echidna 0.9.0

A high-performance automatic differentiation library for Rust
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

use rayon::prelude::*;

use crate::dual::Dual;
use crate::float::Float;

impl<F: Float> super::BytecodeTape<F> {
    /// Parallel gradient: forward + reverse using external buffers.
    ///
    /// Takes `&self` instead of `&mut self`, enabling shared access across threads.
    pub fn gradient_par(&self, inputs: &[F]) -> Vec<F> {
        let mut values_buf = Vec::new();
        self.forward_into(inputs, &mut values_buf);
        let adjoints = self.reverse_from(&values_buf, self.output_index);
        adjoints[..self.num_inputs as usize].to_vec()
    }

    /// Parallel Jacobian: one reverse sweep per output, parallelized.
    ///
    /// Returns `J[i][j] = ∂f_i/∂x_j`.
    pub fn jacobian_par(&self, inputs: &[F]) -> Vec<Vec<F>> {
        let mut values_buf = Vec::new();
        self.forward_into(inputs, &mut values_buf);

        let out_indices = self.all_output_indices();

        let ni = self.num_inputs as usize;
        out_indices
            .par_iter()
            .map(|&out_idx| {
                let adjoints = self.reverse_from(&values_buf, out_idx);
                adjoints[..ni].to_vec()
            })
            .collect()
    }

    /// Parallel Hessian: one HVP per column, parallelized over columns.
    ///
    /// Returns `(value, gradient, hessian)`.
    pub fn hessian_par(&self, x: &[F]) -> (F, Vec<F>, Vec<Vec<F>>) {
        let n = self.num_inputs as usize;
        assert_eq!(x.len(), n, "wrong number of inputs");

        // Compute gradient and value from column 0 (serial).
        let dual_input_buf: Vec<Dual<F>> = (0..n)
            .map(|i| Dual::new(x[i], if i == 0 { F::one() } else { F::zero() }))
            .collect();
        let mut dual_vals_buf = Vec::new();
        let mut adjoint_buf = Vec::new();
        self.forward_tangent_dual(&dual_input_buf, &mut dual_vals_buf);
        self.reverse_tangent_dual(&dual_vals_buf, &mut adjoint_buf);

        let value = dual_vals_buf[self.output_index as usize].re;
        let gradient: Vec<F> = (0..n).map(|i| adjoint_buf[i].re).collect();
        let col0: Vec<F> = (0..n).map(|i| adjoint_buf[i].eps).collect();

        // Parallelize remaining columns.
        let other_cols: Vec<Vec<F>> = (1..n)
            .into_par_iter()
            .map(|j| {
                let inputs: Vec<Dual<F>> = (0..n)
                    .map(|i| Dual::new(x[i], if i == j { F::one() } else { F::zero() }))
                    .collect();
                let mut dv = Vec::new();
                let mut ab = Vec::new();
                self.forward_tangent_dual(&inputs, &mut dv);
                self.reverse_tangent_dual(&dv, &mut ab);
                (0..n).map(|i| ab[i].eps).collect()
            })
            .collect();

        let mut hessian = vec![vec![F::zero(); n]; n];
        for i in 0..n {
            hessian[i][0] = col0[i];
        }
        for (j_minus_1, col) in other_cols.iter().enumerate() {
            let j = j_minus_1 + 1;
            for i in 0..n {
                hessian[i][j] = col[i];
            }
        }

        (value, gradient, hessian)
    }

    /// Parallel sparse Hessian: parallelized over colors.
    ///
    /// Returns `(value, gradient, pattern, hessian_values)`.
    pub fn sparse_hessian_par(
        &self,
        x: &[F],
    ) -> (F, Vec<F>, crate::sparse::SparsityPattern, Vec<F>) {
        let n = self.num_inputs as usize;
        assert_eq!(x.len(), n, "wrong number of inputs");

        let pattern = self.detect_sparsity();
        let (colors, num_colors) = crate::sparse::greedy_coloring(&pattern);

        // Compute value/gradient from color 0 (serial).
        let mut v0 = vec![F::zero(); n];
        for i in 0..n {
            v0[i] = if colors[i] == 0 { F::one() } else { F::zero() };
        }
        let di: Vec<Dual<F>> = (0..n).map(|i| Dual::new(x[i], v0[i])).collect();
        let mut dv = Vec::new();
        let mut ab = Vec::new();
        self.forward_tangent_dual(&di, &mut dv);
        self.reverse_tangent_dual(&dv, &mut ab);
        let value = dv[self.output_index as usize].re;
        let gradient: Vec<F> = (0..n).map(|i| ab[i].re).collect();

