1 files changed, 87 insertions, 0 deletions
diff --git a/gi/posterior-regularisation/projected_gradient.cc b/gi/posterior-regularisation/projected_gradient.cc
new file mode 100644
index 00000000..f7c39817
--- /dev/null
+++ b/gi/posterior-regularisation/projected_gradient.cc
@@ -0,0 +1,87 @@
+//
+// Minimises given functional using the projected gradient method. Based on
+// algorithm and demonstration example in Linear and Nonlinear Programming,
+// Luenberger and Ye, 3rd ed., p 370.
+//
+
+#include "invert.hh"
+#include <iostream>
+
+using namespace std;
+
+double 
+f(double x1, double x2, double x3, double x4)
+{
+    return x1 * x1 + x2 * x2 + x3 * x3 + x4 * x4 - 2 * x1 - 3 * x4;
+}
+
+ublas::vector<double> 
+g(double x1, double x2, double x3, double x4)
+{
+    ublas::vector<double> v(4);
+    v(0) = 2 * x1 - 2;
+    v(1) = 2 * x2;
+    v(2) = 2 * x3;
+    v(3) = 2 * x4 - 3;
+    return v;
+}
+
+ublas::matrix<double> 
+activeConstraints(double x1, double x2, double x3, double x4)
+{
+    int n = 2;
+    if (x1 == 0) ++n;
+    if (x2 == 0) ++n;
+    if (x3 == 0) ++n;
+    if (x4 == 0) ++n;
+
+    ublas::matrix<double> a(n,4);
+    a(0, 0) = 2; a(0, 1) = 1; a(0, 2) = 1; a(0, 3) = 4;
+    a(1, 0) = 1; a(1, 1) = 1; a(1, 2) = 2; a(1, 3) = 1;
+
+    int c = 2;
+    if (x1 == 0) a(c++, 0) = 1;
+    if (x2 == 0) a(c++, 1) = 1;
+    if (x3 == 0) a(c++, 2) = 1;
+    if (x4 == 0) a(c++, 3) = 1;
+
+    return a;
+}
+
+ublas::matrix<double>
+projection(const ublas::matrix<double> &a)
+{
+    ublas::matrix<double> aT = ublas::trans(a);
+    ublas::matrix<double> inv(a.size1(), a.size1());
+    bool ok = invert_matrix(ublas::matrix<double>(ublas::prod(a, aT)), inv);
+    assert(ok && "Failed to invert matrix");
+    return ublas::identity_matrix<double>(4) - 
+        ublas::prod(aT, ublas::matrix<double>(ublas::prod(inv, a)));
+}
+
+int main(int argc, char *argv[])
+{
+    double x1 = 2, x2 = 2, x3 = 1, x4 = 0;
+
+    double fval = f(x1, x2, x3, x4);
+    cout << "f = " << fval << endl;
+    ublas::vector<double> grad = g(x1, x2, x3, x4);
+    cout << "g = " << grad << endl;
+    ublas::matrix<double> A = activeConstraints(x1, x2, x3, x4);
+    cout << "A = " << A << endl;
+    ublas::matrix<double> P = projection(A);
+    cout << "P = " << P << endl;
+    // the direction of movement
+    ublas::vector<double> d = prod(P, grad);
+    cout << "d = " << (d / d(0)) << endl;
+
+    // special case for d = 0
+
+    // next solve for limits on the line search
+
+    // then use golden rule technique between these values (if bounded)
+
+    // or simple Armijo's rule technique
+
+    return 0;
+}