diffsol 0.12.4

A library for solving ordinary differential equations (ODEs) in 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

use super::Op;
use crate::{Matrix, Vector};
use num_traits::{One, Zero};

pub trait ConstantOp: Op {
    fn call_inplace(&self, t: Self::T, y: &mut Self::V);
    fn call(&self, t: Self::T) -> Self::V {
        let mut y = Self::V::zeros(self.nout(), self.context().clone());
        self.call_inplace(t, &mut y);
        y
    }
}

pub trait ConstantOpSens: ConstantOp {
    /// Compute the product of the gradient of F wrt a parameter vector p with a given vector `J_p(x, t) * v`.
    /// Note that the vector v is of size nparams() and the result is of size nstates().
    fn sens_mul_inplace(&self, _t: Self::T, _v: &Self::V, _y: &mut Self::V);

    /// Compute the gradient of the operator wrt a parameter vector p and store it in the matrix `y`.
    /// `y` should have been previously initialised using the output of [Self::sens_sparsity].
    /// The default implementation of this method computes the gradient using [Self::sens_mul_inplace],
    /// but it can be overriden for more efficient implementations.
    fn sens_inplace(&self, t: Self::T, y: &mut Self::M) {
        self._default_sens_inplace(t, y);
    }

    /// Default implementation of the gradient computation (this is the default for [Self::sens_inplace]).
    fn _default_sens_inplace(&self, t: Self::T, y: &mut Self::M) {
        let mut v = Self::V::zeros(self.nparams(), self.context().clone());
        let mut col = Self::V::zeros(self.nout(), self.context().clone());
        for j in 0..self.nparams() {
            v.set_index(j, Self::T::one());
            self.sens_mul_inplace(t, &v, &mut col);
            y.set_column(j, &col);
            v.set_index(j, Self::T::zero());
        }
    }

    /// Compute the gradient of the operator wrt a parameter vector p and return it.
    /// See [Self::sens_inplace] for a non-allocating version.
    fn sens(&self, t: Self::T) -> Self::M {
        let n = self.nstates();
        let m = self.nparams();
        let mut y = Self::M::new_from_sparsity(n, m, self.sens_sparsity(), self.context().clone());
        self.sens_inplace(t, &mut y);
        y
    }
    fn sens_sparsity(&self) -> Option<<Self::M as Matrix>::Sparsity> {
        None
    }
}

pub trait ConstantOpSensAdjoint: ConstantOp {
    /// Compute the product of the transpose of the gradient of F wrt a parameter vector p with a given vector `-J_p^T(x, t) * v`.
    /// Note that the vector v is of size nstates() and the result is of size nparam().
    fn sens_transpose_mul_inplace(&self, t: Self::T, v: &Self::V, y: &mut Self::V);

    /// Compute the negative transpose of the gradient of the operator wrt a parameter vector p and return it.
    /// See [Self::sens_adjoint_inplace] for a non-allocating version.
    fn sens_adjoint(&self, t: Self::T) -> Self::M {
        let n = self.nstates();
        let mut y =
            Self::M::new_from_sparsity(n, n, self.sens_adjoint_sparsity(), self.context().clone());
        self.sens_adjoint_inplace(t, &mut y);
        y
    }

    /// Compute the negative transpose of the gradient of the operator wrt a parameter vector p and store it in the matrix `y`.
    /// `y` should have been previously initialised using the output of [Self::sens_adjoint_sparsity].
    /// The default implementation of this method computes the gradient using [Self::sens_transpose_mul_inplace],
    /// but it can be overriden for more efficient implementations.
    fn sens_adjoint_inplace(&self, t: Self::T, y: &mut Self::M) {
        self._default_sens_adjoint_inplace(t, y);
    }

    /// Default implementation of the gradient computation (this is the default for [Self::sens_adjoint_inplace]).
    fn _default_sens_adjoint_inplace(&self, t: Self::T, y: &mut Self::M) {
        let mut v = Self::V::zeros(self.nstates(), self.context().clone());
        let mut col = Self::V::zeros(self.nout(), self.context().clone());
        for j in 0..self.nstates() {
            v.set_index(j, Self::T::one());
            self.sens_transpose_mul_inplace(t, &v, &mut col);
            y.set_column(j, &col);
            v.set_index(j, Self::T::zero());
        }
    }

    fn sens_adjoint_sparsity(&self) -> Option<<Self::M as Matrix>::Sparsity> {
        None
    }
}

