Some changes.

2 files changed, 1024 insertions, 868 deletions

diff --git a/fits.cpp b/fits.cpp
index f2f3a1d..d86af73 100644
--- a/fits.cpp
+++ b/fits.cpp
@@ -13,7 +13,7 @@ using Real = double;
 using Vector = Eigen::Matrix<Real, Eigen::Dynamic, 1>;
 
 /*
-inline Real basisFunctions(unsigned i, Real x) const {
+inline Real basisFunctions(unsigned N, unsigned i, Real x) {
   if (i == 0) {
     return 1;
   } else {
@@ -22,9 +22,21 @@ inline Real basisFunctions(unsigned i, Real x) const {
 }
 */
 
+Real legendreP(unsigned n, Real x) {
+  if (n == 0) return 1;
+  else if (n == 1) return x;
+  else return ((2 * (n - 1) + 1) * x * legendreP(n - 1, x) - (n - 1) * legendreP(n - 2, x)) / n;
+}
+
+inline Real basisFunctions(unsigned N, unsigned i, Real x) {
+  return legendreP(i, x);
+}
+
+/*
 inline Real basisFunctions(unsigned N, unsigned i, Real x) {
   return abs(x - i / (N - 1.0));
 }
+*/
 
 Real value(const Vector& coeffs, Real x) {
   Real v = 0;
@@ -167,7 +179,7 @@ int main(int argc, char* argv[]) {
 
   Rng r;
 
-  std::list<std::tuple<Real, Real>> data = generateData([](Real x) {return x;}, M, σ, r);
+  std::list<std::tuple<Real, Real>> data = generateData([](Real x) {return std::cos(2 * M_PI * x);}, M, σ, r);
 
   std::cout << std::setprecision(15);
 
@@ -177,7 +189,10 @@ int main(int argc, char* argv[]) {
   std::cout << std::endl;
 
   Vector a₀ = Vector::Zero(N);
-  Vector a = stochasticGradientDescent(data, a₀, r, maxSteps);
+  for (Real& aa : a₀) {
+    aa = r.variate<Real, std::normal_distribution>(0, 0);
+  }
+  Vector a = gradientDescent(data, a₀, maxSteps);
 
   for (unsigned i = 0; i < N; i++) {
     std::cout << a[i] << " ";
diff --git a/fits.nb b/fits.nb
index 79a57b5..74424d5 100644
--- a/fits.nb
+++ b/fits.nb
@@ -10,10 +10,10 @@
 NotebookFileLineBreakTest
 NotebookFileLineBreakTest
 NotebookDataPosition[       154,          7]
-NotebookDataLength[    605529,      10912]
-NotebookOptionsPosition[    600558,      10829]
-NotebookOutlinePosition[    600953,      10845]
-CellTagsIndexPosition[    600910,      10842]
+NotebookDataLength[    614374,      11053]
+NotebookOptionsPosition[    609401,      10970]
+NotebookOutlinePosition[    609796,      10986]
+CellTagsIndexPosition[    609753,      10983]
 WindowFrame->Normal*)
 
 (* Beginning of Notebook Content *)
@@ -9804,7 +9804,7 @@ test.dat\>\"", "]"}]}], ";"}]], "Input",
  CellChangeTimes->{{3.9481307166422443`*^9, 3.948130754169201*^9}, {
   3.9481309111456833`*^9, 3.948130912383401*^9}},
  CellLabel->
-  "In[688]:=",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"],
+  "In[888]:=",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"],
 
 Cell[BoxData[{
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@@ -9819,401 +9819,323 @@ Cell[BoxData[{
     RowBox[{"[", "2", "]"}], "]"}]}], ";"}]}], "Input",
  CellChangeTimes->{{3.9481307549726753`*^9, 3.9481308081074133`*^9}},
  CellLabel->
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+  "In[889]:=",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"],
 
