102 lines
2.3 KiB
TypeScript
102 lines
2.3 KiB
TypeScript
export class MonotonicInterpolant {
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private xs: any
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private ys: any
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private c1s: any
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private c2s: any
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private c3s: any
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public constructor(xs: number[], ys: number[]) {
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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] as number) < (xs[b] as number) ? -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] as number) - (xs[i] as number)
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dy = (ys[i + 1] as number) - (ys[i] as number)
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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] as number
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const mNext = ms[i + 1] as number
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if (m2 * mNext <= 0) {
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c1s.push(0)
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} else {
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dx = dxs[i] as number
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const dxNext = dxs[i + 1] as number
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const common = dx + dxNext
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c1s.push(
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(3 * common) / ((common + dxNext) / m2 + (common + dx) / mNext),
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)
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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] as number
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const c1 = c1s[i] as number
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const invDx = 1 / (dxs[i] as number)
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const common = c1 + (c1s[i + 1] as number) - 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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public interpolate(x: number): number {
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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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} else if (xHere > x) {
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high = mid - 1
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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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