4 files changed, 125 insertions, 0 deletions
diff --git a/.gitmodules b/.gitmodules
new file mode 100644
index 0000000..a14394b
--- /dev/null
+++ b/.gitmodules
@@ -0,0 +1,6 @@
+[submodule "randutils"]
+	path = randutils
+	url = https://gist.github.com/imneme/540829265469e673d045
+[submodule "pcg-cpp"]
+	path = pcg-cpp
+	url = https://github.com/imneme/pcg-cpp
diff --git a/least_squares.cpp b/least_squares.cpp
new file mode 100644
index 0000000..8e7d085
--- /dev/null
+++ b/least_squares.cpp
@@ -0,0 +1,119 @@
+#include <eigen3/Eigen/Dense>
+#include <random>
+#include <getopt.h>
+
+#include "pcg-cpp/include/pcg_random.hpp"
+#include "randutils/randutils.hpp"
+
+
+template <class Real>
+using Vector = Eigen::Matrix<Real, Eigen::Dynamic, 1>;
+
+template <class Real>
+using Matrix = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>;
+
+template <class Real>
+class Model {
+private:
+  Matrix<Real> A;
+  Vector<Real> b;
+
+public:
+  template <class Generator>
+  Model(Real σ, unsigned N, unsigned M, Generator& r) : A(M, N), b(M) {
+    std::normal_distribution<Real> aDistribution(0, 1);
+
+    for (unsigned i = 0; i < M; i++) {
+      for (unsigned j =0; j < N; j++) {
+        A(i, j) = aDistribution(r);
+      }
+    }
+
+    std::normal_distribution<Real> bDistribution(0, σ);
+
+    for (unsigned i = 0; i < M; i++) {
+      b(i) = bDistribution(r);
+    }
+  }
+
+  const unsigned N() {
+    return A.cols();
+  }
+
+  const unsigned M() {
+    return A.rows();
+  }
+
+  const Vector<Real> V(const Vector<Real>& x) {
+    return A * x + b;
+  }
+
+  const Matrix<Real> dV(const Vector<Real>& x) {
+    return A;
+  }
+
+//  const Real ddV(const Vector<Real>& x) {
+//    return Matrix::Zero(;
+//  }
+
+  const Real H(const Vector<Real>& x) {
+    return V(x).squaredNorm();
+  }
+
+  const Vector<Real> dH(const Vector<Real>& x) {
+    return dV(x).transpose() * V(x);
+  }
+
+  const Matrix<Real> ddH(const Vector<Real>& x) {
+    return dV(x).transpose() * dV(x);
+  }
+
+  const Vector<Real> ∇H(const Vector<Real>& x){
+    return dH(x) - dH(x).dot(x) * x / x.squaredNorm();
+  }
+
+  const Matrix<Real> HessH(const Vector<Real>& x) {
+    Matrix<Real> hess = ddH(x) - x.dot(dH(x)) * Matrix<Real>::Identity(N(), N());
+    return hess - (hess * x) * x.transpose() / x.squaredNorm();
+  }
+};
+
+using Rng = randutils::random_generator<pcg32>;
+using Real = double;
+
+int main(int argc, char* argv[]) {
+  unsigned N = 10;
+  unsigned M = 10;
+  Real σ = 1;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "N:M:s:")) != -1) {
+    switch (opt) {
+    case 'N':
+      N = (unsigned)atof(optarg);
+      break;
+    case 'M':
+      M = (unsigned)atof(optarg);
+      break;
+    case 's':
+      σ = atof(optarg);
+      break;
+    default:
+      exit(1);
+    }
+  }
+
+  Rng r;
+
+  Model<Real> leastSquares(σ, N, M, r.engine());
+
+  Vector<Real> x = Vector<Real>::Zero(N);
+  x(0) = N;
+
+  std::cout << leastSquares.H(x) << std::endl;
+  std::cout << leastSquares.∇H(x) << std::endl;
+  std::cout << leastSquares.HessH(x) << std::endl;
+
+  return 0;
+}
diff --git a/pcg-cpp b/pcg-cpp
new file mode 160000
+Subproject 428802d1a5634f96bcd0705fab379ff0113bcf1
diff --git a/randutils b/randutils
new file mode 160000
+Subproject 5afb4439c23a6c060eda72121bff8bf9da59591