minikalman 0.7.0

A microcontroller targeted Kalman filter implementation
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

#![allow(dead_code)]

use proptest::prelude::*;

use minikalman::matrix::{MatrixDataArray, MatrixDataBoxed};
use minikalman::prelude::*;

/// Tolerance for floating-point comparisons in proptest assertions.
pub const EPS: f32 = 1e-3;

/// A more relaxed tolerance for complex operations (e.g. matrix inversion).
pub const EPS_RELAXED: f32 = 1e-2;

/// Generates finite `f32` values in range `[-1e3..1e3]`.
pub fn finite_f32() -> impl Strategy<Value = f32> {
    (-1e3f32..1e3f32).prop_filter("exclude non-finite", |x| x.is_finite())
}

/// Generates finite `f32` values in range `[-5..5]` for well-conditioned filter tests.
pub fn small_finite_f32() -> impl Strategy<Value = f32> {
    (-5f32..5f32).prop_filter("exclude non-finite", |x| x.is_finite())
}

/// Generates a `Vec<T>` of length `len` with small finite entries.
pub fn small_finite_vec(len: usize) -> impl Strategy<Value = Vec<f32>> {
    proptest::collection::vec(small_finite_f32(), len..=len)
}

/// Generates a fixed-size array strategy with small finite entries.
pub fn small_fixed_vec<const N: usize>() -> impl Strategy<Value = [f32; N]> {
    small_finite_vec(N).prop_map(|v| {
        let mut arr = [0.0f32; N];
        arr.copy_from_slice(&v);
        arr
    })
}

/// Generates finite `f64` values in range `[-1e3..1e3]`.
pub fn finite_f64() -> impl Strategy<Value = f64> {
    (-1e3f64..1e3f64).prop_filter("exclude non-finite", |x| x.is_finite())
}

/// Generates a `Vec<T>` of length `len` with finite entries.
pub fn finite_vec(len: usize) -> impl Strategy<Value = Vec<f32>> {
    proptest::collection::vec(finite_f32(), len..=len)
}

/// Generates a fixed-size array strategy for small arrays.
pub fn finite_fixed_vec<const N: usize>() -> impl Strategy<Value = [f32; N]> {
    finite_vec(N).prop_map(|v| {
        let mut arr = [0.0f32; N];
        arr.copy_from_slice(&v);
        arr
    })
}

// ---- Concrete identity / zero matrices for test sizes ----

pub fn identity_2() -> MatrixDataArray<2, 2, 4, f32> {
    MatrixDataArray::new([1.0, 0.0, 0.0, 1.0])
}

pub fn identity_3() -> MatrixDataArray<3, 3, 9, f32> {
    MatrixDataArray::new([1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0])
}

pub fn zero_2x2() -> MatrixDataArray<2, 2, 4, f32> {
    MatrixDataArray::new([0.0; 4])
}

pub fn zero_2x3() -> MatrixDataArray<2, 3, 6, f32> {
    MatrixDataArray::new([0.0; 6])
}

pub fn zero_3x2() -> MatrixDataArray<3, 2, 6, f32> {
    MatrixDataArray::new([0.0; 6])
}

pub fn zero_3x3() -> MatrixDataArray<3, 3, 9, f32> {
    MatrixDataArray::new([0.0; 9])
}

pub fn zero_3x4() -> MatrixDataArray<3, 4, 12, f32> {
    MatrixDataArray::new([0.0; 12])
}

pub fn zero_4x4() -> MatrixDataArray<4, 4, 16, f32> {
    MatrixDataArray::new([0.0; 16])
}

pub fn zero_2x4() -> MatrixDataArray<2, 4, 8, f32> {
    MatrixDataArray::new([0.0; 8])
}

pub fn zero_4x2() -> MatrixDataArray<4, 2, 8, f32> {
    MatrixDataArray::new([0.0; 8])
}

pub fn zero_4x3() -> MatrixDataArray<4, 3, 12, f32> {
    MatrixDataArray::new([0.0; 12])
}

// ---- Random matrix strategies (concrete sizes) ----

pub fn random_matrix_2x2() -> impl Strategy<Value = MatrixDataArray<2, 2, 4, f32>> {
    finite_vec(4).prop_map(|v| {
        let mut data = [0.0f32; 4];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_3x3() -> impl Strategy<Value = MatrixDataArray<3, 3, 9, f32>> {
    finite_vec(9).prop_map(|v| {
        let mut data = [0.0f32; 9];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_2x3() -> impl Strategy<Value = MatrixDataArray<2, 3, 6, f32>> {
    finite_vec(6).prop_map(|v| {
        let mut data = [0.0f32; 6];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_3x2() -> impl Strategy<Value = MatrixDataArray<3, 2, 6, f32>> {
    finite_vec(6).prop_map(|v| {
        let mut data = [0.0f32; 6];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_3x4() -> impl Strategy<Value = MatrixDataArray<3, 4, 12, f32>> {
    finite_vec(12).prop_map(|v| {
        let mut data = [0.0f32; 12];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_4x4() -> impl Strategy<Value = MatrixDataArray<4, 4, 16, f32>> {
    finite_vec(16).prop_map(|v| {
        let mut data = [0.0f32; 16];
        data.copy_from_slice(&v);
        MatrixDataArray::new(data)
    })
}

pub fn random_matrix_boxed_3x3() -> impl Strategy<Value = MatrixDataBoxed<3, 3, f32>> {
    finite_vec(9).prop_map(MatrixDataBoxed::new)
}

