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