diff --git a/DFT.cc b/DFT.cc
index c31c9e9d8aa4baf276ee39c6548b6175e657a5ca..da5e5bb75346616fffa0ac70a2e706ac48517a18 100644
--- a/DFT.cc
+++ b/DFT.cc
@@ -1,82 +1,86 @@
-#include <complex>
#include <cmath>
#include <iomanip>
#include "Header files/DFT.h"
#include <iostream>
#include <fstream>
-#include <string>
using namespace std::complex_literals;
+const double PI{std::acos(-1)};
+
+// Alg start ---------------------------------------------------------------------------------------
+std::vector<std::complex<double>> dft(std::vector<std::complex<double>> f,int n,int flag)
+{
+ std::vector<std::complex<double>> answer;
+ for(int i = 0; i<n; i++)
+ {
+ std::complex<double> s = 0;
+ for(int j = 0; j<n; j++)
+ {
+ std::complex<double> exponent = static_cast<double> (i*j);
+ s += std::exp(flag*2*PI*1i*exponent/static_cast<double>(n)) * f[j];
+ }
+ answer.push_back(s / static_cast<double>(std::sqrt(n)));
+ }
+
+ return answer;
+}
+// Alg slut ---------------------------------------------------------------------------------------
int main()
{
- // PI
- const double PI{std::acos(-1)};
+ DFT call;
+ // inFile innehåller uHatt data och outFile är resulterande filen
+ std::string inFile{"sinus.txt"};
+ std::string outFile{"inversSinusDFT.txt"};
+ int const n{16};
+
+ // Får data från inFile och lägger på en vektor
+ std::vector<std::complex<double>> inputVector = call.getInput(inFile,n);
+ // Anroppar alg ----------------------------------------------------------
+ std::vector<std::complex<double>> transfer = dft(inputVector,n,-1);
+ std::vector<std::complex<double>> invTransfer = dft(transfer,n,1);
+ // -----------------------------------------------------------------------------------
+ call.printToFile(invTransfer,outFile,n);
+ std::cout << "DFT done"<<'\n';
+ return 0;
+}
+
+
+
- // inFile innehåller uHatt data och outFile är resulterande filen
- std::string inFile{"sinus.txt"};
- std::string outFile{"inversSinusDFT.txt"};
-
- // Perioden för funktionen
- double T{2*PI};
-
- int const n{20};
- std::complex<double> inputFunction[n];
- std::complex<double> F[n][n];
- std::complex<double> funcTransf[n];
- std::complex<double> inverseFuncTransf[n];
+std::vector<std::complex<double>> DFT::getInput(std::string inFile, int n)
+{
+ std::vector<std::complex<double>> inputVector;
+ // Hämtar data och sätter den på en vector
+ int loop = 0;
std::string dataLine;
std::ifstream functionData (inFile);
-
- // while-loop variabel samt element i
- int loop = 0;
std::complex<double> element;
-
if (functionData.is_open())
{
while ((std::getline (functionData,dataLine)) && (loop < n) )
{
std::istringstream is(dataLine);
is >> element;
- inputFunction[loop] = element;
+ inputVector.push_back(element);
loop++;
}
functionData.close();
}
+ return inputVector;
+}
- for(int i = 0; i<n; i++)
- {
- for(int j = 0; j<n; j++)
- {
- std::complex<double> exponent = static_cast<double> (i*j);
- F[j][i] = std::exp(-1.0*T*1i*exponent/(n+1.0));
- funcTransf[i] = funcTransf[i] + F[j][i]*inputFunction[i];
- }
-
- }
-
- for(int i = 0; i<n; i++)
- {
- for(int j = 0; j<n; j++)
- {
- std::complex<double> exponent = static_cast<double> (i*j);
