public void SSA_Correlation_Test01()
{
double[] ts = getAirPassengersData(); // Monthly time-series data
//embed
var ssa = new SSA(ts);
//embed
var x = ssa.Embedding(12);
//decompose
ssa.Decompose();
var w = ssa.WCorrelation(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 });
// ssa.PlotwCorrelation(w).Show();
for (int i = 0; i < w.GetLength(0); i++)
{
Assert.True(Math.Round(w[i, i], 5) == 1.0000);
}
}
public void SSA_Correlation_Test02()
{
//
var df = getMonthlyDeatsData(); // Monthly time-series data
//DataFrame.ToCsv("usa_deaths.csv",df);
var ts = df.ToSeries().Select(x => Convert.ToDouble(x));
//embed
var ssa = new SSA(ts);
//embed
var x = ssa.Embedding(24);
PlotMatrix(x).Show();
//decompose
ssa.Decompose();
var plt = new List <XPlot.Plotly.PlotlyChart> ();
foreach (var tm in ssa.EM)
{
plt.Add(PlotMatrix(tm.Value));
}
XPlot.Plotly.Chart.ShowAll(plt);
var f1 = ssa.Reconstruct(1);
var sct1 = new Scatter()
{
name = "Actual", x = Enumerable.Range(1, f1.Length), y = f1, mode = "line",
};
var chart1 = XPlot.Plotly.Chart.Plot <Trace>(new Trace[] { sct1 });
chart1.Show();
var ff = ssa.Forecast(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 }, 6, method: Forecasting.Rforecasing);
var scatters1 = new Scatter()
{
name = "Predicted", x = Enumerable.Range(1, ff.Length), y = ff, mode = "line",
};
var scatters2 = new Scatter()
{
name = "Actual", x = Enumerable.Range(1, ts.Count()), y = ts, mode = "line", fillcolor = "Blue"
};
var chart = XPlot.Plotly.Chart.Plot <Trace>(new Trace[] { scatters1, scatters2 });
// chart.Show();
// int i= 0;
// ssa.PlotComponents(12);
//
ssa.PlotSingularValues().Show();
//
var charts = ssa.PlotEigenPairs();
XPlot.Plotly.Chart.ShowAll(charts);
var w = ssa.WCorrelation(new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 });
ssa.PlotwCorrelation(w).Show();
}
//Test is based on Kaggle notebook and python implementation of SSA
public void SSATest_ToyTimeSeries01()
{
uint L = 70;
var n = 200;
var t = nc.GenerateIntSeries(0, n, 1).Select(x => Convert.ToDouble(x)).ToArray();
var temp1 = t.Substract(100.0).Pow(2);
var trend = temp1.Multiply(0.001);
var p1 = 20.0;
var p2 = 30.0;
var periodic1 = t.Multiply(2.0 * Math.PI / p1).Select(x => 2 * Math.Sin(x)).ToArray();
var periodic2 = t.Multiply(2.0 * Math.PI / p2).Select(x => 0.75 * Math.Sin(x)).ToArray();
var r = Daany.MathStuff.Constant.FixedRandomSeed = true;
//Since we cannot replicate random we take it from the source;
var noise = new double[] {
0.39293837, -0.42772133, -0.54629709, 0.10262954, 0.43893794,
-0.15378708, 0.9615284, 0.36965948, -0.0381362, -0.21576496,
