diff --git a/src/Makefile.am b/src/Makefile.am
index 68bcce7a07cd97154227e7fa7f666801211fa1eb..39fc4c205f221a5f0028753592680c160e5a65f0 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -3,11 +3,15 @@ SUBDIRS =
noinst_PROGRAMS = \
bisection-example \
+ bisection-example-flexible \
bisection-simpler-example \
bisection-simpler-example2 \
bisection-simpler-example2-gradient
bisection_example_SOURCES = bisection-example.cc
+bisection_example_flexible_SOURCES = \
+ bisection-example-flexible.cc \
+ properscalarincreasingconvexfunction.hh
bisection_simpler_example_SOURCES = bisection-simpler-example.cc
bisection_simpler_example2_SOURCES = bisection-simpler-example2.cc
bisection_simpler_example2_gradient_SOURCES = bisection-simpler-example2-gradient.cc
@@ -17,6 +21,7 @@ check-am:
./bisection-simpler-example2
./bisection-simpler-example2-gradient
./bisection-example
+ ./bisection-example-flexible
AM_CXXFLAGS = -Wall -Wextra
diff --git a/src/bisection-example-flexible.cc b/src/bisection-example-flexible.cc
new file mode 100644
index 0000000000000000000000000000000000000000..1ca0347fdcbf22a5c5ee9f3a41f0fd0e212ced34
--- /dev/null
+++ b/src/bisection-example-flexible.cc
@@ -0,0 +1,224 @@
+/* -*- mode:c++; mode: flymake -*- */
+
+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#include <dune/common/exceptions.hh>
+#include <dune/common/stdstreams.hh>
+
+#include <dune/fufem/interval.hh>
+
+#include <dune/tnnmg/nonlinearities/smallfunctional.hh>
+#include <dune/tnnmg/problem-classes/bisection.hh>
+
+#include <cassert>
+#include <cstdlib>
+#include <limits>
+
+#include "properscalarincreasingconvexfunction.hh"
+
+// TODO: default to TrivialFunction
+template <int dimension, class Function = TrivialFunction>
+class SampleFunctional {
+public:
+ typedef Dune::FieldVector<double, dimension> SmallVector;
+ typedef Dune::FieldMatrix<double, dimension, dimension> SmallMatrix;
+
+ // FIXME: hardcoded function H
+ SampleFunctional(SmallMatrix A, SmallVector b) : A_(A), b_(b), func_() {}
+
+ double operator()(const SmallVector v) const {
+ SmallVector y;
+ A_.mv(v, y); // y = Av
+ y /= 2; // y = 1/2 Av
+ y -= b_; // y = 1/2 Av - b
+ return y * v + func_(v.two_norm()); // <1/2 Av - b,v> + H(|v|)
+ }
+
+ double directionalDerivative(const SmallVector x,
+ const SmallVector dir) const {
+ if (x == SmallVector(0.0))
+ // Well, not in this way -- but can we compute them?
+ DUNE_THROW(Dune::Exception,
+ "Directional derivatives cannot be computed at zero.");
+
+ if (x * dir > 0)
+ return PlusGrad(x) * dir;
+ else
+ return MinusGrad(x) * dir;
+ }
+
+ SmallVector minimise(const SmallVector x, unsigned int iterations) const {
+ SmallVector descDir = ModifiedGradient(x);
+
+ Dune::dverb << "Starting at x with J(x) = " << operator()(x) << std::endl;
+ Dune::dverb << "Minimizing in direction w with dJ(x,w) = "
+ << directionalDerivative(x, descDir) << std::endl;
+
+ double l = 0;
+ double r = 1;
+ SmallVector tmp;
+ while (true) {
+ tmp = x;
+ tmp.axpy(r, descDir);
+ if (directionalDerivative(tmp, descDir) >= 0)
+ break;
+
+ l = r;
+ r *= 2;
+ Dune::dverb << "Widened interval!" << std::endl;
+ }
+ Dune::dverb << "Interval now [" << l << "," << r << "]" << std::endl;
+
+ // Debugging
+ {
+ SmallVector tmpl = x;
+ tmpl.axpy(l, descDir);
+ SmallVector tmpr = x;
+ tmpr.axpy(r, descDir);
+ assert(directionalDerivative(tmpl, descDir) < 0);
+ assert(directionalDerivative(tmpr, descDir) > 0);
+ }
+
+ double m = l / 2 + r / 2;
+ SmallVector middle;
+ for (unsigned int count = 0; count < iterations; ++count) {
+ Dune::dverb << "now at m = " << m << std::endl;
+ Dune::dverb << "Value of J here: " << operator()(x + middle) << std::endl;
+
+ middle = descDir;
+ middle *= m;
+
+ double derivative = directionalDerivative(x + middle, descDir);
+
+ if (derivative < 0) {
+ l = m;
+ m = (m + r) / 2;
+ } else if (derivative > 0) {
+ r = m;
+ m = (l + m) / 2;
+ } else
+ break;
+ }
+ return middle;
+ }
+
+private:
+ SmallMatrix A_;
+ SmallVector b_;
+
+ Function func_;
