desys< NINT, T > Class Template Reference

Numerical Integration of a system of differential equations (de's). More...

#include <desys.h>

Collaboration diagram for desys< NINT, T >:

List of all members.

Public Member Functions
T &	yiGet (uintc i, uintc k)
	Write to the yi state matrix.
T const	yiGet (uintc i, uintc k) const
	Access the yi state matrix.
	desys (uintc dim_, uintc order_)
	Allocate memory yi uninitialized.
	~desys ()
	Cleanup.
void	eval ()
	Increment the system.
ostream &	print (ostream &os) const
	Output the state of the de system.
Public Attributes
uint	dim
	The dimension of the system.
uint	order
	The highest order of the derivatives.
T *	dy
	The infinitessimal - small change added to y for the next step.
T	xval
	The independent variable x.
T *	yi
	A 2D matrix of yi[0], yi[1],.
NINT	integrator
	Numerical Integrator.
T	hstep
	The step sizes.

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Detailed Description

template<typename NINT, typename T>
class desys< NINT, T >

Numerical Integration of a system of differential equations (de's).

Theory

The integrators calculate the infinatesimal which is what is added to the previous y to get the new state. ie y[n+1] = y[n] + dy where dy is the infinitesimal.

The infinitesimal is not a derivative except in the simplest case of the Euler method where dy=h*y'. dy approximates (taylor series-y).

Interfaces

The numerical integrator support the following interface.

  void integrator.eval
  ( 
    T & dy,          // Infitesimal or change in y.
    T & h,           // The step size
    T const y,       // dependent variable
    T const x        // independent variable
  );
  integrator(&xval,yi);
  ++integrator.yDorder;

The DE solver has a 2D matrix yi. The first row is yi[0], yi[1], ..., yi[order-1] correspond with y, y', y'', .... y^(order-1). The rows correspond to the dimension, the columns the order.

The numerical integrator is passed the locations to xval and yi[] when it is constructed. This coupling lets the equations see all the variables.

Since there is only one integrator, when the dimension is >1 it needs to behave as the current equation. Since this design eliminated virtual functions it is the clients responsibility to define a ++ operator on D of NINT<D,T> to move to the next equation in the system of equations.

Whether this helps for efficiency I do not know. For when dim>1 the client can use an array of function pointers or a case statement.

Example 1

y'' + y = 0, y(0) = 1 cos(x) is the exact solution.

class desystestf1
{
public:

  double * xval;
  // yi[0] is y, yi[1] is y'
  double * yi;

  desystestf1(double * xval_, double * yi_)
    : xval(xval_), yi(yi_) {}

  void operator ++ () {}

  // y''=-y 
  void operator () (double &  Dz, double const z, double const x) const
    { Dz = -yi[0]; }
};
...
  typedef nintegrationEuler< desystestf1, double > integrator;
  desys< integrator ,double > de(1,2);

  de.yiGet(0,0)=1.0;
  de.yiGet(0,1)=0.0;
  de.hstep=0.001;

  cout << de << endl;

  for (; de.xval < 0.3; de.eval() )
    {}
  cout << de << endl;

Definition at line 93 of file desys.h.

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Constructor & Destructor Documentation

template<typename NINT , typename T >

desys< NINT, T >::desys	(	uintc	dim_,
		uintc	order_
	)			[inline]

Allocate memory yi uninitialized.

Definition at line 181 of file desys.h.

References desys< NINT, T >::dim, desys< NINT, T >::order, and desys< NINT, T >::xval.

  : dim(dim_), order(order_), dy(new T[dim]),
    yi(new T[order*dim]), integrator(&xval,yi) 
{
  assert(dim>0);
  assert(order>0);
  xval=0.0;
}

template<typename NINT , typename T >

desys< NINT, T >::~desys

(

)

[inline]

Cleanup.

Definition at line 174 of file desys.h.

References desys< NINT, T >::dy, and desys< NINT, T >::yi.

{
  delete[] dy;
  delete[] yi;
}

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Member Function Documentation

template<typename NINT , typename T >

void desys< NINT, T >::eval

(

)

[inline]

Increment the system.

cout << SHOW(yi[order+c]) << endl;

Definition at line 192 of file desys.h.

References desys< NINT, T >::dim, desys< NINT, T >::dy, desys< NINT, T >::hstep, desys< NINT, T >::integrator, desys< NINT, T >::order, desys< NINT, T >::xval, and desys< NINT, T >::yi.

Referenced by helixtestscope::helixtest::idle03(), desystest::test01(), desystest::test02(), desystest::test03(), desystest::test04(), and desystest::test05().

