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transform.rs
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344 lines (309 loc) · 11.6 KB
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use crate::geometry::Axis;
use ndarray::prelude::*;
use ndarray::*;
use num_dual::*;
use rustdct::{DctNum, DctPlanner, TransformType2And3};
use rustfft::{num_complex::Complex, Fft, FftPlanner};
use std::f64::consts::PI;
use std::ops::DivAssign;
use std::sync::Arc;
#[derive(Clone, Copy)]
enum SinCosTransform {
SinForward,
SinReverse,
CosForward,
CosReverse,
}
impl SinCosTransform {
fn is_reverse(&self) -> bool {
match self {
Self::CosForward | Self::SinForward => false,
Self::CosReverse | Self::SinReverse => true,
}
}
}
pub(super) trait FourierTransform<T: DualNum<f64>>: Send + Sync {
fn forward_transform(&self, f_r: ArrayView1<T>, f_k: ArrayViewMut1<T>, scalar: bool);
fn back_transform(&self, f_k: ArrayViewMut1<T>, f_r: ArrayViewMut1<T>, scalar: bool);
}
pub(super) struct CartesianTransform<T> {
dct: Arc<dyn TransformType2And3<T>>,
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> CartesianTransform<T> {
pub(super) fn new(axis: &Axis) -> (Arc<dyn FourierTransform<T>>, Array1<f64>) {
let (s, k) = Self::init(axis);
(Arc::new(s), k)
}
pub(super) fn new_cartesian(axis: &Axis) -> (Arc<Self>, Array1<f64>) {
let (s, k) = Self::init(axis);
(Arc::new(s), k)
}
fn init(axis: &Axis) -> (Self, Array1<f64>) {
let points = axis.grid.len();
let length = axis.length();
let k_grid = (0..=points).map(|v| PI * v as f64 / length).collect();
(
Self {
dct: DctPlanner::new().plan_dct2(points),
},
k_grid,
)
}
fn calculate_transform(&self, slice: &mut [T], transform: SinCosTransform) {
match transform {
SinCosTransform::CosForward => self.dct.process_dct2(slice),
SinCosTransform::CosReverse => self.dct.process_dct3(slice),
SinCosTransform::SinForward => self.dct.process_dst2(slice),
SinCosTransform::SinReverse => self.dct.process_dst3(slice),
}
}
fn transform(&self, mut f: ArrayViewMut1<T>, transform: SinCosTransform) {
let mut f_slice = match transform {
SinCosTransform::CosForward | SinCosTransform::CosReverse => f.slice_mut(s![..-1]),
SinCosTransform::SinForward | SinCosTransform::SinReverse => f.slice_mut(s![1..]),
};
match f_slice.as_slice_mut() {
Some(slice) => self.calculate_transform(slice, transform),
None => {
let mut slice = f_slice.to_owned();
self.calculate_transform(slice.as_slice_mut().unwrap(), transform);
f_slice.assign(&slice);
}
}
if transform.is_reverse() {
f.div_assign(T::from_f64(0.5).unwrap() * T::from_usize(self.dct.len()).unwrap())
}
}
pub(super) fn forward_transform_inplace(&self, f: ArrayViewMut1<T>, scalar: bool) {
if scalar {
self.transform(f, SinCosTransform::CosForward);
} else {
self.transform(f, SinCosTransform::SinForward);
}
}
pub(super) fn back_transform_inplace(&self, f: ArrayViewMut1<T>, scalar: bool) {
if scalar {
self.transform(f, SinCosTransform::CosReverse);
} else {
self.transform(f, SinCosTransform::SinReverse);
}
}
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> FourierTransform<T> for CartesianTransform<T> {
