pmcore/routines/evaluation/
ipm.rs

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
use crate::structs::psi::Psi;
use anyhow::bail;
use faer::linalg::triangular_solve::solve_lower_triangular_in_place;
use faer::linalg::triangular_solve::solve_upper_triangular_in_place;
use faer::{Col, Mat, Row};
use rayon::prelude::*;
/// Applies Burke's Interior Point Method (IPM) to solve a convex optimization problem.
///
/// The objective function to maximize is:
///     f(x) = Σ(log(Σ(ψ_ij * x_j)))   for i = 1 to n_sub
///
/// subject to:
///     1. x_j ≥ 0 for all j = 1 to n_point,
///     2. Σ(x_j) = 1,
///
/// where ψ is an n_sub×n_point matrix with non-negative entries and x is a probability vector.
///
/// # Arguments
///
/// * `psi` - A reference to a Psi structure containing the input matrix.
///
/// # Returns
///
/// On success, returns a tuple `(lam, obj)` where:
///   - `lam` is a faer::Col<f64> containing the computed probability vector,
///   - `obj` is the value of the objective function at the solution.
///
/// # Errors
///
/// This function returns an error if any step in the optimization (e.g. Cholesky factorization)
/// fails.
pub fn burke(psi: &Psi) -> anyhow::Result<(Col<f64>, f64)> {
    // Get the underlying matrix. (Assume psi.matrix() returns an ndarray-compatible matrix.)
    let mut psi = psi.matrix().to_owned();

    // Ensure all entries are finite and make them non-negative.
    psi.row_iter_mut()
        .try_for_each(|row| {
            row.iter_mut().try_for_each(|x| {
                if !x.is_finite() {
                    bail!("Input matrix must have finite entries")
                } else {
                    // Coerce negatives to non-negative (could alternatively return an error)
                    *x = x.abs();
                    Ok(())
                }
            })
        })
        .unwrap();

    // Let psi be of shape (n_sub, n_point)
    let (n_sub, n_point) = psi.shape();

    // Create unit vectors:
    // ecol: ones vector of length n_point (used for sums over points)
    // erow: ones row of length n_sub (used for sums over subproblems)
    let ecol: Col<f64> = Col::from_fn(n_point, |_| 1.0);
    let erow: Row<f64> = Row::from_fn(n_sub, |_| 1.0);

    // Compute plam = psi · ecol. This gives a column vector of length n_sub.
    let mut plam: Col<f64> = &psi * &ecol;
    let eps: f64 = 1e-8;
    let mut sig: f64 = 0.0;

    // Initialize lam (the variable we optimize) as a column vector of ones (length n_point).
    let mut lam = ecol.clone();

    // w = 1 ./ plam, elementwise.
    let mut w: Col<f64> = Col::from_fn(plam.nrows(), |i| 1.0 / plam.get(i));

    // ptw = ψᵀ · w, which will be a vector of length n_point.
    let mut ptw: Col<f64> = psi.transpose() * &w;

    // Use the maximum entry in ptw for scaling (the "shrink" factor).
    let ptw_max = ptw.iter().fold(f64::NEG_INFINITY, |acc, &x| x.max(acc));
    let shrink = 2.0 * ptw_max;
    lam *= shrink;
    plam *= shrink;
    w /= shrink;
    ptw /= shrink;

    // y = ecol - ptw (a vector of length n_point).
    let mut y: Col<f64> = &ecol - &ptw;
    // r = erow - (w .* plam) (elementwise product; r has length n_sub).
    let mut r: Col<f64> = Col::from_fn(n_sub, |i| erow.get(i) - w.get(i) * plam.get(i));
    let mut norm_r: f64 = r.iter().fold(0.0, |max, &val| max.max(val.abs()));

    // Compute the duality gap.
    let sum_log_plam: f64 = plam.iter().map(|x| x.ln()).sum();
    let sum_log_w: f64 = w.iter().map(|x| x.ln()).sum();
    let mut gap: f64 = (sum_log_w + sum_log_plam).abs() / (1.0 + sum_log_plam);

