72 lines
2.5 KiB
JavaScript
72 lines
2.5 KiB
JavaScript
module.exports = function(xs, ys) {
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var i, length = xs.length;
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// Deal with length issues
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if (length != ys.length) { throw 'Need an equal count of xs and ys.'; }
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if (length === 0) { return function(x) { return 0; }; }
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if (length === 1) {
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// Impl: Precomputing the result prevents problems if ys is mutated later and allows garbage collection of ys
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// Impl: Unary plus properly converts values to numbers
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var result = +ys[0];
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return function(x) { return result; };
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}
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// Rearrange xs and ys so that xs is sorted
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var indexes = [];
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for (i = 0; i < length; i++) { indexes.push(i); }
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indexes.sort(function(a, b) { return xs[a] < xs[b] ? -1 : 1; });
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var oldXs = xs, oldYs = ys;
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// Impl: Creating new arrays also prevents problems if the input arrays are mutated later
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xs = []; ys = [];
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// Impl: Unary plus properly converts values to numbers
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for (i = 0; i < length; i++) { xs.push(+oldXs[indexes[i]]); ys.push(+oldYs[indexes[i]]); }
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// Get consecutive differences and slopes
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var dys = [], dxs = [], ms = [];
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for (i = 0; i < length - 1; i++) {
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var dx = xs[i + 1] - xs[i], dy = ys[i + 1] - ys[i];
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dxs.push(dx); dys.push(dy); ms.push(dy / dx);
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}
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// Get degree-1 coefficients
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var c1s = [ms[0]];
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for (i = 0; i < dxs.length - 1; i++) {
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var m = ms[i], mNext = ms[i + 1];
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if (m * mNext <= 0) {
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c1s.push(0);
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} else {
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var dx = dxs[i], dxNext = dxs[i + 1], common = dx + dxNext;
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c1s.push(3 * common / ((common + dxNext) / m + (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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var c2s = [], c3s = [];
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for (i = 0; i < c1s.length - 1; i++) {
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var c1 = c1s[i], m = ms[i], invDx = 1 / dxs[i], common = c1 + c1s[i + 1] - m - m;
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c2s.push((m - c1 - common) * invDx); c3s.push(common * invDx * invDx);
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}
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// Return interpolant function
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return function(x) {
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// The rightmost point in the dataset should give an exact result
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var i = xs.length - 1;
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if (x == xs[i]) { return ys[i]; }
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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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var low = 0, mid, high = c3s.length - 1;
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while (low <= high) {
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mid = Math.floor(0.5 * (low + high));
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var xHere = xs[mid];
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if (xHere < x) { low = mid + 1; }
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else if (xHere > x) { high = mid - 1; }
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else { return ys[mid]; }
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}
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i = Math.max(0, high);
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// Interpolate
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var diff = x - xs[i], 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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}; |