- F[j][i] = std::exp(1.0*T*1i*exponent/(n+1.0));
- inverseFuncTransf[i] = inverseFuncTransf[i] + F[j][i]*funcTransf[i];
- }
- }
-
-
+void DFT::printToFile(std::vector<std::complex<double>> printVector, std::string fileName, int n)
+{
+ // Skriver ut inversFuncTransf till en fil
std::ofstream resultFile;
- resultFile.open(outFile);
+ resultFile.open(fileName);
// Sätter önskad antal decimaler
resultFile << std::fixed << std::setprecision(10);
for (int i=0;i<n;i++)
{
- resultFile << inverseFuncTransf[i].real() << "," << inverseFuncTransf[i].imag() << '\n';
+ resultFile << printVector[i].real() << "," << printVector[i].imag() << '\n';
}
resultFile.close();
- std::cout << "DFT done"<<'\n';
- return 0;
-}
-
+}
\ No newline at end of file
diff --git a/FFT.cc b/FFT.cc
new file mode 100644
index 0000000000000000000000000000000000000000..8765e389159d6d5775c9728b537de307ae2a670e
--- /dev/null
+++ b/FFT.cc
@@ -0,0 +1,98 @@
+#include <complex>
+#include <cmath>
+#include <iomanip>
+#include "Header files/FFT.h"
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <bits/stdc++.h>
+using namespace std::complex_literals;
+
+int main()
+{
+ // PI
+ const double PI{std::acos(-1)};
+
+ // inFile innehåller uHatt data och outFile är resulterande filen
+ std::string inFile{"sinus.txt"};
+ std::string outFile{"sinusFFT.txt"};
+
+ // Perioden för funktionen
+ double T{2*PI};
+ int const n{16};
+ std::vector<std::complex<double>> inputVector;
+ std::complex<double> funcTransf[n];
+
+
+ // Hämtar data och sätter den på en vector
+ int loop = 0;
+ std::string dataLine;
+ std::ifstream functionData (inFile);
+ std::complex<double> element;
+
+ if (functionData.is_open())
+ {
+ while ((std::getline (functionData,dataLine)) && (loop < n) )
+ {
+ std::istringstream is(dataLine);
+ is >> element;
+ inputVector.push_back(element);
+ loop++;
+ }
+ functionData.close();
+ }
+
+ // alg start -------------------------------------------------------------
+ std::complex<double> my[n];
+ for(int i=0;i<n;i++)
+ {
+ my[i]=std::exp(-1i*T*static_cast<double> (i)/static_cast<double> (n));
+ }
+
+
+ // "Bitreversal"
+ std::stable_partition(std::begin(inputVector), std::end(inputVector),
+ [&inputVector](std::complex<double> const& a){return 0==((&a-&inputVector[0])%2);});
+
+
+ // F2 mult.
+ for(int i=0;i<n;i+=2)
+ {
+ funcTransf[i]=inputVector[i]+inputVector[i+1];
+ funcTransf[i+1]=inputVector[i]-inputVector[i+1];
+ }
+
+ // I and D mult.
+ for(int m=0;m<n;m++)
+ {
+ std::complex<double> s = 0;
+ if(m % 2 == 0)
+ {
+ for(int j=0;j<n;j+=4)
+ {
+ s = s + funcTransf[j] + std::pow(my[m],m) * funcTransf[j+2];
+ }
+ }
+ else
+ {
+ for(int j=1;j<n;j+=4)
+ {
+ s = s + funcTransf[j] + std::pow(my[m],m) * funcTransf[j+2];
+ }
+ }
+ funcTransf[m]= s / static_cast<double> (std::sqrt(n));
+ }
+ // Alg end ----------------------------------------------------------------
+
+ std::ofstream resultFile;
+ resultFile.open(outFile);
+ // Sätter önskad antal decimaler
+ resultFile << std::fixed << std::setprecision(10);
+ for (int i=0;i<n;i++)
+ {
+ resultFile << funcTransf[i].real() << "," << funcTransf[i].imag() << '\n';
