rustad 0.0.0

A rust Automatic Differentiation 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

// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2025 Bradley M. Bell
//
// Example Hessian
//
use rustad::{
    AD,
    ad_from_value,
    ad_from_vector,
    NumVec,
    start_recording,
    stop_recording,
};
//
// example_hessian
// Simple case where V = f32
fn example_hessian () {
    //
    type V     = f32;
    let nx     = 3;
    let trace  = false;
    //
    // x
    let x  : Vec<V> = vec![ 2.0 as V; nx ];
    //
    // ax
    let ax       = start_recording(x.clone());
    //
    // asum
    let mut asum : AD<V>  = ad_from_value(  0.0 as V );
    for j in 0 .. nx {
        let cubed  = &( &ax[j] * &ax[j] ) * &ax[j];
        asum      += &cubed;
    }
    //
    // f
    // f(x) = x[0] * x[0] * x[0] + ... + x[nx-1] * x[nx-1] * x[nx-1]
    let ay = vec![ asum ];
    let f  = stop_recording(ay);
    //
    // av
    let ax                     = start_recording(x);
    let mut av  : Vec< AD<V> > = Vec::new();
    f.forward_zero_ad(&mut av, ax, trace);
    //
    // g
    // g(x) = df/dx = [ 3 * x[0] * x[0], ..., 3 * x[nx-1] * x[nx-1] ]
    let dy  : Vec<V>  = vec![ 1.0 as V ];
    let ady           = ad_from_vector(dy);
    let adx           = f.reverse_one_ad(&av, ady, trace);
    let g             = stop_recording(adx);
    //
    // x
    // x[j] = j+2
    let mut x  : Vec<V> = Vec::new();
    for j in 0 .. nx {
        x.push( (j+2) as V );
    }
    //
    // v, y
    let mut v  : Vec<V> = Vec::new();
    let y               = g.forward_zero_value(&mut v, x, trace);
    for j in 0 .. nx {
        let check  = 3 * (j+2) * (j+2);
        assert_eq!( y[j], check as V );
    }
    //
    // dy
    // dy[i] = partial g[i] w.r.t x[j] = 6 * x[j]
    for j in 0 .. nx {
        let mut dx : Vec<V> = vec![ 0.0 as V; nx ];
        dx[j]               = 1.0 as V;
        let dy              = g.forward_one_value(&v, dx, trace);
        for i in 0 .. nx {
            if i == j {
                let check  = 6 * (j+2);
                assert_eq!( dy[i], check as V );
            } else {
                assert_eq!( dy[i],  0.0 as V );
            }
        }
    }
}
//
// example_numvec_hessian
// Same function where V = NumVec<f64>
fn example_numvec_hessian () {
    //
    type F     = f64;
    type V     = NumVec<F>;
    let nx     = 3;
    let trace  = false;
    //
    // x
    let mut x  : Vec<V> = Vec::new();
    for _j in 0 .. nx {
        x.push( NumVec::new( vec![ 2.0 as F ] ) );
    }
    //
    // ax
    let ax       = start_recording(x.clone());
    //
    // asum
    let mut asum : AD<V>  = ad_from_value(  NumVec::from( 0.0 as F ) );
    for j in 0 .. nx {
        let cubed  = &( &ax[j] * &ax[j] ) * &ax[j];
        asum      += &cubed;
    }
    //
    // f
    // f(x) = x[0] * x[0] * x[0] + ... + x[nx-1] * x[nx-1] * x[nx-1]
    let ay = vec![ asum ];
    let f  = stop_recording(ay);
    //
    // av
    let ax                     = start_recording(x);
    let mut av  : Vec< AD<V> > = Vec::new();
    f.forward_zero_ad(&mut av, ax, trace);
    //
    // g
    // g(x) = df/dx = [ 3 * x[0] * x[0], ..., 3 * x[nx-1] * x[nx-1] ]
    let dy  : Vec<V>  = vec![ NumVec::from( 1.0 as F ) ];
    let ady           = ad_from_vector(dy);
    let adx           = f.reverse_one_ad(&av, ady, trace);
    let g             = stop_recording(adx);
    //
    // x
    // x[j] = [ j+1, j+2 ]
    let mut x  : Vec<V> = Vec::new();
    for j in 0 .. nx {
        x.push( NumVec::new( vec![ (j+1) as F, (j+2) as F ] ) );
    }
    //
    // v, y
    let mut v  : Vec<V> = Vec::new();
    let y               = g.forward_zero_value(&mut v, x, trace);
    for j in 0 .. nx {
        //
        let check  = 3 * (j+1) * (j+1);
        assert_eq!( y[j].get(0), check as F );
        //
        let check  = 3 * (j+2) * (j+2);
        assert_eq!( y[j].get(1), check as F );
    }
    //
    // dy
    // dy[i] = partial g[i] w.r.t x[j] = 6 * x[j]
    for j in 0 .. nx {
        let mut dx : Vec<V> = vec![ NumVec::from( 0.0 as F ); nx ];
        dx[j]               = NumVec::from( 1.0 as F );
        let dy              = g.forward_one_value(&v, dx, trace);
        for i in 0 .. nx {
            if i == j {
                //
                let check  = 6 * (j+1);
                assert_eq!( dy[i].get(0), check as F );
                //
                let check  = 6 * (j+2);
                assert_eq!( dy[i].get(1), check as F );
            } else {
                for k in 0 .. dy[i].len() {
                    assert_eq!( dy[i].get(k) ,  0.0 as F );
                }
            }
        }
    }
}
fn main() {
    example_hessian();
    example_numvec_hessian();
}