LoessInterpolator { Double smoothOnePoint(final double x, final int left, final int right) { State state = computeNeighborhoodWeights(x, left, right); if (state == State.WEIGHTS_FAILED) return null; if (state == State.LINEAR_OK) updateWeights(x, left, right); double ys = 0.0; for (int i = left; i <= right; ++i) ys += fWeights[i] * fData[i]; return ys; } LoessInterpolator(int width, double[] data, double[] externalWeights);   }
@Test public void constantDataExtrapolatesConstantValues() { double[] data = createConstantDataArray(); for (int degree = 0; degree < 3; ++degree) { LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(7).setDegree(degree).interpolate(data); Double y = loess.smoothOnePoint(-100, 0, data.length - 1); assertNotNull(y); assertEquals("Bad value extrapolating left", data[0], y, 3.0e-9); y = loess.smoothOnePoint(1000.0, 0, data.length - 1); assertNotNull(y); assertEquals("Bad value extrapolating right", data[0], y, 3.0e-9); } }
@Test public void constantDataGivesConstantInterpolatedResults() { double[] data = createConstantDataArray(); for (int degree = 0; degree < 3; ++degree) { LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(7).setDegree(degree).interpolate(data); for (int i = 0; i < 99; ++i) { double x = i + 0.5; Double y = loess.smoothOnePoint(x, 0, data.length - 1); assertNotNull(y); assertEquals(String.format("Bad value at %d", i), data[i], y, 2.0e-11); } } }
@Test public void linearDataReturnsDataOnLine() { double[] data = createLinearDataArray(); LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(5).interpolate(data); for (int i = 0; i < data.length; ++i) { Double y = loess.smoothOnePoint(i, Math.max(0, i - 2), Math.min(i + 2, data.length - 1)); assertNotNull(y); assertEquals(String.format("Bad value at %d", i), data[i], y, 1.0e-8); } }
@Test public void linearDataExtrapolatesLinearValues() { double[] data = new double[100]; for (int i = 0; i < data.length; ++i) data[i] = -0.25 * i; final LoessInterpolator.Builder builder = new LoessInterpolator.Builder(); for (int degree = 1; degree < 3; ++degree) { LoessInterpolator loess = builder.setWidth(7).setDegree(degree).interpolate(data); Double y = loess.smoothOnePoint(-100, 0, data.length - 1); assertNotNull(y); assertEquals("Bad value extrapolating left", -0.25 * -100, y, 1.0e-8); y = loess.smoothOnePoint(1000.0, 0, data.length - 1); assertNotNull(y); assertEquals("Bad value extrapolating right", -0.25 * 1000, y, 1.0e-8); } }
@Test public void smoothingWithLargeWidthGivesLinearRegressionFit() { final double[] scatter100 = new double[] { 45.0641826945, 69.6998783993, 9.81903951235, -75.4079441854, 53.7430205615, 12.1359388898, 84.972441255, 194.467452805, 182.276035711, 128.161856616, 147.021732433, -40.6773185264, 41.1575417261, 111.04115761, 75.0179056538, 278.946359666, 93.3453251262, 103.779785975, 252.750915429, 252.636103208, 457.859165335, 143.021758047, 79.343240193, 280.969547174, 35.650257308, 157.656673765, 29.6984404613, 141.980264706, 263.465758806, 346.309482972, 330.044915761, 135.019120067, 211.801092316, 198.186646037, 206.088498967, 510.89412974, 332.076915483, 530.524264511, 298.21175481, 234.317252809, 573.836352739, 382.708235416, 340.090947574, 452.475239395, 576.134135134, 536.703405146, 545.033194307, 479.525083559, 368.551750848, 588.429801268, 528.672000843, 507.301073925, 432.749370682, 600.239380863, 567.328853536, 481.544306962, 510.42118889, 456.519971302, 565.839651322, 510.505759788, 503.2514057, 491.279917041, 642.319449309, 573.019058995, 574.709858012, 