+
+ // Gradient of the smooth part
+ SmallVector SmoothGrad(const SmallVector x) const {
+ SmallVector y;
+ A_.mv(x, y); // y = Av
+ y -= b_; // y = Av - b
+ return y;
+ }
+
+ SmallVector PlusGrad(const SmallVector x) const {
+ SmallVector y = SmoothGrad(x);
+ y.axpy(func_.rightDifferential(x.two_norm()) / x.two_norm(), x);
+ return y;
+ }
+
+ SmallVector MinusGrad(const SmallVector x) const {
+ SmallVector y = SmoothGrad(x);
+ y.axpy(func_.leftDifferential(x.two_norm()) / x.two_norm(), x);
+ return y;
+ }
+
+ SmallVector ModifiedGradient(const SmallVector x) const {
+ if (x == SmallVector(0.0))
+ // TODO
+ DUNE_THROW(Dune::Exception, "The case x = 0 is not yet handled.");
+
+ SmallVector const pg = PlusGrad(x);
+ SmallVector const mg = MinusGrad(x);
+ SmallVector ret;
+ // TODO: collinearity checks suck
+ if (pg * x == pg.two_norm() * x.two_norm() &&
+ -(mg * x) == mg.two_norm() * x.two_norm()) {
+ return SmallVector(0);
+ } else if (pg * x >= 0 && mg * x >= 0) {
+ ret = pg;
+ } else if (pg * x <= 0 && mg * x <= 0) {
+ ret = mg;
+ } else {
+ ret = project(SmoothGrad(x), x);
+ }
+ ret *= -1;
+ return ret;
+ }
+
+ SmallVector project(const SmallVector z, const SmallVector x) const {
+ SmallVector y = z;
+ y.axpy(-(z * x) / x.two_norm2(), x);
+ return y;
+ }
+};
+
+void testSampleFunction() {
+ int const dim = 2;
+ typedef SampleFunctional<dim, SampleFunction> SampleFunctional;
+
+ SampleFunctional::SmallMatrix A;
+ A[0][0] = 3;
+ A[0][1] = 0;
+ A[1][0] = 0;
+ A[1][1] = 3;
+ SampleFunctional::SmallVector b;
+ b[0] = 1;
+ b[1] = 2;
+
+ SampleFunctional J(A, b);
+
+ std::cout << J.directionalDerivative(b, b) << std::endl;
+ assert(J.directionalDerivative(b, b) == 10 + 2 * sqrt(5));
+
+ SampleFunctional::SmallVector start = b;
+ start *= 17;
+ SampleFunctional::SmallVector correction = J.minimise(start, 20);
+ assert(J(start + correction) <= J(start));
+ assert(std::abs(J(start + correction) + 0.254644) < 1e-8);
+ std::cout << J(start + correction) << std::endl;
+}
+
+void testTrivialFunction() {
+ int const dim = 2;
+ typedef SampleFunctional<dim> SampleFunctional;
+
+ SampleFunctional::SmallMatrix A;
+ A[0][0] = 3;
+ A[0][1] = 0;
+ A[1][0] = 0;
+ A[1][1] = 3;
+ SampleFunctional::SmallVector b;
+ b[0] = 1;
+ b[1] = 2;
+
+ SampleFunctional J(A, b);
+
+ std::cout << J.directionalDerivative(b, b) << std::endl;
+ assert(J.directionalDerivative(b, b) == 10);
+
+ SampleFunctional::SmallVector start = b;
+ start *= 17;
+ SampleFunctional::SmallVector correction = J.minimise(start, 20);
+ assert(J(start + correction) <= J(start));
+ assert(std::abs(J(start + correction) + 0.833333) < 1e-6);
+ std::cout << J(start + correction) << std::endl;
+}
+
+int main() {
+ try {
+ testSampleFunction();
+ testTrivialFunction();
+ return 0;
+ }
+ catch (Dune::Exception &e) {
+ Dune::derr << "Dune reported error: " << e << std::endl;
+ }
+}
diff --git a/src/properscalarincreasingconvexfunction.hh b/src/properscalarincreasingconvexfunction.hh
new file mode 100644
index 0000000000000000000000000000000000000000..da30eb4b0f44c2ea68c929fdea7e30ba89619db0
--- /dev/null
+++ b/src/properscalarincreasingconvexfunction.hh
@@ -0,0 +1,24 @@
+class ProperScalarIncreasingConvexFunction {
+public:
+ virtual double operator()(const double s) const = 0;
+ virtual double leftDifferential(const double s) const = 0;
+ virtual double rightDifferential(const double s) const = 0;
+};
+
+class SampleFunction : public ProperScalarIncreasingConvexFunction {
+public:
+ double operator()(const double s) const { return (s < 1) ? s : (2 * s - 1); }
+
+ double leftDifferential(const double s) const { return (s <= 1) ? 1 : 2; }
+
+ double rightDifferential(const double s) const { return (s < 1) ? 1 : 2; }
+};
+
+class TrivialFunction : public ProperScalarIncreasingConvexFunction {
+public:
+ double operator()(const double) const { return 0; }
+
+ double leftDifferential(const double) const { return 0; }
+
+ double rightDifferential(const double) const { return 0; }
+};