fn forward_transform(&self, f_r: ArrayView1<T>, mut f_k: ArrayViewMut1<T>, scalar: bool) {
if scalar {
f_k.slice_mut(s![..-1]).assign(&f_r);
} else {
f_k.slice_mut(s![1..]).assign(&f_r);
}
self.forward_transform_inplace(f_k, scalar);
}
fn back_transform(&self, mut f_k: ArrayViewMut1<T>, mut f_r: ArrayViewMut1<T>, scalar: bool) {
self.back_transform_inplace(f_k.view_mut(), scalar);
if scalar {
f_r.assign(&f_k.slice(s![..-1]));
} else {
f_r.assign(&f_k.slice(s![1..]));
}
}
}
pub(super) struct SphericalTransform<T> {
r_grid: Array1<f64>,
k_grid: Array1<f64>,
dct: Arc<dyn TransformType2And3<T>>,
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> SphericalTransform<T> {
pub(super) fn new(axis: &Axis) -> (Arc<dyn FourierTransform<T>>, Array1<f64>) {
let points = axis.grid.len();
let length = axis.length();
let k_grid: Array1<_> = (0..=points).map(|v| PI * v as f64 / length).collect();
(
Arc::new(Self {
r_grid: axis.grid.clone(),
k_grid: k_grid.clone(),
dct: DctPlanner::new().plan_dct2(points),
}),
k_grid,
)
}
fn sine_transform<S1, S2>(
&self,
f_in: ArrayBase<S1, Ix1>,
mut f_out: ArrayBase<S2, Ix1>,
reverse: bool,
) where
S1: Data<Elem = T>,
S2: RawData<Elem = T> + DataMut,
{
if reverse {
f_out.assign(&f_in.slice(s![1..]));
self.dct.process_dst3(f_out.as_slice_mut().unwrap());
f_out.div_assign(T::from_f64(0.5).unwrap() * T::from_usize(f_out.len()).unwrap());
} else {
let mut f_slice = f_out.slice_mut(s![1..]);
f_slice.assign(&f_in);
self.dct.process_dst2(f_slice.as_slice_mut().unwrap());
}
}
fn cosine_transform<S1, S2>(
&self,
f_in: ArrayBase<S1, Ix1>,
mut f_out: ArrayBase<S2, Ix1>,
reverse: bool,
) where
S1: Data<Elem = T>,
S2: RawData<Elem = T> + DataMut,
{
if reverse {
f_out.assign(&f_in.slice(s![..-1]));
self.dct.process_dct3(f_out.as_slice_mut().unwrap());
f_out.div_assign(T::from_f64(0.5).unwrap() * T::from_usize(f_out.len()).unwrap());
} else {
let mut f_slice = f_out.slice_mut(s![..-1]);
f_slice.assign(&f_in);
self.dct.process_dct2(f_slice.as_slice_mut().unwrap());
}
}
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> FourierTransform<T> for SphericalTransform<T> {
fn forward_transform(&self, f_r: ArrayView1<T>, mut f_k: ArrayViewMut1<T>, scalar: bool) {
if scalar {
self.sine_transform(&f_r * &self.r_grid, f_k.view_mut(), false);
} else {
let mut f_aux = Array::zeros(f_k.raw_dim());
self.cosine_transform(&f_r * &self.r_grid, f_aux.view_mut(), false);
self.sine_transform(f_r, f_k.view_mut(), false);
f_k.assign(&(&f_k / &self.k_grid - &f_aux));
}
f_k.assign(&(&f_k / &self.k_grid));
f_k[0] = T::zero();
}
fn back_transform(&self, f_k: ArrayViewMut1<T>, mut f_r: ArrayViewMut1<T>, scalar: bool) {
if scalar {
self.sine_transform(&f_k * &self.k_grid, f_r.view_mut(), true);
} else {
let mut f_aux = Array::zeros(f_r.raw_dim());
self.cosine_transform(&f_k * &self.k_grid, f_aux.view_mut(), true);
self.sine_transform(f_k, f_r.view_mut(), true);
f_r.assign(&(&f_r / &self.r_grid - &f_aux));
}
f_r.assign(&(&f_r / &self.r_grid));
}
}
pub(super) struct PolarTransform<T: DctNum> {
r_grid: Array1<f64>,
k_grid: Array1<f64>,
fft: Arc<dyn Fft<T>>,
j: [Array1<Complex<T>>; 2],
k0: [f64; 2],
alpha: f64,
gamma: f64,
l: f64,
