numr 0.5.1

High-performance numerical computing with multi-backend GPU acceleration (CPU/CUDA/WebGPU)
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

//! Arithmetic operations on dual tensors

use crate::autograd::DualTensor;
use crate::error::Result;
use crate::ops::{BinaryOps, UnaryOps};
use crate::runtime::{Runtime, RuntimeClient};
use crate::tensor::Tensor;

/// Add two optional tangents: Some + Some = Some, Some + None = Some, None + None = None
pub(crate) fn add_tangents<R, C>(
    t1: Option<&Tensor<R>>,
    t2: Option<&Tensor<R>>,
    client: &C,
) -> Result<Option<Tensor<R>>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R>,
{
    match (t1, t2) {
        (Some(a), Some(b)) => Ok(Some(client.add(a, b)?)),
        (Some(a), None) => Ok(Some(a.clone())),
        (None, Some(b)) => Ok(Some(b.clone())),
        (None, None) => Ok(None),
    }
}

/// Subtract two optional tangents
pub(crate) fn sub_tangents<R, C>(
    t1: Option<&Tensor<R>>,
    t2: Option<&Tensor<R>>,
    client: &C,
) -> Result<Option<Tensor<R>>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R> + UnaryOps<R>,
{
    match (t1, t2) {
        (Some(a), Some(b)) => Ok(Some(client.sub(a, b)?)),
        (Some(a), None) => Ok(Some(a.clone())),
        (None, Some(b)) => Ok(Some(client.neg(b)?)),
        (None, None) => Ok(None),
    }
}

/// Dual addition: (a, ȧ) + (b, ḃ) = (a + b, ȧ + ḃ)
pub fn dual_add<R, C>(a: &DualTensor<R>, b: &DualTensor<R>, client: &C) -> Result<DualTensor<R>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R>,
{
    let primal = client.add(a.primal(), b.primal())?;
    let tangent = add_tangents(a.tangent(), b.tangent(), client)?;
    Ok(DualTensor::new(primal, tangent))
}

/// Dual subtraction: (a, ȧ) - (b, ḃ) = (a - b, ȧ - ḃ)
pub fn dual_sub<R, C>(a: &DualTensor<R>, b: &DualTensor<R>, client: &C) -> Result<DualTensor<R>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R> + UnaryOps<R>,
{
    let primal = client.sub(a.primal(), b.primal())?;
    let tangent = sub_tangents(a.tangent(), b.tangent(), client)?;
    Ok(DualTensor::new(primal, tangent))
}

/// Dual multiplication: (a, ȧ) * (b, ḃ) = (a*b, ȧ*b + a*ḃ)
///
/// Product rule: d(a*b) = da*b + a*db
pub fn dual_mul<R, C>(a: &DualTensor<R>, b: &DualTensor<R>, client: &C) -> Result<DualTensor<R>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R>,
{
    let primal = client.mul(a.primal(), b.primal())?;

    let tangent = match (a.tangent(), b.tangent()) {
        (Some(at), Some(bt)) => {
            let term1 = client.mul(at, b.primal())?;
            let term2 = client.mul(a.primal(), bt)?;
            Some(client.add(&term1, &term2)?)
        }
        (Some(at), None) => Some(client.mul(at, b.primal())?),
        (None, Some(bt)) => Some(client.mul(a.primal(), bt)?),
        (None, None) => None,
    };

