public void LinearDataExtrapolatesLinearValues()
{
double[] data = new double[100];
for (int i = 0; i < data.Length; ++i)
{
data[i] = -0.25 * i;
}
var builder = new LoessInterpolatorBuilder();
for (int degree = 1; degree < 3; ++degree)
{
var loess = builder
.SetWidth(7)
.SetDegree(degree)
.Build(data);
var y = loess.Smooth(-100, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, -0.25 * -100, 1.0e-8);
y = loess.Smooth(1000.0, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, -0.25 * 1000, 1.0e-8);
}
}
public void TestDegreeBuilt()
{
var data = new[] { 1.0, 2.0, 3.0 };
{
var interpolator = new LoessInterpolatorBuilder()
.SetDegree(0)
.SetWidth(1)
.Build(data);
Assert.AreEqual(typeof(FlatLoessInterpolator), interpolator.GetType());
}
{
var interpolator = new LoessInterpolatorBuilder()
.SetDegree(1)
.SetWidth(1)
.Build(data);
Assert.AreEqual(typeof(LinearLoessInterpolator), interpolator.GetType());
}
{
var interpolator = new LoessInterpolatorBuilder()
.SetDegree(2)
.SetWidth(1)
.Build(data);
Assert.AreEqual(typeof(QuadraticLoessInterpolator), interpolator.GetType());
}
Assert.ThrowsException <ArgumentException>(() => {
var interpolator = new LoessInterpolatorBuilder()
.SetDegree(3)
.SetWidth(1)
.Build(data);
});
}
public void ConstantDataGivesConstantValuesAtNodes()
{
double[] data = CreateConstantDataArray();
for (int degree = 0; degree < 3; ++degree)
{
var loess = new LoessInterpolatorBuilder()
.SetWidth(7)
.SetDegree(degree)
.Build(data);
CheckFitToData(data, loess, 2.0e-11);
}
}
public void LinearDataReturnsDataOnLine2()
{
double[] data = CreateLinearDataArray();
var builder = new LoessInterpolatorBuilder();
for (int degree = 1; degree < 3; ++degree)
{
var loess = builder
.SetWidth(5000)
.SetDegree(degree)
.Build(data);
CheckFitToData(data, loess, 1.0e-12);
}
}
public void LinearDataReturnsDataOnLine()
{
double[] data = CreateLinearDataArray();
var loess = new LoessInterpolatorBuilder()
.SetWidth(5)
.Build(data);
for (int i = 0; i < data.Length; ++i)
{
var y = loess.Smooth(i, Math.Max(0, i - 2), Math.Min(i + 2, data.Length - 1));
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, data[i], 1.0e-8, $"Bad value at {i}.");
}
}
public void QuadraticDataReturnsDataOnParabolaWithQuadraticInterpolation()
{
double[] data = CreateQuadraticDataArray();
var loess = new LoessInterpolatorBuilder()
.SetWidth(500000)
.SetDegree(2)
.Build(data);
for (int i = -100; i < data.Length + 100; ++i)
{
var y = loess.Smooth(i, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, 3.7 - 0.25 * i + 0.7 * i * i, 1.0e-10, $"Bad value at {i}.");
}
}
public void QuadraticSmoothingWithLargeWidthGivesQuadraticFit()
{
// Half-period of sine plus noise, generated in Python with
//
// >>> x = np.arange(0, 100)
// >>> y = 100 * np.sin(x * np.pi / 100.0)
// >>> y = y + 20*np.random.randn(100)
//
// Quadratic fit:
//
// >>> np.polyfit(x, y, 2)
// array([-0.042576513162, 4.318963328925, -9.80856523083 ])
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 };
var loess = new LoessInterpolatorBuilder()
.SetWidth(500000)
.SetDegree(2)
.Build(data);
for (int i = 0; i < data.Length; ++i)
{
var y = loess.Smooth(i, 0, data.Length - 1);
Assert.IsNotNull(y);
double y0 = -0.042576513162 * i * i + 4.318963328925 * i - 9.80856523083;
Assert.AreEqual(y.Value, y0, 1.0e-8, $"Bad value at {i}.");
}
}
public void SmoothingWithLargeWidthGivesLinearRegressionFit()
{
// 100 point sample of linear data plus noise generated in Python with
//
// x = np.arange(0, 100)
// y = 10.0 * x + 100.0*np.random.randn(100)
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 };
// Linear fit from Python
double testSlope = 9.9564197212156671;
double testIntercept = -12.894457726954045;
// Choose a loess width sufficiently large that tri-cube weights for all of the data will be 1.0.
var loess = new LoessInterpolatorBuilder()
.SetWidth(1000000)
.Build(scatter100);
double x = -5.0;
while (x < 105.0)
{
var y = loess.Smooth(x, 0, scatter100.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, testSlope * x + testIntercept, 1.0e-8);
x += 0.5;
}
}
public void ConstantDataGivesConstantInterpolatedResults()
{
double[] data = CreateConstantDataArray();
for (int degree = 0; degree < 3; ++degree)
{
var loess = new LoessInterpolatorBuilder()
.SetWidth(7)
.SetDegree(degree)
.Build(data);
for (int i = 0; i < 99; ++i)
{
double x = i + 0.5;
var y = loess.Smooth(x, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, data[i], 2.0e-11, $"Bad value at {i}.");
}
}
}
public void ConstantDataExtrapolatesConstantValues()
{
double[] data = CreateConstantDataArray();
for (int degree = 0; degree < 3; ++degree)
{
var loess = new LoessInterpolatorBuilder()
.SetWidth(7)
.SetDegree(degree)
.Build(data);
var y = loess.Smooth(-100, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, data[0], 3.0e-9);
y = loess.Smooth(1000.0, 0, data.Length - 1);
Assert.IsNotNull(y);
Assert.AreEqual(y.Value, data[0], 3.0e-9);
}
}
