From afb4ff049c8040189de152ebbb3782f9fa407f76 Mon Sep 17 00:00:00 2001 From: Mario Mulansky Date: Sun, 27 Nov 2011 20:59:18 +0100 Subject: [PATCH] more docs --- .../concepts.html | 9 +- .../concepts/controlled_stepper.html | 45 ++-- .../concepts/dense_output_stepper.html | 45 ++-- .../concepts/error_stepper.html | 41 ++- .../concepts/implicit_system.html | 29 ++- .../concepts/observer.html | 27 +- .../concepts/simple_symplectic_system.html | 27 +- .../concepts/state_algebra_operations.html | 80 +++--- .../concepts/state_wrapper.html | 27 +- .../concepts/stepper.html | 57 +++-- .../concepts/symplectic_system.html | 27 +- .../concepts/system.html | 27 +- .../extend_odeint.html | 9 +- .../adapt_your_own_operations.html | 9 +- .../adapt_your_own_state_types.html | 236 ++++++++++++++---- .../extend_odeint/write_own_steppers.html | 9 +- .../getting_started.html | 9 +- .../getting_started/overview.html | 27 +- .../getting_started/short_example.html | 20 +- .../usage__compilation__headers.html | 12 +- .../odeint_in_detail.html | 9 +- .../algebras_and_operations.html | 9 +- .../generation_functions.html | 9 +- .../odeint_in_detail/integrate_functions.html | 63 +++-- .../odeint_in_detail/steppers.html | 109 +++++--- .../odeint_in_detail/using_boost__range.html | 9 +- .../odeint_in_detail/using_boost__ref.html | 9 +- .../old_concepts.html | 9 +- .../old_concepts/basic_stepper.html | 33 ++- .../old_concepts/compositestepper.html | 9 +- .../old_concepts/controlled_stepper.html | 31 ++- .../old_concepts/dense_ouput_stepper.html | 9 +- .../old_concepts/error_stepper.html | 35 ++- .../old_concepts/size_adjusting_stepper.html | 9 +- .../old_reference.html | 9 +- .../old_reference/algebras.html | 9 +- .../old_reference/integration_functions.html | 13 +- .../old_reference/operations.html | 9 +- .../old_reference/resizing.html | 9 +- .../old_reference/stepper_classes.html | 9 +- .../tutorial.html | 9 +- .../tutorial/all_examples.html | 9 +- ...haotic_systems_and_lyapunov_exponents.html | 41 +-- .../tutorial/harmonic_oscillator.html | 26 +- .../tutorial/references.html | 9 +- .../tutorial/solar_system.html | 41 +-- .../tutorial/special_topics.html | 117 +++++---- .../tutorial/stiff_systems.html | 13 +- .../tutorial/using_cuda_and_thrust.html | 157 ++++++------ doc/index.html | 17 +- doc/odeint/reference.html | 9 +- libs/numeric/odeint/doc/extend.qbk | 67 +++-- libs/numeric/odeint/examples/point_type.hpp | 24 +- 53 files changed, 961 insertions(+), 760 deletions(-) diff --git a/doc/boost_sandbox_numeric_odeint/concepts.html b/doc/boost_sandbox_numeric_odeint/concepts.html index 47bf8e5f..4b916cc1 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts.html +++ b/doc/boost_sandbox_numeric_odeint/concepts.html @@ -3,8 +3,8 @@ Concepts - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+
@@ -44,8 +44,7 @@
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/controlled_stepper.html b/doc/boost_sandbox_numeric_odeint/concepts/controlled_stepper.html index f5e3cc46..104f5f29 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/controlled_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/controlled_stepper.html @@ -3,8 +3,8 @@ Controlled Stepper - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+

Controlled Stepper @@ -25,9 +25,9 @@ to be used within integrate functions.

-

- - Description +
+ + Description

A controlled stepper following this Controlled Stepper concept provides the @@ -36,9 +36,9 @@ with a given step-size dt. Depending on an error estimate of the solution the step might be rejected and a smaller step-size is suggested.

-
- - Notation +
+ + Notation

@@ -77,9 +77,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -178,32 +178,31 @@
-
- - Models +
+ + Models
-
    -
  • +
      +
    • controlled_error_stepper< runge_kutta_cash_karp54 >
      • -
    • +
    • controlled_error_stepper_fsal< runge_kutta_dopri5 >
      • -
    • +
    • controlled_error_stepper< runge_kutta_fehlberg78 >
      • -
    • +
    • rosenbrock4_controller
      • -
    • +
    • bulirsch_stoer
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/dense_output_stepper.html b/doc/boost_sandbox_numeric_odeint/concepts/dense_output_stepper.html index 2e9f4fc9..7ead6367 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/dense_output_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/dense_output_stepper.html @@ -3,8 +3,8 @@ Dense Output Stepper - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+

Dense Output Stepper @@ -25,9 +25,9 @@ to be used within integrate functions.

-

- - Description +
+ + Description

A dense ouput stepper following this Dense Output Stepper concept provides @@ -37,9 +37,9 @@ to calculate the state x(t') at any point t <= t' <= t+dt.

-
- - Associated +
+ + Associated types
@@ -55,9 +55,9 @@

-
- - Notation +
+ + Notation

@@ -92,9 +92,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -284,24 +284,23 @@
-
- - Models +
+ + Models
-
    -
  • +
      +
    • dense_output_controlled_explicit_fsal< controlled_error_stepper_fsal< runge_kutta_dopri5 >
      • -
    • +
    • bulirsch_stoer_dense_out
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/error_stepper.html b/doc/boost_sandbox_numeric_odeint/concepts/error_stepper.html index 041deb17..8b8ece9e 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/error_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/error_stepper.html @@ -3,8 +3,8 @@ Error Stepper - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+

Error Stepper @@ -24,9 +24,9 @@ This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper.

-

- - Description +
+ + Description

An error stepper following this Error Stepper concept is capable of doing @@ -40,9 +40,9 @@ Symplectic System or Implicit System.

-
- - Notation +
+ + Notation

@@ -90,9 +90,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -187,26 +187,25 @@
-
- - Models +
+ + Models
-
    -
  • +
      +
    • runge_kutta_cash_karp54
      • -
    • +
    • runge_kutta_dopri5
      • -
    • +
    • runge_kutta_fehlberg78
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/implicit_system.html b/doc/boost_sandbox_numeric_odeint/concepts/implicit_system.html index 6f195b64..4610c182 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/implicit_system.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/implicit_system.html @@ -3,8 +3,8 @@ Implicit System - - + + @@ -15,27 +15,27 @@
PrevUpHomeNext
-
+
-
- - Description +
+ + Description

This concept describes how to define a ODE that can be solved by an implicit routine. Implicit routines need not only the function f(x,t) - but also the Jacobian df/dx = A(x,t). A + but also the Jacobian /dfdx = A(x,t). A is a matrix and implicit routines need to solve the linear problem Ax = b. In odeint this is implemented with use of Boost.UBlas, therefore, the state_type implicit routines is ublas::vector and the matrix is defined as ublas::matrix.

-
- - Notation +
+ + Notation

@@ -70,9 +70,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -162,8 +162,7 @@
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/observer.html b/doc/boost_sandbox_numeric_odeint/concepts/observer.html index c58f79c1..0edb1d42 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/observer.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/observer.html @@ -3,8 +3,8 @@ Observer - - + + @@ -15,13 +15,13 @@
PrevUpHomeNext
-
+
-
- - Description +
+ + Description

The Observer concept is used in integrate @@ -32,9 +32,9 @@ or at user defined time points depending on which integrate function is used.

-
- - Notation +
+ + Notation

@@ -65,9 +65,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -128,8 +128,7 @@
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/simple_symplectic_system.html b/doc/boost_sandbox_numeric_odeint/concepts/simple_symplectic_system.html index ca0ef162..70478d4f 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/simple_symplectic_system.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/simple_symplectic_system.html @@ -3,8 +3,8 @@ Simple Symplectic System - - + + @@ -15,14 +15,14 @@
PrevUpHomeNext
-
+
-
- - Description +
+ + Description

In most Hamiltonian systems the kinetic term is a quadratic term in the momentum @@ -44,9 +44,9 @@ equation for p' has to be provided to the symplectic stepper. We call this concept Simple_Symplectic_System

-
- - Notation +
+ + Notation

@@ -77,9 +77,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -166,8 +166,7 @@
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/state_algebra_operations.html b/doc/boost_sandbox_numeric_odeint/concepts/state_algebra_operations.html index 3e61e5c6..8548076d 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/state_algebra_operations.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/state_algebra_operations.html @@ -3,8 +3,8 @@ State Algebra Operations - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+

State Algebra Operations @@ -40,9 +40,9 @@ and no algebra/operations are used.

-
- - Description +
+ + Description

The State, Algebra and Operations @@ -78,13 +78,13 @@ Algebra and Operations are used together within the stepper implementations.

-
+
-
- - Notation +
+ + Notation

@@ -111,7 +111,7 @@ Type that represents a general scale_sum operation, N should be replaced by a number from 1 to 14.

-
scale_sum/N/
+
scale_sumN

Object of type ScaleSumN, N should be replaced by a @@ -142,9 +142,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -258,18 +258,21 @@ @@ -281,13 +284,13 @@

- Operations::scale_sum/N/< Value1 , ... , ValueN > + Operations::scale_sumN< Value1 + , ... , ValueN >

- ScaleSum/N/ + ScaleSumN

- Get the ScaleSum/N/ type from Operations, N - should be replaced by a number from 1 to 14. + Get the ScaleSumN type + from Operations, + N should be replaced + by a number from 1 to 14.

- ScaleSum/N/< Value1 , ... , ValueN >( a1 , ... - , aN ) + ScaleSumN< Value1 , ... , ValueN + >( a1 , ... , aN )

- ScaleSum/N/ + ScaleSumN

@@ -307,7 +310,7 @@

- scale_sum/N/( y , x1 , ... , xN ) + scale_sumN( y , x1 , ... , xN )

@@ -410,13 +413,13 @@
-
+
-
- - Notation +
+ + Notation

@@ -429,7 +432,7 @@

The algebra type

-
Operation/N/
+
OperationN

An N-ary operation type, N should be a number from @@ -439,7 +442,7 @@

Object of type Algebra

-
operation/N/
+
operationN

Object of type Operation/N

@@ -452,9 +455,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -554,8 +557,8 @@

- algebra.for_each/N/( y , x1 , ... , xN , operation/N/ - ) + algebra.for_eachN( y , x1 , ... + , xN , operationN )

@@ -565,8 +568,8 @@

- Calls operation/N/( y_i , x1_i , ... , xN_i ) - for each element y_i + Calls operationN( y_i , x1_i , + ... , xN_i ) for each element y_i of y and x1_i of x1 and so on. N should be replaced by a number between 1 and 14. @@ -576,7 +579,7 @@

-
+

Pre-Defined implementations @@ -743,7 +746,7 @@

-
+

Example expressions @@ -814,8 +817,7 @@

-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/state_wrapper.html b/doc/boost_sandbox_numeric_odeint/concepts/state_wrapper.html index 587376e0..af174459 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/state_wrapper.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/state_wrapper.html @@ -3,8 +3,8 @@ State Wrapper - - + + @@ -15,14 +15,14 @@
PrevUpHomeNext
-
+
-
- - Description +
+ + Description

The State Wrapper @@ -30,9 +30,9 @@ intermediate results within the stepper's do_step methods.