    Ok(DualTensor::new(primal, tangent))
}

/// Dual division: (a, ȧ) / (b, ḃ) = (a/b, (ȧ*b - a*ḃ) / b²)
///
/// Quotient rule: d(a/b) = (da*b - a*db) / b²
pub fn dual_div<R, C>(a: &DualTensor<R>, b: &DualTensor<R>, client: &C) -> Result<DualTensor<R>>
where
    R: Runtime,
    C: RuntimeClient<R> + BinaryOps<R> + UnaryOps<R>,
{
    let primal = client.div(a.primal(), b.primal())?;

    let tangent = match (a.tangent(), b.tangent()) {
        (Some(at), Some(bt)) => {
            let term1 = client.mul(at, b.primal())?;
            let term2 = client.mul(a.primal(), bt)?;
            let numer = client.sub(&term1, &term2)?;
            let b_sq = client.mul(b.primal(), b.primal())?;
            Some(client.div(&numer, &b_sq)?)
        }
        (Some(at), None) => Some(client.div(at, b.primal())?),
        (None, Some(bt)) => {
            let term = client.mul(a.primal(), bt)?;
            let b_sq = client.mul(b.primal(), b.primal())?;
            let neg_term = client.neg(&term)?;
            Some(client.div(&neg_term, &b_sq)?)
        }
        (None, None) => None,
    };

    Ok(DualTensor::new(primal, tangent))
}

/// Dual negation: -(a, ȧ) = (-a, -ȧ)
pub fn dual_neg<R, C>(a: &DualTensor<R>, client: &C) -> Result<DualTensor<R>>
where
    R: Runtime,
    C: RuntimeClient<R> + UnaryOps<R>,
{
    let primal = client.neg(a.primal())?;
    let tangent = match a.tangent() {
        Some(t) => Some(client.neg(t)?),
        None => None,
    };
    Ok(DualTensor::new(primal, tangent))
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::runtime::cpu::{CpuClient, CpuDevice, CpuRuntime};

    fn setup() -> (CpuDevice, CpuClient) {
        let device = CpuDevice::new();
        let client = CpuRuntime::default_client(&device);
        (device, client)
    }

    #[test]
    fn test_dual_add() {
        let (device, client) = setup();

        let a_primal = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 2.0, 3.0], &[3], &device);
        let a_tangent = Tensor::<CpuRuntime>::from_slice(&[1.0f32, 0.0, 0.0], &[3], &device);
        let a = DualTensor::with_tangent(a_primal, a_tangent);

        let b_primal = Tensor::<CpuRuntime>::from_slice(&[4.0f32, 5.0, 6.0], &[3], &device);
        let b_tangent = Tensor::<CpuRuntime>::from_slice(&[0.0f32, 1.0, 0.0], &[3], &device);
        let b = DualTensor::with_tangent(b_primal, b_tangent);

        let c = dual_add(&a, &b, &client).unwrap();

        assert_eq!(c.primal().to_vec::<f32>(), [5.0, 7.0, 9.0]);
        assert_eq!(c.tangent().unwrap().to_vec::<f32>(), [1.0, 1.0, 0.0]);
    }

    #[test]
    fn test_dual_mul() {
        let (device, client) = setup();

        // f(x) = x² at x=3, tangent v=1 → df = 2*3*1 = 6
        let x_primal = Tensor::<CpuRuntime>::from_slice(&[3.0f32], &[1], &device);
        let x_tangent = Tensor::<CpuRuntime>::from_slice(&[1.0f32], &[1], &device);
        let x = DualTensor::with_tangent(x_primal, x_tangent);

        let y = dual_mul(&x, &x, &client).unwrap();

        assert_eq!(y.primal().to_vec::<f32>(), [9.0]);
        assert_eq!(y.tangent().unwrap().to_vec::<f32>(), [6.0]);
    }

    #[test]
    fn test_dual_constant_no_tangent() {
        let (device, client) = setup();

        let a = DualTensor::constant(Tensor::<CpuRuntime>::from_slice(
            &[1.0f32, 2.0],
            &[2],
            &device,
        ));
        let b = DualTensor::constant(Tensor::<CpuRuntime>::from_slice(
            &[3.0f32, 4.0],
            &[2],
            &device,
        ));

        let c = dual_add(&a, &b, &client).unwrap();

        assert_eq!(c.primal().to_vec::<f32>(), [4.0, 6.0]);
        assert!(!c.has_tangent());
    }
}