solvr 0.2.0

Advanced computing library for real-world problem solving - optimization, differential equations, interpolation, statistics, and more
Documentation 
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//! 1D interpolation generic implementation.
//!
//! Provides linear, nearest neighbor, and cubic interpolation for 1D data.
//! All computation uses tensor operations.
use crate::DType;

use crate::interpolate::error::InterpolateResult;
use crate::interpolate::traits::interp1d::InterpMethod;
use numr::ops::{CompareOps, ScalarOps, TensorOps};
use numr::runtime::{Runtime, RuntimeClient};
use numr::tensor::Tensor;

/// Evaluate 1D interpolation at new x coordinates.
///
/// Uses tensor operations for GPU-accelerated batch evaluation.
pub fn interp1d_evaluate<R, C>(
    client: &C,
    x: &Tensor<R>,
    y: &Tensor<R>,
    x_new: &Tensor<R>,
    method: InterpMethod,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: TensorOps<R> + ScalarOps<R> + CompareOps<R> + RuntimeClient<R>,
{
    match method {
        InterpMethod::Nearest => evaluate_nearest(client, x, y, x_new),
        InterpMethod::Linear => evaluate_linear(client, x, y, x_new),
        InterpMethod::Cubic => evaluate_cubic(client, x, y, x_new),
    }
}

/// Nearest neighbor interpolation using tensor ops.
fn evaluate_nearest<R, C>(
    client: &C,
    x: &Tensor<R>,
    y: &Tensor<R>,
    x_new: &Tensor<R>,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: TensorOps<R> + ScalarOps<R> + RuntimeClient<R>,
{
    let m = x_new.shape()[0];
    let n = x.shape()[0];
    let device = client.device();

    // Find interval indices using searchsorted
    let indices = client.searchsorted(x, x_new, false)?;

    // Create constant tensors for clamping
    let ones = Tensor::<R>::from_slice(&vec![1i64; m], &[m], device);
    let n_minus_1 = Tensor::<R>::from_slice(&vec![(n - 1) as i64; m], &[m], device);

    // Clamp indices to valid range [1, n-1], then get interval [0, n-2]
    let indices_clamped = client.maximum(&client.minimum(&indices, &n_minus_1)?, &ones)?;
    let idx = client.sub(&indices_clamped, &ones)?;
    let idx_plus_1 = client.add(&idx, &ones)?;

    // Get x values at interval endpoints
    let x0 = client.index_select(x, 0, &idx)?;
    let x1 = client.index_select(x, 0, &idx_plus_1)?;
    let y0 = client.index_select(y, 0, &idx)?;
    let y1 = client.index_select(y, 0, &idx_plus_1)?;

    // Compute distances: d0 = xi - x0, d1 = x1 - xi
    let d0 = client.sub(x_new, &x0)?;
    let d1 = client.sub(&x1, x_new)?;

    // Create indicator for which point is closer
    // indicator = 1 if d0 <= d1 (closer to x0), 0 otherwise
    // Use smooth indicator: (d1 - d0 + |d1 - d0|) / (2 * |d1 - d0| + eps)
    let diff = client.sub(&d1, &d0)?;
    let diff_abs = client.abs(&diff)?;
    let epsilon = Tensor::<R>::from_slice(&vec![1e-14; m], &[m], device);
    let sum = client.add(&diff, &diff_abs)?;
    let denom = client.add(&client.mul_scalar(&diff_abs, 2.0)?, &epsilon)?;
    let indicator = client.div(&sum, &denom)?; // ~1 if d0 <= d1

    // result = y0 * indicator + y1 * (1 - indicator)
    let ones_f64 = Tensor::<R>::from_slice(&vec![1.0; m], &[m], device);
    let one_minus_ind = client.sub(&ones_f64, &indicator)?;
    let term0 = client.mul(&y0, &indicator)?;
    let term1 = client.mul(&y1, &one_minus_ind)?;
    let result = client.add(&term0, &term1)?;

    Ok(result)
}

/// Linear interpolation using tensor ops.
fn evaluate_linear<R, C>(
    client: &C,
    x: &Tensor<R>,
    y: &Tensor<R>,
    x_new: &Tensor<R>,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: TensorOps<R> + ScalarOps<R> + RuntimeClient<R>,
{
    let m = x_new.shape()[0];
    let n = x.shape()[0];
    let device = client.device();

    // Find interval indices using searchsorted
    let indices = client.searchsorted(x, x_new, false)?;

