182 lines
4.4 KiB
Rust
182 lines
4.4 KiB
Rust
//! 通用插值过程
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//!
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//! 原始 Fortran: interp.f
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//! 支持 (NPOL-1) 阶插值，可选对数插值
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use crate::state::MDEPTH;
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/// 通用插值过程
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///
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/// 对给定点进行 (NPOL-1) 阶拉格朗日插值
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///
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/// # 参数
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/// - `x`: 原始 x 坐标数组 (可能被修改)
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/// - `y`: 原始 y 值数组 (可能被修改)
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/// - `xx`: 新 x 坐标数组 (可能被修改)
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/// - `yy`: 输出的插值结果
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/// - `nx`: 原始数组大小
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/// - `nxx`: 新数组大小
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/// - `npol`: 插值阶数+1
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/// - `ilogx`: 1 表示对 x 取对数插值
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/// - `ilogy`: 1 表示对 y 取对数插值
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///
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/// # 说明
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/// - 当 NPOL <= 0 或 NX <= 0 时，直接复制数据
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/// - 对数插值会修改输入数组
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pub fn interp(
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x: &mut [f64],
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y: &mut [f64],
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xx: &mut [f64],
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yy: &mut [f64],
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nx: usize,
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nxx: usize,
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npol: i32,
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ilogx: i32,
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ilogy: i32,
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) {
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// 常量
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const LN10: f64 = 2.30258509299405;
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// 无效情况: 直接复制
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if npol <= 0 || nx == 0 {
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let n = if nxx >= nx { nxx } else { nx };
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for i in 0..n.min(MDEPTH) {
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if i < xx.len() && i < x.len() {
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xx[i] = x[i];
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}
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if i < yy.len() && i < y.len() {
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yy[i] = y[i];
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}
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}
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return;
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}
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// 对数插值预处理
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if ilogx > 0 {
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for i in 0..nx.min(x.len()) {
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x[i] = x[i].ln() / LN10; // log10
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}
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for i in 0..nxx.min(xx.len()) {
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xx[i] = xx[i].ln() / LN10; // log10
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}
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}
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if ilogy > 0 {
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for i in 0..nx.min(y.len()) {
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y[i] = y[i].ln() / LN10; // log10
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}
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}
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// 插值参数
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let nm = (npol + 1) as usize / 2;
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let nm1 = nm + 1;
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let nup = nx + nm1 - npol as usize;
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// 对每个目标点进行插值
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for id in 0..nxx {
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let xxx = xx[id];
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// 找到插值区间
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let mut i = nm1;
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while i <= nup && xxx > x[i - 1] {
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i += 1;
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}
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if i > nup {
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i = nup;
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}
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let j = i - nm;
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let jj = j + npol as usize - 1;
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// 拉格朗日插值
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let mut yyy = 0.0;
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for k in j..=jj {
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let mut t = 1.0;
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for m in j..=jj {
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if k != m {
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t *= (xxx - x[m - 1]) / (x[k - 1] - x[m - 1]);
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}
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}
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yyy += y[k - 1] * t;
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}
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yy[id] = yyy;
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}
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// 对数插值后处理: 恢复原值
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if ilogx > 0 {
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for i in 0..nx.min(x.len()) {
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x[i] = (x[i] * LN10).exp();
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}
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for i in 0..nxx.min(xx.len()) {
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xx[i] = (xx[i] * LN10).exp();
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}
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}
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if ilogy > 0 {
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for i in 0..nx.min(y.len()) {
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y[i] = (y[i] * LN10).exp();
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}
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for i in 0..nxx.min(yy.len()) {
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yy[i] = (yy[i] * LN10).exp();
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}
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_interp_linear() {
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// 线性函数 y = 2x
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let mut x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
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let mut y = vec![2.0, 4.0, 6.0, 8.0, 10.0];
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let mut xx = vec![1.5, 2.5, 3.5, 4.5];
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let mut yy = vec![0.0; 4];
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interp(
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&mut x, &mut y, &mut xx, &mut yy,
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5, 4, 2, 0, 0 // npol=2 (线性), 无对数
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);
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assert!((yy[0] - 3.0).abs() < 1e-10);
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assert!((yy[1] - 5.0).abs() < 1e-10);
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assert!((yy[2] - 7.0).abs() < 1e-10);
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assert!((yy[3] - 9.0).abs() < 1e-10);
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}
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#[test]
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fn test_interp_quadratic() {
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// 二次函数 y = x^2
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let mut x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
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let mut y = vec![1.0, 4.0, 9.0, 16.0, 25.0];
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let mut xx = vec![2.5];
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let mut yy = vec![0.0];
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interp(
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&mut x, &mut y, &mut xx, &mut yy,
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5, 1, 3, 0, 0 // npol=3 (二次)
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);
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// 2.5^2 = 6.25
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assert!((yy[0] - 6.25).abs() < 1e-10);
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}
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#[test]
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fn test_interp_log() {
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// 对数插值测试
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let mut x = vec![1.0, 10.0, 100.0, 1000.0];
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let mut y = vec![1.0, 2.0, 3.0, 4.0];
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let mut xx = vec![10.0_f64.sqrt()]; // sqrt(10)
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let mut yy = vec![0.0];
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interp(
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&mut x, &mut y, &mut xx, &mut yy,
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4, 1, 2, 1, 0 // 对数 x
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);
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// 在 log10 空间中，sqrt(10) ≈ 0.5，应该得到 1.5
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assert!((yy[0] - 1.5).abs() < 1e-10);
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}
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}
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