eyepiece 0.1.0

A crate to generate star fields as seen with different telescopes
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249

use num_complex::Complex;
use rustfft::{num_traits::Zero, Fft, FftPlanner};
use std::sync::Arc;

type Cpx = Complex<f64>;

/// Zero-Padded Discrete Fourier Transform
///
/// Two-dimensions discrete fourier transfrom
pub struct ZpDft {
    zero_padded_buffer: Vec<Cpx>,
    scratch: Vec<Cpx>,
    len: i64,
    fft: Arc<dyn Fft<f64>>,
}
impl ZpDft {
    /// Forward Fourier transfrom
    pub fn forward(len: usize) -> Self {
        let mut planner = FftPlanner::new();
        let fft = planner.plan_fft_forward(len);
        Self {
            zero_padded_buffer: vec![Complex::zero(); len * len],
            scratch: vec![Complex::zero(); fft.get_inplace_scratch_len()],
            fft,
            len: len as i64,
        }
    }
    pub fn reset(&mut self) -> &mut Self {
        self.zero_padded_buffer = vec![Complex::zero(); (self.len * self.len) as usize];
        self
    }
    /// Inverse Fourier transfrom
    pub fn inverse(len: usize) -> Self {
        let mut planner = FftPlanner::new();
        Self {
            zero_padded_buffer: vec![Complex::zero(); len * len],
            scratch: vec![Complex::zero(); len],
            fft: planner.plan_fft_inverse(len),
            len: len as i64,
        }
    }
    // Zero-pads the FFT buffer
    fn zero_padding(&mut self, buffer: &[Cpx]) {
        let n2 = buffer.len() as i64;
        let n = (n2 as f64).sqrt() as i64;
        assert_eq!(n2, n * n, "DFT input is not a square array");
        self.zero_padded_buffer = vec![Complex::zero(); self.zero_padded_buffer.len()];
        for i in 0..n {
            let ii = (i - n / 2).rem_euclid(self.len);
            for j in 0..n {
                let jj = (j - n / 2).rem_euclid(self.len);
                let k = (i * n + j) as usize;
                let kk = (ii * self.len + jj) as usize;
                self.zero_padded_buffer[kk].re = buffer[k].re;
                self.zero_padded_buffer[kk].im = buffer[k].im;
            }
        }
    }
    // Shift zero frequency back to center
    fn shift(&mut self) {
        let mut buffer: Vec<Cpx> = vec![Complex::zero(); self.zero_padded_buffer.len()];
        for i in 0..self.len {
            let ii = (i + self.len / 2) % self.len;
            for j in 0..self.len {
                let jj = (j + self.len / 2) % self.len;
                let k = (i * self.len + j) as usize;
                let kk = (ii * self.len + jj) as usize;
                buffer[kk] = self.zero_padded_buffer[k];
            }
        }
        self.zero_padded_buffer.copy_from_slice(buffer.as_slice());
    }
    /// Compute the 2D Fourier transfrom
    pub fn process(&mut self, buffer: &[Cpx]) -> &mut Self {
        self.zero_padding(buffer);
        self.fft.process_with_scratch(
            self.zero_padded_buffer.as_mut_slice(),
            self.scratch.as_mut_slice(),
        );
        self.zero_padded_buffer = (0..self.len as usize)
            .flat_map(|k| {
                self.zero_padded_buffer
                    .iter()
                    .skip(k)
                    .step_by(self.len as usize)
                    .cloned()
                    .collect::<Vec<Cpx>>()
            })
            .collect();
        self.fft.process_with_scratch(
            self.zero_padded_buffer.as_mut_slice(),
            self.scratch.as_mut_slice(),
        );
        self.shift();
        self
    }
    /// FFT buffer real part
    pub fn real(&self) -> Vec<f64> {
        self.zero_padded_buffer.iter().map(|b| b.re).collect()
    }
    /// FFT buffer imaginary part
    pub fn imag(&self) -> Vec<f64> {
        self.zero_padded_buffer.iter().map(|b| b.im).collect()
    }
    /// FFT buffer norm
    pub fn norm(&self) -> Vec<f64> {
        self.zero_padded_buffer.iter().map(|b| b.norm()).collect()
    }
    /// FFT buffer norm squared
    pub fn norm_sqr(&self) -> Vec<f64> {
        self.zero_padded_buffer
            .iter()
            .map(|b| b.norm_sqr())
            .collect()
    }
    pub fn crop(&mut self, new_len: usize) -> &mut Self {
        let ij0 = self.len as usize / 2 - new_len / 2;
        let buffer = self.zero_padded_buffer.clone();
        self.zero_padded_buffer = vec![Complex::zero(); new_len * new_len];
        for i in 0..new_len {
            for j in 0..new_len {
                let k = i * new_len + j;
                let kk = (i + ij0) * self.len as usize + j + ij0;
                self.zero_padded_buffer[k] = buffer[kk];
            }
        }
        self
    }
    pub fn resize(&mut self, new_len: usize) -> &mut Self {
        let old_len = self.len as usize;
        if old_len > new_len {
            self.crop(new_len);
        } else {
            let ij0 = (new_len - old_len) / 2;
            let buffer = self.zero_padded_buffer.clone();
            self.zero_padded_buffer = vec![Complex::zero(); new_len * new_len];
            for i in 0..old_len {
                for j in 0..old_len {
                    let k = i * old_len + j;
                    let kk = (i + ij0) * new_len + j + ij0;
                    self.zero_padded_buffer[kk] = buffer[k];
                }
            }
        }
        self
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn zero_padding() {
        let n = 8;
        let n_fft = 16;
        let mut zp_dft = ZpDft::forward(n_fft);
        let buffer: Vec<Cpx> = vec![Complex::new(1f64, 0f64); n * n];
        zp_dft.zero_padding(buffer.as_slice());
        println!("REAL");
        zp_dft.real().chunks(n_fft).for_each(|c| println!("{c:?}"));
        println!("IMAG");
        zp_dft.imag().chunks(n_fft).for_each(|c| println!("{c:?}"));
        zp_dft.process(buffer.as_slice());
        println!("REAL");
        zp_dft
            .real()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("IMAG");
        zp_dft
            .imag()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("NORM");
        zp_dft
            .norm()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
    }