-
- - Notation +
+ + Notation

@@ -56,9 +56,9 @@

-
- - Valid +
+ + Valid Expressions
@@ -267,8 +267,7 @@
-
Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

+

Copyright © 2009 -2011 Karsten Ahnert and 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)

diff --git a/doc/boost_sandbox_numeric_odeint/concepts/stepper.html b/doc/boost_sandbox_numeric_odeint/concepts/stepper.html index c4633fb5..cb333d85 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/stepper.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/stepper.html @@ -3,8 +3,8 @@ Stepper - - + + @@ -15,7 +15,7 @@
PrevUpHomeNext
-
+
@@ -24,9 +24,9 @@ be used within the integrate functions.

-
- - Description +
+ + Description

The basic stepper concept. A basic stepper following this Stepper concept @@ -40,22 +40,22 @@ Symplectic System or Implicit System. Note that all error steppers are also basic steppers.

-
- - Refinement +
+ + Refinement of
-
    -
  • +
      +
    • DefaultConstructable
      • -
    • +
    • CopyConstructable
    -
    - - Notation +
    + + Notation

    @@ -95,9 +95,9 @@

    -
    - - Valid +
    + + Valid Expressions
    @@ -187,32 +187,31 @@
    -
    - - Models +
    + + Models
    -
      -
    • +
        +
      • runge_kutta4
        • -
      • +
      • euler
        • -
      • +
      • runge_kutta_cash_karp54
        • -
      • +
      • runge_kutta_dopri5
        • -
      • +
      • runge_kutta_fehlberg78
    -
    Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

    +

    Copyright © 2009 -2011 Karsten Ahnert and 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)

    diff --git a/doc/boost_sandbox_numeric_odeint/concepts/symplectic_system.html b/doc/boost_sandbox_numeric_odeint/concepts/symplectic_system.html index 58ffdf3f..7ee61a09 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/symplectic_system.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/symplectic_system.html @@ -3,8 +3,8 @@ Symplectic System - - + + @@ -15,14 +15,14 @@
    PrevUpHomeNext
    -
    +
    -
    - - Description +
    + + Description

    This concept describes how to define a symplectic system written with generalized @@ -58,9 +58,9 @@ std::pair of functions or a functors. Symplectic systems are used in symplectic steppers like symplectic_rkn_sb3a_mclachlan.

    -
    - - Notation +
    + + Notation

    @@ -107,9 +107,9 @@

    -
    - - Valid +
    + + Valid expressions
    @@ -220,8 +220,7 @@
    -
    Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

    +

    Copyright © 2009 -2011 Karsten Ahnert and 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)

    diff --git a/doc/boost_sandbox_numeric_odeint/concepts/system.html b/doc/boost_sandbox_numeric_odeint/concepts/system.html index d3e50519..0f6478b7 100644 --- a/doc/boost_sandbox_numeric_odeint/concepts/system.html +++ b/doc/boost_sandbox_numeric_odeint/concepts/system.html @@ -3,8 +3,8 @@ System - - + + @@ -15,13 +15,13 @@
    PrevUpHomeNext
    -
    +
    -
    - - Description +
    + + Description

    The System concept models the algorithmic implementation of the rhs. of the @@ -34,9 +34,9 @@ System and Implicit System.

    -
    - - Notation +
    + + Notation

    @@ -75,9 +75,9 @@

    -
    - - Valid +
    + + Valid expressions
    @@ -138,8 +138,7 @@
    -
    Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

    +

    Copyright © 2009 -2011 Karsten Ahnert and 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)

    diff --git a/doc/boost_sandbox_numeric_odeint/extend_odeint.html b/doc/boost_sandbox_numeric_odeint/extend_odeint.html index 2cc175a4..561f0252 100644 --- a/doc/boost_sandbox_numeric_odeint/extend_odeint.html +++ b/doc/boost_sandbox_numeric_odeint/extend_odeint.html @@ -3,8 +3,8 @@ Extend odeint - - + + @@ -15,7 +15,7 @@
    PrevUpHomeNext
    -
    +
    @@ -33,8 +33,7 @@
    -
    Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

    +

    Copyright © 2009 -2011 Karsten Ahnert and 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)

    diff --git a/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html b/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html index c76bbb5f..36e2bd8a 100644 --- a/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html +++ b/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html @@ -3,8 +3,8 @@ Adapt your own operations - - + + @@ -15,7 +15,7 @@
    PrevUpHomeNext
    -
    +

    Adapt your own operations @@ -29,8 +29,7 @@

    -
    Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

    +

    Copyright © 2009 -2011 Karsten Ahnert and 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)

    diff --git a/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_state_types.html b/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_state_types.html index b84516e8..0df5f409 100644 --- a/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_state_types.html +++ b/doc/boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_state_types.html @@ -3,8 +3,8 @@ Adapt your own state types - - + + @@ -15,7 +15,7 @@
    PrevUpHomeNext
    -
    +

    Adapt your own state types @@ -44,14 +44,14 @@ are to be performed on state types. So when introducing new state types to odeint, the following points have to be considered:

    -
      -
    • +
        +
      • construction/destruction
        • -
      • +
      • resizing (if possible/required)
        • -
      • +
      • algebraic operations
      @@ -61,7 +61,7 @@ or a boost::array as state type no additional work is required, they just work out of the box.

      -
      +
      @@ -366,7 +366,7 @@

    -
    +
    Vectors derived from std::vector @@ -381,10 +381,7 @@ as resizeable as it is a dynamically sized array:

    -<<<<<<< HEAD -======= ->>>>>>> 730d9205ac4754193e77fe15092e7003f6153a31 

    class my_vector : public std::vector< double >
 {
@@ -397,11 +394,11 @@
         : std::vector< double >()
     { }
 
-// ...
-};
-
-// define my_vector as reizeable
+// ...
+};
 
+// define my_vector as reizeable
+
 namespace boost { namespace numeric { namespace odeint {
 
 template<>
@@ -423,7 +420,7 @@
             can be found in my_vector.cpp
    -
    +
    @@ -518,10 +515,7 @@ to work with odeint. The following code shows the required template specializations:

    -<<<<<<< HEAD -======= ->>>>>>> 730d9205ac4754193e77fe15092e7003f6153a31 

    typedef std::list< double > state_type;
 
@@ -529,15 +523,15 @@
 
 template< >
 struct is_resizeable< state_type >
-{ // declare resizeablility
-    typedef boost::true_type type;
+{ // declare resizeablility
+    typedef boost::true_type type;
     const static bool value = type::value;
 };
 
-template< >
+template< > 
 struct same_size_impl< state_type , state_type >
-{ // define how to check size
-    static bool same_size( const state_type &v1 ,
+{ // define how to check size
+    static bool same_size( const state_type &v1 ,
                            const state_type &v2 )
     {
         return v1.size() == v2.size();
@@ -546,15 +540,15 @@
 
 template< >
 struct resize_impl< state_type , state_type >
-{ // define how to resize
-    static void resize( state_type &v1 ,
+{ // define how to resize
+    static void resize( state_type &v1 ,
                         const state_type &v2 )
     {
         v1.resize( v2.size() );
     }
 };
 
-} } }
+} } }

    @@ -565,12 +559,14 @@

    -
    +
    +
    Vector + Space Algebra
    Boost.Ublas
    GSL Vector
    @@ -579,31 +575,152 @@ If your state type is not supported by Boost.Range there are several possibilities to tell odeint how to do algebraic operations:

    -
      -
    • +
        +
      • Implement boost::begin and boost::end for your state type so it works with Boost.Range.
        • -
      • +
      • Implement vector-vector addition operator + and scalar-vector multiplication operator * and use the non-standard vector_space_algebra.
        • -
      • +
      • Implement your own algebra that defines the required operations.
      -
      +
      +
      +

      + The standard way of performing algebraic operations on container-like + state types in odeint is to iterate through the elements of the container + and perform the operations element-wise on the underlying value type. + This is realized by means of the range_algebra + that uses Boost.Range + for obtaining iterators of the state types. However, there are other + ways to implement the algebraic operations on containers, one of which + is defining the addition/multiplication operators for the containers + directly and then using the vector_space_algebra. + If you use this algebra, the following operators have to be defined for + the state_type: +

      +
      ++++++ + + + + + + + + + + + + + + + + + + + + + + + + + + +
      +

      + Name +

      +       		+

      + Expression +

      +       		+

      + Type +

      +       		+

      + Semantics +

      +
      +

      + Addition +

      +       		+

      + x + + y +

      +       		+

      + state_type +

      +       		+

      + Calculates the vector sum 'x+y'. +

      +
      +

      + Assign addition +

      +       		+

      + x += + y +

      +       		+

      + state_type +

      +       		+

      + Performs x+y in place. +

      +
      +

      + Scalar multiplication +

      +       		+

      + a * + x +

      +       		+

      + state_type +

      +       		+

      + Performs multiplication of vector x with scalar a. +

      +
      +
      +

      - As an example of the above we will adopt ublas::vector - from Boost.UBlas + As an example for the employment of the vector_space_algebra + we will adopt ublas::vector from Boost.UBlas to work as a state type in odeint. This is particularily easy because - ublas::vector supports Boost.Range, - including boost::size. It also has a resize member function - so all that has to be done in this case is to declare resizability: + ublas::vector supports vector-vector addition + and scalar-vector multiplication as well as boost::size. + It also has a resize member function so all that has to be done in this + case is to declare resizability:

      @@ -624,12 +741,30 @@

      - This immediately makes ublas::vector - working with odeint as all other requirements are fullfilled by default - in this case. You can find the full example in lorenz_ublas.cpp. + Now ublas::vector can be used as state type in odeint by specifying the + vector_space_algebra + as algebra in the template parameter list of the stepper. The following + code shows the corresponding definitions: +

      +

      + +

      +
      int main()
+{
+    state_type x(3);
+    x[0] = 10.0; x[1] = 5.0 ; x[2] = 0.0;
+    typedef runge_kutta4< state_type , double , state_type , double , vector_space_algebra > stepper;
+    integrate_const( stepper() , lorenz , x , 
+                     0.0 , 10.0 , 0.1 );
+}
+
      +

      +

      +

      + You can find the full example in lorenz_ublas.cpp.

