Fix w type 1 calculation of lagrange model (#1027)

Author: ishii-norimi

lib/model/lagrange.js

@@ -55,10 +55,16 @@ export default class LagrangeInterpolation {
 		const w = x.map((d, j) => 1 / x.reduce((p, v, i) => (i === j ? p : p * (d - v)), 1))
 		if (this._w_type === 1) {
 			return target.map(t => {
-				const l = x.reduce((p, k) => p * (t - k), 1)
-				return x.reduce((s, d, j) => {
-					return s + (y[j] * l * w[j]) / (t - d + 1.0e-8)
-				}, 0)
+				let l = 1
+				let v = 0
+				for (let i = 0; i < x.length; i++) {
+					if (t === x[i]) {
+						return y[i]
+					}
+					l *= t - x[i]
+					v += (y[i] * w[i]) / (t - x[i])
+				}
+				return l * v
 			})
 		} else {
 			return target.map(t => {

tests/lib/model/lagrange.test.js

@@ -23,3 +23,25 @@ test.each([undefined, '', 'weighted', 'newton'])('interpolation %s', { retry: 3
 	const err = rmse(y0, x0.map(Math.sin))
 	expect(err).toBeLessThan(0.1)
 })
+
+test('interpolation w type 1', () => {
+	const model = new LagrangeInterpolation()
+	model._w_type = 1
+	const x = Matrix.random(20, 1, -2, 2).value
+	const t = []
+	for (let i = 0; i < x.length; i++) {
+		t[i] = Math.sin(x[i])
+	}
+	model.fit(x, t)
+
+	const y = model.predict(x)
+	expect(y).toHaveLength(x.length)
+	for (let i = 0; i < y.length; i++) {
+		expect(y[i]).toBeCloseTo(t[i])
+	}
+
+	const x0 = Matrix.random(100, 1, -2, 2).value
+	const y0 = model.predict(x0)
+	const err = rmse(y0, x0.map(Math.sin))
+	expect(err).toBeLessThan(0.1)
+})