    #[test]
    fn cropping() {
        let n = 8;
        let n_fft = 16;
        let mut zp_dft = ZpDft::forward(n_fft);
        let buffer: Vec<Cpx> = vec![Complex::new(1f64, 0f64); n * n];
        zp_dft.zero_padding(buffer.as_slice());
        println!("REAL");
        zp_dft.real().chunks(n_fft).for_each(|c| println!("{c:?}"));
        println!("IMAG");
        zp_dft.imag().chunks(n_fft).for_each(|c| println!("{c:?}"));
        zp_dft.process(buffer.as_slice());
        println!("REAL");
        zp_dft
            .real()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("IMAG");
        zp_dft
            .imag()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("NORM");
        zp_dft
            .norm()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        zp_dft.crop(7);
        println!("NORM");
        zp_dft.norm().chunks(7).for_each(|c| println!("{c:+7.2?}"));
    }

    #[test]
    fn resizing() {
        let n = 7;
        let n_fft = 12;
        let mut zp_dft = ZpDft::forward(n_fft);
        let buffer: Vec<Cpx> = vec![Complex::new(1f64, 0f64); n * n];
        zp_dft.zero_padding(buffer.as_slice());
        println!("REAL");
        zp_dft.real().chunks(n_fft).for_each(|c| println!("{c:?}"));
        println!("IMAG");
        zp_dft.imag().chunks(n_fft).for_each(|c| println!("{c:?}"));
        zp_dft.process(buffer.as_slice());
        println!("REAL");
        zp_dft
            .real()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("IMAG");
        zp_dft
            .imag()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        println!("NORM");
        zp_dft
            .norm()
            .chunks(n_fft)
            .for_each(|c| println!("{c:+7.2?}"));
        let new_len = 18;
        zp_dft.resize(new_len);
        println!("NORM");
        zp_dft
            .norm()
            .chunks(new_len)
            .for_each(|c| println!("{c:+7.2?}"));
    }
}