      -
      +
      GSL Vector @@ -732,7 +867,9 @@ 
      /*
  * defines an iterator for gsl_vector
  */
-class gsl_vector_iterator : public boost::iterator_facade< gsl_vector_iterator , double , boost::random_access_traversal_tag >
+class gsl_vector_iterator 
+      : public boost::iterator_facade< gsl_vector_iterator , double , 
+                                       boost::random_access_traversal_tag >
 {
 public :
 
@@ -775,14 +912,14 @@
             Finally, the bindings for Boost.Range
             are added: 
 
      
-
      // template<>
-inline gsl_vector_iterator range_begin( gsl_vector *x )
+
      // template<>
+inline gsl_vector_iterator range_begin( gsl_vector *x )
 {
     return gsl_vector_iterator( x );
 }
 
-// template<>
-inline gsl_vector_iterator range_end( gsl_vector *x )
+// template<>
+inline gsl_vector_iterator range_end( gsl_vector *x )
 {
     return end_iterator( x );
 }
@@ -800,8 +937,7 @@
      -
      Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

      +

      Copyright © 2009 -2011 Karsten Ahnert and 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)

      diff --git a/doc/boost_sandbox_numeric_odeint/extend_odeint/write_own_steppers.html b/doc/boost_sandbox_numeric_odeint/extend_odeint/write_own_steppers.html index d025a5b3..b2fec6f7 100644 --- a/doc/boost_sandbox_numeric_odeint/extend_odeint/write_own_steppers.html +++ b/doc/boost_sandbox_numeric_odeint/extend_odeint/write_own_steppers.html @@ -3,8 +3,8 @@ Write own steppers - - + + @@ -15,14 +15,13 @@
      PrevUpHomeNext
      -

      +
      -
      Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

      +

      Copyright © 2009 -2011 Karsten Ahnert and 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)

      diff --git a/doc/boost_sandbox_numeric_odeint/getting_started.html b/doc/boost_sandbox_numeric_odeint/getting_started.html index 4bb7bb1b..a92d20fa 100644 --- a/doc/boost_sandbox_numeric_odeint/getting_started.html +++ b/doc/boost_sandbox_numeric_odeint/getting_started.html @@ -3,8 +3,8 @@ Getting started - - + + @@ -15,7 +15,7 @@
      PrevUpHomeNext
      -
      +
      @@ -29,8 +29,7 @@
      -
      Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

      +

      Copyright © 2009 -2011 Karsten Ahnert and 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)

      diff --git a/doc/boost_sandbox_numeric_odeint/getting_started/overview.html b/doc/boost_sandbox_numeric_odeint/getting_started/overview.html index 963854c8..1f1578e5 100644 --- a/doc/boost_sandbox_numeric_odeint/getting_started/overview.html +++ b/doc/boost_sandbox_numeric_odeint/getting_started/overview.html @@ -3,8 +3,8 @@ Overview - - + + @@ -15,7 +15,7 @@
      PrevUpHomeNext
      -
      +
      @@ -57,33 +57,33 @@ or a boost::array, we provide native support for the following libraries:

      -
        -
      • +
        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/getting_started/short_example.html b/doc/boost_sandbox_numeric_odeint/getting_started/short_example.html index c4096118..b79da97e 100644 --- a/doc/boost_sandbox_numeric_odeint/getting_started/short_example.html +++ b/doc/boost_sandbox_numeric_odeint/getting_started/short_example.html @@ -3,8 +3,8 @@ Short Example - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Short Example @@ -30,6 +30,7 @@ = (p,-q+γ p):

        + 

        /* The type of container used to hold the state vector */
 typedef std::vector< double > state_type;
@@ -59,10 +60,11 @@
         start:
       
        
 
        
+        
 
        
 
        state_type x(2);
-x[0] = 1.0; // start at x=1.0, p=0.0
-x[1] = 0.0;
+x[0] = 1.0; // start at x=1.0, p=0.0
+x[1] = 0.0;
 
        
 
        
       
        
@@ -73,6 +75,7 @@
         stepper (5th order) and uses adaptive stepsize.
       
        
 
        
+        
 
        
 
        size_t steps = integrate( harmonic_oscillator ,
         x , 0.0 , 10.0 , 0.1 );
@@ -93,6 +96,7 @@
         rhs must then be implemented as a functor having defined the ()-operator:
       
        
 
        
+        
 
        
 
        /* The rhs of x' = f(x) defined as a class */
 class harm_osc {
@@ -115,6 +119,7 @@
         which can be used via
       
        
 
        
+        
 
        
 
        harm_osc ho(0.15);
 steps = integrate( ho ,
@@ -129,6 +134,7 @@
         to provide a reasonable observer. An example is
       
        
 
        
+        
 
        
 
        struct push_back_state_and_time
 {
@@ -152,6 +158,7 @@
         pass this container to the integration function:
       
        
 
        
+        
 
        
 
        vector<state_type> x_vec;
 vector<double> times;
@@ -179,8 +186,7 @@

        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/getting_started/usage__compilation__headers.html b/doc/boost_sandbox_numeric_odeint/getting_started/usage__compilation__headers.html index 81c1cb6e..3cf5f598 100644 --- a/doc/boost_sandbox_numeric_odeint/getting_started/usage__compilation__headers.html +++ b/doc/boost_sandbox_numeric_odeint/getting_started/usage__compilation__headers.html @@ -3,8 +3,8 @@ Usage, Compilation, Headers - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Usage, Compilation, Headers @@ -25,12 +25,13 @@ library. It can be include by

        + 

        #include <boost/numeric/odeint.hpp>

        which includes all headers in the library. All functions and classes from - odeint live in the namespace + odeint live in the namespace 

        using namespace boost::numeric::odeint;
        @@ -39,8 +40,7 @@

        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail.html index 0aa2a1b4..4d673c88 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail.html @@ -3,8 +3,8 @@ Odeint in detail - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Odeint in detail @@ -36,8 +36,7 @@

        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/algebras_and_operations.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/algebras_and_operations.html index 03255a30..4014b28e 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/algebras_and_operations.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/algebras_and_operations.html @@ -3,8 +3,8 @@ Algebras and operations - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Algebras and operations @@ -26,8 +26,7 @@

        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/generation_functions.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/generation_functions.html index ff172bd6..7be49e9f 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/generation_functions.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/generation_functions.html @@ -3,8 +3,8 @@ Generation functions - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Generation functions @@ -195,8 +195,7 @@

        -
        Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

        +

        Copyright © 2009 -2011 Karsten Ahnert and 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)

        diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/integrate_functions.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/integrate_functions.html index ea854d8e..3161ac2d 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/integrate_functions.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/integrate_functions.html @@ -3,8 +3,8 @@ Integrate functions - - + + @@ -15,7 +15,7 @@
        PrevUpHomeNext
        -
        +

        Integrate functions @@ -35,9 +35,9 @@ Output Stepper. Depending on the abilities of the stepper, the integrate functions make use of step-size control or dense output.

        -

        - - Equidistant +
        + + Equidistant observer calls

        @@ -81,15 +81,15 @@ steps you should prefer the integrate_n_steps function below.

        -
          -
        • +
            +
          • If stepper is a Stepper or Error Stepper then dt is also the step size used for integration and the observer is called just after every step.
            • -
          • +
          • If stepper is a Controlled Stepper then dt is the initial step size. The actual step size will change due to error @@ -100,7 +100,7 @@ Stepper is reasonable here only if dt is considerably larger than typical step sizes used by the stepper.
            • -
          • +
          • If stepper is a __dense_out_stepper then dt is the initial step size. The actual step size will be adjusted during integration due @@ -108,9 +108,9 @@ calculate x(t) at t = t0 + n dt.
          -
          - - Observer +
          + + Observer calls at each step

          @@ -149,8 +149,8 @@ step of the provided stepper (and before the first step at t0). integrate_adaptive returns the number of steps performed during the integration.

          -
            -
          • +
              +
            • If stepper is a Stepper or Error Stepper then dt @@ -160,7 +160,7 @@ exactly at t1. If provided, the observer is called at each step.
              • -
            • +
            • If stepper is a Controlled Stepper then dt is the initial step size. The actual step size is changed according to @@ -169,16 +169,16 @@ If provided, the observer is called after each time step (and before the first step at t0).
              • -
            • +
            • If stepper is a __dense_out_stepper then dt is the initial step size and integrate_adaptive behaves just like for Controlled Stepper above. No dense output is used.
            -
            - - Observer +
            + + Observer calls at given time points

            @@ -225,8 +225,8 @@ integrate_times returns the number of steps performed during the integration.

            -
              -
            • +
                +
              • If stepper is a Stepper or Error Stepper dt is @@ -235,7 +235,7 @@ will be reduced to obtain the state x(t) exactly at the time point.
                • -
              • +
              • If stepper is a Controlled Stepper then dt is the initial step size. The actual step size is adjusted during integration @@ -243,7 +243,7 @@ is approached the step size is reduced to obtain the state x(t) exactly at the time point.
                • -
              • +
              • If stepper is a __dense_out_stepper then dt is the initial step size. The actual step size is adjusted during integration according @@ -251,9 +251,9 @@ at the time points from the sequence.
              -
              - - Integrate +
              + + Integrate a given number of steps

              @@ -308,9 +308,9 @@ This function returns the end time t0 + n*dt.

              -
              - - Convenience +
              + + Convenience integrate function

              @@ -344,8 +344,7 @@

            -
            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

            +

            Copyright © 2009 -2011 Karsten Ahnert and 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)

            diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html index 27a5b4e1..1d024cc7 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html @@ -3,8 +3,8 @@ Steppers - - + + @@ -15,7 +15,7 @@
            PrevUpHomeNext
            -
            +
            @@ -94,7 +94,7 @@ Since the system function is strongly related to the stepper type, such an introduction of a new stepper might result in a new type of system function.

