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88 lines
2.7 KiB
88 lines
2.7 KiB
export default class MonotonicInterpolant {
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constructor(xs, ys) {
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const { length } = xs;
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// Rearrange xs and ys so that xs is sorted
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const indexes = [];
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for (let i = 0; i < length; i++) {
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indexes.push(i);
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}
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indexes.sort((a, b) => (xs[a] < xs[b] ? -1 : 1));
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// Get consecutive differences and slopes
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const dys = [];
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const dxs = [];
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const ms = [];
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let dx;
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let dy;
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for (let i = 0; i < length - 1; i++) {
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dx = xs[i + 1] - xs[i];
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dy = ys[i + 1] - ys[i];
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dxs.push(dx);
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dys.push(dy);
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ms.push(dy / dx);
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}
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// Get degree-1 coefficients
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const c1s = [ms[0]];
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for (let i = 0; i < dxs.length - 1; i++) {
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const m2 = ms[i];
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const mNext = ms[i + 1];
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if (m2 * mNext <= 0) {
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c1s.push(0);
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}
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else {
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dx = dxs[i];
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const dxNext = dxs[i + 1];
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const common = dx + dxNext;
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c1s.push((3 * common) / ((common + dxNext) / m2 + (common + dx) / mNext));
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}
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}
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c1s.push(ms[ms.length - 1]);
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// Get degree-2 and degree-3 coefficients
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const c2s = [];
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const c3s = [];
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let m;
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for (let i = 0; i < c1s.length - 1; i++) {
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m = ms[i];
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const c1 = c1s[i];
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const invDx = 1 / dxs[i];
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const common = c1 + c1s[i + 1] - m - m;
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c2s.push((m - c1 - common) * invDx);
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c3s.push(common * invDx * invDx);
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}
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this.xs = xs;
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this.ys = ys;
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this.c1s = c1s;
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this.c2s = c2s;
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this.c3s = c3s;
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}
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interpolate(x) {
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const { xs, ys, c1s, c2s, c3s } = this;
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// The rightmost point in the dataset should give an exact result
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let i = xs.length - 1;
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if (x === xs[i]) {
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return ys[i];
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}
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// Search for the interval x is in, returning the corresponding y if x is one of the original xs
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let low = 0;
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let high = c3s.length - 1;
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let mid;
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while (low <= high) {
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mid = Math.floor(0.5 * (low + high));
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const xHere = xs[mid];
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if (xHere < x) {
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low = mid + 1;
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}
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else if (xHere > x) {
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high = mid - 1;
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}
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else {
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return ys[mid];
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}
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}
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i = Math.max(0, high);
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// Interpolate
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const diff = x - xs[i];
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const diffSq = diff * diff;
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return ys[i] + c1s[i] * diff + c2s[i] * diffSq + c3s[i] * diff * diffSq;
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}
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}
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