-0.31364397, 0.45809941, -0.12285551, -0.88064421, -0.20391149,
0.47599081, -0.63501654, -0.64909649, 0.06310275, 0.06365517,
0.26880192, 0.69886359, 0.44891065, 0.22204702, 0.44488677,
-0.35408217, -0.27642269, -0.54347354, -0.41257191, 0.26195225,
-0.81579012, -0.13259765, -0.13827447, -0.0126298, -0.14833942,
-0.37547755, -0.14729739, 0.78677833, 0.88832004, 0.00367335,
0.2479059, -0.76876321, -0.36542904, -0.17034758, 0.73261832,
-0.49908927, -0.03393147, 0.97111957, 0.03897024, 0.22578905,
-0.75874267, 0.6526816, 0.20612026, 0.09013601, -0.31447233,
-0.39175842, -0.16595558, 0.36260153, 0.75091368, 0.02084467,
0.33862757, 0.17187311, 0.249807, 0.3493781, 0.68468488,
-0.83361002, 0.52736568, -0.51266725, -0.61155408, 0.14491391,
-0.80857497, 0.77065365, 0.25449794, 0.44683272, -0.96774159,
0.18886376, 0.11357038, -0.68208071, -0.69385897, 0.39105906,
-0.36246715, 0.38394059, 0.1087665, -0.22209885, 0.85026498,
0.68333999, -0.28520487, -0.91281707, -0.39046385, -0.20362864,
0.40991766, 0.99071696, -0.28817027, 0.52509563, 0.18635383,
0.3834036, -0.6977451, -0.20224741, -0.5182882, -0.31308797,
0.02625631, 0.3332491, -0.78818303, -0.7382101, -0.35603879,
0.32312867, 0.69301245, 0.10651469, 0.70890498, -0.23032438,
-0.36642421, -0.29147065, -0.65783634, 0.65822527, -0.32265831,
0.10474015, 0.15710294, 0.04306612, -0.99462387, 0.97669084,
0.81068315, -0.58472828, -0.41502117, 0.04002031, 0.80382275,
0.96726177, -0.48491587, 0.12871809, 0.61393737, -0.21125989,
0.46214607, -0.67786197, 0.20139714, 0.73172892, 0.96704322,
-0.84126842, -0.14330545, -0.59091428, -0.09872702, 0.09552715,
-0.81334658, -0.40627845, 0.85516848, 0.13800746, -0.085176,
0.50705198, 0.4837243, -0.90284193, 0.41739479, 0.6784867,
-0.66812423, 0.56199588, -0.42692677, -0.38706049, 0.33052293,
-0.77721566, 0.3297449, 0.77571359, 0.39262254, -0.11934425,
-0.12357123, 0.53019219, 0.131284, -0.83019167, 0.16534218,
0.62968741, -0.32586723, 0.85515316, 0.501434, 0.14812765,
0.50328798, -0.84170208, 0.71877815, 0.64300823, 0.81974332,
-0.7427376, -0.83643983, -0.72316885, -0.20124258, -0.15138628,
0.12443676, -0.7555129, -0.597201, 0.6232887, -0.06402485,
0.61587642, -0.98514724, 0.10318545, 0.8638643, 0.16435092,
-0.58780855, 0.43551512, -0.2420283, 0.33676789, -0.94136055,
0.27180072, -0.93560413, 0.48956131, -0.054174, -0.75649129
}; //nc.Rand(200, 0d,1d).Select(x=>(double)x).ToArray().Substract(0.5).Multiply(2);
//toy function
var f = trend.Add(periodic1.Add(periodic2).Add(noise));
//construct and decompose the time series.