            -
            +

            Explicit steppers @@ -130,14 +130,15 @@ is the Runge Kutta stepper of fourth order:

            + 

            runge_kutta4< state_type > rk;
-rk.do_step( sys1 , inout , t , dt );               // In-place transformation of inout
-rk.do_step( sys2 , inout , t , dt );               // Ok
-rk.do_step( sys1 , in , t , out , dt );            // Out-of-place transformation
-rk.do_step( sys1 , inout , dxdtin , t , dt );      // In-place tranformation of inout
-rk.do_step( sys1 , in , dxdtin , t , out , dt );   // Out-of-place transformation
-
            +rk.do_step( sys1 , inout , t , dt ); // In-place transformation of inout +rk.do_step( sys2 , inout , t , dt ); // Ok +rk.do_step( sys1 , in , t , out , dt ); // Out-of-place transformation +rk.do_step( sys1 , inout , dxdtin , t , dt ); // In-place tranformation of inout +rk.do_step( sys1 , in , dxdtin , t , out , dt ); // Out-of-place transformation +

            @@ -174,20 +175,21 @@ how the FSAL steppers can be used is

            + 

            runge_kutta_dopri5< state_type > rk;
 rk.do_step( sys1 , in , t , out , dt );
-rk.do_step( sys2 , in , t , out , dt );         // DONT do this, sys1 is assumed
-
+rk.do_step( sys2 , in , t , out , dt );         // DONT do this, sys1 is assumed
+
 rk.do_step( sys2 , in2 , t , out , dt );
-rk.do_step( sys2 , in3 , t , out , dt );        // DONT do this, in2 is assumed
-
+rk.do_step( sys2 , in3 , t , out , dt );        // DONT do this, in2 is assumed
+
 rk.do_step( sys1 , inout , dxdtinout , t , dt );
-rk.do_step( sys2 , inout , dxdtinout , t , dt );           // Ok, internal derivative is not used, dxdtinout is updated
-
+rk.do_step( sys2 , inout , dxdtinout , t , dt );           // Ok, internal derivative is not used, dxdtinout is updated
+
 rk.do_step( sys1 , in , dxdtin , t , out , dxdtout , dt );
-rk.do_step( sys2 , in , dxdtin , t , out , dxdtout , dt ); // Ok, internal derivative is not used
-
            +rk.do_step( sys2 , in , dxdtin , t , out , dxdtout , dt ); // Ok, internal derivative is not used +

            @@ -207,7 +209,7 @@

            -
            +

            Symplectic solvers @@ -239,6 +241,7 @@ again simple C-functions of functors. An example is the harmonic oscillator:

            + 

            typedef boost::array< double , 1 > vector_type;
 
@@ -260,6 +263,7 @@
           example for the harmonic oscillator is now:
         
            
 
            
+          
 
            
 
            pair< vector_type , vector_type > x;
 x.first[0] = 1.0; x.second[0] = 0.0;
@@ -273,6 +277,7 @@
           two public method:
         
            
 
            
+          
 
            
 
            struct harm_osc
 {
@@ -290,6 +295,7 @@
 
            
         
            
 
            
+          
 
            
 
            harm_osc h;
 rkn.do_step( make_pair( boost::bind( &harm_osc::f1 , h , _1 , _2 ) , boost::bind( &harm_osc::f2 , h , _1 , _2 ) ) ,
@@ -309,6 +315,7 @@
           can be written as
         
            
 
            
+          
 
            
 
            pair< vector_type , vector_type > x;
 x.first[0] = 1.0; x.second[0] = 0.0;
@@ -332,6 +339,7 @@
           takes q and p without combining them into a pair:
         
            
 
            
+          
 
            
 
            rkn.do_step( harm_osc_f1 , make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
 rkn.do_step( harm_osc_f1 , q , p , t , dt );
@@ -340,7 +348,7 @@

            -
            +

            Implicit solvers @@ -375,7 +383,7 @@ by ublas::matrix.

            -
            +

            Multistep methods @@ -397,6 +405,7 @@ steps is instantiated and initialized;

            + 

            adams_bashforth_moulton< 5 , state_type > abm;
 abm.initialize( sys , inout , t , dt );
@@ -414,6 +423,7 @@
           state of the Adams-Bashforth-Stepper:
         
            
 
            
+          
 
            
 
            abm.initialize( runge_kutta_fehlberg78< state_type >() , sys , inout , t , dt );
 
            
@@ -440,7 +450,7 @@

        -
        +

        Controlled steppers @@ -450,15 +460,15 @@ stepsize control. Adaptive step size integration works in principle as follows:

        -
          -
        1. +
            +
          1. The error of one step is calculated. This is usually done by performing two steps with different orders. The difference between these two steps is then used as a measure for the error. Stepper which can calculate the error are Error Stepper and they form a own class with an separate concept.
            2. -
          2. +
          3. This error is compared against some predefined error tolerances. Are the tolerance violated the step is reject and the stepsize is decreases. Otherwise the step is accepted and possibly the stepsize is increased. @@ -658,7 +668,7 @@ stepper. The generation functions are explained in detail in XYZ.

          -
          +

          Dense output steppers @@ -676,6 +686,7 @@ An example is

          + 

          dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > > dense;
 dense.initialize( in , t , dt );
@@ -701,6 +712,7 @@
           exist:
         
          
 
          
+          
 
          
 
          result_of::make_dense_output< runge_kutta_dopri5< state_type > >::type dense2 = make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() );
 
          
@@ -718,13 +730,14 @@
           for easy use with the integrate functions:
         
          
 
          
+          
 
          
 
          integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() ) , sys , inout , t_start , t_end , dt );

          -
          +

          Using steppers @@ -744,6 +757,15 @@

          Steppers might have a internal state

          +
          + + + + + +
          [Caution]Caution

          + Some of the features described in this section are not yet implemented +

          Some steppers require to store some informations about the state of the ODE between two steps. Examples are the multistep method which store a @@ -774,16 +796,22 @@ 4 internal derivatives of the solution at times (t-dt,t-2dt,t-3dt,t-4dt).

          + 

          adams_bashforth_moulton< 4 , state_type > stepper;
-stepper.do_step( sys , x , t , dt );   // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-4dt
-stepper.do_step( sys , x , t , dt );   // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-3dt
-stepper.do_step( sys , x , t , dt );   // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-2dt
-stepper.do_step( sys , x , t , dt );   // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-dt
-stepper.do_step( sys , x , t , dt );   // make one step with Adam-Bashforth-Moulton, the internal array of states is now rotated
-
          +stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-4dt +stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-3dt +stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-2dt +stepper.do_step( sys , x , t , dt ); // make one step with the classical Runge-Kutta stepper and initialize the first internal state at time t-dt +stepper.do_step( sys , x , t , dt ); // make one step with Adam-Bashforth-Moulton, the internal array of states is now rotated +

          +

          + In the stepper table at the bottom of this page one can see which stepper + have an internal state and hence provide the reset + and initialize methods. +

          Stepper might be resizable

          @@ -798,26 +826,26 @@ user is left with the question of which stepper fits his needs. In the following we give our (personal) recommendations

          -
            -
          • +
              +
            • runge_kutta_dopri5 is maybe the best default stepper. It has step size control as well as dense-output functionality. Simple create a dense-output stepper by make_dense_output( 1.0e-6 , 1.0e-5 , runge_kutta_dopri5< state_type >() ).
              • -
            • +
            • runge_kutta4 is a good stepper for constant step sizes. It is widely used and very well known. If you need to create artifical time series this stepper should be the first choice.
              • -
            • +
            • 'runge_kutta_fehlberg78' is similar to the 'runge_kutta4' with the advantage that it has higher precision. It can also be used with step size control.
              • -
            • +
            • adams_bashforth_moulton is very well suited for ODEs where the r.h.s. is expensive (in terms of computation time). It will calculate the system function only once @@ -825,7 +853,7 @@
          -
          +

          Stepper overview @@ -1829,8 +1857,7 @@

          -
          Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

          +

          Copyright © 2009 -2011 Karsten Ahnert and 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)

          diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html index 871f3c9e..657ea5af 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html @@ -3,8 +3,8 @@ Using boost::range - - + + @@ -15,14 +15,13 @@
          PrevUpHomeNext
          -

          +
          -
          Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

          +

          Copyright © 2009 -2011 Karsten Ahnert and 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)

          diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html index c358536c..e93491f2 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html @@ -3,8 +3,8 @@ Using boost::ref - - + + @@ -15,14 +15,13 @@
          PrevUpHomeNext
          -

          +
          -
          Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

          +

          Copyright © 2009 -2011 Karsten Ahnert and 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)

          diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts.html b/doc/boost_sandbox_numeric_odeint/old_concepts.html index 14ce2958..0e3192e9 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts.html @@ -3,8 +3,8 @@ Old Concepts - - + + @@ -15,7 +15,7 @@
          PrevUpHomeNext
          -
          +
          @@ -41,8 +41,7 @@
          -
          Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

          +

          Copyright © 2009 -2011 Karsten Ahnert and 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)

          diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/basic_stepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/basic_stepper.html index d169bea7..8fb795ec 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/basic_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/basic_stepper.html @@ -3,8 +3,8 @@ Basic stepper - - + + @@ -15,7 +15,7 @@
          PrevUpHomeNext
          -
          +

          Basic stepper @@ -123,18 +123,18 @@

          Methods

          -
            -
          • +
              +
            • Stepper() Constructor.
              • -
            • +
            • Stepper( container_type &x ) Constructor that allocates internal memory to store intermediate results of the same size as x.
              • -
            • +
            • void do_step( DynamicalSystem &system , container_type @@ -246,7 +246,7 @@ The result of this method is the (approximate) state of the system x(t+dt) and is stored in the variable x (in-place). Note, that the time t is not automatically increased by this method.

              -
              • +
                • void do_step( DynamicalSystem &system , container_type @@ -261,15 +261,15 @@ that represents the derivative x'(t) = f(x,t) at the time t.

                  -
                    -
                  • +
                      +
                    • void adjust_size( const container_type &x ) Adjusts the internal memory to store intermediate results of the same size as x. This function must be called whenever the system size changes during the integration.
                      • -
                    • +
                    • order_type order_step() Returns the order of the algorithm. If n is the order of a method, then the result of one iteration with the timestep dt @@ -280,22 +280,21 @@

                      Stepper that model this concept

                      -
                        -
                      • +
                          +
                        • stepper_euler
                          • -
                        • +
                        • stepper_rk4
                          • -
                        • +
                        • stepper_rk78_fehlberg
                      -
                      Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                      +

                      Copyright © 2009 -2011 Karsten Ahnert and 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)

                      diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/compositestepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/compositestepper.html index 2a8227a3..638b9bb4 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/compositestepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/compositestepper.html @@ -3,8 +3,8 @@ CompositeStepper - - + + @@ -15,13 +15,12 @@
                      PrevUpHomeNext
                      -

                      +
                      -
                      Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                      +

                      Copyright © 2009 -2011 Karsten Ahnert and 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)

                      diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/controlled_stepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/controlled_stepper.html index c31fc178..3bb7951e 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/controlled_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/controlled_stepper.html @@ -3,8 +3,8 @@ Controlled stepper - - + + @@ -15,7 +15,7 @@
                      PrevUpHomeNext
                      -
                      +

                      Controlled stepper @@ -35,7 +35,7 @@

                      Methods

                      -
                      • +
                        • Controlled_Stepper( time_type abs_err, time_type rel_err, @@ -60,8 +60,8 @@ If the estimated error is less than half of the desired error, an increased stepsize will be suggested.

                          -
                            -
                          • +
                              +
                            • Controlled_Stepper( container_type &x, time_type abs_err, time_type rel_err, @@ -70,7 +70,7 @@ Same as above, but with additional allocation of the internal memory to store intermediate results of the same size as x.
                              • -
                            • +
                            • controlled_step_result try_step( DynamicalSystem &system, container_type &x, time_type &t, time_type &dt )
                              • @@ -186,8 +186,8 @@ dt now containes the suggested reduced stepsize that should give an error below the desired level.

