imgal 0.3.1

A fast and open-source scientific image processing and algorithm library.
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
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296

use imgal::prelude::*;
use imgal::simulation::blob::gaussian_metaballs;
use imgal::statistics::{
    effective_sample_size, kahan_sum, linear_percentile, max, min, min_max, sum,
    weighted_kendall_tau_b, weighted_merge_sort_mut,
};
use ndarray::arr2;

const TOLERANCE: f64 = 1e-10;
const CENTER: [[f64; 2]; 1] = [[25.0, 25.0]];
const RADIUS: [f64; 1] = [20.0];
const INTENSITY: [f64; 1] = [10.0];
const FALLOFF: [f64; 1] = [2.0];
const BACKGROUND: f64 = 0.0;
const SHAPE: [usize; 2] = [50, 50];
const THREADS: Option<usize> = Some(0);

fn approx_equal(a: f64, b: f64) -> bool {
    (a - b).abs() < TOLERANCE
}

/// Tests that `effective_sample_size` returns the expected results for data
/// that is dominated by a single weight, partially zero, uniform and all zeros.
#[test]
fn statistics_effective_sample_size_expected_results() {
    let dominant_w: [f64; 5] = [0.99, 0.001, 0.001, 0.001, 0.001];
    let part_zero_w: [f64; 5] = [1.0, 2.0, 0.0, 0.0, 0.0];
    let uniform_w: [f64; 5] = [1.0, 1.0, 1.0, 1.0, 1.0];
    let zero_w: [f64; 5] = [0.0, 0.0, 0.0, 0.0, 0.0];
    assert!((approx_equal(effective_sample_size(&dominant_w), 1.0080930187)));
    assert_eq!(effective_sample_size(&part_zero_w), 1.8);
    assert_eq!(effective_sample_size(&uniform_w), 5.0);
    assert_eq!(effective_sample_size(&zero_w), 0.0);
}

/// Tests that `kahan_sum` returns the expected compensated sum results for
/// integer and floating point data.
#[test]
fn statistics_kahan_sum_expected_results() -> Result<(), ImgalError> {
    let i32_data = vec![2, 5, 10, 23];
    let f64_data = vec![1.0, 10.5, 3.25, 37.11];
    let f64_error_data = vec![0.1_f64; 1000];
    let mut large_small_data = vec![1e-7_f64; 1_000_000];
    large_small_data.insert(0, 1_000_000.0);
    assert_eq!(kahan_sum(&i32_data)?, 40);
    assert_eq!(kahan_sum(&f64_data)?, 51.86);
    assert_eq!(kahan_sum(&f64_error_data)?, 100.0);
    assert_eq!(kahan_sum(&large_small_data)?, 1_000_000.1);
    Ok(())
}

/// Tests that `linear_percentile` returns the expected results for flat and
/// axis compute.
#[test]
fn statistics_linear_percentile_expected_results() -> Result<(), ImgalError> {
    let data = gaussian_metaballs(
        &arr2(&CENTER),
        &RADIUS,
        &INTENSITY,
        &FALLOFF,
        BACKGROUND,
        &SHAPE,
        None,
    )?;
    let axis_par = linear_percentile(&data, 99.8, Some(0), None, THREADS)?;
    let axis_seq = linear_percentile(&data, 99.8, Some(0), None, None)?;
    let mm_par = min_max(&axis_par, None)?;
    let mm_seq = min_max(&axis_seq, None)?;
    let flat_par = linear_percentile(&data, 99.8, None, None, THREADS)?;
    let flat_seq = linear_percentile(&data, 99.8, None, None, None)?;
    assert_eq!(axis_par.shape(), [50,]);
    assert_eq!(axis_seq.shape(), [50,]);
    assert!(approx_equal(mm_par.0, 4.5777731222));
    assert!(approx_equal(mm_seq.0, 4.5777731222));
    assert!(approx_equal(mm_par.1, 9.9987757653));
    assert!(approx_equal(mm_seq.1, 9.9987757653));
    assert!(approx_equal(flat_par[0], 9.9750561771));
    assert!(approx_equal(flat_seq[0], 9.9750561771));
    Ok(())
}

/// Tests that `max` returns the maximum value from integer, floating point,
/// string arrays and images.
#[test]
fn statistics_max_expected_results() -> Result<(), ImgalError> {
    let image_data = gaussian_metaballs(
        &arr2(&CENTER),
        &RADIUS,
        &INTENSITY,
        &FALLOFF,
        BACKGROUND,
        &SHAPE,
        None,
    )?;
    let i32_data: [i32; 10] = [1, 5, 3, 9, 2, 3, 0, 4, 6, 15];
    let f64_data: [f64; 10] = [1.0, 5.0, 3.0, 9.0, 2.0, 3.0, 0.0, 4.0, 6.0, 15.0];
    let str_data: [&str; 8] = ["1.0", "5.0", "3.0", "4.0", "15.0", "9.0", "0.0", "8.0"];
    assert_eq!(max(&i32_data, THREADS)?, 15);
    assert_eq!(max(&i32_data, None)?, 15);
    assert_eq!(max(&f64_data, THREADS)?, 15.0);
    assert_eq!(max(&f64_data, None)?, 15.0);
    assert_eq!(max(&str_data, THREADS)?, "9.0");
    assert_eq!(max(&str_data, None)?, "9.0");
    assert_eq!(max(&image_data, THREADS)?, 10.0);
    assert_eq!(max(&image_data, None)?, 10.0);
    Ok(())
}

