hologram 0.1.1

Interpolation library with multipurpose Radial Basis Function (RBF).
Documentation 
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use crate::numeric::Numeric;

#[cfg(any(feature = "openblas", feature = "intel-mkl"))]
use ndarray::{Array1, Array2};
#[cfg(any(feature = "openblas", feature = "intel-mkl"))]
use ndarray_linalg::Solve;

pub fn lu_linear_solver<T>(mat: &[Vec<f64>], rhs: &[T]) -> Result<Vec<T>, String>
where
    T: Numeric,
{
    let mat_rows = mat.len();

    if mat_rows != rhs.len() {
        return Err(String::from(
            "Incompatible design matrix and right-hand side sizes!",
        ));
    }

    let (lu, p) = lu_decomposition(mat)?;

    // Forward substitution: Solve Ly = Pb
    let mut y = T::zeros(mat_rows, &rhs[p[0]]);
    y[0] = rhs[p[0]].subtract(&T::zero(&rhs[p[0]]));

    for i in 1..mat_rows {
        let sum = T::sum((0..i).map(|j| y[j].multiply_scalar(lu[i][j])));
        y[i] = rhs[p[i]].subtract(&sum);
    }

    // Backward substitution: Solve Ux = y
    let mut x = T::zeros(mat_rows, &y[mat_rows - 1]);
    x[mat_rows - 1] = y[mat_rows - 1].divide_scalar(lu[mat_rows - 1][mat_rows - 1]);

    for i in (0..mat_rows - 1).rev() {
        let sum = T::sum((i + 1..mat_rows).map(|j| x[j].multiply_scalar(lu[i][j])));
        x[i] = y[i].subtract(&sum).divide_scalar(lu[i][i]);

        if x[i].is_instance_nan() {
            return Err(format!(
                "NaN detected in backward substitution at index {}",
                i
            ));
        }
    }

    Ok(x)
}

/// Performs LU decomposition with partial pivoting on a given square matrix.
/// The function decomposes a square matrix `mat` into its lower triangular
/// (L) and upper triangular (U) components, along with a permutation vector `p`
/// to handle row swaps due to partial pivoting.
///
/// # Arguments
/// * `mat` - A reference to a square matrix.
///
/// # Returns
/// A tuple of `lu` and `p` as `Ok((lu, p))`
/// - `lu` is a matrix where the diagonal and above contain elements of U,
///                       and below the diagonal contains elements of L.
/// - `p` is a permutation vector, representing the row swaps applied to `mat`.
///
/// Or an `Err(String)` if the decomposition fails, such as encountering a zero pivot.
pub fn lu_decomposition(mat: &[Vec<f64>]) -> Result<(Vec<Vec<f64>>, Vec<usize>), String> {
    let mut lu = mat.to_vec();
    let mut p = (0..mat.len()).collect::<Vec<usize>>();

    for k in 0..mat.len() - 1 {
        let mut max_row = k;
        for i in k + 1..mat.len() {
            if lu[i][k].abs() > lu[max_row][k].abs() {
                max_row = i;
            }
        }
        if lu[max_row][k] == 0.0 {
            return Err(String::from("Zero obtained in LU[max_row][k]!"));
        }
        if max_row != k {
            lu.swap(k, max_row);
            p.swap(k, max_row);
        }
        for i in k + 1..mat.len() {
            let factor = lu[i][k] / lu[k][k];
            lu[i][k] = factor;
            for j in k + 1..mat.len() {
                lu[i][j] -= factor * lu[k][j];
            }
        }
    }

    Ok((lu, p))
}

/// Builds a design matrix based on two sets of input vectors and a kernel function.
///
/// # Arguments
/// * `x0`: A slice of vectors representing the first set of input data.
/// * `x1`: A slice of vectors representing the second set of input data.
/// * `kernel`: A function that takes two f64 values and returns a f64 value.
/// * `epsilon`: The kernel function's parameter.
///
/// # Returns
/// A vector of vectors representing the design matrix.
pub fn build_design_matrix<X>(
    x0: &[X],
    x1: &[X],
    kernel: &fn(f64, f64) -> f64,
    epsilon: f64,
) -> Vec<Vec<f64>>
where
    X: Numeric,
{
    (0..x0.len())
        .map(|i| {
            (0..x1.len())
                .map(|j| {
                    let dist = x0[i].squared_distance(&x1[j]).max(f64::EPSILON);
                    kernel(dist, epsilon)
                })
                .collect::<Vec<f64>>()
        })
        .collect::<Vec<Vec<f64>>>()
}

pub fn compute_determinant(mat: &[Vec<f64>]) -> f64 {
    let n = mat.len();

    if mat.iter().any(|row| row.len() != n) {
        panic!("Matrix must be square to compute determinant!");
    }

    // Perform LU decomposition
    let (lu, p) = match lu_decomposition(mat) {
        Ok((lu, p)) => (lu, p),
        Err(_) => return 0.0, // If decomposition fails, assume singular matrix
    };

    // Determinant is product of diagonal elements of U
    let mut det = 1.0;
    for i in 0..n {
        det *= lu[i][i]; // Product of diagonal elements
    }

    // Adjust sign based on number of row swaps in permutation vector `p`
    let num_swaps = permutation_parity(&p);
    if num_swaps % 2 != 0 {
        det = -det;
    }

    det
}

// Helper function to determine permutation parity (odd or even swaps)
fn permutation_parity(p: &[usize]) -> usize {
    let mut visited = vec![false; p.len()];
    let mut swaps = 0;

    for i in 0..p.len() {
        if visited[i] {
            continue;
        }

        let mut j = i;
        while !visited[j] {
            visited[j] = true;
            j = p[j];
            if j != i {
                swaps += 1;
            }
        }
    }

    swaps
}

#[cfg(any(feature = "openblas", feature = "intel-mkl"))]
pub fn ndarray_linear_solver<T: Numeric>(
    design_matrix: &[Vec<f64>],
    rhs: &[T],
) -> Result<Vec<T>, String> {
    let n = design_matrix.len();

    if rhs.len() != n {
        return Err(format!(
            "Design matrix and rhs have different lengths: {} vs {}",
            n,
            rhs.len()
        ));
    }

    // Convert design matrix to Array2
    let design_array =
        Array2::from_shape_vec((n, n), design_matrix.iter().flatten().copied().collect())
            .map_err(|e| format!("Design matrix conversion failed: {}", e))?;

    // Get dimension from first RHS element
    let dim = rhs[0].to_flattened().len();

    // Check all elements have consistent dimension
    for (i, val) in rhs.iter().enumerate() {
        if val.to_flattened().len() != dim {
            return Err(format!(
                "Inconsistent dimension at index {}: expected {}, got {}",
                i,
                dim,
                val.to_flattened().len()
            ));
        }
    }

    // Solve each dimension separately
    let mut weights_matrix = Array2::zeros((n, dim));
    for d in 0..dim {
        // Extract column from RHS
        let rhs_column: Array1<f64> = Array1::from_iter(rhs.iter().map(|x| x.to_flattened()[d]));

        // Solve for this dimension
        let w = design_array
            .solve(&rhs_column)
            .map_err(|e| format!("Linear solve failed for dimension {}: {}", d, e))?;

        weights_matrix.column_mut(d).assign(&w);
    }

    // Convert back to output type
    weights_matrix
        .outer_iter()
        .map(|row| T::from_flattened(row.to_vec()))
        .collect()
}