+ }
+ resultFile.close();
+ std::cout << "FFT done"<<'\n';
+ return 0;
+}
\ No newline at end of file
diff --git a/Header files/DFT.h b/Header files/DFT.h
index 0f8bf18c6a63aa5874e20182121085658ea66c8f..d55533fd49e1787eab65f65602db97ee2a04eb0b 100644
--- a/Header files/DFT.h
+++ b/Header files/DFT.h
@@ -1,7 +1,11 @@
#include <complex>
+#include <vector>
+#include <string>
class DFT
{
public:
+ void printToFile(std::vector<std::complex<double>> printVector, std::string fileName, int n);
+ std::vector<std::complex<double>> getInput(std::string inFile, int n);
private:
};
diff --git a/Header files/FFT.h b/Header files/FFT.h
new file mode 100644
index 0000000000000000000000000000000000000000..8fe06a9eb6a1cd40108d27e940b4ac90b77b95d1
--- /dev/null
+++ b/Header files/FFT.h
@@ -0,0 +1,7 @@
+#include <complex>
+
+class FFT
+{
+public:
+private:
+};
diff --git a/Header files/RECFFT.h b/Header files/RECFFT.h
new file mode 100644
index 0000000000000000000000000000000000000000..312ee57add95dc09a46c311e597e5a486a435baf
--- /dev/null
+++ b/Header files/RECFFT.h
@@ -0,0 +1,11 @@
+#include <complex>
+#include <vector>
+#include <string>
+
+class RECFFT
+{
+public:
+ void printToFile(std::vector<std::complex<double>> printVector, std::string fileName, int n);
+ std::vector<std::complex<double>> getInput(std::string inFile, int n);
+private:
+};
diff --git a/PlotData.py b/PlotData.py
index e8754785ef91680081cf748e69c8c175fe1a34d9..389ce3b2a88d312855d613ad10fcf8293a5bf350 100644
--- a/PlotData.py
+++ b/PlotData.py
@@ -4,10 +4,12 @@ import numpy as np
filename0 = 'sinus.txt'
filename1 = 'inversSinusDFT.txt'
filename2 = 'inversSinusFFTW.txt'
+filename3 = 'inversSinusRECFFT.txt'
name0 = filename0[:len(filename0)-4]
name1 = filename1[:len(filename1)-4]
name2 = filename2[:len(filename2)-4]
+name3 = filename3[:len(filename3)-4]
# Tar fram data och plotar datan i filename0 mot x=1...len()
Y = np.loadtxt(filename0, unpack=True)
@@ -27,6 +29,12 @@ XHat2 = list(range(0,len((YHat2))))
plt.plot(XHat2, YHat2, label = name2, color='k')
plt.scatter(XHat2, YHat2, color='k')
+# Tar fram data och plotar datan i filename2 mot xHat2=1...len()
+YHat3,Imaginary = np.loadtxt(filename3, delimiter =',',unpack=True)
+XHat3 = list(range(0,len((YHat3))))
+plt.plot(XHat3, YHat3, label = name3, color='c')
+plt.scatter(XHat3, YHat3, color='c')
+
plt.legend()
plt.title(name0)
plt.xlabel('X')
diff --git a/RECFFT.cc b/RECFFT.cc
new file mode 100644
index 0000000000000000000000000000000000000000..b2ddd016a8e735cbcee6822c48800c6e78226527
--- /dev/null
+++ b/RECFFT.cc
@@ -0,0 +1,122 @@
+#include <complex>
+#include <cmath>
+#include <iomanip>
+#include "Header files/RECFFT.h"
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <vector>
+using namespace std::complex_literals;
+
+const double PI{std::acos(-1)};
+
+// Alg start -----------------------------------------------------------------------------------------------
+std::vector<std::complex<double>> fftrec(std::vector<std::complex<double>> f,int NN,std::vector<std::complex<double>> fftv, int flag)
+{
+ int N = f.size();
+ std::complex<double> w = std::exp(flag*2*PI*1i/static_cast<double> (N));