/// Tests that `min` returns the minimum value from integer, floating point,
/// string arrays and images.
#[test]
fn statistics_min_expected_results() -> Result<(), ImgalError> {
    let image_data = gaussian_metaballs(
        &arr2(&CENTER),
        &RADIUS,
        &INTENSITY,
        &FALLOFF,
        BACKGROUND,
        &SHAPE,
        None,
    )?;
    let i32_data: [i32; 10] = [1, 5, 3, 9, 2, 3, 0, 4, 6, 15];
    let f64_data: [f64; 10] = [1.0, 5.0, 3.0, 9.0, 2.0, 3.0, 0.0, 4.0, 6.0, 15.0];
    let str_data: [&str; 8] = ["1.0", "5.0", "3.0", "4.0", "15.0", "9.0", "0.0", "8.0"];
    assert_eq!(min(&i32_data, THREADS)?, 0);
    assert_eq!(min(&i32_data, None)?, 0);
    assert_eq!(min(&f64_data, THREADS)?, 0.0);
    assert_eq!(min(&f64_data, None)?, 0.0);
    assert_eq!(min(&str_data, THREADS)?, "0.0");
    assert_eq!(min(&str_data, None)?, "0.0");
    assert!(approx_equal(min(&image_data, THREADS)?, 2.0961138715));
    assert!(approx_equal(min(&image_data, None)?, 2.0961138715));
    Ok(())
}

/// Tests that `min_max` returns the minimum and maximum values from integer,
/// floating ppoint, string arrays and images.
#[test]
fn statistics_min_max_expected_results() -> Result<(), ImgalError> {
    let image_data = gaussian_metaballs(
        &arr2(&CENTER),
        &RADIUS,
        &INTENSITY,
        &FALLOFF,
        BACKGROUND,
        &SHAPE,
        None,
    )?;
    let i32_data: [i32; 10] = [1, 5, 3, 9, 2, 3, 0, 4, 6, 15];
    let f64_data: [f64; 10] = [1.0, 5.0, 3.0, 9.0, 2.0, 3.0, 0.0, 4.0, 6.0, 15.0];
    let str_data: [&str; 8] = ["1.0", "5.0", "3.0", "4.0", "15.0", "9.0", "0.0", "8.0"];
    assert_eq!(min_max(&i32_data, THREADS)?, (0, 15));
    assert_eq!(min_max(&i32_data, None)?, (0, 15));
    assert_eq!(min_max(&f64_data, THREADS)?, (0.0, 15.0));
    assert_eq!(min_max(&f64_data, None)?, (0.0, 15.0));
    assert_eq!(min_max(&str_data, THREADS)?, ("0.0", "9.0"));
    assert_eq!(min_max(&str_data, None)?, ("0.0", "9.0"));
    assert!(approx_equal(min_max(&image_data, THREADS)?.0, 2.0961138715));
    assert!(approx_equal(min_max(&image_data, None)?.0, 2.0961138715));
    assert!(approx_equal(min_max(&image_data, THREADS)?.1, 10.0));
    assert!(approx_equal(min_max(&image_data, None)?.1, 10.0));
    Ok(())
}

/// Tests that `sum` returns expected sum from integer and floating point arrays
/// as well as images.
#[test]
fn statistics_sum_expected_results() -> Result<(), ImgalError> {
    let image_data = gaussian_metaballs(
        &arr2(&CENTER),
        &RADIUS,
        &INTENSITY,
        &FALLOFF,
        BACKGROUND,
        &SHAPE,
        None,
    )?;
    let i32_data = vec![2, 5, 10, 23];
    let f64_data = vec![1.0, 10.5, 3.25, 37.11];
    let f64_error_data = vec![0.1_f64; 1000];
    assert_eq!(sum(&i32_data, THREADS), 40);
    assert_eq!(sum(&i32_data, None), 40);
    assert_eq!(sum(&f64_data, THREADS), 51.86);
    assert_eq!(sum(&f64_data, None), 51.86);
    assert!(approx_equal(sum(&f64_error_data, THREADS), 100.0));
    assert!(approx_equal(sum(&f64_error_data, None), 99.9999999999));
    assert!(approx_equal(sum(&image_data, THREADS), 15630.0102099582));
    assert!(approx_equal(sum(&image_data, None), 15630.0102099582));
    Ok(())
}