var ssa = new SSA(f);
var em = ssa.Embedding(L);
ssa.Decompose();
//
var rTrend = ssa.Reconstruct(new int[] { 1, 2, 7 });
var rPer1 = ssa.Reconstruct(new int[] { 3, 4 });
var rPer2 = ssa.Reconstruct(new int[] { 5, 6 });
//Test reconstructed components
var testTrend = new double[]
{
1.12794763e+01, 1.11222948e+01, 1.10169536e+01, 1.08863655e+01,
1.06853902e+01, 1.03931489e+01, 1.00688871e+01, 9.68813466e+00,
9.28032006e+00, 8.87127467e+00, 8.47568239e+00, 8.10084450e+00,
7.74515661e+00, 7.42221287e+00, 7.14337328e+00, 6.90399929e+00,
6.69367292e+00, 6.52195814e+00, 6.38280912e+00, 6.26390036e+00,
6.15777257e+00, 6.05979873e+00, 5.95877019e+00, 5.84764883e+00,
5.72693409e+00, 5.59038886e+00, 5.44691196e+00, 5.29435361e+00,
5.13710987e+00, 4.97537350e+00, 4.80894410e+00, 4.65007745e+00,
4.49642526e+00, 4.34888363e+00, 4.21004949e+00, 4.08456981e+00,
3.97474947e+00, 3.87778441e+00, 3.78439997e+00, 3.69259752e+00,
3.60301152e+00, 3.51188069e+00, 3.42230365e+00, 3.32920568e+00,
3.23153049e+00, 3.12161348e+00, 3.00660092e+00, 2.88435775e+00,
2.75172388e+00, 2.61500546e+00, 2.47898457e+00, 2.35062530e+00,
2.22490094e+00, 2.10649533e+00, 1.99896709e+00, 1.90696915e+00,
1.82970455e+00, 1.76354502e+00, 1.70611509e+00, 1.65440231e+00,
1.60749250e+00, 1.56233040e+00, 1.51545707e+00, 1.46496011e+00,
1.40862476e+00, 1.34441016e+00, 1.27480842e+00, 1.19600873e+00,
1.11222764e+00, 1.02613571e+00, 9.44345682e-01, 8.66692292e-01,
7.87494873e-01, 7.11183116e-01, 6.38442347e-01, 5.75885062e-01,
5.19243744e-01, 4.69368629e-01, 4.28402880e-01, 3.96665950e-01,
3.68825607e-01, 3.44908911e-01, 3.21862795e-01, 2.98967748e-01,
2.76413872e-01, 2.49845487e-01, 2.18670761e-01, 1.86623538e-01,
1.57237382e-01, 1.29348700e-01, 1.02360562e-01, 7.45365654e-02,
4.58600349e-02, 2.27543772e-02, 2.55500371e-03, -1.12901539e-02,
-2.00612450e-02, -2.05302337e-02, -1.43955736e-02, -1.96362344e-03,
1.43138815e-02, 3.02983258e-02, 4.34823994e-02, 5.90085959e-02,
7.54443450e-02, 8.95641407e-02, 9.67971875e-02, 9.70562193e-02,
9.55311566e-02, 9.15592170e-02, 9.01994445e-02, 9.41480445e-02,
1.04052993e-01, 1.23400059e-01, 1.48492716e-01, 1.83582911e-01,
2.26294682e-01, 2.75626392e-01, 3.32998578e-01, 4.00528271e-01,
4.67934973e-01, 5.32690412e-01, 6.00663214e-01, 6.69237915e-01,
7.35044063e-01, 7.92103549e-01, 8.40125444e-01, 8.85118228e-01,
9.26710071e-01, 9.63585313e-01, 9.99416886e-01, 1.03370618e+00,
1.07058016e+00, 1.10912625e+00, 1.14910105e+00, 1.19208798e+00,
1.24438037e+00, 1.30576440e+00, 1.37735963e+00, 1.45664249e+00,
1.54193024e+00, 1.63454464e+00, 1.73351863e+00, 1.83294504e+00,
1.93370136e+00, 2.03402182e+00, 2.13233740e+00, 2.22839848e+00,
2.32598392e+00, 2.41995397e+00, 2.51115761e+00, 2.60621539e+00,
2.70227033e+00, 2.80455557e+00, 2.91302734e+00, 3.02734125e+00,
3.15428983e+00, 3.28767069e+00, 3.42238855e+00, 3.55859521e+00,
3.69743476e+00, 3.83768499e+00, 3.97463035e+00, 4.10736914e+00,
4.24048865e+00, 4.36720598e+00, 4.48434912e+00, 4.59589214e+00,
4.69648125e+00, 4.78858713e+00, 4.87648490e+00, 4.96283704e+00,