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-      RowBox[{"as", " ", 
-       RowBox[{"(", 
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-         RowBox[{"edgeBasis", "[", 
-          RowBox[{"Length", "[", "as", "]"}], "]"}]}], ")"}]}], "]"}], ",", 
      RowBox[{"{", 
-      RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]}], "]"}]], "Input",
+      RowBox[{
+       RowBox[{"Cos", "[", 
+        RowBox[{"2", "\[Pi]", " ", "x"}], "]"}], ",", 
+       RowBox[{"Total", "[", 
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+     RowBox[{"{", 
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-            "PlotRange" -> {{0, 1}, {-1.0240079276269844`, 
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+Sqs=
+           "]]}, "Charting`Private`Tag#2"]}}, {}}, <|
      "HighlightElements" -> <|
        "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>, 
       "LayoutOptions" -> <|
        "PanelPlotLayout" -> <||>, 
-        "PlotRange" -> {{0, 1}, {-1.0240079276269844`, 0.9402978510595014}}, 
+        "PlotRange" -> {{0, 1}, {-1.000120855436617, 1.0000941443631546`}}, 
         "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, 0}, 
         "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, 
         "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> {
           Directive[
            Opacity[1.], 
+           RGBColor[0.95, 0.627, 0.1425], 
+           AbsoluteThickness[2]], 
+          Directive[
+           Opacity[1.], 
            RGBColor[0.24, 0.6, 0.8], 
            AbsoluteThickness[2]]}, 
         "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({
@@ -10729,7 +10784,127 @@ RtQ=
             Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> False|>, 
       "Meta" -> <|
        "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> 
-        Plot, "GroupHighlight" -> False|>|>, "DynamicHighlight"]]},
+        Plot, "GroupHighlight" -> False|>|>, "DynamicHighlight"]], {{}, 
+    InterpretationBox[{
+      TagBox[
+       TagBox[
+        {GrayLevel[0], PointSize[0.012833333333333334`], AbsoluteThickness[2],
+          PointBox[{{0., 1.}, {0.111111111111111, 0.766044443118978}, {
+          0.222222222222222, 0.17364817766693}, {0.333333333333333, -0.5}, {
+          0.444444444444444, -0.939692620785908}, {
+          0.555555555555556, -0.939692620785908}, {0.666666666666667, -0.5}, {
+          0.777777777777778, 0.17364817766693}, {0.888888888888889, 
+          0.766044443118978}, {1., 1.}}]},
+        Annotation[#, "Charting`Private`Tag#1"]& ],
+       {"WolframDynamicHighlight", <|
+        "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>}], 
+      StyleBox[
+       DynamicBox[(Charting`HighlightActionBox["DynamicHighlight", {}, 
+         Slot["HighlightElements"], 
+         Slot["LayoutOptions"], 
+         Slot["Meta"], 
+         Charting`HighlightActionFunction["DynamicHighlight", {{
+            Annotation[{
+              Directive[
+               PointSize[0.012833333333333334`], 
+               AbsoluteThickness[2], 
+               GrayLevel[0]], 
+              
+              Point[{{0., 1.}, {0.111111111111111, 0.766044443118978}, {
+               0.222222222222222, 0.17364817766693}, {
+               0.333333333333333, -0.5}, {
+               0.444444444444444, -0.939692620785908}, {
+               0.555555555555556, -0.939692620785908}, {
+               0.666666666666667, -0.5}, {0.777777777777778, 
+               0.17364817766693}, {0.888888888888889, 0.766044443118978}, {1.,
+                1.}}]}, "Charting`Private`Tag#1"]}}, <|
+          "HighlightElements" -> <|
+            "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, 
+           "LayoutOptions" -> <|
+            "PanelPlotLayout" -> <||>, 
+             "PlotRange" -> {{0, 1.}, {-0.939692620785908, 1.}}, 
+             "Frame" -> {{False, False}, {False, False}}, 
+             "AxesOrigin" -> {0, 0}, "ImageSize" -> {360, 360/GoldenRatio}, 
+             "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> 
+             GoldenRatio^(-1), "DefaultStyle" -> {
+               Directive[
+                PointSize[0.012833333333333334`], 