        // Collect all color results in parallel.
        let color_results: Vec<Vec<Dual<F>>> = (0..num_colors)
            .into_par_iter()
            .map(|color| {
                let mut v = vec![F::zero(); n];
                for i in 0..n {
                    v[i] = if colors[i] == color {
                        F::one()
                    } else {
                        F::zero()
                    };
                }
                let inputs: Vec<Dual<F>> = (0..n).map(|i| Dual::new(x[i], v[i])).collect();
                let mut dv_local = Vec::new();
                let mut ab_local = Vec::new();
                self.forward_tangent_dual(&inputs, &mut dv_local);
                self.reverse_tangent_dual(&dv_local, &mut ab_local);
                ab_local
            })
            .collect();

        let mut hessian_values = vec![F::zero(); pattern.nnz()];
        for (k, (&row, &col)) in pattern.rows.iter().zip(pattern.cols.iter()).enumerate() {
            let color = colors[col as usize] as usize;
            hessian_values[k] = color_results[color][row as usize].eps;
        }

        (value, gradient, pattern, hessian_values)
    }

    /// Parallel sparse Jacobian: parallelized over colors.
    ///
    /// Auto-selects forward (column compression) or reverse (row compression)
    /// based on `num_outputs` vs `num_inputs`.
    pub fn sparse_jacobian_par(
        &self,
        x: &[F],
    ) -> (Vec<F>, crate::sparse::JacobianSparsityPattern, Vec<F>) {
        let n = self.num_inputs as usize;
        assert_eq!(x.len(), n, "wrong number of inputs");

        let mut values_buf = Vec::new();
        self.forward_into(x, &mut values_buf);

        let out_indices = self.all_output_indices();
        let m = out_indices.len();
        let outputs: Vec<F> = out_indices
            .iter()
            .map(|&oi| values_buf[oi as usize])
            .collect();

        let jac_pattern = self.detect_jacobian_sparsity();
        let ni = self.num_inputs as usize;

        if m <= n {
            // Row compression (reverse mode)
            let (row_colors, num_colors) = crate::sparse::row_coloring(&jac_pattern);

            let color_results: Vec<Vec<F>> = (0..num_colors)
                .into_par_iter()
                .map(|color| {
                    let n_vars = self.num_variables as usize;
                    let mut adjoints = vec![F::zero(); n_vars];
                    for (i, &oi) in out_indices.iter().enumerate() {
                        if row_colors[i] == color {
                            adjoints[oi as usize] = F::one();
                        }
                    }

                    self.reverse_sweep_core(&mut adjoints, &values_buf, None);
                    adjoints[..ni].to_vec()
                })
                .collect();

            let mut jac_values = vec![F::zero(); jac_pattern.nnz()];
            for (k, (&row, &col)) in jac_pattern
                .rows
                .iter()
                .zip(jac_pattern.cols.iter())
                .enumerate()
            {
                let color = row_colors[row as usize] as usize;
                jac_values[k] = color_results[color][col as usize];
            }

            (outputs, jac_pattern, jac_values)
        } else {
            // Column compression (forward mode) — parallelize forward tangent sweeps
            let (col_colors, num_colors) = crate::sparse::column_coloring(&jac_pattern);

            let color_results: Vec<Vec<F>> = (0..num_colors)
                .into_par_iter()
                .map(|color| {
                    let dir: Vec<F> = (0..n)
                        .map(|i| {
                            if col_colors[i] == color {
                                F::one()
                            } else {
                                F::zero()
                            }
                        })
                        .collect();
                    let inputs: Vec<Dual<F>> = (0..n).map(|i| Dual::new(x[i], dir[i])).collect();
                    let mut dv = Vec::new();
                    self.forward_tangent_dual(&inputs, &mut dv);
                    out_indices.iter().map(|&oi| dv[oi as usize].eps).collect()
                })
                .collect();

            let mut jac_values = vec![F::zero(); jac_pattern.nnz()];
            for (k, (&row, &col)) in jac_pattern
                .rows
                .iter()
                .zip(jac_pattern.cols.iter())
                .enumerate()
            {
                let color = col_colors[col as usize] as usize;
                jac_values[k] = color_results[color][row as usize];
            }

            (outputs, jac_pattern, jac_values)
        }
    }

    /// Evaluate the gradient at multiple input points in parallel.
    ///
    /// Uses `forward_into` + `reverse_from` with per-thread buffers.
    pub fn gradient_batch_par(&self, inputs: &[&[F]]) -> Vec<Vec<F>> {
        let ni = self.num_inputs as usize;
        let out_idx = self.output_index;

        inputs
            .par_iter()
            .map(|x| {
                let mut values_buf = Vec::new();
                self.forward_into(x, &mut values_buf);
                let adjoints = self.reverse_from(&values_buf, out_idx);
                adjoints[..ni].to_vec()
            })
            .collect()
    }

    /// Compute Hessian at multiple input points in parallel.
    ///
    /// Returns `(value, gradient, hessian)` for each input point.
    pub fn hessian_batch_par(&self, inputs: &[&[F]]) -> Vec<(F, Vec<F>, Vec<Vec<F>>)> {
        inputs.par_iter().map(|x| self.hessian_par(x)).collect()
    }
}