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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 SIR-DDFT model under periodic boundary conditions in
//! one spatial dimension
#[cfg(not(target_arch = "wasm32"))]
use itertools::izip;
use crate::{
SIRStateSpatial1D, SIRParameters, SIRDiffusionParameters, SIRDDFTParameters,
Grid1D,
helpers::*,
ode::{ODEIVP, StopCondition},
sir::{SIRStateSpatial1DBorrowed}
};
/// Initial value problem for the SIR-DDFT model in one spatial dimension
///
/// Note: The model is technically a PDE, but is transformed to a high-dimensional
/// ODE via the finite difference method.
pub struct SIRDDFT1DIVP {
/// Flattened SIRStateSpatial1D (during integration ownership is passed to the
/// integrator so state is None then!)
state: Option<Vec<f64>>,
/// Distance between gridpoints (currently only equidistant grids are supported!)
dx: f64,
/// Originally passed grid
grid: Grid1D,
/// Model parameters for all SIR models
sir_params: SIRParameters,
/// Model parameters for diffusion
diff_params: SIRDiffusionParameters,
/// Model parameters specific to the SIR DDFT model
ddft_params: SIRDDFTParameters,
/// Current time of integration
time: f64,
/// Total duration of integration
duration: f64,
/// Precalculated social distancing kernel
kernel_sd: Vec<f64>,
/// Precalculated self isolation kernel
kernel_si: Vec<f64>,
/// Thread pool for parallel convolution
#[cfg(not(target_arch = "wasm32"))]
thread_pool: scoped_threadpool::Pool
}
/// 1D convolution with the symmetric (!) kernel of the SIR DDFT model
/// Returns (in this order):
/// Convolution of sd kernel with S+R + convolution of si kernel with I
/// Convolution of si kernel with S+I+R
#[allow(non_snake_case)]
fn convolve_sirddft(S: &[f64], I: &[f64], R: &[f64], kernel_sd: &[f64], kernel_si: &[f64],
amp_sd: f64, amp_si: f64, offset: usize, dx: f64) -> (f64,f64)
{
let n = S.len();
let mut conv_sd_SR = 0.0;
let mut conv_si_I = 0.0;
let mut conv_si_SIR = 0.0;
// Note: the auto vectorizer does not seem to see much vectorization opportunity here
// so this might call for some manual SIMD stuff
// TODO: Fix this mess once inline closures become stable
#[inline(always)]
fn add_contrib(kidx: usize, idx:usize, kernel_sd: &[f64], kernel_si: &[f64],
conv_sd_SR: &mut f64, conv_si_I: &mut f64, conv_si_SIR: &mut f64,
dx: f64, S: &[f64], I: &[f64], R: &[f64])
{
let kernel_sd_fac = kernel_sd[kidx];
let kernel_si_fac = kernel_si[kidx];
*conv_sd_SR += (S[idx] + R[idx]) * kernel_sd_fac * dx;
*conv_si_I += I[idx] * kernel_si_fac * dx;
*conv_si_SIR += (S[idx] + I[idx] + R[idx]) * kernel_si_fac * dx;
}
// Putting the add_contrib code directly into the macro is ~7% slower in the
// benchmark (why?)