#[cfg(test)]
mod tests {
    use crate::{
        context::nalgebra::NalgebraContext, matrix::dense_nalgebra_serial::NalgebraMat, ConstantOp,
        ConstantOpSens, ConstantOpSensAdjoint, DenseMatrix, Matrix, Op, Vector,
    };

    type M = NalgebraMat<f64>;

    struct FakeConstantOp {
        ctx: NalgebraContext,
    }

    impl FakeConstantOp {
        fn new() -> Self {
            Self {
                ctx: NalgebraContext,
            }
        }
    }

    impl Op for FakeConstantOp {
        type T = f64;
        type V = crate::NalgebraVec<f64>;
        type M = M;
        type C = NalgebraContext;

        fn context(&self) -> &Self::C {
            &self.ctx
        }
        fn nstates(&self) -> usize {
            2
        }
        fn nout(&self) -> usize {
            2
        }
        fn nparams(&self) -> usize {
            2
        }
    }

    impl ConstantOp for FakeConstantOp {
        fn call_inplace(&self, t: Self::T, y: &mut Self::V) {
            y.copy_from(&Self::V::from_vec(vec![1.0 + t, 2.0 - t], self.ctx));
        }
    }

    impl ConstantOpSens for FakeConstantOp {
        fn sens_mul_inplace(&self, _t: Self::T, v: &Self::V, y: &mut Self::V) {
            y.copy_from(&Self::V::from_vec(
                vec![
                    v.get_index(0) + 2.0 * v.get_index(1),
                    3.0 * v.get_index(0) - v.get_index(1),
                ],
                self.ctx,
            ));
        }
    }

    impl ConstantOpSensAdjoint for FakeConstantOp {
        fn sens_transpose_mul_inplace(&self, _t: Self::T, v: &Self::V, y: &mut Self::V) {
            y.copy_from(&Self::V::from_vec(
                vec![
                    -v.get_index(0) - 3.0 * v.get_index(1),
                    -2.0 * v.get_index(0) + v.get_index(1),
                ],
                self.ctx,
            ));
        }
    }

    #[test]
    fn constant_op_default_helpers_construct_expected_outputs() {
        let op = FakeConstantOp::new();
        let value = op.call(0.25);
        value.assert_eq_st(
            &crate::NalgebraVec::from_vec(vec![1.25, 1.75], NalgebraContext),
            1e-12,
        );

        let sens = op.sens(0.0);
        assert_eq!(sens.get_index(0, 0), 1.0);
        assert_eq!(sens.get_index(1, 0), 3.0);
        assert_eq!(sens.get_index(0, 1), 2.0);
        assert_eq!(sens.get_index(1, 1), -1.0);

        let mut sens_inplace = M::zeros(2, 2, NalgebraContext);
        op.sens_inplace(0.0, &mut sens_inplace);
        assert_eq!(sens_inplace.get_index(0, 0), 1.0);
        assert_eq!(sens_inplace.get_index(1, 0), 3.0);
        assert_eq!(sens_inplace.get_index(0, 1), 2.0);
        assert_eq!(sens_inplace.get_index(1, 1), -1.0);

        let sens_adj = op.sens_adjoint(0.0);
        assert_eq!(sens_adj.get_index(0, 0), -1.0);
        assert_eq!(sens_adj.get_index(1, 0), -2.0);
        assert_eq!(sens_adj.get_index(0, 1), -3.0);
        assert_eq!(sens_adj.get_index(1, 1), 1.0);

        let mut sens_adj_inplace = M::zeros(2, 2, NalgebraContext);
        op.sens_adjoint_inplace(0.0, &mut sens_adj_inplace);
        assert_eq!(sens_adj_inplace.get_index(0, 0), -1.0);
        assert_eq!(sens_adj_inplace.get_index(1, 0), -2.0);
        assert_eq!(sens_adj_inplace.get_index(0, 1), -3.0);
        assert_eq!(sens_adj_inplace.get_index(1, 1), 1.0);
    }
}