                              -
                                -
                              • +
                                  +
                                • controlled_step_result try_step( DynamicalSystem &system, container_type &x, const container_type &dxdt, time_type @@ -198,33 +198,32 @@ represents the derivative x'(t) = f(x,t) at the time t.
                                  • -
                                • +
                                • void adjust_size( const container_type &x ) Adjusts the internal memory to store intermediate results of the same size as x. This function must be called whenever the system size changes during the integration.
                                  • -
                                • +
                                • order_type order_error_step() Returns the order of the result x(t+dt) of the algorithm.

                                Stepper that model this concept

                                -
                                  -
                                • +
                                    +
                                  • controlled_stepper_standard
                                    • -
                                  • +
                                  • controlled_stepper_bs
                                -
                                Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                +

                                Copyright © 2009 -2011 Karsten Ahnert and 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)

                                diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/dense_ouput_stepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/dense_ouput_stepper.html index 92bc7e8f..125b75c4 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/dense_ouput_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/dense_ouput_stepper.html @@ -3,8 +3,8 @@ Dense ouput stepper - - + + @@ -15,14 +15,13 @@
                                PrevUpHomeNext
                                -

                                +
                                -
                                Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                +

                                Copyright © 2009 -2011 Karsten Ahnert and 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)

                                diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/error_stepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/error_stepper.html index d669dc9a..bce3b512 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/error_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/error_stepper.html @@ -3,8 +3,8 @@ Error stepper - - + + @@ -15,7 +15,7 @@
                                PrevUpHomeNext
                                -
                                +

                                Error stepper @@ -40,18 +40,18 @@

                                Methods

                                -
                                  -
                                • +
                                    +
                                  • Error_Stepper() Constructor.
                                    • -
                                  • +
                                  • Error_Stepper( container_type &x ) Constructor that allocates internal memory to store intermediate results of the same size as x.
                                    • -
                                  • +
                                  • void do_step( DynamicalSystem &system , container_type @@ -183,7 +183,7 @@ Note, that the time t is not automatically increased by this method.

                                    -
                                    • +
                                      • void do_step( DynamicalSystem &system , container_type @@ -199,18 +199,18 @@ that represents the derivative x'(t) = f(x,t) at the time t.

                                        -
                                          -
                                        • +
                                            +
                                          • void adjust_size( const container_type &x ) Adjusts the internal memory to store intermediate results of the same size as x. This function must be called whenever the system size changes during the integration.
                                            • -
                                          • +
                                          • order_type order_error_step() Returns the order of the result x(t+dt) of the algorithm.
                                            • -
                                          • +
                                          • order_type order_error() Returns the order of the error estimation of the algorithm.
                                            • @@ -218,22 +218,21 @@

                                            Stepper that model this concept

                                            -
                                              -
                                            • +
                                                +
                                              • stepper_rk5_ck
                                                • -
                                              • +
                                              • stepper_rk78_fehlberg
                                                • -
                                              • +
                                              • stepper_half_step
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_concepts/size_adjusting_stepper.html b/doc/boost_sandbox_numeric_odeint/old_concepts/size_adjusting_stepper.html index 8b51376c..c54bc218 100644 --- a/doc/boost_sandbox_numeric_odeint/old_concepts/size_adjusting_stepper.html +++ b/doc/boost_sandbox_numeric_odeint/old_concepts/size_adjusting_stepper.html @@ -3,8 +3,8 @@ Size adjusting stepper - - + + @@ -15,14 +15,13 @@
                                            PrevUpHomeNext
                                            -

                                            +
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference.html b/doc/boost_sandbox_numeric_odeint/old_reference.html index 9f32316b..bc0874da 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference.html @@ -3,8 +3,8 @@ Old Reference - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +
                                            @@ -31,8 +31,7 @@
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference/algebras.html b/doc/boost_sandbox_numeric_odeint/old_reference/algebras.html index 35ae5a85..33abc8dc 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference/algebras.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference/algebras.html @@ -3,8 +3,8 @@ Algebras - - + + @@ -15,13 +15,12 @@
                                            PrevUpHomeNext
                                            -

                                            +
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference/integration_functions.html b/doc/boost_sandbox_numeric_odeint/old_reference/integration_functions.html index 7cc7b3bc..6c4b3705 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference/integration_functions.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference/integration_functions.html @@ -3,8 +3,8 @@ Integration functions - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +
                                            -

                                            +
                                            -
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference/operations.html b/doc/boost_sandbox_numeric_odeint/old_reference/operations.html index ef8a45a3..d9d8d5ca 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference/operations.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference/operations.html @@ -3,8 +3,8 @@ Operations - - + + @@ -15,13 +15,12 @@
                                            PrevUpHomeNext
                                            -

                                            +
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference/resizing.html b/doc/boost_sandbox_numeric_odeint/old_reference/resizing.html index 14749420..9a88f763 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference/resizing.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference/resizing.html @@ -3,8 +3,8 @@ Resizing - - + + @@ -14,13 +14,12 @@
                                            PrevUpHome
                                            -

                                            +
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/old_reference/stepper_classes.html b/doc/boost_sandbox_numeric_odeint/old_reference/stepper_classes.html index 5f52e624..0775a70a 100644 --- a/doc/boost_sandbox_numeric_odeint/old_reference/stepper_classes.html +++ b/doc/boost_sandbox_numeric_odeint/old_reference/stepper_classes.html @@ -3,8 +3,8 @@ Stepper classes - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +

                                            Stepper classes @@ -191,8 +191,7 @@

                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/tutorial.html b/doc/boost_sandbox_numeric_odeint/tutorial.html index 0ba767e6..0ea093c8 100644 --- a/doc/boost_sandbox_numeric_odeint/tutorial.html +++ b/doc/boost_sandbox_numeric_odeint/tutorial.html @@ -3,8 +3,8 @@ Tutorial - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +
                                            @@ -39,8 +39,7 @@
                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/all_examples.html b/doc/boost_sandbox_numeric_odeint/tutorial/all_examples.html index 7705102e..4ab2eadd 100644 --- a/doc/boost_sandbox_numeric_odeint/tutorial/all_examples.html +++ b/doc/boost_sandbox_numeric_odeint/tutorial/all_examples.html @@ -3,8 +3,8 @@ All examples - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +

                                            All examples @@ -236,8 +236,7 @@

                                            -
                                            Copyright © 2009-2011 Karsten Ahnert - and Mario Mulansky

                                            +

                                            Copyright © 2009 -2011 Karsten Ahnert and 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)

                                            diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html b/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html index 566791b9..8494961e 100644 --- a/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html +++ b/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html @@ -3,8 +3,8 @@ Chaotic systems and Lyapunov exponents - - + + @@ -15,7 +15,7 @@
                                            PrevUpHomeNext
                                            -
                                            +

                                            Chaotic systems and Lyapunov exponents @@ -61,6 +61,7 @@ The implementation of the Lorenz system is

                                            + 

                                            const double sigma = 10.0;
 const double R = 28.0;
@@ -83,6 +84,7 @@
         the perturbation could look like:
       
                                            
 
                                            
+        
 
                                            
 
                                            const size_t n = 3;
 const size_t num_of_lyap = 3;
@@ -114,6 +116,7 @@
         inside a functor with templatized arguments:
       
                                            
 
                                            
+        
 
                                            
 
                                            struct lorenz
 {
@@ -135,11 +138,11 @@
 
                                            
 
                                            
         This works fine and lorenz_with_lyap
-        can be used for example via
+        can be used for example via 
 
                                            
 
                                            state_type x;
-// initialize x
-explicit_rk4< state_type > rk4;
+// initialize x
+explicit_rk4< state_type > rk4;
 integrate_n_steps( rk4 , lorenz_with_lyap , x , 0.0 , 0.01 , 1000 );
 
                                            
 
                                            
@@ -151,10 +154,11 @@
         current state lies on the attractor, hence it would look like
       
                                            
 
                                            
+        
 
                                            
 
                                            state_type x;
-// initialize x
-explicit_rk4< state_type > rk4;
+// initialize x
+explicit_rk4< state_type > rk4;
 integrate_n_steps( rk4 , lorenz , x , 0.0 , 0.01 , 1000 );
 
                                            
 
                                            
@@ -166,6 +170,7 @@
         by pointer to the state and an appropriate length, something similar to
       
                                            
 
                                            
+        
 
                                            
 
                                            void lorenz( double* x , double *dxdt , double t, void* params )
 {
@@ -183,6 +188,7 @@
         the system has to by changed:
       
                                            
 
                                            
+        
 
                                            
 
                                            struct lorenz
 {
@@ -205,9 +211,10 @@
         with an suited range:
       
                                            
 
                                            
+        
 
                                            
-
                                            // perform 10000 transient steps
-integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
+
                                            // perform 10000 transient steps
+integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
 
                                            
 
                                            
       
                                            
@@ -215,26 +222,27 @@
         Having integrated a sufficient number of transients steps we are now able
         to calculate the Lyapunov exponents:
       
                                            
-
                                              
-
                                            1. 
+
                                                
+
                                              1. 
             We initialize the perturbations. They are stored linearly behind the
             state of the Lorenz system. The perturbation are initialized such that
             they fullfill < p ​i , p​j > = δ ​ij  where <,>
             is the classical scalar product and δ ​ij is the Kronecker
             symbol.
           
                                                2. 
-
                                              2. 
+
                                              3. 
             Integrate 100 steps of the full system with perturbations
           
                                                4. 
-
                                              4. 
+
                                              5. 
             Orthonormalize the perturbation using Gram-Schmidt orthonormalization
             algorithm.
           
                                                6. 
-
                                              6. 
+
                                              7. 
             Repeat step 2 and 3. Every 10000 steps write the current Lyapunov exponent.
           
                                                8. 
 