    // Compute the duality measure mu.
    let mut mu = lam.transpose() * &y / n_point as f64;

    let mut psi_inner: Mat<f64> = Mat::zeros(psi.nrows(), psi.ncols());

    let n_threads = faer::get_global_parallelism().degree();

    let rows = psi.nrows();

    let mut output: Vec<Mat<f64>> = (0..n_threads).map(|_| Mat::zeros(rows, rows)).collect();

    let mut h: Mat<f64> = Mat::zeros(rows, rows);

    while mu > eps || norm_r > eps || gap > eps {
        let smu = sig * mu;
        // inner = lam ./ y, elementwise.
        let inner = Col::from_fn(lam.nrows(), |i| lam.get(i) / y.get(i));
        // w_plam = plam ./ w, elementwise (length n_sub).
        let w_plam = Col::from_fn(plam.nrows(), |i| plam.get(i) / w.get(i));

        // Scale each column of psi by the corresponding element of 'inner'

        if psi.ncols() > n_threads * 128 {
            psi_inner
                .par_col_partition_mut(n_threads)
                .zip(psi.par_col_partition(n_threads))
                .zip(inner.par_partition(n_threads))
                .zip(output.par_iter_mut())
                .for_each(|(((mut psi_inner, psi), inner), output)| {
                    psi_inner
                        .as_mut()
                        .col_iter_mut()
                        .zip(psi.col_iter())
                        .zip(inner.iter())
                        .for_each(|((col, psi_col), inner_val)| {
                            col.iter_mut().zip(psi_col.iter()).for_each(|(x, psi_val)| {
                                *x = psi_val * inner_val;
                            });
                        });
                    faer::linalg::matmul::triangular::matmul(
                        output.as_mut(),
                        faer::linalg::matmul::triangular::BlockStructure::TriangularLower,
                        faer::Accum::Replace,
                        &psi_inner,
                        faer::linalg::matmul::triangular::BlockStructure::Rectangular,
                        psi.transpose(),
                        faer::linalg::matmul::triangular::BlockStructure::Rectangular,
                        1.0,
                        faer::Par::Seq,
                    );
                });

            let mut first_iter = true;
            for output in &output {
                if first_iter {
                    h.copy_from(output);
                    first_iter = false;
                } else {
                    h += output;
                }
            }
        } else {
            psi_inner
                .as_mut()
                .col_iter_mut()
                .zip(psi.col_iter())
                .zip(inner.iter())
                .for_each(|((col, psi_col), inner_val)| {
                    col.iter_mut().zip(psi_col.iter()).for_each(|(x, psi_val)| {
                        *x = psi_val * inner_val;
                    });
                });
            faer::linalg::matmul::triangular::matmul(
                h.as_mut(),
                faer::linalg::matmul::triangular::BlockStructure::TriangularLower,
                faer::Accum::Replace,
                &psi_inner,
                faer::linalg::matmul::triangular::BlockStructure::Rectangular,
                psi.transpose(),
                faer::linalg::matmul::triangular::BlockStructure::Rectangular,
                1.0,
                faer::Par::Seq,
            );
        }

        for i in 0..h.nrows() {
            h[(i, i)] += w_plam[i];
        }

        let uph = match h.llt(faer::Side::Lower) {
            Ok(llt) => llt,
            Err(_) => {
                bail!("Error during Cholesky decomposition")
            }
        };
        let uph = uph.L().transpose().to_owned();

        // smuyinv = smu * (ecol ./ y)
        let smuyinv: Col<f64> = Col::from_fn(ecol.nrows(), |i| smu * (ecol[i] / y[i]));

        // let smuyinv = smu * (&ecol / &y);
        // rhsdw = (erow ./ w) - (psi · smuyinv)
        let psi_dot_muyinv: Col<f64> = &psi * &smuyinv;

        let rhsdw: Row<f64> = Row::from_fn(erow.ncols(), |i| erow[i] / w[i] - psi_dot_muyinv[i]);

        //let rhsdw = (&erow / &w) - psi * &smuyinv;
        // Reshape rhsdw into a column vector.
        let mut dw = Mat::from_fn(rhsdw.ncols(), 1, |i, _j| *rhsdw.get(i));