macro_rules! add_contrib_macro {
($kidx: expr, $idx: expr) => {
add_contrib($kidx, $idx, kernel_sd, kernel_si, &mut conv_sd_SR, &mut conv_si_I, &mut conv_si_SIR, dx, S, I, R);
}
}
// -- end of mess --
add_contrib_macro!(0,offset);
for i in 1..(n/2) {
let left = (offset + n - i) % n;
let right = (offset + i) % n;
add_contrib_macro!(i, left);
add_contrib_macro!(i, right);
}
let i = n/2 + 1;
let left = (offset + n - i) % n;
let right = (offset + i) % n;
add_contrib_macro!(i, left);
if n % 2 == 1 {
add_contrib_macro!(i, right);
}
(conv_sd_SR * amp_sd + conv_si_I * amp_si, conv_si_SIR * amp_si)
// // Old version
// let n = S.len();
// let mut conv_sd_SR = 0.0;
// let mut conv_si_I = 0.0;
// let mut conv_si_SIR = 0.0;
// for i in 0..(n/2)+1 {
// let left = (offset + n - i) % n;
// let right = (offset + i) % n;
// let kernel_sd_fac = kernel_sd[i];
// let kernel_si_fac = kernel_si[i];
// conv_sd_SR += (S[left] + R[left]) * kernel_sd_fac * dx;
// conv_si_I += I[left] * kernel_si_fac * dx;
// conv_si_SIR += (S[left] + I[left] + R[left]) * kernel_si_fac * dx;
// // Don't count the last field double if n is even
// if left != right {
// conv_si_I += I[right] * kernel_si_fac * dx;
// conv_sd_SR += (S[right] + R[right]) * kernel_sd_fac * dx;
// conv_si_SIR += (S[right] + I[right] + R[right]) * kernel_si_fac * dx;
// }
// }
// (conv_sd_SR * amp_sd + conv_si_I * amp_si, conv_si_SIR * amp_si)
}
impl<S> ODEIVP<S,f64> for SIRDDFT1DIVP {
#[allow(non_snake_case)]
fn rhs(&mut self, _ : f64, y: &[f64], rhs: &mut[f64]) {
// Number of gridpoints
let n = y.len() / 3;
// Split state vector into S,I,R
let (S,IR) = y.split_at(n);
let (I,R) = IR.split_at(n);
// Split RHS vector
let (dS,dIR) = rhs.split_at_mut(n);
let (dI,dR) = dIR.split_at_mut(n);
// Shorthands for parameters
let inf_param = self.sir_params.infection_parameter;
let rec_rate = self.sir_params.recovery_rate;
let mort_rate = self.sir_params.mortality_rate;
let diff_S = self.diff_params.diffusivity_S;
let diff_I = self.diff_params.diffusivity_I;
let diff_R = self.diff_params.diffusivity_R;
let mob_S = self.ddft_params.mobility_S;
let mob_I = self.ddft_params.mobility_I;
let mob_R = self.ddft_params.mobility_R;
let amp_sd = self.ddft_params.social_distancing_amplitude;
let amp_si = self.ddft_params.self_isolation_amplitude;
let dx = self.dx;
let kernel_sd = self.kernel_sd.as_ref();
let kernel_si = self.kernel_si.as_ref();
// Direct convolution (less efficient than FFT, but can be easily run in parallel)
let calc_rhs = |start: usize, end: usize, dS: &mut [f64], dI: &mut [f64], dR: &mut[f64]| {
// We can save time by reusing evaluations of the convolution in the next step, so we
// only need to calculate one convolution tuple per cell
// First step calculations:
let mut conv_prevprev =
convolve_sirddft(S, I, R, kernel_sd, kernel_si, amp_sd, amp_si, (start+n-2)%n, dx);
let mut conv_prev =
convolve_sirddft(S, I, R, kernel_sd, kernel_si, amp_sd, amp_si, (start+n-1)%n, dx);
let mut conv_curr =
convolve_sirddft(S, I, R, kernel_sd, kernel_si, amp_sd, amp_si, start, dx);
let mut conv_next =
convolve_sirddft(S, I, R, kernel_sd, kernel_si, amp_sd, amp_si, (start+1)%n, dx);
// Calculate RHS
for i in start..end {
let prev = i as i64 - 1;
let mut next = i+1;
// Periodic boundary conditions
let prev = if prev < 0 { n-1 } else {
// Only need to check if prev is not < 0
if next >= n {
next = 0;
}
prev as usize
};
// Calculate next convolution:
let conv_nextnext =