                                              
 
                                              
+        
 
                                              
 
                                              fill( x.begin()+n , x.end() , 0.0 );
 for( size_t i=0 ; i<num_of_lyap ; ++i ) x[n+n*i+i] = 1.0;
@@ -265,8 +273,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html b/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
index 171361d0..26036355 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
@@ -3,8 +3,8 @@
 
 Harmonic oscillator
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Define
         the ODE
@@ -52,6 +52,7 @@
           to just define a function, e.g:
         
                                            
 
                                            
+          
 
                                            
 
                                            /* The type of container used to hold the state vector */
 typedef std::vector< double > state_type;
@@ -78,6 +79,7 @@
           parameter structure as above:
         
                                            
 
                                            
+          
 
                                            
 
                                            /* The rhs of x' = f(x) defined as a class */
 class harm_osc {
@@ -101,7 +103,7 @@
           which allows for cleaner code.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Stepper
         Types
@@ -1118,7 +1120,7 @@
           which kind of steppers should be applied.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Integration
         with Constant Step Size
@@ -1136,6 +1138,7 @@
           ) function from odeint:
         
                                            
 
                                            
+          
 
                                            
 
                                            runge_kutta4< state_type > stepper;
 integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
@@ -1152,6 +1155,7 @@
           method which can used directly. So, you write down the above example as
         
                                            
 
                                            
+          
 
                                            
 
                                            const double dt = 0.01;
 for( double t=0.0 ; t<10.0 ; t+= dt )
@@ -1160,7 +1164,7 @@
 
                                            
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Integration
         with Adaptive Step Size
@@ -1175,6 +1179,7 @@
           with 4th order error estimation and coefficients introduced by Cash-Karp.
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
 
                                            
@@ -1187,6 +1192,7 @@
           stepper exists which can be used via
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
 controlled_stepper_type controlled_stepper;
@@ -1213,6 +1219,7 @@
           by using make_controlled:
         
                                            
 
                                            
+          
 
                                            
 
                                            integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
 
                                            
@@ -1228,6 +1235,7 @@
           is
         
                                            
 
                                            
+          
 
                                            
 
                                            integrate_adaptive( make_controlled( 1.0e-10 , 1.0e-6 , error_stepper_type() ) , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
 
                                            
@@ -1243,6 +1251,7 @@
           with all parameters is therefore
         
                                            
 
                                            
+          
 
                                            
 
                                            double abs_err = 1.0e-10 , rel_err = 1.0e-6 , a_x = 1.0 , a_dxdt = 1.0;
 controlled_stepper_type controlled_stepper( default_error_checker< double >( abs_err , rel_err , a_x , a_dxdt ) );
@@ -1444,8 +1453,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/references.html b/doc/boost_sandbox_numeric_odeint/tutorial/references.html
index 86871b10..03ce8a67 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/references.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/references.html
@@ -3,8 +3,8 @@
 
 References
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
@@ -74,8 +74,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html b/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
index 927dddd0..d7e89781 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
@@ -3,8 +3,8 @@
 
 Solar system
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Gravitation
         and energy conservation
@@ -88,7 +88,7 @@
           f( q​i ).
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Define
         the system function
@@ -98,6 +98,7 @@
           space as well as the velocity. Therefore, we use the operators from Boost.Operators:
         
                                            
 
                                            
+          
 
                                            
 
                                            /*the point type */
 template< class T , size_t Dim >
@@ -113,20 +114,20 @@
         typedef T value_type;
         typedef point< value_type , dim > point_type;
 
-        // ...
-        // constructors
-
-        // ...
-        // operators
-
+        // ...
+        // constructors
+
+        // ...
+        // operators
+
     private:
 
         T m_val[dim];
     };
 
-    //...
-    // more operators
-    
                                            
+    //...
+    // more operators
+    
 
                                            
         
                                            
 
                                            
@@ -135,9 +136,10 @@
           type we use std::tr1::array
         
                                            
 
                                            
+          
 
                                            
-
                                            // we simulate 5 planets and the sun
-const size_t n = 6;
+
                                            // we simulate 5 planets and the sun
+const size_t n = 6;
 
 typedef point< double , 3 > point_type;
 typedef boost::array< point_type , n > container_type;
@@ -157,6 +159,7 @@
           As system function we have to provide f(p) and f(q):
         
                                            
 
                                            
+          
 
                                            
 
                                            const double gravitational_constant = 2.95912208286e-4;
 
@@ -176,6 +179,7 @@
 
                                            
         
                                            
 
                                            
+          
 
                                            
 
                                            struct solar_system_momentum
 {
@@ -217,6 +221,7 @@
           apply here:
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
 const double dt = 100.0;
@@ -241,6 +246,7 @@
           The reference wrapper is also passed, but this is not a problem at all:
         
                                            
 
                                            
+          
 
                                            
 
                                            struct streaming_observer
 {
@@ -267,8 +273,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html b/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
index 313c7480..2ec48199 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
@@ -3,8 +3,8 @@
 
 Special topics
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
 Special
       topics
@@ -43,7 +43,7 @@
 
                                            
         explain boost::ref
       
                                            
-
                                            
+
                                            
 
                                            
 Complex
         state types
@@ -63,6 +63,7 @@
           code is very simple
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef boost::array< complex< double > , 1 > state_type;
 
@@ -88,6 +89,7 @@
           function. In this cast the Stuart-Landau oscillator looks like
         
                                            
 
                                            
+          
 
                                            
 
                                            double eta = 1.0;
 double alpha = 1.0;
@@ -109,6 +111,7 @@
           Integration is also very easy:
         
                                            
 
                                            
+          
 
                                            
 
                                            state_type x = {{ complex< double >( 1.0 , 0.0 ) }};
 
@@ -124,7 +127,7 @@
           The full cpp file for the Stuart Landau example can be found here stuart_landau.cpp
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Lattice
         systems
@@ -153,6 +156,7 @@
           components. Here, is how this function looks like
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef vector< double > container_type;
 
@@ -162,8 +166,8 @@
 
     fpu( const double beta = 1.0 ) : m_beta( beta ) { }
 
-    // system function defining the ODE
-    void operator()( const container_type &q , container_type &dpdt ) const
+    // system function defining the ODE
+    void operator()( const container_type &q , container_type &dpdt ) const
     {
         size_t n = q.size();
         double tmp = q[0] - 0.0;
@@ -181,17 +185,17 @@
         dpdt[n-1] += tmp2;
     }
 
-    // calculates the energy of the system
-    double energy( const container_type &q , const container_type &p ) const
+    // calculates the energy of the system
+    double energy( const container_type &q , const container_type &p ) const
     {
-        // ...
-    }
+        // ...
+    }
 
-    // calculates the local energy of the system
-    void local_energy( const container_type &q , const container_type &p , container_type &e ) const
+    // calculates the local energy of the system
+    void local_energy( const container_type &q , const container_type &p , container_type &e ) const
     {
-        // ...
-    }
+        // ...
+    }
 };
 
                                            
 
                                            
@@ -204,6 +208,7 @@
           All this can be easily done with the following piece of code:
         
                                            
 
                                            
+          
 
                                            
 
                                            const size_t n = 64;
 container_type q( n , 0.0 ) , p( n , 0.0 );
@@ -230,6 +235,7 @@
           The observer is more or less trivial
         
                                            
 
                                            
+          
 
                                            
 
                                            struct streaming_observer
 {
@@ -267,7 +273,7 @@
           The full cpp file for this FPU example can be found here fpu.cpp
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Ensembles
         of oscillators
@@ -298,6 +304,7 @@
           also need to store the individual frequencies of each oscillator.
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef vector< double > container_type;
 
@@ -360,6 +367,7 @@
           and we record Z for different values of ε.
         
                                            
 
                                            
+          
 
                                            
 
                                            struct statistics_observer
 {
@@ -392,6 +400,7 @@
           2.
         
                                            
 
                                            
+          
 
                                            
 
                                            const size_t n = 16384;
 const double dt = 0.1;
@@ -402,8 +411,8 @@
 boost::uniform_real<> unif( 0.0 , 2.0 * M_PI );
 boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
 
-// gamma = 1, the phase transition occurs at epsilon = 2
-phase_ensemble ensemble( n , 1.0 );
+// gamma = 1, the phase transition occurs at epsilon = 2
+phase_ensemble ensemble( n , 1.0 );
 statistics_observer obs;
 
 for( double epsilon = 0.0 ; epsilon < 5.0 ; epsilon += 0.1 )
@@ -411,14 +420,14 @@
     ensemble.set_epsilon( epsilon );
     obs.reset();
 
-    // start with random initial conditions
-    generate( x.begin() , x.end() , gen );
+    // start with random initial conditions
+    generate( x.begin() , x.end() , gen );
 
-    // calculate some transients steps
-    integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 10.0 , dt );
+    // calculate some transients steps
+    integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 10.0 , dt );
 
-    // integrate and compute the statistics
-    integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 100.0 , dt , boost::ref( obs ) );
+    // integrate and compute the statistics
+    integrate_const( runge_kutta4< container_type >() , boost::ref( ensemble ) , x , 0.0 , 100.0 , dt , boost::ref( obs ) );
     cout << epsilon << "\t" << obs.get_K_mean() << endl;
 }
 
@@ -430,7 +439,7 @@
           The full cpp file for this example can be found here phase_oscillator_ensemble.cpp
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Using
         boost::units
@@ -449,6 +458,7 @@
           all quantities
         
                                            
 
                                            
+          
 
                                            
 
                                            #include <boost/numeric/odeint.hpp>
 #include <boost/numeric/odeint/algebra/fusion_algebra.hpp>
@@ -486,6 +496,7 @@
           equivalent to the example in the first section of this tutorial
         
                                            
 
                                            
+          
 
                                            
 
                                            struct oscillator
 {
@@ -509,6 +520,7 @@
           Furthermore, the basic calculations are now performed by the fusion_algebra which must also be given.
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef runge_kutta_dopri5< state_type , double , deriv_type , time_type , fusion_algebra > stepper_type;
 
@@ -523,6 +535,7 @@
           the observer is defined a bit different
         
                                            
 
                                            
+          
 
                                            
 
                                            struct streaming_observer
 {
@@ -569,7 +582,7 @@
           The full cpp file for this example can be found here harmonic_oscillator_units.cpp.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Using
         matrices as state types
@@ -594,6 +607,7 @@
           The definition of the system is
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef boost::numeric::ublas::matrix< double > state_type;
 
@@ -645,7 +659,7 @@
           The full cpp for this example can be found here two_dimensional_phase_lattice.cpp.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Partial
         differential equations
@@ -660,11 +674,11 @@
           Ginzburg-Landau
         
                                            
 
                                            
-
                                            
+
                                            
-
                                            
+
                                            
 
                                            
 Using
         arbitrary precision floating point types
@@ -687,6 +701,7 @@
           Here is a simple example:
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef mpf_class value_type;
 typedef boost::array< value_type , 3 > state_type;
@@ -711,6 +726,7 @@
           which can be used
         
                                            
 
                                            
+          
 
                                            
 
                                            const int precision = 1024;
 mpf_set_default_prec( precision );
@@ -747,7 +763,7 @@
           The full example can be found at lorenz_gmpxx.cpp.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Self
         expanding lattices
@@ -772,6 +788,7 @@
           is kept which should be changed whenever the states' size change.
         
