solvr 0.2.0-beta.2

Advanced computing library for real-world problem solving - optimization, differential equations, interpolation, statistics, and more
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

//! CPU implementation of spectral PDE solvers.

use numr::runtime::cpu::{CpuClient, CpuRuntime};
use numr::tensor::Tensor;

use crate::pde::error::PdeResult;
use crate::pde::impl_generic::{spectral_1d_impl, spectral_2d_impl};
use crate::pde::traits::SpectralAlgorithms;
use crate::pde::types::{BoundarySpec, SpectralResult};

impl SpectralAlgorithms<CpuRuntime> for CpuClient {
    fn spectral_1d(
        &self,
        f_rhs: &Tensor<CpuRuntime>,
        q: Option<&Tensor<CpuRuntime>>,
        n: usize,
        boundary: &[BoundarySpec<CpuRuntime>],
    ) -> PdeResult<SpectralResult<CpuRuntime>> {
        spectral_1d_impl(self, f_rhs, q, n, boundary)
    }

    fn spectral_2d(
        &self,
        f_rhs: &Tensor<CpuRuntime>,
        nx: usize,
        ny: usize,
        boundary: &[BoundarySpec<CpuRuntime>],
    ) -> PdeResult<SpectralResult<CpuRuntime>> {
        spectral_2d_impl(self, f_rhs, nx, ny, boundary)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::pde::types::{BoundaryCondition, BoundarySide};
    use numr::runtime::cpu::CpuDevice;
    fn setup() -> (CpuClient, CpuDevice) {
        let device = CpuDevice::new();
        let client = CpuClient::new(device.clone());
        (client, device)
    }

    #[test]
    fn test_spectral_1d_polynomial() {
        let (client, device) = setup();

        // -u'' = 2 on [-1,1], u(-1) = u(1) = 0
        // Exact: u(x) = 1 - x^2
        let n = 16;
        let np1 = n + 1;

        let f_data = vec![2.0; np1];
        let f_rhs = Tensor::<CpuRuntime>::from_slice(&f_data, &[np1], &device);

        let boundary = vec![
            BoundarySpec {
                side: BoundarySide::Left,
                condition: BoundaryCondition::Dirichlet(Tensor::<CpuRuntime>::from_slice(
                    &[0.0],
                    &[1],
                    &device,
                )),
            },
            BoundarySpec {
                side: BoundarySide::Right,
                condition: BoundaryCondition::Dirichlet(Tensor::<CpuRuntime>::from_slice(
                    &[0.0],
                    &[1],
                    &device,
                )),
            },
        ];

        let result = client
            .spectral_1d(&f_rhs, None, n, &boundary)
            .expect("Spectral 1D solve failed");

        let sol: Vec<f64> = result.solution.to_vec();
        let nodes: Vec<f64> = result.nodes.to_vec();

        // Check interior points against exact solution u(x) = 1 - x^2
        for i in 1..n {
            let x = nodes[i];
            let exact = 1.0 - x * x;
            assert!(
                (sol[i] - exact).abs() < 1e-8,
                "Spectral 1D at x={}: numerical={}, exact={}, error={}",
                x,
                sol[i],
                exact,
                (sol[i] - exact).abs()
            );
        }
    }

    #[test]
    fn test_spectral_2d_poisson() {
        let (client, device) = setup();

        // -nabla^2 u = f on [-1,1]^2, u=0 on boundary
        let nx = 8;
        let ny = 8;
        let npx = nx + 1;
        let npy = ny + 1;
        let total = npx * npy;

        // Simple constant RHS
        let f_data = vec![1.0; total];
        let f_rhs = Tensor::<CpuRuntime>::from_slice(&f_data, &[total], &device);

        let boundary = vec![BoundarySpec {
            side: BoundarySide::All,
            condition: BoundaryCondition::Dirichlet(Tensor::<CpuRuntime>::from_slice(
                &[0.0],
                &[1],
                &device,
            )),
        }];

        let result = client
            .spectral_2d(&f_rhs, nx, ny, &boundary)
            .expect("Spectral 2D solve failed");

        let sol: Vec<f64> = result.solution.to_vec();

        // Boundary should be zero
        for j in 0..npy {
            assert!(sol[j].abs() < 1e-10, "Top boundary not zero");
            assert!(sol[nx * npy + j].abs() < 1e-10, "Bottom boundary not zero");
        }

        // Interior should be positive (Laplacian of positive function with zero BC)
        let center = (npx / 2) * npy + npy / 2;
        assert!(
            sol[center] > 0.0,
            "Center should be positive, got {}",
            sol[center]
        );
    }
}