597.316826688, 602.361341448, 622.312708681, 506.669245531, 640.120714982, 699.793133288, 672.969830555, 656.645808774, 901.375994679, 573.903581507, 906.472771298, 719.604429516, 759.262994619, 786.970584025, 717.422383977, 899.007418786, 745.516032607, 748.049043698, 876.99080793, 810.985707949, 888.762045358, 947.030030816, 1007.48402395, 830.251382179, 921.078927761, 810.212273661, 926.740829016, 787.965498372, 944.230542154, 808.215987256, 1044.74526488, 866.568085766, 1068.6479395, 776.566771785, 1190.32090194 }; final double testSlope = 9.9564197212156671; final double testIntercept = -12.894457726954045; LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(1000000).interpolate(scatter100); double x = -5.0; while (x < 105.0) { Double y = loess.smoothOnePoint(x, 0, scatter100.length - 1); assertNotNull(y); assertEquals("Fit is on regression line", testSlope * x + testIntercept, y, 1.0e-8); x += 0.5; } }
@Test public void quadraticDataReturnsDataOnParabolaWithQuadraticInterpolation() { double[] data = createQuadraticDataArray(); LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(500000).setDegree(2).interpolate(data); for (int i = -100; i < data.length + 100; ++i) { Double y = loess.smoothOnePoint(i, 0, data.length - 1); assertNotNull(y); assertEquals(String.format("Bad value at %d", i), 3.7 - 0.25 * i + 0.7 * i * i, y, 1.0e-10); } }
@Test public void quadraticSmoothingWithLargeWidthGivesQuadraticFit() { final double[] data = { -10.073853166025, -47.578434834077, 9.969567309914, 13.607475640614, 26.336724862687, 20.24315196619, 8.522203731921, 40.879813612701, 20.348936031958, 34.851420490978, 23.004883874872, 54.308938782219, 15.829781536312, 48.719668671254, 8.119311766507, 1.318458454996, 47.063368648646, 53.312795063592, 83.823883969792, 59.110160316898, 77.957952679217, 27.187112586324, 58.265304568637, 58.51100724642, 66.008865742665, 72.672400306629, 81.552532336694, 49.790263630259, 97.490016206155, 100.088531750104, 67.022085750862, 101.72944638112, 76.523955444828, 109.879122870237, 103.156426935471, 97.440990018768, 96.326853943821, 100.002052764625, 97.901908920881, 81.907764661345, 104.608286357414, 70.096952411082, 87.900737922771, 123.466069349253, 86.36343272932, 96.898061547722, 105.2409423246, 84.473529980995, 87.589406762096, 107.145948743204, 103.924243272493, 86.327435697654, 122.078243981121, 82.664603304996, 90.610134349843, 94.333055790992, 130.280210790056, 106.70486524105, 76.506903917192, 81.412062643472, 93.910953769154, 106.832729589699, 115.642049987031, 84.975670522389, 97.761576968675, 111.855362368863, 72.717525044868, 81.957250239574, 61.808571079313, 70.85792217601, 40.898527454521, 97.782149960766, 97.913155063949, 101.714088071105, 86.227528826015, 67.255531559075, 80.13052355131, 74.988502831106, 96.560985475347, 65.285104731415, 62.127365337288, 28.616465130641, 82.768020843782, 52.291991098773, 64.194294668567, 38.225290216514, 20.662635351816, 26.091102513734, 24.5632772509, 23.281240785751, 23.800117109909, 52.816749904647, 33.332347686135, 28.2914005902, 14.683404049683, 53.212854193497, 1.829566520138, 18.404833513506, -9.019769796879, 9.006983482915 }; LoessInterpolator loess = new LoessInterpolator.Builder().setWidth(500000).setDegree(2).interpolate(data); for (int i = 0; i < data.length; ++i) { Double y = loess.smoothOnePoint(i, 0, data.length - 1); assertNotNull(y); double y0 = -0.042576513162 * i * i + 4.318963328925 * i - 9.80856523083; assertEquals(String.format("Bad value at %d", i), y0, y, 1.0e-8); } }