                                            
 
                                            
+          
 
                                            
 
                                            typedef vector< double > coord_type;
 typedef pair< coord_type , coord_type > state_type;
@@ -787,8 +804,8 @@
         : m_max_N( max_N ) , m_beta( beta ) , m_pot_start_index( pot_start_index ) , m_pot( max_N )
     {
         srand( time( NULL ) );
-        // fill random potential with iid values from [0,1]
-        boost::mt19937 rng;
+        // fill random potential with iid values from [0,1]
+        boost::mt19937 rng;
         boost::uniform_real<> unif( 0.0 , 1.0 );
         boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
         generate( m_pot.begin() , m_pot.end() , gen );
@@ -796,9 +813,9 @@
 
     void operator()( const coord_type &q , coord_type &dpdt )
     {
-        // calculate dpdt = -dH/dq of this hamiltonian system
-        // dp_i/dt = - V_i * q_i^3 - beta*(q_i - q_{i-1})^3 + beta*(q_{i+1} - q_i)^3
-        const int N = q.size();
+        // calculate dpdt = -dH/dq of this hamiltonian system
+        // dp_i/dt = - V_i * q_i^3 - beta*(q_i - q_{i-1})^3 + beta*(q_{i+1} - q_i)^3
+        const int N = q.size();
         double diff = q[0] - q[N-1];
         for( int i=0 ; i<N ; ++i )
         {
@@ -811,8 +828,8 @@
 
     void energy_distribution( const coord_type &q , const coord_type &p , coord_type &energies )
     {
-        // computes the energy per lattice site normalized by total energy
-        const size_t N = q.size();
+        // computes the energy per lattice site normalized by total energy
+        const size_t N = q.size();
         double en = 0.0;
         for( size_t i=0 ; i<N ; i++ )
         {
@@ -831,8 +848,8 @@
 
     double energy( const coord_type &q , const coord_type &p )
     {
-        // calculates the total energy of the excitation
-        const size_t N = q.size();
+        // calculates the total energy of the excitation
+        const size_t N = q.size();
         double en = 0.0;
         for( size_t i=0 ; i<N ; i++ )
         {
@@ -857,24 +874,25 @@
           of 60.
         
                                            
 
                                            
+          
 
                                            
-
                                            //start with 60 sites
-const int N_start = 60;
+
                                            //start with 60 sites
+const int N_start = 60;
 coord_type q( N_start , 0.0 );
 q.reserve( max_N );
 coord_type p( N_start , 0.0 );
 p.reserve( max_N );
-// start with uniform momentum distribution over 20 sites
-fill( p.begin()+20 , p.end()-20 , 1.0/sqrt(20) );
+// start with uniform momentum distribution over 20 sites
+fill( p.begin()+20 , p.end()-20 , 1.0/sqrt(20) );
 
 coord_type distr( N_start , 0.0 );
 distr.reserve( max_N );
 
-// create the system
-compacton_lattice lattice( max_N , beta , (max_N-N_start)/2 );
+// create the system
+compacton_lattice lattice( max_N , beta , (max_N-N_start)/2 );
 
-//create the stepper, note that we use an always_resizer because state size might change during steps
-typedef symplectic_rkn_sb3a_mclachlan< coord_type , coord_type , double , coord_type , coord_type , double ,
+//create the stepper, note that we use an always_resizer because state size might change during steps
+typedef symplectic_rkn_sb3a_mclachlan< coord_type , coord_type , double , coord_type , coord_type , double ,
         range_algebra , default_operations , always_resizer > hamiltonian_stepper;
 hamiltonian_stepper stepper;
 hamiltonian_stepper::state_type state = make_pair( q , p );
@@ -892,6 +910,7 @@
           the start index of the potential changes in this case.
         
                                            
 
                                            
+          
 
                                            
 
                                            double t = 0.0;
 const double dt = 0.1;
@@ -924,6 +943,7 @@
           , p and distr.
         
                                            
 
                                            
+          
 
                                            
 
                                            void do_resize( coord_type &q , coord_type &p , coord_type &distr , const int N )
 {
@@ -941,8 +961,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html b/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
index 149e2be5..6732f950 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
@@ -3,8 +3,8 @@
 
 Stiff systems
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
 Stiff
       systems
@@ -45,6 +45,7 @@
         is needed. Here is the definition of the above example
       
                                            
 
                                            
+        
 
                                            
 
                                            typedef boost::numeric::ublas::vector< double > vector_type;
 typedef boost::numeric::ublas::matrix< double > matrix_type;
@@ -81,6 +82,7 @@
         just templatize the operator():
       
                                            
 
                                            
+        
 
                                            
 
                                            typedef boost::numeric::ublas::vector< double > vector_type;
 typedef boost::numeric::ublas::matrix< double > matrix_type;
@@ -116,6 +118,7 @@
         all the other stepper:
       
                                            
 
                                            
+        
 
                                            
 
                                            vector_type x( 3 , 1.0 );
 
@@ -132,6 +135,7 @@
         5 method with step size control and dense output yields 1531 steps.
       
                                            
 
                                            
+        
 
                                            
 
                                            vector_type x2( 3 , 1.0 );
 
@@ -151,8 +155,7 @@
 
                                            
 
-
                                            
 
                                            Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                            
+
                                            Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                            
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html b/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
index 1c6a5b82..57a56968 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
@@ -3,8 +3,8 @@
 
 Using Cuda and Thrust
 
-
-
+
+
 
 
 
@@ -15,7 +15,7 @@
 
                                            
 PrevUpHomeNext
 
                                            
-
                                            
+
                                            
 
                                            
 Using
       Cuda and Thrust
@@ -66,7 +66,7 @@
           in the last example.
         
                                            
 
                                            
-
                                            
+
                                            
 
                                            
 Phase
         oscillator ensemble
@@ -87,14 +87,15 @@
           website.
         
                                            
 
                                            
+          
 
                                            
-
                                            //change this to float if your device does not support double computation
-typedef double value_type;
+
                                            //change this to float if your device does not support double computation
+typedef double value_type;
 
-//change this to host_vector< ... > of you want to run on CPU
-typedef thrust::device_vector< value_type > state_type;
-// typedef thrust::host_vector< value_type > state_type;
-
                                            
+//change this to host_vector< ... > of you want to run on CPU
+typedef thrust::device_vector< value_type > state_type;
+// typedef thrust::host_vector< value_type > state_type;
+
                                            
 
                                            
         
                                            
 
                                            
@@ -102,7 +103,7 @@
           a calculation on the GPU you usually have to call a global function like
           thrust::for_each, thrust::reduce,
           ... with an appropriate local functor which performs the basic operation.
-          An example is
+          An example is 
 
                                            
 
                                            struct add_two
 {
@@ -114,8 +115,8 @@
     }
 };
 
-// ...
-
+// ...
+
 thrust::for_each( x.begin() , x.end() , add_two() );
 
                                            
 
                                            
@@ -124,11 +125,11 @@
 
                                            
           For the purpose of integrating the phase oscillator ensemble we need
         
                                            
-
                                              
-
                                            • 
+
                                                
+
                                              • 
               to calculate the system function, hence the r.h.s. of the ODE.
             
                                                • 
-
                                              • 
+
                                              • 
               this involves computing the mean field of the oscillator example, i.e.
               the values of R and θ
             
                                                • 
@@ -137,6 +138,7 @@
           The mean field is calculated in a class mean_field_calculator
         
                                                
 
                                                
+          
 
                                                
 
                                                struct mean_field_calculator
 {
@@ -190,6 +192,7 @@
           GPU as well as on the CPU. The line
         
                                                
 
                                                
+          
 
                                                
 
                                                value_type sin_sum = thrust::reduce(
         thrust::make_transform_iterator( x.begin() , sin_functor() ) ,
@@ -205,6 +208,7 @@
           The system function is defined via
         
                                                
 
                                                
+          
 
                                                
 
                                                class phase_oscillator_ensemble
 {
@@ -226,8 +230,8 @@
         }
     };
 
-    // ...
-
+    // ...
+
     void operator() ( const state_type &x , state_type &dxdt , const value_type dt ) const
     {
         std::pair< value_type , value_type > mean_field = mean_field_calculator::get_mean( x );
@@ -239,8 +243,8 @@
                 );
     }
 
-    // ...
-};
+    // ...
+};
 
                                                
 
                                                
         
                                                
@@ -260,6 +264,7 @@
           thrust algebra:
         
                                                
 
                                                
+          
 
                                                
 
                                                typedef runge_kutta4< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
 
                                                
@@ -269,6 +274,7 @@
           Of course, you can also use a controlled or dense output stepper, e.g.
         
                                                
 
                                                
+          
 
                                                
 
                                                typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
 
                                                
@@ -279,12 +285,14 @@
           an instance of the rhs class and using an integration function:
         
                                                
 
                                                
+          
 
                                                
 
                                                phase_oscillator_ensemble ensemble( N , 1.0 );
 
                                                
 
                                                
         
                                                
 
                                                
+          
 
                                                
 
                                                size_t steps1 = integrate_const( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
 
                                                
@@ -301,7 +309,7 @@
           The full example can be found at phase_oscillator_example.cu.
         
                                                
 
                                              
-
                                              
+
                                              
 
                                              
 Large
         oscillator chains
@@ -326,13 +334,14 @@
           in front. The full system class is:
         
                                              
 
                                              
+          
 
                                              
-
                                              //change this to host_vector< ... > of you want to run on CPU
-typedef thrust::device_vector< value_type > state_type;
+
                                              //change this to host_vector< ... > of you want to run on CPU
+typedef thrust::device_vector< value_type > state_type;
 typedef thrust::device_vector< size_t > index_vector_type;
-//typedef thrust::host_vector< value_type > state_type;
-//typedef thrust::host_vector< size_t > index_vector_type;
-
+//typedef thrust::host_vector< value_type > state_type;
+//typedef thrust::host_vector< size_t > index_vector_type;
+
 class phase_oscillators
 {
 
@@ -342,29 +351,29 @@
     {
         template< class Tuple >
         __host__ __device__
-        void operator()( Tuple t )  // this functor works on tuples of values
-        {
-            // first, unpack the tuple into value, neighbors and omega
-            const value_type phi = thrust::get<0>(t);
-            const value_type phi_left = thrust::get<1>(t);  // left neighbor
-            const value_type phi_right = thrust::get<2>(t); // right neighbor
-            const value_type omega = thrust::get<3>(t);
-            // the dynamical equation
-            thrust::get<4>(t) = omega + sin( phi_right - phi ) + sin( phi - phi_left );
+        void operator()( Tuple t )  // this functor works on tuples of values
+        {
+            // first, unpack the tuple into value, neighbors and omega
+            const value_type phi = thrust::get<0>(t);
+            const value_type phi_left = thrust::get<1>(t);  // left neighbor
+            const value_type phi_right = thrust::get<2>(t); // right neighbor
+            const value_type omega = thrust::get<3>(t);
+            // the dynamical equation
+            thrust::get<4>(t) = omega + sin( phi_right - phi ) + sin( phi - phi_left );
         }
     };
 
     phase_oscillators( const state_type &omega )
         : m_omega( omega ) , m_N( omega.size() ) , m_prev( omega.size() ) , m_next( omega.size() )
     {
-        // build indices pointing to left and right neighbours
-        thrust::counting_iterator<size_t> c( 0 );
+        // build indices pointing to left and right neighbours
+        thrust::counting_iterator<size_t> c( 0 );
         thrust::copy( c , c+m_N-1 , m_prev.begin()+1 );
-        m_prev[0] = 0; // m_prev = { 0 , 0 , 1 , 2 , 3 , ... , N-1 }
-
+        m_prev[0] = 0; // m_prev = { 0 , 0 , 1 , 2 , 3 , ... , N-1 }
+
         thrust::copy( c+1 , c+m_N , m_next.begin() );
-        m_next[m_N-1] = m_N-1; // m_next = { 1 , 2 , 3 , ... , N-1 , N-1 }
-    }
+        m_next[m_N-1] = m_N-1; // m_next = { 1 , 2 , 3 , ... , N-1 , N-1 }
+    }
 
     void operator() ( const state_type &x , state_type &dxdt , const value_type dt )
     {
@@ -414,33 +423,34 @@
           current state, hence the phase of each oscillator.
         
