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+// Copyright Jim Bosch 2010-2012.
+// Distributed under the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+
+#include <boost/python/numpy.hpp>
+
+#include <cmath>
+#include <memory>
+
+#ifndef M_PI
+#include <boost/math/constants/constants.hpp>
+const double M_PI = boost::math::constants::pi<double>();
+#endif
+
+namespace bp = boost::python;
+namespace bn = boost::python::numpy;
+
+/**
+ * A 2x2 matrix class, purely for demonstration purposes.
+ *
+ * Instead of wrapping this class with Boost.Python, we'll convert it to/from numpy.ndarray.
+ */
+class matrix2 {
+public:
+
+ double & operator()(int i, int j) {
+ return _data[i*2 + j];
+ }
+
+ double const & operator()(int i, int j) const {
+ return _data[i*2 + j];
+ }
+
+ double const * data() const { return _data; }
+
+private:
+ double _data[4];
+};
+
+/**
+ * A 2-element vector class, purely for demonstration purposes.
+ *
+ * Instead of wrapping this class with Boost.Python, we'll convert it to/from numpy.ndarray.
+ */
+class vector2 {
+public:
+
+ double & operator[](int i) {
+ return _data[i];
+ }
+
+ double const & operator[](int i) const {
+ return _data[i];
+ }
+
+ double const * data() const { return _data; }
+
+ vector2 operator+(vector2 const & other) const {
+ vector2 r;
+ r[0] = _data[0] + other[0];
+ r[1] = _data[1] + other[1];
+ return r;
+ }
+
+ vector2 operator-(vector2 const & other) const {
+ vector2 r;
+ r[0] = _data[0] - other[0];
+ r[1] = _data[1] - other[1];
+ return r;
+ }
+
+private:
+ double _data[2];
+};
+
+/**
+ * Matrix-vector multiplication.
+ */
+vector2 operator*(matrix2 const & m, vector2 const & v) {
+ vector2 r;
+ r[0] = m(0, 0) * v[0] + m(0, 1) * v[1];
+ r[1] = m(1, 0) * v[0] + m(1, 1) * v[1];
+ return r;
+}
+
+/**
+ * Vector inner product.
+ */
+double dot(vector2 const & v1, vector2 const & v2) {
+ return v1[0] * v2[0] + v1[1] * v2[1];
+}
+
+/**
+ * This class represents a simple 2-d Gaussian (Normal) distribution, defined by a
+ * mean vector 'mu' and a covariance matrix 'sigma'.
+ */
+class bivariate_gaussian {
+public:
+
+ vector2 const & get_mu() const { return _mu; }
+
+ matrix2 const & get_sigma() const { return _sigma; }
+
+ /**
+ * Evaluate the density of the distribution at a point defined by a two-element vector.
+ */
+ double operator()(vector2 const & p) const {
+ vector2 u = _cholesky * (p - _mu);
+ return 0.5 * _cholesky(0, 0) * _cholesky(1, 1) * std::exp(-0.5 * dot(u, u)) / M_PI;
+ }
+
+ /**
+ * Evaluate the density of the distribution at an (x, y) point.
+ */
+ double operator()(double x, double y) const {
+ vector2 p;
+ p[0] = x;
+ p[1] = y;
+ return operator()(p);
+ }
+
+ /**
+ * Construct from a mean vector and covariance matrix.
+ */
+ bivariate_gaussian(vector2 const & mu, matrix2 const & sigma)
+ : _mu(mu), _sigma(sigma), _cholesky(compute_inverse_cholesky(sigma))
+ {}
+
+private:
+
+ /**
+ * This evaluates the inverse of the Cholesky factorization of a 2x2 matrix;
+ * it's just a shortcut in evaluating the density.
+ */
+ static matrix2 compute_inverse_cholesky(matrix2 const & m) {
+ matrix2 l;
+ // First do cholesky factorization: l l^t = m
+ l(0, 0) = std::sqrt(m(0, 0));
+ l(0, 1) = m(0, 1) / l(0, 0);
+ l(1, 1) = std::sqrt(m(1, 1) - l(0,1) * l(0,1));
+ // Now do forward-substitution (in-place) to invert:
+ l(0, 0) = 1.0 / l(0, 0);
+ l(1, 0) = l(0, 1) = -l(0, 1) / l(1, 1);
+ l(1, 1) = 1.0 / l(1, 1);
+ return l;
+ }
+
+ vector2 _mu;
+ matrix2 _sigma;
+ matrix2 _cholesky;
+
+};
+
+/*
+ * We have a two options for wrapping get_mu and get_sigma into NumPy-returning Python methods:
+ * - we could deep-copy the data, making totally new NumPy arrays;
+ * - we could make NumPy arrays that point into the existing memory.
+ * The latter is often preferable, especially if the arrays are large, but it's dangerous unless
+ * the reference counting is correct: the returned NumPy array needs to hold a reference that
+ * keeps the memory it points to from being deallocated as long as it is alive. This is what the
+ * "owner" argument to from_data does - the NumPy array holds a reference to the owner, keeping it
+ * from being destroyed.
+ *
+ * Note that this mechanism isn't completely safe for data members that can have their internal
+ * storage reallocated. A std::vector, for instance, can be invalidated when it is resized,
+ * so holding a Python reference to a C++ class that holds a std::vector may not be a guarantee
+ * that the memory in the std::vector will remain valid.
+ */
+
+/**
+ * These two functions are custom wrappers for get_mu and get_sigma, providing the shallow-copy
+ * conversion with reference counting described above.