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> PolarTransform<T> {
pub(super) fn new(axis: &Axis) -> (Arc<dyn FourierTransform<T>>, Array1<f64>) {
let points = axis.grid.len();
let mut alpha = 0.002_f64;
for _ in 0..20 {
alpha = -(1.0 - (-alpha).exp()).ln() / (points - 1) as f64;
}
let x0 = 0.5 * ((-alpha * points as f64).exp() + (-alpha * (points - 1) as f64).exp());
let gamma = (alpha * (points - 1) as f64).exp();
let l = axis.length();
let k_grid: Array1<_> = (0..points)
.map(|i| x0 * (alpha * i as f64).exp() * gamma / l)
.collect();
let k0 = (2.0 * alpha).exp() * (2.0 * alpha.exp() + (2.0 * alpha).exp() - 1.0)
/ ((1.0 + alpha.exp()).powi(2) * ((2.0 * alpha).exp() - 1.0));
let k0v = (2.0 * alpha).exp() * (2.0 * alpha.exp() + (2.0 * alpha).exp() - 5.0 / 3.0)
/ ((1.0 + alpha.exp()).powi(2) * ((2.0 * alpha).exp() - 1.0));
let fft = FftPlanner::new().plan_fft_forward(2 * points);
let ifft = FftPlanner::new().plan_fft_inverse(2 * points);
let mut j = Array1::from_shape_fn(2 * points, |i| {
Complex::from(T::from(
(gamma * x0 * (alpha * ((i + 1) as f64 - points as f64)).exp()).bessel_j1()
/ ((2 * points) as f64),
))
});
ifft.process(j.as_slice_mut().unwrap());
let mut jv = Array1::from_shape_fn(2 * points, |i| {
Complex::from(T::from(
(gamma * x0 * (alpha * ((i + 1) as f64 - points as f64)).exp()).bessel_j2()
/ ((2 * points) as f64),
))
});
ifft.process(jv.as_slice_mut().unwrap());
(
Arc::new(Self {
r_grid: axis.grid.clone(),
k_grid: k_grid.clone(),
fft,
j: [j, jv],
k0: [k0, k0v],
alpha,
gamma,
l,
}),
k_grid,
)
}
fn transform(
&self,
f_in: ArrayView1<T>,
mut f_out: ArrayViewMut1<T>,
scalar: bool,
x_in: &Array1<f64>,
x_out: &Array1<f64>,
mut factor: f64,
) {
let n = f_in.len();
let (f_in, alpha, k0, j) = if scalar {
(f_in.to_owned(), self.alpha, self.k0[0], &self.j[0])
} else {
factor *= factor;
(&f_in / x_in, 2.0 * self.alpha, self.k0[1], &self.j[1])
};
let mut phi = Array1::from_shape_fn(2 * n, |i| {
if i < n - 1 {
(f_in[i] - f_in[i + 1]) * (-alpha * (n - i - 1) as f64).exp()
} else {
T::zero()
}
});
phi[0] *= k0;
let mut phi = phi.mapv(Complex::from);
self.fft.process(phi.as_slice_mut().unwrap());
phi *= j;
self.fft.process(phi.as_slice_mut().unwrap());
f_out.assign(&(phi.slice(s![..n]).map(|phi| phi.re * factor) / x_out));
}
}
impl<T: DualNum<f64> + DctNum + ScalarOperand> FourierTransform<T> for PolarTransform<T> {
fn forward_transform(&self, f_r: ArrayView1<T>, f_k: ArrayViewMut1<T>, scalar: bool) {
self.transform(f_r, f_k, scalar, &self.r_grid, &self.k_grid, self.l);
}
fn back_transform(&self, f_k: ArrayViewMut1<T>, f_r: ArrayViewMut1<T>, scalar: bool) {
self.transform(
f_k.view(),
f_r,
scalar,
&self.k_grid,
&self.r_grid,
self.gamma / self.l,
);
}
}
pub(super) struct NoTransform();
impl NoTransform {
pub(super) fn new<T: DualNum<f64>>() -> (Arc<dyn FourierTransform<T>>, Array1<f64>) {
(Arc::new(Self()), arr1(&[0.0]))
}
}
impl<T: DualNum<f64>> FourierTransform<T> for NoTransform {
fn forward_transform(&self, f: ArrayView1<T>, mut f_k: ArrayViewMut1<T>, _: bool) {
f_k.assign(&f);
}
fn back_transform(&self, f_k: ArrayViewMut1<T>, mut f_r: ArrayViewMut1<T>, _: bool) {
f_r.assign(&f_k);
}
}