+ if(N==2)
+ {
+ for(int i=0; i <= NN-1; i++)
+ {
+ fftv[i] = f[0]+std::pow(w,-NN/2+i)*f[2];
+ }
+ }
+ else
+ {
+ std::vector<std::complex<double>> a1;
+ std::vector<std::complex<double>> b1;
+ for(int i=0;i<=N;i++)
+ {
+ if(i%2==0)
+ {
+ a1.push_back(f[i]);
+ }
+ else
+ {
+ b1.push_back(f[i]);
+ }
+ }
+ std::vector<std::complex<double>> a2 = fftrec(a1,NN,fftv,flag);
+ std::vector<std::complex<double>> b2 = fftrec(b1,NN,fftv,flag);
+ for(int k = 0; k <= NN-1; k++)
+ {
+ fftv[k] = a2[k] + b2[k]*std::pow(w,k-NN/2.0);
+ }
+ }
+ return fftv;
+}
+// Alg slut -----------------------------------------------------------------------------------------------
+
+int main()
+{
+ RECFFT call;
+ std::string inFile{"sinus.txt"};
+ std::string outFile{"inversSinusRECFFT.txt"};
+
+ int const n{16};
+ // Får data från inFile och lägger på en vektor
+ std::vector<std::complex<double>> inputVector = call.getInput(inFile,n);
+
+ // Skapar två vektorer av storlek n med nollor i sig
+ std::vector<std::complex<double>> fftv1;
+ std::vector<std::complex<double>> fftv2;
+ for(int i=0;i<n;i++)
+ {
+ fftv1.push_back(0);
+ fftv2.push_back(0);
+ }
+
+ // Anroppar alg ----------------------------------------------------------------
+ std::vector<std::complex<double>> transf = fftrec(inputVector,n,fftv1,-1);
+ std::vector<std::complex<double>> invTransf = fftrec(transf,n,fftv2,1);
+ // -----------------------------------------------------------------------------
+ call.printToFile(invTransf,outFile,n);
+
+ std::cout<<"RECFFT done"<<'\n';
+
+}
+
+
+
+
+
+
+
+
+std::vector<std::complex<double>> RECFFT::getInput(std::string inFile, int n)
+{
+ std::vector<std::complex<double>> inputVector;
+ // Hämtar data och sätter den på en vector
+ int loop = 0;
+ std::string dataLine;
+ std::ifstream functionData (inFile);
+ std::complex<double> element;
+
+ if (functionData.is_open())
+ {
+ while ((std::getline (functionData,dataLine)) && (loop < n) )
+ {
+ std::istringstream is(dataLine);
+ is >> element;
+ inputVector.push_back(element);
+ loop++;
+ }
+ functionData.close();
+ }
+ return inputVector;
+}
+
+void RECFFT::printToFile(std::vector<std::complex<double>> printVector, std::string fileName, int n)
+{
+ // Skriver ut inversFuncTransf till en fil
+ std::ofstream resultFile;
+ resultFile.open(fileName);
+ // Sätter önskad antal decimaler
+ resultFile << std::fixed << std::setprecision(10);
+ for (int i=0;i<n;i++)
+ {
+ resultFile << printVector[i].real() << "," << printVector[i].imag() << '\n';
+ }
+ resultFile.close();
+}
\ No newline at end of file
diff --git a/a.out b/a.out
index 634c2f9334a48227c91bb4fc0d65bfa8266b8775..b2d99b83c42f7267193543eec5e9786faa298bda 100755
Binary files a/a.out and b/a.out differ
diff --git a/inversSinusDFT.txt b/inversSinusDFT.txt
index 936556e578e0d655c6b739af2e08970c999ff6e9..20eb3e7c965afb5c6a38b137db392dbb7393c3a6 100644
--- a/inversSinusDFT.txt
+++ b/inversSinusDFT.txt
@@ -2,19 +2,15 @@
0.8414709848,-0.0000000000
0.9092974268,0.0000000000
0.1411200081,-0.0000000000
--0.7568024953,-0.0000000000
+-0.7568024953,0.0000000000
-0.9589242747,0.0000000000
--0.2794154982,-0.0000000000
