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-rw-r--r--compile_flags.txt3
-rw-r--r--fits.cpp173
-rw-r--r--fits.nb1152
3 files changed, 1268 insertions, 60 deletions
diff --git a/compile_flags.txt b/compile_flags.txt
new file mode 100644
index 0000000..4cb2489
--- /dev/null
+++ b/compile_flags.txt
@@ -0,0 +1,3 @@
+-std=c++17
+-Wno-mathematical-notation-identifier-extension
+-Wall
diff --git a/fits.cpp b/fits.cpp
index a342791..923712b 100644
--- a/fits.cpp
+++ b/fits.cpp
@@ -1,5 +1,6 @@
#include <getopt.h>
#include <iomanip>
+#include<list>
#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
@@ -10,3 +11,175 @@ using Rng = randutils::random_generator<pcg32>;
using Real = double;
using Vector = Eigen::Matrix<Real, Eigen::Dynamic, 1>;
+
+class fitModel {
+public:
+ unsigned N;
+
+ fitModel(unsigned N) : N(N) {}
+
+ /*
+ virtual Real basisFunctions(unsigned i, Real x) const {
+ if (i == 0) {
+ return 1;
+ } else {
+ return pow(x, i);
+ }
+ }
+ */
+
+ Real basisFunctions(unsigned i, Real x) const {
+ return abs(x - i / (N - 1.0));
+ }
+
+ Real value(const Vector& coeffs, Real x) const {
+ Real v = 0;
+
+ for (unsigned j = 0; j < N; j++) {
+ v += coeffs[j] * basisFunctions(j, x);
+ }
+
+ return v;
+ }
+
+ Real cost(const std::list<std::tuple<Real, Real>>& data, const Vector& coeffs) const {
+ Real c = 0;
+
+ for (std::tuple<Real, Real> xy : data) {
+ Real x = std::get<0>(xy);
+ Real y = std::get<1>(xy);
+ c += 0.5 * pow(value(coeffs, x) - y, 2);
+ }
+
+ return c;
+ }
+
+ Vector dCost(const std::list<std::tuple<Real, Real>>& data, const Vector& coeffs) const {
+ Vector dC = Vector::Zero(N);
+
+ for (unsigned j = 0; j < N; j++) {
+ for (std::tuple<Real, Real> xy : data) {
+ Real x = std::get<0>(xy);
+ Real y = std::get<1>(xy);
+ dC[j] += (value(coeffs, x) - y) * basisFunctions(j, x);
+ }
+ }
+
+ return dC;
+ }
+};
+
+Vector gradientDescent(const fitModel& M, const std::list<std::tuple<Real, Real>>& data, const Vector& a₀, unsigned maxSteps, Real ε = 1e-12) {
+ Vector xₜ = a₀;
+ Real Hₜ = M.cost(data, a₀);
+ Real α = 1.0;
+ Real m;
+ Vector ∇H;
+ unsigned steps = 0;
+
+ while (
+ ∇H = M.dCost(data, xₜ), m = ∇H.squaredNorm(),
+ m > ε && steps < maxSteps
+ ) {
+ Vector xₜ₊₁;
+ Real Hₜ₊₁;
+
+ while (
+ xₜ₊₁ = xₜ - α * ∇H, Hₜ₊₁ = M.cost(data, xₜ₊₁),
+ Hₜ₊₁ > Hₜ - 0.5 * α * m
+ ) {
+ α /= 2;
+ }
+
+ xₜ = xₜ₊₁;
+ Hₜ = Hₜ₊₁;
+ α *= 1.25;
+ steps++;
+ }
+
+ return xₜ;
+}
+
+Vector stochasticGradientDescent(const fitModel& M, const std::list<std::tuple<Real, Real>>& data, const Vector& a₀, Rng& r, unsigned maxSteps, Real ε = 1e-12) {
+ Vector xₜ = a₀;
+ Real α = 1e-3;
+ Real m;
+ Vector ∇H;
+ unsigned steps = 0;
+
+ while (
+ ∇H = M.dCost(data, xₜ), m = ∇H.squaredNorm(),
+ m > ε && steps < maxSteps
+ ) {
+ Vector γ(M.N);
+ for (Real& γi : γ) {
+ γi = r.variate<Real, std::normal_distribution>(0, 1e-4);
+ }
+ xₜ = xₜ - α * ∇H + γ;
+ steps++;
+ }
+
+ return xₜ;
+}
+
+std::list<std::tuple<Real, Real>> generateData(Real(*f)(Real), unsigned M, Real σ, Rng& r) {
+ std::list<std::tuple<Real, Real>> data;
+
+ for (unsigned i = 0; i < M; i++) {
+ Real x = ((Real)i) / (M - 1.0);
+ data.push_back({x, f(x) + r.variate<Real, std::normal_distribution>(0, σ)});
+ }
+
+ return data;
+}
+
+int main(int argc, char* argv[]) {
+ unsigned N = 10;
+ unsigned M = 10;
+ Real σ = 0.2;
+ unsigned maxSteps = 1e5;
+
+ int opt;
+
+ while ((opt = getopt(argc, argv, "N:M:s:S:")) != -1) {
+ switch (opt) {
+ case 'N':
+ N = (unsigned)atof(optarg);
+ break;
+ case 'M':
+ M = (unsigned)atof(optarg);
+ break;
+ case 's':
+ σ = atof(optarg);
+ break;
+ case 'S':
+ maxSteps = (unsigned)atof(optarg);
+ break;
+ default:
+ exit(1);
+ }
+ }
+
+ Rng r;
+
+ std::list<std::tuple<Real, Real>> data = generateData([](Real x) {return sin(2 * M_PI * x);}, M, σ, r);
+
+ std::cout << std::setprecision(15);
+