        // let a = rhsdw
        //     .into_shape((n_sub, 1))
        //     .context("Failed to reshape rhsdw").unwrap();

        // Solve the triangular systems:

        solve_lower_triangular_in_place(uph.transpose().as_ref(), dw.as_mut(), faer::Par::rayon(0));

        solve_upper_triangular_in_place(uph.as_ref(), dw.as_mut(), faer::Par::rayon(0));

        // Extract dw (a column vector) from the solution.
        let dw = dw.col(0);

        // let dw = dw_aux.column(0);
        // Compute dy = - (ψᵀ · dw)
        let dy = -(psi.transpose() * dw);

        let inner_times_dy = Col::from_fn(ecol.nrows(), |i| inner[i] * dy[i]);

        let dlam: Row<f64> =
            Row::from_fn(ecol.nrows(), |i| smuyinv[i] - lam[i] - inner_times_dy[i]);
        // let dlam = &smuyinv - &lam - inner.transpose() * &dy;

        // Compute the primal step length alfpri.
        let ratio_dlam_lam = Row::from_fn(lam.nrows(), |i| dlam[i] / lam[i]);
        //let ratio_dlam_lam = &dlam / &lam;
        let min_ratio_dlam = ratio_dlam_lam.iter().cloned().fold(f64::INFINITY, f64::min);
        let mut alfpri: f64 = -1.0 / min_ratio_dlam.min(-0.5);
        alfpri = (0.99995 * alfpri).min(1.0);

        // Compute the dual step length alfdual.
        let ratio_dy_y = Row::from_fn(y.nrows(), |i| dy[i] / y[i]);
        // let ratio_dy_y = &dy / &y;
        let min_ratio_dy = ratio_dy_y.iter().cloned().fold(f64::INFINITY, f64::min);
        let ratio_dw_w = Row::from_fn(dw.nrows(), |i| dw[i] / w[i]);
        //let ratio_dw_w = &dw / &w;
        let min_ratio_dw = ratio_dw_w.iter().cloned().fold(f64::INFINITY, f64::min);
        let mut alfdual = -1.0 / min_ratio_dy.min(-0.5);
        alfdual = alfdual.min(-1.0 / min_ratio_dw.min(-0.5));
        alfdual = (0.99995 * alfdual).min(1.0);

        // Update the iterates.
        lam += alfpri * dlam.transpose();
        w += alfdual * dw;
        y += alfdual * &dy;

        mu = lam.transpose() * &y / n_point as f64;
        plam = &psi * &lam;

        // mu = lam.dot(&y) / n_point as f64;
        // plam = psi.dot(&lam);
        r = Col::from_fn(n_sub, |i| erow.get(i) - w.get(i) * plam.get(i));
        ptw -= alfdual * dy;

        norm_r = r.norm_max();
        let sum_log_plam: f64 = plam.iter().map(|x| x.ln()).sum();
        let sum_log_w: f64 = w.iter().map(|x| x.ln()).sum();
        gap = (sum_log_w + sum_log_plam).abs() / (1.0 + sum_log_plam);

        // Adjust sigma.
        if mu < eps && norm_r > eps {
            sig = 1.0;
        } else {
            let candidate1 = (1.0 - alfpri).powi(2);
            let candidate2 = (1.0 - alfdual).powi(2);
            let candidate3 = (norm_r - mu) / (norm_r + 100.0 * mu);
            sig = candidate1.max(candidate2).max(candidate3).min(0.3);
        }
    }
    // Scale lam.
    lam /= n_sub as f64;
    // Compute the objective function value: sum(ln(psi·lam)).
    let obj = (psi * &lam).iter().map(|x| x.ln()).sum();
    // Normalize lam to sum to 1.
    let lam_sum: f64 = lam.iter().sum();
    lam = &lam / lam_sum;

    Ok((lam, obj))
}

// fn pprint(x: &Mat<f64>, name: &str) {
//     println!("Matrix: {}", name);
//     x.row_iter().for_each(|row| {
//         println!("{:.unwrap()}", row);
//     });
// }