fdars-core 0.13.0

Functional Data Analysis algorithms 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

//! Basis-coefficient semimetric for functional data.
//!
//! Each curve is projected onto a chosen basis (B-spline or Fourier) and
//! the Euclidean distance between the resulting coefficient vectors is
//! used as a semimetric.

use crate::basis::{fdata_to_basis, ProjectionBasisType};
use crate::matrix::FdMatrix;

use super::{cross_distance_matrix, self_distance_matrix};

/// Euclidean distance between two rows of an `FdMatrix`.
#[inline]
fn row_euclidean(mat: &FdMatrix, i: usize, j: usize, ncols: usize) -> f64 {
    let mut sum = 0.0;
    for k in 0..ncols {
        let diff = mat[(i, k)] - mat[(j, k)];
        sum += diff * diff;
    }
    sum.sqrt()
}

/// Euclidean distance between row `i` of `mat1` and row `j` of `mat2`.
#[inline]
fn row_euclidean_cross(mat1: &FdMatrix, i: usize, mat2: &FdMatrix, j: usize, ncols: usize) -> f64 {
    let mut sum = 0.0;
    for k in 0..ncols {
        let diff = mat1[(i, k)] - mat2[(j, k)];
        sum += diff * diff;
    }
    sum.sqrt()
}

/// Compute the basis-coefficient semimetric self-distance matrix.
///
/// Each curve is projected onto `nbasis` functions of the specified
/// `basis_type`, and the Euclidean distance in coefficient space is
/// returned.
///
/// # Arguments
///
/// * `data` - Functional data matrix (`n x m`, column-major).
/// * `argvals` - Evaluation grid (length `m`).
/// * `nbasis` - Number of basis functions.
/// * `basis_type` - [`ProjectionBasisType::Bspline`] or [`ProjectionBasisType::Fourier`].
///
/// # Examples
///
/// ```
/// use fdars_core::matrix::FdMatrix;
/// use fdars_core::basis::ProjectionBasisType;
/// use fdars_core::metric::basis_coef_self_1d;
///
/// let argvals: Vec<f64> = (0..20).map(|i| i as f64 / 19.0).collect();
/// let data = FdMatrix::from_column_major(
///     (0..100).map(|i| (i as f64 * 0.1).sin()).collect(), 5, 20,
/// ).unwrap();
/// let dist = basis_coef_self_1d(&data, &argvals, 7, ProjectionBasisType::Fourier);
/// assert_eq!(dist.shape(), (5, 5));
/// assert!(dist[(0, 0)].abs() < 1e-10);
/// ```
pub fn basis_coef_self_1d(
    data: &FdMatrix,
    argvals: &[f64],
    nbasis: usize,
    basis_type: ProjectionBasisType,
) -> FdMatrix {
    let n = data.nrows();
    if n == 0 || data.ncols() == 0 {
        return FdMatrix::zeros(0, 0);
    }

    let proj = match fdata_to_basis(data, argvals, nbasis, basis_type) {
        Some(p) => p,
        None => return FdMatrix::zeros(0, 0),
    };
    let coefs = &proj.coefficients;
    let nb = proj.n_basis;

    self_distance_matrix(n, |i, j| row_euclidean(coefs, i, j, nb))
}

/// Compute the basis-coefficient semimetric cross-distance matrix.
///
/// Both datasets are independently projected onto the same basis
/// specification, and pairwise Euclidean distances in coefficient space
/// are computed.
///
/// # Arguments
///
/// * `data1` - First dataset (`n1 x m`, column-major).
/// * `data2` - Second dataset (`n2 x m`, column-major).
/// * `argvals` - Evaluation grid (length `m`).
/// * `nbasis` - Number of basis functions.
/// * `basis_type` - [`ProjectionBasisType::Bspline`] or [`ProjectionBasisType::Fourier`].
///
/// # Examples
///
/// ```
/// use fdars_core::matrix::FdMatrix;
/// use fdars_core::basis::ProjectionBasisType;
/// use fdars_core::metric::basis_coef_cross_1d;
///
/// let argvals: Vec<f64> = (0..20).map(|i| i as f64 / 19.0).collect();
/// let data1 = FdMatrix::from_column_major(
///     (0..60).map(|i| (i as f64 * 0.1).sin()).collect(), 3, 20,
/// ).unwrap();
/// let data2 = FdMatrix::from_column_major(
///     (0..40).map(|i| (i as f64 * 0.2).cos()).collect(), 2, 20,
/// ).unwrap();
/// let dist = basis_coef_cross_1d(&data1, &data2, &argvals, 7, ProjectionBasisType::Fourier);
/// assert_eq!(dist.shape(), (3, 2));
/// ```
pub fn basis_coef_cross_1d(
    data1: &FdMatrix,
    data2: &FdMatrix,
    argvals: &[f64],
    nbasis: usize,
    basis_type: ProjectionBasisType,
) -> FdMatrix {
    let n1 = data1.nrows();
    let n2 = data2.nrows();
    let m = data1.ncols();

    if n1 == 0 || n2 == 0 || m == 0 || data2.ncols() != m {
        return FdMatrix::zeros(0, 0);
    }

    let proj1 = match fdata_to_basis(data1, argvals, nbasis, basis_type) {
        Some(p) => p,
        None => return FdMatrix::zeros(0, 0),
    };
    let proj2 = match fdata_to_basis(data2, argvals, nbasis, basis_type) {
        Some(p) => p,
        None => return FdMatrix::zeros(0, 0),
    };
    let coefs1 = &proj1.coefficients;
    let coefs2 = &proj2.coefficients;
    let nb = proj1.n_basis.min(proj2.n_basis);

    cross_distance_matrix(n1, n2, |i, j| row_euclidean_cross(coefs1, i, coefs2, j, nb))
}