-0.6569865987,0.0000000000
-0.9893582466,-0.0000000000
+-0.2794154982,0.0000000000
+0.6569865987,-0.0000000000
+0.9893582466,0.0000000000
0.4121184852,0.0000000000
-0.5440211109,-0.0000000000
--0.9999902066,-0.0000000000
+-0.9999902066,0.0000000000
-0.5365729180,-0.0000000000
-0.4201670368,0.0000000000
-0.9906073557,-0.0000000000
-0.6502878402,-0.0000000000
--0.2879033167,-0.0000000000
--0.9613974919,-0.0000000000
--0.7509872468,0.0000000000
-0.1498772097,0.0000000000
+0.4201670368,-0.0000000000
+0.9906073557,0.0000000000
+0.6502878402,0.0000000000
diff --git a/inversSinusRECFFT.txt b/inversSinusRECFFT.txt
new file mode 100644
index 0000000000000000000000000000000000000000..696c25a14291906db305be413574579273801acf
--- /dev/null
+++ b/inversSinusRECFFT.txt
@@ -0,0 +1,16 @@
+9.1398206044,-5.4536844553
+9.6809334767,-2.9346356508
+-4.8533132756,5.9696298177
+3.1631893166,-3.1673031952
+-1.0681141449,-3.9889275745
+2.5085516570,4.2659503988
+-2.0451485834,-2.2295090922
+-0.9188801268,0.4380280064
+-0.9681317764,-0.3772564925
+-9.1997883841,3.8848288233
+-1.0035716440,-21.6139703680
+10.2159678974,8.3013102465
+0.3726256441,0.3068522515
+-12.6332527731,5.2140573888
+-3.2499819989,-13.7342402161
+4.0199196309,-4.8413742979
diff --git a/sinusDFT.txt b/sinusDFT.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f036fd0dd46b3c9fcc17d3f176827db0e10b9389
--- /dev/null
+++ b/sinusDFT.txt
@@ -0,0 +1,16 @@
+0.4839218698,0.0000000000
+0.5728138574,0.0359040572
+1.2704524334,0.1525576481
+-1.2704178589,-0.2109423635
+-0.3451213350,-0.0666069980
+-0.1871078472,-0.0360227643
+-0.1290856034,-0.0204001227
+-0.1046463980,-0.0094059210
+-0.0976963665,0.0000000000
+-0.1046463980,0.0094059210
+-0.1290856034,0.0204001227
+-0.1871078472,0.0360227643
+-0.3451213350,0.0666069980
+-1.2704178589,0.2109423635
+1.2704524334,-0.1525576481
+0.5728138574,-0.0359040572
diff --git a/sinusFFT.txt b/sinusFFT.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f05a2aa79188f72a07ca10a754d392bc73841de
--- /dev/null
+++ b/sinusFFT.txt
@@ -0,0 +1,16 @@
+0.4839218698,0.0000000000
+-0.2052369891,0.3683901055
+0.3309945693,-0.0465834113
+1.7495228981,-0.2762925791
+0.7193811213,-0.0116458528
+1.2616069280,0.0005730662
+0.3878597128,-0.3912980152
+0.3907509831,0.1837652531
+0.7713484365,-0.1123818198
+0.8513163208,0.0427193630
+0.2372245699,-0.4028497890
+0.7708398190,0.1524420635
+0.8533283588,-0.2411897220
+0.2049880275,0.3455750247
+0.4968121427,-0.5979377809
+1.1531292822,-0.0533400012
diff --git a/sinusRECFFT.txt b/sinusRECFFT.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fe98e1cfc9d914c762b6726756f3671508adf047
--- /dev/null
+++ b/sinusRECFFT.txt
@@ -0,0 +1,16 @@
+-0.4512556488,-2.0328835177
+-1.0583024753,1.6556270252
+-0.5953326772,-2.0157905705
+0.5477123041,0.7768255909
+-5.3680736541,0.6023996661
+3.3988211217,3.4049866271
+0.5281248517,0.9961761991
+1.1167614080,-0.5013865645
+1.2853996392,0.0000000000
+1.1167614080,0.5013865645
+0.5281248517,-0.9961761991
+3.3988211217,-3.4049866271
+-5.3680736541,-0.6023996661
+0.5477123041,-0.7768255909
+-0.5953326772,2.0157905705
+-1.0583024753,-1.6556270252