                                              
 
                                              
+          
 
                                              
-
                                              // create random number generators
-boost::mt19937 rng;
+
                                              // create random number generators
+boost::mt19937 rng;
 boost::uniform_real< value_type > unif( 0.0 , 2.0 * pi );
 boost::variate_generator< boost::mt19937&, boost::uniform_real< value_type > > gen( rng , unif );
 
-// create initial conditions and omegas on host:
-vector< value_type > x_host( N );
+// create initial conditions and omegas on host:
+vector< value_type > x_host( N );
 vector< value_type > omega_host( N );
 for( size_t i=0 ; i<N ; ++i )
 {
     x_host[i] = gen();
-    omega_host[i] = ( N - i ) * epsilon; // decreasing frequencies
-}
+    omega_host[i] = ( N - i ) * epsilon; // decreasing frequencies
+}
 
-// copy to device
-state_type x = x_host;
+// copy to device
+state_type x = x_host;
 state_type omega = omega_host;
 
-// create stepper
-runge_kutta4< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper;
+// create stepper
+runge_kutta4< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper;
 
-// create phase oscillator system function
-phase_oscillators sys( omega );
+// create phase oscillator system function
+phase_oscillators sys( omega );
 
-// integrate
-integrate_const( stepper , sys , x , 0.0 , 10.0 , dt );
+// integrate
+integrate_const( stepper , sys , x , 0.0 , 10.0 , dt );
 
 thrust::copy( x.begin() , x.end() , std::ostream_iterator< value_type >( std::cout , "\n" ) );
 std::cout << std::endl;
@@ -451,7 +461,7 @@
           The full example can be found at phase_oscillator_chain.cu.
         
                                              
 
                                              
-
                                              
+
                                              
 
                                              
 Parameter
         studies
@@ -481,6 +491,7 @@
           >.
         
                                              
 
                                              
+          
 
                                              
 
                                              boost::mt19937 rng;
 boost::uniform_real< value_type > unif( 0.0 , 1.0 );
@@ -502,6 +513,7 @@
           calculates one particular realization of the Lorenz ensemble
         
                                              
 
                                              
+          
 
                                              
 
                                              struct lorenz_system
 {
@@ -511,8 +523,8 @@
         __host__ __device__
         void operator()( T t ) const
         {
-            // unpack the parameter we want to vary and the Lorenz variables
-            value_type R = thrust::get< 3 >( t );
+            // unpack the parameter we want to vary and the Lorenz variables
+            value_type R = thrust::get< 3 >( t );
             value_type x = thrust::get< 0 >( t );
             value_type y = thrust::get< 1 >( t );
             value_type z = thrust::get< 2 >( t );
@@ -584,6 +596,7 @@
           which is used within this observer is defined
         
                                              
 
                                              
+          
 
                                              
 
                                              struct lyap_functor
 {
@@ -623,32 +636,33 @@
           and written to stdout.
         
                                              
 
                                              
+          
 
                                              
 
                                              state_type x( 6 * N );
 
-// initialize x,y,z
-thrust::fill( x.begin() , x.begin() + 3 * N , 10.0 );
+// initialize x,y,z
+thrust::fill( x.begin() , x.begin() + 3 * N , 10.0 );
 
-// initial dx
-thrust::fill( x.begin() + 3 * N , x.begin() + 4 * N , 1.0 );
+// initial dx
+thrust::fill( x.begin() + 3 * N , x.begin() + 4 * N , 1.0 );
 
-// initialize dy,dz
-thrust::fill( x.begin() + 4 * N , x.end() , 0.0 );
+// initialize dy,dz
+thrust::fill( x.begin() + 4 * N , x.end() , 0.0 );
 
 
-// create error stepper, can be used with make_controlled or make_dense_output
-typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
+// create error stepper, can be used with make_controlled or make_dense_output
+typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
 
 
 lorenz_system lorenz( N , beta );
 lorenz_perturbation_system lorenz_perturbation( N , beta );
 lyap_observer obs( N , 1 );
 
-// calculate transients
-integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz , std::make_pair( x.begin() , x.begin() + 3 * N ) , 0.0 , 10.0 , dt );
+// calculate transients
+integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz , std::make_pair( x.begin() , x.begin() + 3 * N ) , 0.0 , 10.0 , dt );
 
-// calculate the Lyapunov exponents -- the main loop
-double t = 0.0;
+// calculate the Lyapunov exponents -- the main loop
+double t = 0.0;
 while( t < 10000.0 )
 {
     integrate_adaptive( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , lorenz_perturbation , x , t , t + 1.0 , 0.1 );
@@ -671,8 +685,7 @@
 
                                              
 
-
                                              
 
                                              Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                              
+
                                              Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                              
diff --git a/doc/index.html b/doc/index.html
index 3ed24068..d6455445 100644
--- a/doc/index.html
+++ b/doc/index.html
@@ -3,15 +3,15 @@
 
 Chapter 1. boost.sandbox.numeric.odeint
 
-
-
+
+
 
 
 
 
                                              
 
                                              
 
                                              Next
                                              
-
                                              
+
                                              
 
                                              
 
                                              
 Chapter 1. boost.sandbox.numeric.odeint
                                              
@@ -21,10 +21,9 @@
 
                                              
 Mario Mulansky
 
                                              
-
                                              Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                              
+
                                              Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                              
@@ -134,11 +133,7 @@
 
                                              
 
                                              
 
-<<<<<<< HEAD
-
-=======
-
->>>>>>> 730d9205ac4754193e77fe15092e7003f6153a31
+
                                              Last revised: November 25, 2011 at 17:55:09 GMT
                                              Last revised: November 22, 2011 at 17:52:03 GMT
                                              Last revised: November 27, 2011 at 15:44:29 GMT
                                              		
 
                                              		
 
                                              
 
                                              
diff --git a/doc/odeint/reference.html b/doc/odeint/reference.html
index e8a7c0df..06c2dd53 100644
--- a/doc/odeint/reference.html
+++ b/doc/odeint/reference.html
@@ -3,8 +3,8 @@
 
 Reference
 
-
-
+
+
 
 
 
@@ -15,12 +15,11 @@
 
                                              
 PrevUpHomeNext
 
                                              
-
                                              
+
                                              
 Reference
                                              
 
-
                                              
 
                                              Copyright © 2009-2011 Karsten Ahnert
-      and Mario Mulansky
                                              
+
                                              Copyright © 2009 -2011 Karsten Ahnert and 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)
       
                                              
diff --git a/libs/numeric/odeint/doc/extend.qbk b/libs/numeric/odeint/doc/extend.qbk
index d8519052..ef4e5059 100644
--- a/libs/numeric/odeint/doc/extend.qbk
+++ b/libs/numeric/odeint/doc/extend.qbk
@@ -147,30 +147,6 @@ with Boost.Range.
 multiplication operator `*` and use the non-standard `vector_space_algebra`.
 * Implement your own algebra that defines the required operations.
 
-[section Boost.Ublas]
-As an example for the employment of the `vector_space_algebra` we will adopt
-`ublas::vector` from __ublas to work as a state type in odeint.
-This is particularily easy because `ublas::vector` supports vector-vector
-addition and scalar-vector multiplication as well as `boost::size`.
-It also has a resize member function so all that has to be done in this case
-is to declare resizability:
-
-[import ../examples/ublas/lorenz_ublas.cpp]
-
-[ublas_resizeable]
-
-Now ublas::vector can be used as state type in odeint by specifying the 
-`vector_space_algebra` as algebra in the template parameter list of the
-stepper. 
-The following code shows the corresponding definitions:
-
-[ublas_main]
-
-You can find the full example in [github_link
-libs/numeric/odeint/examples/ublas/lorenz_ublas.cpp lorenz_ublas.cpp].
-
-[endsect]
-
 [section GSL Vector]
 
 All the above examples use __boost_range to iterate through the elements of the
@@ -320,6 +296,49 @@ library so it is quite an achievement that it's possible to get it working at
 all in the first place.
 [endsect]
 
+
+[section Vector Space Algebra]
+
+As seen above, the standard way of performing algebraic operations on container-like state types in odeint is to iterate through the elements of the container and perform the operations element-wise on the underlying value type.
+This is realized by means of the `range_algebra` that uses __boost_range for obtaining iterators of the state types.
+However, there are other ways to implement the algebraic operations on containers, one of which is defining the addition/multiplication operators for the containers directly and then using the `vector_space_algebra`.
+If you use this algebra, the following operators have to be defined for the state_type:
+
+[table
+  [[Name] [Expression] [Type] [Semantics]]
+  [[Addition] [`x + y`] [`state_type`] [Calculates the vector sum 'x+y'.]]
+  [[Assign addition] [`x += y`] [`state_type`] [Performs x+y in place.]]
+  [[Scalar multiplication] [`a * x `] [`state_type`] [Performs multiplication of vector x with scalar a.]]
+  [[Assign scalar multiplication] [`x *= a`] [`state_type`] [Performs in-place multiplication of vector x with scalar a.]]
+]
+
+
+[endsect]
+
+[section Boost.Ublas]
+As an example for the employment of the `vector_space_algebra` we will adopt
+`ublas::vector` from __ublas to work as a state type in odeint.
+This is particularily easy because `ublas::vector` supports vector-vector
+addition and scalar-vector multiplication as well as `boost::size`.
+It also has a resize member function so all that has to be done in this case
+is to declare resizability:
+
+[import ../examples/ublas/lorenz_ublas.cpp]
+
+[ublas_resizeable]
+
+Now ublas::vector can be used as state type in odeint by specifying the 
+`vector_space_algebra` as algebra in the template parameter list of the
+stepper. 
+The following code shows the corresponding definitions:
+
+[ublas_main]
+
+You can find the full example in [github_link
+libs/numeric/odeint/examples/ublas/lorenz_ublas.cpp lorenz_ublas.cpp].
+
+[endsect]
+
 [endsect]
 
 [endsect]
diff --git a/libs/numeric/odeint/examples/point_type.hpp b/libs/numeric/odeint/examples/point_type.hpp
index d3c71d60..7bd2bfd7 100644
--- a/libs/numeric/odeint/examples/point_type.hpp
+++ b/libs/numeric/odeint/examples/point_type.hpp
@@ -61,46 +61,46 @@ class point :
         T& operator[]( size_t i ) { return m_val[i]; }
 
         point_type& operator+=( const point_type& p )
-		        {
+        {
             for( size_t i=0 ; i