5.06076331e+00, 5.15916588e+00, 5.26102971e+00, 5.36878962e+00,
5.49923056e+00, 5.65359704e+00, 5.83209320e+00, 6.03534268e+00,
6.25949176e+00, 6.49756945e+00, 6.75355801e+00, 7.02179657e+00,
7.28684141e+00, 7.54783554e+00, 7.78890776e+00, 8.02756007e+00,
8.24485944e+00, 8.41762883e+00, 8.56386667e+00, 8.70045401e+00,
8.79791358e+00, 8.86760620e+00, 8.89660240e+00, 8.93821625e+00,
8.96249649e+00, 9.01373384e+00, 9.03171593e+00, 9.02370461e+00
};
var testPer1 = new double[]
{
-0.80020077, -0.20799692, 0.34058598, 0.79812753, 1.11234431,
1.26627552, 1.24296279, 1.04435011, 0.700797, 0.25219845,
-0.25319069, -0.75880308, -1.21529466, -1.56925367, -1.77808467,
-1.82163868, -1.69270393, -1.39533391, -0.95647582, -0.42056558,
0.16110082, 0.73001779, 1.22991918, 1.61448026, 1.84535913,
1.90093538, 1.77635869, 1.48465622, 1.05407977, 0.5267259,
-0.04708132, -0.61084437, -1.11063844, -1.49620291, -1.73032528,
-1.79054622, -1.67088411, -1.38391355, -0.95775676, -0.4339794,
0.13813546, 0.70329124, 1.20664338, 1.59845943, 1.83860363,
1.90318627, 1.78592608, 1.49700388, 1.06300559, 0.52709454,
-0.06013703, -0.64052324, -1.15758081, -1.56061871, -1.80985932,
-1.88067834, -1.76510211, -1.47340338, -1.03424322, -0.49027391,
0.1069, 0.69860768, 1.22807982, 1.64300383, 1.90256571,
1.98059464, 1.8708777, 1.58215114, 1.1426878, 0.59451356,
-0.01776822, -0.62619539, -1.17329314, -1.60635986, -1.88378628,
-1.97765929, -1.88005299, -1.60091012, -1.16577305, -0.61724179,
-0.00962269, 0.59931731, 1.14897868, 1.58687717, 1.87105722,
1.97233196, 1.8811974, 1.60741854, 1.17791583, 0.6336449,
0.02733875, -0.58286743, -1.13868809, -1.58457863, -1.87713153,
-1.98777608, -1.90540126, -1.63633736, -1.20731554, -0.65961451,
-0.04683626, 0.57122652, 1.13417009, 1.58723187, 1.88576591,
1.99983319, 1.91797844, 1.64736758, 1.21411434, 0.65951476,
0.03881991, -0.58738637, -1.15717097, -1.61474627, -1.91712043,
-2.03383836, -1.95332229, -1.68267916, -1.24865504, -0.69220392,
-0.06875556, 0.56213332, 1.13957463, 1.60784606, 1.9208251,
2.0480416, 1.97649791, 1.71478315, 1.28696975, 0.73427712,
0.11180259, -0.52213658, -1.10131413, -1.56989044, -1.88275321,
-2.0099503, -1.93685931, -1.67181406, -1.24014776, -0.68456918,
-0.06007609, 0.57333983, 1.15222245, 1.61836307, 1.9266784,
2.04795906, 1.96883273, 1.69699325, 1.26139978, 0.70321934,
0.07603428, -0.55656503, -1.13432999, -1.59903982, -1.90448993,
-2.02179409, -1.93727912, -1.65913972, -1.21424054, -0.64542751,
-0.00742886, 0.63697835, 1.2237692, 1.69683144, 2.01074899,
2.1331573, 2.05076264, 1.77374564, 1.32586246, 0.75070573,
0.10436375, -0.55123658, -1.15012341, -1.63600488, -1.96236899,
-2.09900554, -2.03060716, -1.76373843, -1.32481644, -0.76003157,
-0.12338318, 0.5217479, 1.11522784, 1.59784859, 1.91573826,
2.0415897, 1.96001876, 1.686063, 1.24281843, 0.67253564,
0.03025695, -0.6129921, -1.19289926, -1.64345407, -1.92236339,
-1.98832954, -1.84458753, -1.46644984, -0.91565827, -0.24748056
};
var testPer2 = new double[]
{