+ for (std::tuple<Real, Real> datum : data) {
+ std::cout << std::get<0>(datum) << " " << std::get<1>(datum) << " ";
+ }
+ std::cout << std::endl;
+
+ fitModel model(N);
+
+ Vector a₀ = Vector::Zero(N);
+ Vector a = gradientDescent(model, data, a₀, maxSteps);
+
+ for (unsigned i = 0; i < N; i++) {
+ std::cout << a[i] << " ";
+ }
+ std::cout << std::endl;
+
+ return 0;
+}
diff --git a/fits.nb b/fits.nb
index a87a6bf..79a57b5 100644
--- a/fits.nb
+++ b/fits.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 154, 7]
-NotebookDataLength[ 549603, 9880]
-NotebookOptionsPosition[ 544961, 9802]
-NotebookOutlinePosition[ 545356, 9818]
-CellTagsIndexPosition[ 545313, 9815]
+NotebookDataLength[ 605529, 10912]
+NotebookOptionsPosition[ 600558, 10829]
+NotebookOutlinePosition[ 600953, 10845]
+CellTagsIndexPosition[ 600910, 10842]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -776,29 +776,27 @@ Cell[BoxData[
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RowBox[{
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- RowBox[{"(",
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- RowBox[{"0", ",",
- RowBox[{"m", "-", "2"}]}], "]"}]}], "]"}], ",",
- RowBox[{"1", "&"}]}], "]"}]}]], "Input",
+ RowBox[{
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+ RowBox[{"x", "\[Function]",
+ RowBox[{"Abs", "[",
+ RowBox[{"x", "-",
+ RowBox[{"#", "/",
+ RowBox[{"(",
+ RowBox[{"m", "-", "1"}], ")"}]}]}], "]"}]}], ")"}], "&"}], ",",
+ RowBox[{"Range", "[",
+ RowBox[{"0", ",",
+ RowBox[{"m", "-", "1"}]}], "]"}]}], "]"}]}]], "Input",
CellChangeTimes->{{3.948119521796258*^9, 3.948119527674906*^9}, {
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3.948120146260414*^9, 3.948120149652207*^9}, {3.9481203905183697`*^9,
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CellLabel->
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@@ -4807,7 +4805,7 @@ Cell[BoxData[
CellLabel->
"In[588]:=",ExpressionUUID->"68019ef8-0ad0-4736-bcd3-369769400c1d"],
-Cell[BoxData["0.027261670813651672`"], "Output",
+Cell[BoxData["$Aborted"], "Output",
CellChangeTimes->{
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@@ -4829,9 +4827,10 @@ Cell[BoxData["0.027261670813651672`"], "Output",
3.948123472343184*^9, 3.94812349749905*^9}, 3.948123736651988*^9, {
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3.9481247089443493`*^9, 3.9481247114935417`*^9}, {3.948124743284782*^9,
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CellLabel->
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+ "Out[588]=",ExpressionUUID->"e79c5a28-1937-4270-9088-db58dd375331"]
}, Open ]],
Cell[CellGroupData[{
@@ -9795,10 +9794,1038 @@ Cell[BoxData["0.`"], "Output",
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+Cell[BoxData[
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+ "HighlightElements" -> <|
+ "Label" -> {"XYLabel"}, "Ball" -> {"InterpolatedBall"}|>,
+ "LayoutOptions" -> <|
+ "PanelPlotLayout" -> <||>,
+ "PlotRange" -> {{0, 1}, {-1.0240079276269844`, 0.9402978510595014}},
+ "Frame" -> {{False, False}, {False, False}}, "AxesOrigin" -> {0, 0},
+ "ImageSize" -> {360, 360/GoldenRatio}, "Axes" -> {True, True},
+ "LabelStyle" -> {}, "AspectRatio" -> GoldenRatio^(-1), "DefaultStyle" -> {
+ Directive[
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+ RGBColor[0.24, 0.6, 0.8],
+ AbsoluteThickness[2]]},
+ "HighlightLabelingFunctions" -> <|"CoordinatesToolOptions" -> ({
+ (Identity[#]& )[
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+ (Identity[#]& )[
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+ "Meta" -> <|
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+ FrameLabel->{{None, None}, {None, None}},
+ FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
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+ "Effects" -> {
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