+                AbsoluteThickness[2], 
+                GrayLevel[0]]}, 
+             "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({
+                 (Identity[#]& )[
+                  Part[#, 1]], 
+                 (Identity[#]& )[
+                  Part[#, 2]]}& ), 
+               "ScalingFunctions" -> {{Identity, Identity}, {
+                 Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> 
+             False|>, 
+           "Meta" -> <|
+            "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, 
+             "Function" -> ListPlot, "GroupHighlight" -> False|>|>]]& )[<|
+         "HighlightElements" -> <|
+           "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, 
+          "LayoutOptions" -> <|
+           "PanelPlotLayout" -> <||>, 
+            "PlotRange" -> {{0, 1.}, {-0.939692620785908, 1.}}, 
+            "Frame" -> {{False, False}, {False, False}}, 
+            "AxesOrigin" -> {0, 0}, "ImageSize" -> {360, 360/GoldenRatio}, 
+            "Axes" -> {True, True}, "LabelStyle" -> {}, "AspectRatio" -> 
+            GoldenRatio^(-1), "DefaultStyle" -> {
+              Directive[
+               PointSize[0.012833333333333334`], 
+               AbsoluteThickness[2], 
+               GrayLevel[0]]}, 
+            "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({
+                (Identity[#]& )[
+                 Part[#, 1]], 
+                (Identity[#]& )[
+                 Part[#, 2]]}& ), 
+              "ScalingFunctions" -> {{Identity, Identity}, {
+                Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> 
+            False|>, 
+          "Meta" -> <|
+           "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> 
+            ListPlot, "GroupHighlight" -> False|>|>]],
+       Selectable->False]},
+     Annotation[{{
+        Annotation[{
+          Directive[
+           PointSize[0.012833333333333334`], 
+           AbsoluteThickness[2], 
+           GrayLevel[0]], 
+          
+          Point[{{0., 1.}, {0.111111111111111, 0.766044443118978}, {
+           0.222222222222222, 0.17364817766693}, {0.333333333333333, -0.5}, {
+           0.444444444444444, -0.939692620785908}, {
+           0.555555555555556, -0.939692620785908}, {
+           0.666666666666667, -0.5}, {0.777777777777778, 0.17364817766693}, {
+           0.888888888888889, 0.766044443118978}, {1., 1.}}]}, 
+         "Charting`Private`Tag#1"]}}, <|
+      "HighlightElements" -> <|
+        "Label" -> {"XYLabel"}, "Ball" -> {"IndicatedBall"}|>, 
+       "LayoutOptions" -> <|
+        "PanelPlotLayout" -> <||>, 
+         "PlotRange" -> {{0, 1.}, {-0.939692620785908, 1.}}, 
+         "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, 0}, 
+         "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True}, 
+         "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), 
+         "DefaultStyle" -> {
+           Directive[
+            PointSize[0.012833333333333334`], 
+            AbsoluteThickness[2], 
+            GrayLevel[0]]}, 
+         "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({
+             (Identity[#]& )[
+              Part[#, 1]], 
+             (Identity[#]& )[
+              Part[#, 2]]}& ), 
+           "ScalingFunctions" -> {{Identity, Identity}, {
+             Identity, Identity}}|>, "Primitives" -> {}, "GCFlag" -> False|>, 
+       "Meta" -> <|
+        "DefaultHighlight" -> {"Dynamic", None}, "Index" -> {}, "Function" -> 
+         ListPlot, "GroupHighlight" -> False|>|>, 
+      "DynamicHighlight"]], {{}, {}}}},
   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
   Axes->{True, True},
   AxesLabel->{None, None},
@@ -10741,8 +10916,9 @@ RtQ=
   GridLines->{None, None},
   GridLinesStyle->Directive[
     GrayLevel[0.5, 0.4]],
+  ImagePadding->All,
   Method->{
-   "AxisPadding" -> Scaled[0.02], "DefaultBoundaryStyle" -> Automatic, 
+   "DefaultBoundaryStyle" -> Automatic, 
     "DefaultGraphicsInteraction" -> {
      "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
       "Effects" -> {
@@ -10750,55 +10926,7 @@ RtQ=
         "Droplines" -> {
          "freeformCursorMode" -> True, 
           "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