+ *
+ * It's also worth noting that these return NumPy arrays that cannot be modified in Python;
+ * the const overloads of vector::data() and matrix::data() return const references,
+ * and passing a const pointer to from_data causes NumPy's 'writeable' flag to be set to false.
+ */
+static bn::ndarray py_get_mu(bp::object const & self) {
+ vector2 const & mu = bp::extract<bivariate_gaussian const &>(self)().get_mu();
+ return bn::from_data(
+ mu.data(),
+ bn::dtype::get_builtin<double>(),
+ bp::make_tuple(2),
+ bp::make_tuple(sizeof(double)),
+ self
+ );
+}
+static bn::ndarray py_get_sigma(bp::object const & self) {
+ matrix2 const & sigma = bp::extract<bivariate_gaussian const &>(self)().get_sigma();
+ return bn::from_data(
+ sigma.data(),
+ bn::dtype::get_builtin<double>(),
+ bp::make_tuple(2, 2),
+ bp::make_tuple(2 * sizeof(double), sizeof(double)),
+ self
+ );
+}
+
+/**
+ * To allow the constructor to work, we need to define some from-Python converters from NumPy arrays
+ * to the matrix/vector types. The rvalue-from-python functionality is not well-documented in Boost.Python
+ * itself; you can learn more from boost/python/converter/rvalue_from_python_data.hpp.
+ */
+
+/**
+ * We start with two functions that just copy a NumPy array into matrix/vector objects. These will be used
+ * in the templated converted below. The first just uses the operator[] overloads provided by
+ * bp::object.
+ */
+static void copy_ndarray_to_mv2(bn::ndarray const & array, vector2 & vec) {
+ vec[0] = bp::extract<double>(array[0]);
+ vec[1] = bp::extract<double>(array[1]);
+}
+
+/**
+ * Here, we'll take the alternate approach of using the strides to access the array's memory directly.
+ * This can be much faster for large arrays.
+ */
+static void copy_ndarray_to_mv2(bn::ndarray const & array, matrix2 & mat) {
+ // Unfortunately, get_strides() can't be inlined, so it's best to call it once up-front.
+ Py_intptr_t const * strides = array.get_strides();
+ for (int i = 0; i < 2; ++i) {
+ for (int j = 0; j < 2; ++j) {
+ mat(i, j) = *reinterpret_cast<double const *>(array.get_data() + i * strides[0] + j * strides[1]);
+ }
+ }
+}
+
+/**
+ * Here's the actual converter. Because we've separated the differences into the above functions,
+ * we can write a single template class that works for both matrix2 and vector2.
+ */
+template <typename T, int N>
+struct mv2_from_python {
+
+ /**
+ * Register the converter.
+ */
+ mv2_from_python() {
+ bp::converter::registry::push_back(
+ &convertible,
+ &construct,
+ bp::type_id< T >()
+ );
+ }
+
+ /**
+ * Test to see if we can convert this to the desired type; if not return zero.
+ * If we can convert, returned pointer can be used by construct().
+ */
+ static void * convertible(PyObject * p) {
+ try {
+ bp::object obj(bp::handle<>(bp::borrowed(p)));
+ std::auto_ptr<bn::ndarray> array(
+ new bn::ndarray(
+ bn::from_object(obj, bn::dtype::get_builtin<double>(), N, N, bn::ndarray::V_CONTIGUOUS)
+ )
+ );
+ if (array->shape(0) != 2) return 0;
+ if (N == 2 && array->shape(1) != 2) return 0;
+ return array.release();
+ } catch (bp::error_already_set & err) {
+ bp::handle_exception();
+ return 0;
+ }
+ }
+
+ /**
+ * Finish the conversion by initializing the C++ object into memory prepared by Boost.Python.
+ */
+ static void construct(PyObject * obj, bp::converter::rvalue_from_python_stage1_data * data) {
+ // Extract the array we passed out of the convertible() member function.
+ std::auto_ptr<bn::ndarray> array(reinterpret_cast<bn::ndarray*>(data->convertible));
+ // Find the memory block Boost.Python has prepared for the result.
+ typedef bp::converter::rvalue_from_python_storage<T> storage_t;
+ storage_t * storage = reinterpret_cast<storage_t*>(data);
+ // Use placement new to initialize the result.
+ T * m_or_v = new (storage->storage.bytes) T();
+ // Fill the result with the values from the NumPy array.
+ copy_ndarray_to_mv2(*array, *m_or_v);
+ // Finish up.
+ data->convertible = storage->storage.bytes;
+ }
+
+};
+
+
+BOOST_PYTHON_MODULE(gaussian) {
+ bn::initialize();
+
+ // Register the from-python converters
+ mv2_from_python< vector2, 1 >();
+ mv2_from_python< matrix2, 2 >();
+
+ typedef double (bivariate_gaussian::*call_vector)(vector2 const &) const;
+
+ bp::class_<bivariate_gaussian>("bivariate_gaussian", bp::init<bivariate_gaussian const &>())
+
+ // Declare the constructor (wouldn't work without the from-python converters).
+ .def(bp::init< vector2 const &, matrix2 const & >())
+
+ // Use our custom reference-counting getters
+ .add_property("mu", &py_get_mu)
+ .add_property("sigma", &py_get_sigma)
+
+ // First overload accepts a two-element array argument
+ .def("__call__", (call_vector)&bivariate_gaussian::operator())
+
+ // This overload works like a binary NumPy universal function: you can pass
+ // in scalars or arrays, and the C++ function will automatically be called
+ // on each element of an array argument.
+ .def("__call__", bn::binary_ufunc<bivariate_gaussian,double,double,double>::make())
+ ;
+}