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Dateien nach „BSP_1_D“ hochladen

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Georg Thomas Mandl 2025-10-22 23:15:15 +02:00
commit dde42b7628
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40
BSP_1_D/bsp_1_d.cbp Normal file
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<?xml version="1.0" encoding="UTF-8" standalone="yes" ?>
<CodeBlocks_project_file>
<FileVersion major="1" minor="6" />
<Project>
<Option title="bsp_1_d" />
<Option pch_mode="2" />
<Option compiler="gcc" />
<Build>
<Target title="Debug">
<Option output="bin/Debug/bsp_1_d" prefix_auto="1" extension_auto="1" />
<Option object_output="obj/Debug/" />
<Option type="1" />
<Option compiler="gcc" />
<Compiler>
<Add option="-g" />
</Compiler>
</Target>
<Target title="Release">
<Option output="bin/Release/bsp_1_d" prefix_auto="1" extension_auto="1" />
<Option object_output="obj/Release/" />
<Option type="1" />
<Option compiler="gcc" />
<Compiler>
<Add option="-O2" />
</Compiler>
<Linker>
<Add option="-s" />
</Linker>
</Target>
</Build>
<Compiler>
<Add option="-Wall" />
<Add option="-fexceptions" />
</Compiler>
<Unit filename="bsp_1_d.cpp" />
<Unit filename="bsp_1_d.h" />
<Unit filename="main.cpp" />
<Extensions />
</Project>
</CodeBlocks_project_file>

34
BSP_1_D/bsp_1_d.cpp Normal file
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#include "bsp_1_d.h"
#include <cassert> // assert()
#include <cmath>
using namespace std;
double scalar(vector<double> const &x, vector<double> const &y)
{
assert(x.size() == y.size()); // switch off via compile flag: -DNDEBUG
size_t const N = x.size();
double sum = 0.0;
for (size_t i = 0; i < N; ++i)
{
sum += x[i] * y[i];
}
return sum;
}
double Kahan_skalar(vector<double> const &x, vector<double> const &y)
{
assert(x.size() == y.size()); // switch off via compile flag: -DNDEBUG
size_t const N = x.size();
double sum = 0.0;
double c = 0.0;
for (size_t i = 0; i < N; ++i)
{
double z = x[i]*y[i] - c;
double t = sum + z;
c = (t - sum) - z;
sum = t;
}
return sum;
}

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BSP_1_D/bsp_1_d.h Normal file
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#ifndef BSP_1_D_H_INCLUDED
#define BSP_1_D_H_INCLUDED
#include <vector>
/** \brief Berechnet das Skalarprodukt zweier Vektoren
*
* \param[in] x erster Vektor
* \param[in] y zweiter Vektor
* \return Skalarprodukt von @x und @y
*
*/
double scalar(std::vector<double> const &x, std::vector<double> const &y);
/** \brief Berechnet das Skalarprodukt zweier Vektoren unter Anwendung der Kahan-Summation
*
* \param[in] x erster Vektor
* \param[in] y zweiter Vektor
* \return Skalarprodukt von @x und @y
*
*/
double Kahan_skalar(std::vector<double> const &x, std::vector<double> const &y);
#endif // BSP_1_D_H_INCLUDED

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BSP_1_D/main.cpp Normal file
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#include "bsp_1_d.h"
#include <iostream>
#include <math.h>
// BSP 1_D
using namespace std;
int main()
{
vector<int> nvec{100,500,1000,10000,100000,1000000,10000000,100000000}; // Vektor mit verschiedene n zum Testen
double exact = M_PI*M_PI/6;
for(size_t k = 0; k<nvec.size(); ++k)
{
vector<double> x;
for(int i = 0; i<nvec[k]; ++i)
{
x.push_back(1.0/(i+1));
}
double sum = scalar(x,x);
double sumkahan = Kahan_skalar(x,x);
cout << "n = " << nvec[k] << endl;
cout << "sum = " << sum << endl;
cout << "sumkahan = " << sumkahan << endl;
cout << "Differenz mit/ohne Kahan: " << abs(sum - sumkahan) << endl;
cout << "Differenz zu exakt fuer n to inf (mit/ohne Kahan): " << abs(exact - sum) << " / " << abs(exact - sumkahan) << endl << endl;
}
return 0;
}