob_S * ddft_term!(S,conv_sz);
dZ[curr-offset] = diff_Z * laplace_2d9(Z,
prev_x, ix, next_x, prev_y, iy, next_y, nx, dx, dy)
+ (bite_param - kill_param) * S[curr] * Z[curr]
+ mob_Z * ddft_term!(Z,conv_zs);
}
};
// Single threaded?
#[cfg(not(target_arch = "wasm32"))]
if num_threads < 2 {
for iy in 0..ny {
add_contrib(iy,0,dS,dZ);
}
}
// Else multi-threaded
else {
thread_pool.scoped(|s|{
// Size of chunk in numbers of rows
let chunk_size_y = ceil_div(ny, num_threads as usize);
// Size of chunk in numbers of gridpoints
let chunk_size = chunk_size_y * nx;
// Split output slice into chunks
let dS_chunks = dS.chunks_mut(chunk_size);
let dZ_chunks = dZ.chunks_mut(chunk_size);
// One thread per chunk will calculate all RHS values in said chunk
for (i,dS,dZ) in izip![0..num_threads as usize, dS_chunks, dZ_chunks] {
s.execute(move || {
for iy in (i*chunk_size_y)..((i+1)*chunk_size_y).min(ny) {
add_contrib(iy, i*chunk_size, dS, dZ);
}
});
}
});
}
#[cfg(target_arch = "wasm32")] {
for iy in 0..ny {
add_contrib(iy,0,dS,dI,dR);
}
}
}
fn initial_state(&mut self) -> (f64, Vec<f64>) {
(self.time, self.state.take().unwrap())
}
fn end_step(&mut self, _ : f64, _: &[f64], _: &S) -> StopCondition {
StopCondition::ContinueUntil(self.duration)
}
fn final_state(&mut self, t: f64, y: Vec<f64>) {
self.state = Some(y);
self.time = t;
}
}
impl SZDDFT2DIVP {
/// Creates a new IVP for the SIR DDFT model
///
/// **Note that for now only square grid (i.e. `n x n` grid points) with equal lattice spacing
/// in x and y are supported!**
pub fn new(sir_params: SZParameters, diff_params: SZDiffusionParameters,
ddft_params: SZDDFTParameters, state: SZStateSpatial2D, num_threads: usize)
-> Self {
// Validate grid
// TODO: proper errors
let ((dx,nx,lx),(dy,ny,_ly)) = match &state.grid {
Grid2D::Cartesian(cart_grid) => {
(
match &cart_grid.grid_x {
Grid1D::Equidistant(grid) => { (grid.delta(), grid.n, grid.xlim.1 - grid.xlim.0) },
#[allow(unreachable_patterns)]
_ => { unimplemented!("Only equidistant grids in x are supported for now") }
},
match &cart_grid.grid_y {
Grid1D::Equidistant(grid) => { (grid.delta(), grid.n, grid.xlim.1 - grid.xlim.0) },
#[allow(unreachable_patterns)]
_ => { unimplemented!("Only equidistant grids in y are supported for now") }
},
)
},
#[allow(unreachable_patterns)]
_ => unimplemented!("Only cartesian grids are supported for now")
};
if nx < 3 || ny < 3 {
panic!("Must have at least 3 grid points in every direction");
}
if nx != ny {
panic!("Lattice must be square, i.e. have the same number of grid points in x and y");
}
if dx != dy {
panic!("Lattice spacing must be equal in x and y");
}
if nx > i32::MAX as usize || ny > i32::MAX as usize {
panic!("nx and ny must fit in a i32 variable");
}
// Threading is not available (yet) in WASM
#[cfg(target_arch = "wasm32")]
{
if num_threads > 1 {
panic!("Multithreading not supported in WASM");
}
}
// Copy state into flattened state vector
let state_vector = [state.S, state.Z].concat();
// Create Fourier transforms
let mut fftplanner = FftPlanner::new();
let fft = fftplanner.plan_fft(nx, FftDirection::Forward);
let ifft = fftplanner.plan_fft(nx, FftDirection::Inverse);
let scratch = vec![Complex64::new(0.0, 0.0); nx*ny];
// Generate kernels
let kernel_sz_fft = Self::generate_kernel_fft(ddft_params.fear_range,
ddft_params.fear_amplitude, dx, nx, lx, fft.clone());
let kernel_zs_fft = Self::generate_kernel_fft(ddft_params.hunger_range,
ddft_params.hunger_amplitude, dx, nx, lx, fft.clone());
// Allocate convolution buffers
let conv_sz = vec![Complex64::new(0.0,0.0); nx*ny];
let conv_zs = vec![Complex64::new(0.0,0.0); nx*ny];
Self {
state: Some(state_vector),
dx,dy,
nx,ny,
grid: state.grid,
sz_params: sir_params,
diff_params,
ddft_params,
time: 0.,
duration: 0.,
kernel_sz_fft,
kernel_zs_fft,
fft, ifft,
scratch,
conv_sz, conv_zs,
#[cfg(not(target_arch = "wasm32"))]
thread_pool: scoped_threadpool::Pool::new(num_threads as u32)
}
}
fn generate_kernel_fft(range: f64, amp: f64, dx: f64, nx: usize, lx: f64, fft: Arc<dyn Fft<f64>>) -> Vec<Complex64> {
// Assume square grid
let ny = nx;
let _dy = dx;
// Create kernel
let mut kernel = Vec::with_capacity(nx*ny);
for iy in 0..ny {
for ix in 0..nx {
let dist_top_left = ix.pow(2) + iy.pow(2);
let dist_top_right = (nx-ix).pow(2) + iy.pow(2);
let dist_bottom_left = ix.pow(2) + (ny-iy).pow(2);
let dist_bottom_right = (nx-ix).pow(2) + (ny-iy).pow(2);
let dist = dist_top_left.min(dist_top_right.min(
dist_bottom_left.min(dist_bottom_right)));
kernel.push(Complex64::new(amp*(-range * dist as f64 * dx*dx).exp(), 0.0));
}
}
// Fourier transform kernel
let mut scratch = vec![Complex64::new(0.0, 0.0); nx*ny];
fft.process_with_scratch(kernel.as_mut_slice(), scratch.as_mut_slice());
transpose_2d(kernel.as_mut_slice(), nx);
fft.process_with_scratch(kernel.as_mut_slice(), scratch.as_mut_slice());
// Normalize kernel FFT
for x in &mut kernel {
*x /= (nx as f64).powi(4) / (lx*lx); // Bake all normalization factors into kernel (why is this n**4 and not n**3?)
}
kernel
}
/// Increase integration time
pub fn add_time(&mut self, time: f64) {
assert!(time >= 0.);
self.duration += time;
}
/// Get current time and state
///
/// Note that the type of the return value is not SIRStateSpatial2D, but a
/// similar construct with references
#[allow(non_snake_case)]
pub fn get_result(&self) -> (f64, SZStateSpatial2DBorrowed) {
let state = self.state.as_ref().unwrap();
(self.time, SZStateSpatial2DBorrowed::from_vec(state, &self.grid))
}
/// Raw read access to the state (used in profiling)
pub fn clone_state(&self) -> Vec<f64> {
self.state.as_ref().unwrap().clone()
}
/// Raw write access to the state (used in profiling)
pub fn set_state(&mut self, state: &[f64]) {
self.state.as_mut().unwrap().copy_from_slice(state);
}
}