convolve_sirddft(S, I, R, kernel_sd, kernel_si, amp_sd, amp_si, (i+2) % n, dx);
// Semantic naming:
let (conv_SR_prevprev, conv_I_prevprev) = conv_prevprev;
let (conv_SR_curr, conv_I_curr) = conv_curr;
let (conv_SR_nextnext, conv_I_nextnext) = conv_nextnext;
// Calculate convolution gradients
let conv_grad_SR_prev = grad_1d_val(conv_SR_prevprev, conv_SR_curr, dx);
let conv_grad_SR_next = grad_1d_val(conv_SR_curr, conv_SR_nextnext, dx);
let conv_grad_I_prev = grad_1d_val(conv_I_prevprev, conv_I_curr, dx);
let conv_grad_I_next = grad_1d_val(conv_I_curr, conv_I_nextnext, dx);
// Discretized form of model equations
dS[i-start] = diff_S * laplace_1d(S, prev, i, next, dx)
- inf_param * S[i] * I[i]
- mob_S * (grad_1d_val(S[prev] * conv_grad_SR_prev, S[next] * conv_grad_SR_next, dx));
dI[i-start] = diff_I * laplace_1d(I, prev, i, next, dx)
+ inf_param * S[i] * I[i] - rec_rate * I[i] - mort_rate * I[i]
- mob_I * (grad_1d_val(I[prev] * conv_grad_I_prev, I[next] * conv_grad_I_next, dx));
dR[i-start] = diff_R * laplace_1d(R, prev, i, next, dx)
+ rec_rate * I[i]
- mob_R * (grad_1d_val(R[prev] * conv_grad_SR_prev, R[next] * conv_grad_SR_next, dx));
// Shift all stored convolutions
conv_prevprev = conv_prev;
conv_prev = conv_curr;
conv_curr = conv_next;
conv_next = conv_nextnext;
}
};
#[cfg(not(target_arch = "wasm32"))]
{
let num_threads = self.thread_pool.thread_count() as usize;
self.thread_pool.scoped(|s| {
let chunk_size = ceil_div(n,num_threads);
let dS_chunks = dS.chunks_mut(chunk_size);
let dI_chunks = dI.chunks_mut(chunk_size);
let dR_chunks = dR.chunks_mut(chunk_size);
for (i,dS,dI,dR) in izip!(0..num_threads, dS_chunks, dI_chunks, dR_chunks) {
s.execute(move || {
calc_rhs(i*chunk_size, ((i+1)*chunk_size).min(n), dS, dI, dR);
});
}
});
}
#[cfg(target_arch = "wasm32")]
{
// TODO: Switch to FFT based convolution
calc_rhs(0,n,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 SIRDDFT1DIVP {
/// Creates a new IVP for the SIR diffusion model
pub fn new(sir_params: SIRParameters, diff_params: SIRDiffusionParameters,
ddft_params: SIRDDFTParameters, state: SIRStateSpatial1D, num_threads: usize)
-> Self {
// Check grid length
let length = state.S.len();
if length < 3 {
panic!("Must have at least 3 gridpoints!"); // TODO: proper errors
}
let dx = match &state.grid {
Grid1D::Equidistant(grid) => { grid.delta() },
#[allow(unreachable_patterns)]
_ => { unimplemented!("Only equidistant grids are supported for now!") }
};
// 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.I, state.R].concat();
// Generate kernels
let kernel_sd = Self::generate_kernel(ddft_params.social_distancing_range, dx, length);
let kernel_si = Self::generate_kernel(ddft_params.self_isolation_range, dx, length);
Self {
state: Some(state_vector),
dx,
grid: state.grid,
sir_params,
diff_params,
ddft_params,
time: 0.,
duration: 0.,
kernel_sd,
kernel_si,
#[cfg(not(target_arch = "wasm32"))]
thread_pool: scoped_threadpool::Pool::new(num_threads as u32)
}
}
fn generate_kernel(range: f64, dx: f64, length: usize) -> Vec<f64> {
(0..length).map(|i| (-range * dx*dx * (i*i) as f64).exp()).collect()
}
/// 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 SIRStateSpatial1D, but a
/// similar construct with references
#[allow(non_snake_case)]
pub fn get_result(&self) -> (f64, SIRStateSpatial1DBorrowed) {
let state = self.state.as_ref().unwrap();
(self.time, SIRStateSpatial1DBorrowed::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);
}
}