/// Tests that `weighted_kendall_tau_b` returns the expected results for perfect
/// positive correlation, perfect negative correlation, tie corretion and order
/// invariance.
#[test]
fn statistics_weighted_kendall_tau_b_expected_results() -> Result<(), ImgalError> {
    let perfect_pos_corr = ([1, 2, 3, 4, 5], [1, 2, 3, 4, 5], [1.0_f64; 5]);
    let perfect_neg_corr = ([1, 2, 3, 4, 5], [5, 4, 3, 2, 1], [1.0_f64; 5]);
    let single_diff_corr = ([1, 2, 3, 4, 5], [1, 2, 3, 5, 4], [1.0_f64; 5]);
    let all_ties_corr = ([2, 2, 2, 2, 2], [3, 3, 3, 3, 3], [1.0_f64; 5]);
    let no_ties_fwd = (
        [10, 21, 22, 23, 30, 40, 50],
        [5, 3, 8, 6, 2, 9, 10],
        [1.0_f64; 7],
    );
    let no_ties_rev = (
        [50, 40, 30, 23, 22, 21, 10],
        [10, 9, 2, 6, 8, 3, 5],
        [1.0_f64; 7],
    );
    let with_ties_fwd = (
        [10, 20, 20, 20, 30, 40, 50],
        [50, 40, 30, 20, 20, 20, 10],
        [1.0_f64; 7],
    );
    let with_ties_rev = (
        [50, 40, 30, 20, 20, 20, 10],
        [10, 20, 20, 20, 30, 40, 50],
        [1.0_f64; 7],
    );
    assert_eq!(
        weighted_kendall_tau_b(
            &perfect_pos_corr.0,
            &perfect_pos_corr.1,
            &perfect_pos_corr.2
        )?,
        1.0
    );
    assert_eq!(
        weighted_kendall_tau_b(
            &perfect_neg_corr.0,
            &perfect_neg_corr.1,
            &perfect_neg_corr.2
        )?,
        -1.0
    );
    assert_eq!(
        weighted_kendall_tau_b(
            &single_diff_corr.0,
            &single_diff_corr.1,
            &single_diff_corr.2
        )?,
        0.8
    );
    assert!(weighted_kendall_tau_b(&all_ties_corr.0, &all_ties_corr.1, &all_ties_corr.2)?.is_nan(),);
    assert!(approx_equal(
        weighted_kendall_tau_b(&no_ties_fwd.0, &no_ties_fwd.1, &no_ties_fwd.2)?,
        0.4285714285
    ));
    assert!(approx_equal(
        weighted_kendall_tau_b(&no_ties_rev.0, &no_ties_rev.1, &no_ties_rev.2)?,
        0.4285714285
    ));
    assert!(approx_equal(
        weighted_kendall_tau_b(&with_ties_fwd.0, &with_ties_fwd.1, &with_ties_fwd.2)?,
        -0.6666666666
    ));
    assert!(approx_equal(
        weighted_kendall_tau_b(&with_ties_rev.0, &with_ties_rev.1, &with_ties_rev.2)?,
        -0.6666666666
    ));
    Ok(())
}

/// Tests that `weighted_merge_sort_mut` returns the expected weighted inversion
/// count and correctly orders the data and weights arrays. The "ping pong" data
/// tests the ping pong buffer used in the function. The short ping pong data
/// avoids a final copy while the long requires it.
#[test]
fn statistics_weighted_merge_sort_mut_expected_results() -> Result<(), ImgalError> {
    let mut simple_data = (
        [3, 10, 87, 22, 5, 15, 36, 8, 54, 1],
        [0.51, 12.83, 4.24, 9.25, 0.32, 3.22, 1.97, 0.72, 4.10, 10.7],
    );
    let mut ping_pong_short = ([8, 3, 1, 7], [1.0; 4]);
    let mut ping_pong_long = (
        [64, 34, 25, 12, 22, 11, 90, 45],
        [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0],
    );
    let simple_swaps = weighted_merge_sort_mut(&mut simple_data.0, &mut simple_data.1)?;
    let pp_short_swaps = weighted_merge_sort_mut(&mut ping_pong_short.0, &mut ping_pong_short.1)?;
    let pp_long_swaps = weighted_merge_sort_mut(&mut ping_pong_long.0, &mut ping_pong_long.1)?;
    assert_eq!(simple_data.0, [1, 3, 5, 8, 10, 15, 22, 36, 54, 87]);
    assert_eq!(
        simple_data.1,
        [10.7, 0.51, 0.32, 0.72, 12.83, 3.22, 9.25, 1.97, 4.1, 4.24]
    );
    assert_eq!(ping_pong_short.0, [1, 3, 7, 8]);
    assert_eq!(ping_pong_short.1, [1.0; 4]);
    assert_eq!(ping_pong_long.0, [11, 12, 22, 25, 34, 45, 64, 90]);
    assert_eq!(ping_pong_long.1, [6.0, 4.0, 5.0, 3.0, 2.0, 8.0, 1.0, 7.0]);
    assert_eq!(simple_swaps, 537.1162);
    assert_eq!(pp_short_swaps, 4.0);
    assert_eq!(pp_long_swaps, 219.0);
    Ok(())
}