-    AbsolutePointSize[6], "DefaultPlotStyle" -> {
-      Directive[
-       RGBColor[0.24, 0.6, 0.8], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.95, 0.627, 0.1425], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.455, 0.7, 0.21], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.922526, 0.385626, 0.209179], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.578, 0.51, 0.85], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.772079, 0.431554, 0.102387], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.4, 0.64, 1.], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[1., 0.75, 0.], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.8, 0.4, 0.76], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.637, 0.65, 0.], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.915, 0.3325, 0.2125], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.40082222609352647`, 0.5220066643438841, 0.85], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.9728288904374106, 0.621644452187053, 0.07336199581899142], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.736782672705901, 0.358, 0.5030266573755369], 
-       AbsoluteThickness[2]], 
-      Directive[
-       RGBColor[0.28026441037696703`, 0.715, 0.4292089322474965], 
-       AbsoluteThickness[2]]}, "DomainPadding" -> Scaled[0.02], 
-    "PointSizeFunction" -> "SmallPointSize", "RangePadding" -> Scaled[0.05], 
-    "OptimizePlotMarkers" -> True, "IncludeHighlighting" -> "CurrentPoint", 
-    "HighlightStyle" -> Automatic, "OptimizePlotMarkers" -> True, 
+    AbsolutePointSize[6], "ScalingFunctions" -> None, 
     "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
         (Identity[#]& )[
          Part[#, 1]], 
@@ -10808,7 +10936,7 @@ RtQ=
          Part[#, 1]], 
         (Identity[#]& )[
          Part[#, 2]]}& )}},
-  PlotRange->{{0, 1.}, {-1.21648146673872, 1.01647550616545}},
+  PlotRange->{{0, 1}, {-1.000120855436617, 1.0000941443631546`}},
   PlotRangeClipping->True,
   PlotRangePadding->{{
      Scaled[0.02], 
@@ -10822,9 +10950,22 @@ RtQ=
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    3.94813298206507*^9}, 3.9481331151859083`*^9, 3.948133145872796*^9, 
    3.9481331931940002`*^9, {3.9481332275257883`*^9, 3.948133248903883*^9}, {
-   3.948134412219392*^9, 3.948134424786851*^9}},
+   3.948134412219392*^9, 3.948134424786851*^9}, {3.948134704214121*^9, 
+   3.9481347225143414`*^9}, 3.9481349678419323`*^9, 3.948135406718172*^9, {
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+   3.948135770136162*^9}, 3.9481358244100657`*^9, 3.948136618752692*^9, 
+   3.948137070588904*^9, {3.948137311093301*^9, 3.948137353352693*^9}, 
+   3.948137434492918*^9, {3.948137472737005*^9, 3.948137518400502*^9}, 
+   3.94813761059442*^9, {3.9481377242665577`*^9, 3.948137728731876*^9}, {
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+   3.948137915198165*^9, 3.948137961831544*^9}, {3.948138010326825*^9, 
+   3.9481380852616253`*^9}, {3.948138171771494*^9, 3.948138194121057*^9}, 
+   3.9481382402556753`*^9, {3.948138284976859*^9, 3.948138289201264*^9}, 
+   3.948138338382262*^9, 3.948138452037212*^9, 3.948138831793432*^9, 
+   3.948139774880522*^9, 3.948139820496393*^9, 3.94813985677387*^9, 
+   3.948139978928771*^9, 3.948140059803281*^9},
  CellLabel->
-  "Out[691]=",ExpressionUUID->"30f05ce4-ff7f-4315-9ed3-24cb1532e4e3"]
+  "Out[891]=",ExpressionUUID->"17f846e6-caa0-4daf-91be-6b65626b2b8f"]
 }, Open  ]]
 },
 WindowSize->{1024.5, 561},
@@ -10911,8 +11052,8 @@ Cell[544253, 9786, 521, 7, 25, "Output",ExpressionUUID->"1f8c8629-c764-4604-b0fe
 Cell[544789, 9796, 394, 10, 23, "Input",ExpressionUUID->"b6f65d11-1714-42cd-b279-8e2c0eb8fe70"],
 Cell[545186, 9808, 482, 13, 40, "Input",ExpressionUUID->"788c910c-c901-4771-95a4-a21a3056ef4d"],
 Cell[CellGroupData[{
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-Cell[546407, 9846, 54135, 980, 182, "Output",ExpressionUUID->"30f05ce4-ff7f-4315-9ed3-24cb1532e4e3"]
+Cell[545693, 9825, 1329, 33, 23, "Input",ExpressionUUID->"64b9d7b0-4d42-4971-a779-d26a172dddb6"],
+Cell[547025, 9860, 62360, 1107, 182, "Output",ExpressionUUID->"17f846e6-caa0-4daf-91be-6b65626b2b8f"]
 }, Open  ]]
 }
 ]