Squashed 'third_party/boostorg/odeint/' content from commit 6ff2719

Change-Id: If4892e29c1a5e6cf3a7aa51486a2725c251b0c7d
git-subtree-dir: third_party/boostorg/odeint
git-subtree-split: 6ff2719b6907b86596c3d43e88c1bcfdf29df560
diff --git a/examples/vexcl/lorenz_ensemble.cpp b/examples/vexcl/lorenz_ensemble.cpp
new file mode 100644
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+++ b/examples/vexcl/lorenz_ensemble.cpp
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+/*
+ * Copyright 2012 Karsten Ahnert
+ * Copyright 2013 Mario Mulansky
+ *
+ * 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 <iostream>
+#include <vector>
+
+#include <vexcl/vexcl.hpp>
+
+#include <boost/numeric/odeint.hpp>
+//[ vexcl_includes
+#include <boost/numeric/odeint/external/vexcl/vexcl.hpp>
+//]
+
+namespace odeint = boost::numeric::odeint;
+
+//[ vexcl_state_types
+typedef vex::vector< double >    vector_type;
+typedef vex::multivector< double, 3 > state_type;
+//]
+
+
+//[ vexcl_system
+const double sigma = 10.0;
+const double b = 8.0 / 3.0;
+
+struct sys_func
+{
+    const vector_type &R;
+
+    sys_func( const vector_type &_R ) : R( _R ) { }
+
+    void operator()( const state_type &x , state_type &dxdt , double t ) const
+    {
+        dxdt(0) = -sigma * ( x(0) - x(1) );
+        dxdt(1) = R * x(0) - x(1) - x(0) * x(2);
+        dxdt(2) = - b * x(2) + x(0) * x(1);
+    }
+};
+//]
+
+
+int main( int argc , char **argv )
+{
+    using namespace std;
+    using namespace odeint;
+
+    //[ vexcl_main
+    // setup the opencl context
+    vex::Context ctx( vex::Filter::Type(CL_DEVICE_TYPE_GPU) );
+    std::cout << ctx << std::endl;
+
+    // set up number of system, time step and integration time
+    const size_t n = 1024 * 1024;
+    const double dt = 0.01;
+    const double t_max = 1000.0;
+
+    // initialize R
+    double Rmin = 0.1 , Rmax = 50.0 , dR = ( Rmax - Rmin ) / double( n - 1 );
+    std::vector<double> x( n * 3 ) , r( n );
+    for( size_t i=0 ; i<n ; ++i ) r[i] = Rmin + dR * double( i );
+    vector_type R( ctx.queue() , r );
+
+    // initialize the state of the lorenz ensemble
+    state_type X(ctx.queue(), n);
+    X(0) = 10.0;
+    X(1) = 10.0;
+    X(2) = 10.0;
+
+    // create a stepper
+    runge_kutta4< state_type > stepper;
+
+    // solve the system
+    integrate_const( stepper , sys_func( R ) , X , 0.0 , t_max , dt );
+    //]
+
+    std::vector< double > res( 3 * n );
+    vex::copy( X(0) , res );
+    for( size_t i=0 ; i<n ; ++i )
+        cout << r[i] << "\t" << res[i] << "\t" << "\n";
+}