    // Create constant tensors for clamping
    let ones = Tensor::<R>::from_slice(&vec![1i64; m], &[m], device);
    let n_minus_1 = Tensor::<R>::from_slice(&vec![(n - 1) as i64; m], &[m], device);

    // Clamp indices to valid range [1, n-1], then get interval [0, n-2]
    let indices_clamped = client.maximum(&client.minimum(&indices, &n_minus_1)?, &ones)?;
    let idx = client.sub(&indices_clamped, &ones)?;
    let idx_plus_1 = client.add(&idx, &ones)?;

    // Gather values at interval endpoints
    let x0 = client.index_select(x, 0, &idx)?;
    let x1 = client.index_select(x, 0, &idx_plus_1)?;
    let y0 = client.index_select(y, 0, &idx)?;
    let y1 = client.index_select(y, 0, &idx_plus_1)?;

    // Linear interpolation: y = y0 + (y1 - y0) * (x - x0) / (x1 - x0)
    let dx = client.sub(&x1, &x0)?;
    let dy = client.sub(&y1, &y0)?;
    let x_offset = client.sub(x_new, &x0)?;

    // t = (x - x0) / (x1 - x0)
    let epsilon = Tensor::<R>::from_slice(&vec![1e-14; m], &[m], device);
    let dx_safe = client.add(&dx, &epsilon)?;
    let t = client.div(&x_offset, &dx_safe)?;

    // result = y0 + dy * t
    let scaled_dy = client.mul(&dy, &t)?;
    let result = client.add(&y0, &scaled_dy)?;

    Ok(result)
}

/// Cubic interpolation using tensor ops (Catmull-Rom style).
fn evaluate_cubic<R, C>(
    client: &C,
    x: &Tensor<R>,
    y: &Tensor<R>,
    x_new: &Tensor<R>,
) -> InterpolateResult<Tensor<R>>
where
    R: Runtime<DType = DType>,
    C: TensorOps<R> + ScalarOps<R> + RuntimeClient<R>,
{
    let m = x_new.shape()[0];
    let n = x.shape()[0];
    let device = client.device();

    // Find interval indices using searchsorted
    let indices = client.searchsorted(x, x_new, false)?;

    // Create constant tensors
    let zeros_i64 = Tensor::<R>::from_slice(&vec![0i64; m], &[m], device);
    let ones_i64 = Tensor::<R>::from_slice(&vec![1i64; m], &[m], device);
    let n_minus_1 = Tensor::<R>::from_slice(&vec![(n - 1) as i64; m], &[m], device);

    // Clamp main indices to valid range [1, n-1], then get interval [0, n-2]
    let indices_clamped = client.maximum(&client.minimum(&indices, &n_minus_1)?, &ones_i64)?;
    let i1 = client.sub(&indices_clamped, &ones_i64)?; // Main interval start
    let i2 = client.add(&i1, &ones_i64)?; // Main interval end

    // Get 4-point stencil with clamping at boundaries
    // i0 = max(0, i1 - 1)
    let i1_minus_1 = client.sub(&i1, &ones_i64)?;
    let i0 = client.maximum(&i1_minus_1, &zeros_i64)?;

    // i3 = min(n-1, i2 + 1)
    let i2_plus_1 = client.add(&i2, &ones_i64)?;
    let i3 = client.minimum(&i2_plus_1, &n_minus_1)?;

    // Gather x and y values at all 4 points
    let x0 = client.index_select(x, 0, &i0)?;
    let x1 = client.index_select(x, 0, &i1)?;
    let x2 = client.index_select(x, 0, &i2)?;
    let x3 = client.index_select(x, 0, &i3)?;

    let y0 = client.index_select(y, 0, &i0)?;
    let y1 = client.index_select(y, 0, &i1)?;
    let y2 = client.index_select(y, 0, &i2)?;
    let y3 = client.index_select(y, 0, &i3)?;

    // Compute intervals
    let h1 = client.sub(&x2, &x1)?; // Main interval
    let h0 = client.sub(&x1, &x0)?; // Left interval
    let h2 = client.sub(&x3, &x2)?; // Right interval

    // Epsilon for safe division
    let epsilon = Tensor::<R>::from_slice(&vec![1e-14; m], &[m], device);
    let h1_safe = client.add(&h1, &epsilon)?;
    let h0_safe = client.add(&h0, &epsilon)?;
    let h2_safe = client.add(&h2, &epsilon)?;

    // Compute slopes for tangent estimation
    let slope_01 = client.div(&client.sub(&y1, &y0)?, &h0_safe)?;
    let slope_12 = client.div(&client.sub(&y2, &y1)?, &h1_safe)?;
    let slope_23 = client.div(&client.sub(&y3, &y2)?, &h2_safe)?;

