/***
* FUNCTION: Integrates equation using Simpson method
* RETURN: Definite integral of equation
* PARAM: [IN] equation - equation to integrate
* PARAM: [IN] start - left integration border
* PARAM: [IN] end - right integration border
* PARAM: [IN] numIterations - number of iterations
* SEE: write me
* AUTHOR: Eliseev Dmitry
***/
Equation ParametricIntegrator::Simpson( const Equation &equation, const double start, const double end, const unsigned int numIterations )
{
unsigned int i = 0;
/* Timer creation */
Timer timer;
/* Result equation */
Equation result = Equation(start) + Equation(end);
/* Odd members */
Equation oddResult("0");
for (i = 1; i <= 2 * numIterations - 1; i+=2)
oddResult += equation.GetEquation(start + (end - start) * i / (2 * numIterations));
/* Even members */
Equation evenResult("0");
for (i = 2; i <= 2 * numIterations - 2; i+=2)
evenResult += equation.GetEquation(start + (end - start) * i / (2 * numIterations));
/* Add calculated values */
result += Equation("4") * oddResult + Equation("2") * evenResult;
/* That's it */
result *= Equation((end - start) / (6 * numIterations));
result.Simplify();
/* Determine spent time */
numSeconds = timer.GetTimePassed();
return result;
} /* End of 'Integrator::Simpson' method */
/***
* FUNCTION: Integrates equation using center-rectangles method
* RETURN: Definite integral of equation
* PARAM: [IN] equation - equation to integrate
* PARAM: [IN] start - left integration border
* PARAM: [IN] end - right integration border
* PARAM: [IN] numIterations - number of iterations
* SEE: write me
* AUTHOR: Eliseev Dmitry
***/
Equation ParametricIntegrator::Rectangles( const Equation &equation, const double start, const double end, const unsigned int numIterations )
{
double step = (end - start) / numIterations;
unsigned int i = 0;
/* Result equation */
Equation result("0");
Equation width(step);
/* Timer creation */
Timer timer;
/* For each iteration */
for (i = 0; i < numIterations; i++)
result += width * equation.GetEquation(step * i);
/* That's it */
result.Simplify();
/* Determine spent time */
numSeconds = timer.GetTimePassed();
return result;
} /* End of 'Integrator::Rectangles' method */