// ---- SPD matrix strategies (concrete sizes) ----

/// Generates a 2x2 SPD matrix via L*L^T + eps*I.
pub fn spd_matrix_2x2() -> impl Strategy<Value = MatrixDataArray<2, 2, 4, f32>> {
    (
        proptest::collection::vec(-10f32..10f32, 1..=1),
        proptest::collection::vec(-10f32..10f32, 2..=2),
    )
        .prop_map(|(offdiag, diag)| {
            let l_data = [0.5 + diag[0].abs(), 0.0, offdiag[0], 0.5 + diag[1].abs()];
            let l = MatrixDataArray::<2, 2, 4, f32>::new(l_data);
            let mut m = zero_2x2();
            l.mult_transb(&l, &mut m);
            m.as_mut_slice()[0] += 1e-3;
            m.as_mut_slice()[3] += 1e-3;
            m
        })
}

/// Generates a 3x3 SPD matrix via L*L^T + eps*I.
pub fn spd_matrix_3x3() -> impl Strategy<Value = MatrixDataArray<3, 3, 9, f32>> {
    (
        proptest::collection::vec(-10f32..10f32, 3..=3),
        proptest::collection::vec(-10f32..10f32, 3..=3),
    )
        .prop_map(|(offdiag, diag)| {
            let mut l_data = [0.0f32; 9];
            l_data[0] = 0.5 + diag[0].abs();
            l_data[3] = offdiag[0];
            l_data[4] = 0.5 + diag[1].abs();
            l_data[6] = offdiag[1];
            l_data[7] = offdiag[2];
            l_data[8] = 0.5 + diag[2].abs();
            let l = MatrixDataArray::<3, 3, 9, f32>::new(l_data);
            let mut m = zero_3x3();
            l.mult_transb(&l, &mut m);
            for i in 0..3 {
                m.as_mut_slice()[i * 3 + i] += 1e-3;
            }
            m
        })
}

/// Generates a 4x4 SPD matrix via L*L^T + eps*I.
pub fn spd_matrix_4x4() -> impl Strategy<Value = MatrixDataArray<4, 4, 16, f32>> {
    (
        proptest::collection::vec(-10f32..10f32, 6..=6),
        proptest::collection::vec(-10f32..10f32, 4..=4),
    )
        .prop_map(|(offdiag, diag)| {
            let mut l_data = [0.0f32; 16];
            l_data[0] = 0.5 + diag[0].abs();
            l_data[4] = offdiag[0];
            l_data[5] = 0.5 + diag[1].abs();
            l_data[8] = offdiag[1];
            l_data[9] = offdiag[2];
            l_data[10] = 0.5 + diag[2].abs();
            l_data[12] = offdiag[3];
            l_data[13] = offdiag[4];
            l_data[14] = offdiag[5];
            l_data[15] = 0.5 + diag[3].abs();
            let l = MatrixDataArray::<4, 4, 16, f32>::new(l_data);
            let mut m = zero_4x4();
            l.mult_transb(&l, &mut m);
            for i in 0..4 {
                m.as_mut_slice()[i * 4 + i] += 1e-3;
            }
            m
        })
}

// ---- Reference implementations ----

pub fn ref_mult(a: &[f32], b: &[f32], rows_a: usize, cols_a: usize, cols_b: usize) -> Vec<f32> {
    let rows_b = cols_a;
    let mut c = vec![0.0f32; rows_a * cols_b];
    for i in 0..rows_a {
        for j in 0..cols_b {
            let mut sum = 0.0f32;
            for k in 0..rows_b {
                sum += a[i * cols_a + k] * b[k * cols_b + j];
            }
            c[i * cols_b + j] = sum;
        }
    }
    c
}

pub fn ref_add(a: &[f32], b: &[f32], len: usize) -> Vec<f32> {
    let mut c = vec![0.0f32; len];
    for i in 0..len {
        c[i] = a[i] + b[i];
    }
    c
}

pub fn ref_transpose(a: &[f32], rows: usize, cols: usize) -> Vec<f32> {
    let mut t = vec![0.0f32; rows * cols];
    for i in 0..rows {
        for j in 0..cols {
            t[j * rows + i] = a[i * cols + j];
        }
    }
    t
}

// ---- Assertions ----

pub fn assert_matrix_close(a: &[f32], b: &[f32], eps: f32) {
    assert_eq!(a.len(), b.len(), "matrix length mismatch");
    for (i, (&av, &bv)) in a.iter().zip(b.iter()).enumerate() {
        let diff = (av - bv).abs();
        let max_abs = av.abs().max(bv.abs());
        let tol = eps + eps * max_abs;
        assert!(
            diff <= tol,
            "element {} differs: {} vs {} (diff={}, tol={})",
            i,
            av,
            bv,
            diff,
            tol
        );
    }
}

pub fn is_symmetric(data: &[f32], n: usize, eps: f32) -> bool {
    for i in 0..n {
        for j in (i + 1)..n {
            let diff = (data[i * n + j] - data[j * n + i]).abs();
            if diff > eps {
                return false;
            }
        }
    }
    true
}