    // Detect boundaries using interval widths (h0 ≈ 0 means left boundary, h2 ≈ 0 means right)
    // When i0 == i1 (clamped), x0 == x1, so h0 = 0
    // left_boundary_indicator ≈ 1 when h0 ≈ 0, ≈ 0 otherwise
    let ones_f64 = Tensor::<R>::from_slice(&vec![1.0; m], &[m], device);
    let half = Tensor::<R>::from_slice(&vec![0.5; m], &[m], device);

    // Smooth boundary indicator: 1 - h / (h + eps) ≈ 1 if h ≈ 0
    let h0_abs = client.abs(&h0)?;
    let h0_ratio = client.div(&h0_abs, &client.add(&h0_abs, &epsilon)?)?;
    let left_boundary = client.sub(&ones_f64, &h0_ratio)?;

    let h2_abs = client.abs(&h2)?;
    let h2_ratio = client.div(&h2_abs, &client.add(&h2_abs, &epsilon)?)?;
    let right_boundary = client.sub(&ones_f64, &h2_ratio)?;

    // m1 = left_boundary ? slope_12 : 0.5 * (slope_01 + slope_12)
    let avg_m1 = client.mul(&half, &client.add(&slope_01, &slope_12)?)?;
    let one_minus_left = client.sub(&ones_f64, &left_boundary)?;
    let m1 = client.add(
        &client.mul(&left_boundary, &slope_12)?,
        &client.mul(&one_minus_left, &avg_m1)?,
    )?;

    // m2 = right_boundary ? slope_12 : 0.5 * (slope_12 + slope_23)
    let avg_m2 = client.mul(&half, &client.add(&slope_12, &slope_23)?)?;
    let one_minus_right = client.sub(&ones_f64, &right_boundary)?;
    let m2 = client.add(
        &client.mul(&right_boundary, &slope_12)?,
        &client.mul(&one_minus_right, &avg_m2)?,
    )?;

    // Compute t = (x - x1) / h1
    let x_offset = client.sub(x_new, &x1)?;
    let t = client.div(&x_offset, &h1_safe)?;
    let t2 = client.mul(&t, &t)?;
    let t3 = client.mul(&t2, &t)?;

    // Hermite basis functions
    // h00 = 2t³ - 3t² + 1
    let h00 = client.add_scalar(
        &client.sub(&client.mul_scalar(&t3, 2.0)?, &client.mul_scalar(&t2, 3.0)?)?,
        1.0,
    )?;

    // h10 = t³ - 2t² + t
    let h10 = client.add(&client.sub(&t3, &client.mul_scalar(&t2, 2.0)?)?, &t)?;

    // h01 = -2t³ + 3t²
    let h01 = client.add(
        &client.mul_scalar(&t3, -2.0)?,
        &client.mul_scalar(&t2, 3.0)?,
    )?;

    // h11 = t³ - t²
    let h11 = client.sub(&t3, &t2)?;

    // Cubic Hermite: p(t) = h00*y1 + h10*h1*m1 + h01*y2 + h11*h1*m2
    let term1 = client.mul(&h00, &y1)?;
    let term2 = client.mul(&h10, &client.mul(&h1, &m1)?)?;
    let term3 = client.mul(&h01, &y2)?;
    let term4 = client.mul(&h11, &client.mul(&h1, &m2)?)?;

    let result = client.add(&client.add(&term1, &term2)?, &client.add(&term3, &term4)?)?;

    Ok(result)
}

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

    fn setup() -> (CpuDevice, CpuClient) {
        let device = CpuDevice::new();
        let client = CpuClient::new(device.clone());
        (device, client)
    }

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

        let x = Tensor::<CpuRuntime>::from_slice(&[0.0, 1.0, 2.0, 3.0], &[4], &device);
        let y = Tensor::<CpuRuntime>::from_slice(&[0.0, 2.0, 4.0, 6.0], &[4], &device);

        let x_new = Tensor::<CpuRuntime>::from_slice(&[0.5, 1.5, 2.5], &[3], &device);
        let y_new = interp1d_evaluate(&client, &x, &y, &x_new, InterpMethod::Linear).unwrap();
        let y_result: Vec<f64> = y_new.to_vec();

        assert!((y_result[0] - 1.0).abs() < 1e-10);
        assert!((y_result[1] - 3.0).abs() < 1e-10);
        assert!((y_result[2] - 5.0).abs() < 1e-10);
    }
}