{
  uint c;
  assert(hstep!=0);
  for (uint i=0; i<dim; ++i )
  {
    c = i*order+order-1;

//cout << SHOW(xval) << endl;

//cout << SHOW(order) << endl;
//cout << SHOW(c) << endl;
//cout << SHOW(order+c) << endl;
//cout << SHOW(i*(order+1)) << endl;
//cout << SHOW(yi[c]) << endl;
    integrator.eval(dy[i],hstep,yi[c],xval); 
//print(cout); cout << endl;
    yi[c] += dy[i];
//cout << SHOW(yi[c]) << endl;
//cout << SHOW(yi[order-1+c]) << endl;
//cout << "*";
//print(cout); cout << endl;

    ++integrator.yDorder;
  }
  xval += hstep;

  if (order<=1)
    return;
    
  for (uint i=0; i<dim; ++i )
  {
    c = i*order + order;

    for (uint k=2; k<=order; ++k ) 
      yi[c-k] += yi[c-k+1]*hstep;
  }
}

template<typename NINT , typename T >

ostream & desys< NINT, T >::print

(

ostream &

os

)

const [inline]

Output the state of the de system.

Definition at line 150 of file desys.h.

References desys< NINT, T >::dim, desys< NINT, T >::hstep, desys< NINT, T >::order, desys< NINT, T >::xval, and desys< NINT, T >::yi.

{
  os << "dim=" << dim << endl;
  os << "order=" << order << endl;
  os << "hstep=" << hstep << endl;
  os << "xval=" << xval << endl;
  os << "(y0, y0', ...)" << endl;
  os << "(y1, y1', ...)" << endl;
  os << "=" << endl;

  os << "yi" << endl;
  for (uint i=0; i<dim; ++i)
  {
    os << "[" << i << "]: ";
    for (uint k=0; k<order; ++k)
      os << yi[i*order+k] << " ";
    os << endl;
  }
 
  return os;
}

template<typename NINT, typename T>

T const desys< NINT, T >::yiGet	(	uintc	i,
		uintc	k
	)			const [inline]

Access the yi state matrix.

Definition at line 118 of file desys.h.

References desys< NINT, T >::dim, desys< NINT, T >::order, and desys< NINT, T >::yi.

    { assert(i<dim); assert(k<order); return yi[k+i*order]; }

template<typename NINT, typename T>

T& desys< NINT, T >::yiGet	(	uintc	i,
		uintc	k
	)			[inline]

Write to the yi state matrix.

Definition at line 114 of file desys.h.

References desys< NINT, T >::dim, desys< NINT, T >::order, and desys< NINT, T >::yi.

Referenced by helixtestscope::helixtest::idle03(), desystest::test02(), helixtestscope::helixtest::test03(), desystest::test03(), desystest::test04(), and desystest::test05().

    { assert(i<dim); assert(k<order); return yi[k+i*order]; }

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Member Data Documentation

template<typename NINT, typename T>

uint desys< NINT, T >::dim

The dimension of the system.

Definition at line 101 of file desys.h.

Referenced by desys< NINT, T >::desys(), desys< NINT, T >::eval(), desys< NINT, T >::print(), and desys< NINT, T >::yiGet().

template<typename NINT, typename T>

T* desys< NINT, T >::dy

The infinitessimal - small change added to y for the next step.

Definition at line 106 of file desys.h.

Referenced by desys< NINT, T >::eval(), and desys< NINT, T >::~desys().

template<typename NINT, typename T>

T desys< NINT, T >::hstep

The step sizes.

Definition at line 125 of file desys.h.

Referenced by desys< NINT, T >::eval(), desys< NINT, T >::print(), desystest::test01(), desystest::test02(), helixtestscope::helixtest::test03(), desystest::test03(), desystest::test04(), and desystest::test05().

template<typename NINT, typename T>

NINT desys< NINT, T >::integrator

Numerical Integrator.

Definition at line 122 of file desys.h.

Referenced by desys< NINT, T >::eval(), helixtestscope::helixtest::test03(), and desystest::test05().

template<typename NINT, typename T>

uint desys< NINT, T >::order

The highest order of the derivatives.

Definition at line 103 of file desys.h.

Referenced by desys< NINT, T >::desys(), desys< NINT, T >::eval(), desys< NINT, T >::print(), and desys< NINT, T >::yiGet().

template<typename NINT, typename T>

T desys< NINT, T >::xval

The independent variable x.

Definition at line 109 of file desys.h.

Referenced by desys< NINT, T >::desys(), desys< NINT, T >::eval(), desys< NINT, T >::print(), desystest::test01(), desystest::test02(), desystest::test03(), desystest::test04(), and desystest::test05().

template<typename NINT, typename T>

T* desys< NINT, T >::yi

A 2D matrix of yi[0], yi[1],.

..,yi[Order] variable rows for each dimension.

Definition at line 111 of file desys.h.

Referenced by desys< NINT, T >::eval(), desys< NINT, T >::print(), desys< NINT, T >::yiGet(), and desys< NINT, T >::~desys().

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The documentation for this class was generated from the following file:

• nintegration/desys.h