-0.29921287, -0.19345375, -0.09264466, 0.00538367, 0.0907433,
0.16907797, 0.23281512, 0.27667018, 0.30375439, 0.31264929,
0.30318964, 0.27683397, 0.23051852, 0.1691338, 0.09786924,
0.01567301, -0.07382499, -0.16253747, -0.24723623, -0.32657007,
-0.39565374, -0.45213328, -0.49290679, -0.51314143, -0.51150822,
-0.48620446, -0.43678634, -0.3637922, -0.27010747, -0.15922197,
-0.03680229, 0.09234732, 0.22141066, 0.34493897, 0.45608176,
0.54878997, 0.61836517, 0.66011225, 0.67133841, 0.65086931,
0.60048771, 0.52207301, 0.41941025, 0.2969615, 0.15963949,
0.01425226, -0.13160233, -0.27130424, -0.39893947, -0.50709348,
-0.591491, -0.64698753, -0.67141509, -0.66373644, -0.62440791,
-0.55546672, -0.45986244, -0.34231455, -0.20917714, -0.06712453,
0.07799069, 0.2187835, 0.3494885, 0.46369719, 0.55647288,
0.62355095, 0.66384701, 0.67455501, 0.65630649, 0.61023269,
0.53794124, 0.44180212, 0.32482084, 0.19242304, 0.05034762,
-0.0936652, -0.2344481, -0.3660088, -0.4812901, -0.57572488,
-0.64618439, -0.68844124, -0.70207956, -0.68591189, -0.64000472,
-0.5679019, -0.47237943, -0.35672993, -0.22535624, -0.0844686,
0.05999953, 0.2009793, 0.33150171, 0.44722197, 0.5425109,
0.61305958, 0.65569418, 0.66973158, 0.65376309, 0.60885867,
0.53658775, 0.43994741, 0.3228424, 0.19075384, 0.04938327,
-0.09548885, -0.23760632, -0.37145314, -0.49108451, -0.59206643,
-0.66878423, -0.71801811, -0.73697631, -0.7245778, -0.68268287,
-0.61202535, -0.51581889, -0.39788717, -0.26378834, -0.11818053,
0.03113469, 0.17851163, 0.31805561, 0.44402114, 0.55053608,
0.63279649, 0.68684265, 0.71205093, 0.70628458, 0.66945202,
0.6042364, 0.51449515, 0.40259484, 0.27271194, 0.12985762,
-0.0203204, -0.16917514, -0.31115496, -0.43933442, -0.5478243,
-0.63234952, -0.68745967, -0.71128844, -0.70371168, -0.66444627,
-0.59399224, -0.49673506, -0.37714367, -0.2387792, -0.08907026,
0.06422394, 0.21577591, 0.35679647, 0.48165979, 0.58521375,
0.66142591, 0.70818757, 0.72285868, 0.7052971, 0.65734491,
0.58244398, 0.48432965, 0.36716518, 0.23761659, 0.10275575,
-0.03205726, -0.16190241, -0.27887718, -0.38049791, -0.46243047,
-0.52139587, -0.55627585, -0.56520695, -0.55042255, -0.51355427,
-0.45825986, -0.3854348, -0.29895221, -0.20322302, -0.10530744,
-0.00819016, 0.08336356, 0.16881468, 0.24426875, 0.30256322,
0.3450472, 0.36713917, 0.37428971, 0.36234736, 0.32987369,
0.27673663, 0.20708934, 0.11892907, 0.01975251, -0.09113284,
-0.2043234, -0.33148174, -0.44418749, -0.56488906, -0.69471798
};
//test reconstructed components
for (int i = 0; i < rTrend.Length; i++)
{
Assert.Equal(testTrend[i], rTrend[i], 5);
Assert.Equal(testPer1[i], rPer1[i], 5);
Assert.Equal(testPer2[i], rPer2[i], 5);
}
//PlotMatrix(em).Show();
////
//var plt = new List<XPlot.Plotly.PlotlyChart>();
//foreach (var m in ssa.EM)
// plt.Add(PlotMatrix(m.Value));
//Chart.ShowAll(plt);
///test correlations
var w = ssa.WCorrelation();
var df = getwCorrelationMatrix();
for (int i = 0; i < w.GetLength(0); i++)
{
for (int j = 0; j < w.GetLength(0); j++)
{
Assert.Equal(df[i, j], Convert.ToSingle(w[i, j]));
}
}
}