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285abgabe6.cpp
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//g++ abgabe6.cpp -std=c++14 -o abgabe6
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// ./abgabe6
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// Pauline Maas, Ariane Ufer
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#include <stdlib.h>
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#include <stdio.h>
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#include <string.h>
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#include <ctype.h>
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#include <math.h>
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#include <complex>
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#include <vector>
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using namespace std; |
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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typedef struct { |
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long n; |
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double b, a, beta, alpha; |
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double tmin, tmax,h,tl; |
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int m; |
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int sign; |
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} fft_param; |
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//Pseudo-Zufallszahlen-Generator
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//Part of a C-program for MT19937, with initialization improved 2002/1/26.
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//Coded by Takuji Nishimura and Makoto Matsumoto.
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/* Period parameters */ |
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#define N 624
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#define M 397
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#define MATRIX_A 0x9908b0dfUL /* constant vector a */
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#define UPPER_MASK 0x80000000UL /* most significant w-r bits */
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#define LOWER_MASK 0x7fffffffUL /* least significant r bits */
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static unsigned long mt[N]; /* the array for the state vector */ |
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static int mti=N+1; /* mti==N+1 means mt[N] is not initialized */ |
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/* initializes mt[N] with a seed */ |
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void init_genrand(unsigned long s) |
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{ |
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mt[0]= s & 0xffffffffUL; |
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for (mti=1; mti<N; mti++) { |
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mt[mti] = |
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(1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti); |
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/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */ |
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/* In the previous versions, MSBs of the seed affect */ |
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/* only MSBs of the array mt[]. */ |
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/* 2002/01/09 modified by Makoto Matsumoto */ |
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mt[mti] &= 0xffffffffUL; |
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/* for >32 bit machines */ |
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} |
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} |
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/* initialize by an array with array-length */ |
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/* init_key is the array for initializing keys */ |
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/* key_length is its length */ |
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/* slight change for C++, 2004/2/26 */ |
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void init_by_array(unsigned long init_key[], int key_length) |
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{ |
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int i, j, k; |
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init_genrand(19650218UL); |
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i=1; j=0; |
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k = (N>key_length ? N : key_length); |
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for (; k; k--) { |
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525UL)) |
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+ init_key[j] + j; /* non linear */ |
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mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
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i++; j++; |
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if (i>=N) { mt[0] = mt[N-1]; i=1; } |
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if (j>=key_length) j=0; |
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} |
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for (k=N-1; k; k--) { |
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL)) |
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- i; /* non linear */ |
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mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */ |
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i++; |
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if (i>=N) { mt[0] = mt[N-1]; i=1; } |
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} |
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mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */ |
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} |
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/* generates a random number on [0,0xffffffff]-interval */ |
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unsigned long genrand_int32(void) |
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{ |
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unsigned long y; |
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static unsigned long mag01[2]={0x0UL, MATRIX_A}; |
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/* mag01[x] = x * MATRIX_A for x=0,1 */ |
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if (mti >= N) { /* generate N words at one time */ |
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int kk; |
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if (mti == N+1) /* if init_genrand() has not been called, */ |
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init_genrand(5489UL); /* a default initial seed is used */ |
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for (kk=0;kk<N-M;kk++) { |
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK); |
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mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1UL]; |
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} |
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for (;kk<N-1;kk++) { |
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK); |
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mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1UL]; |
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} |
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y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK); |
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mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1UL]; |
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mti = 0; |
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} |
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y = mt[mti++]; |
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/* Tempering */ |
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y ^= (y >> 11); |
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y ^= (y << 7) & 0x9d2c5680UL; |
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y ^= (y << 15) & 0xefc60000UL; |
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y ^= (y >> 18); |
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return y; |
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} |
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/* generates a random number on [0,1) with 53-bit resolution*/ |
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double genrand_res53(void) |
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{ |
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unsigned long a=genrand_int32()>>5, b=genrand_int32()>>6; |
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return(a*67108864.0+b)*(1.0/9007199254740992.0); |
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} |
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// End of C-program for MT19937
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complex<double> expo(fft_param *fp,int k) { |
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int sign = fp->sign; |
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int n=fp->n; |
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return exp(sign*2.0 * M_PI * 1i* ((double)(k/n))); |
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} |
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vector<complex<double>> fourierTrafo(fft_param *fp, vector<complex<double>> x) { |
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long n = x.size(); //Länge des x vektors
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int sign=fp->sign; |
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vector<complex<double>> gerPkt(n / 2); //Vektoren um x in gerade und ungerade Teile aufzuteilen
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vector<complex<double>> ungerPkt(n / 2); //Haben dann Länge n/2
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if (n == 1) { |
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return x; |
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} else { |
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//Aufteilen
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for (int k = 0; k < n / 2; k++) { |
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gerPkt[k] = x[2 * k]; |
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ungerPkt[k] = x[2 * k + 1]; |
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} |
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vector<complex<double>> ftger = fourierTrafo(fp, gerPkt); //rekursives Aufrufen der Funktion um weiter zu Teilen
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vector<complex<double>> ftunger = fourierTrafo(fp, ungerPkt); |
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vector<complex<double>> out(n); |
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for (int k = 0; k < n / 2; k++) { |
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//In out ergebnis nach FFT routine Speichern
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if(sign==-1){ |
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out[k] = (ftger[k] + ftunger[k] * expo(fp,k)); |
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out[k + n / 2] = (ftger[k] - ftunger[k] *expo(fp,k)); |
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} |
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else{ |
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out[k] = (ftger[k] + ftunger[k] * expo(fp,k)); |
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out[k + n / 2] = (ftger[k] - ftunger[k] *expo(fp,k)); |
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} |
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} |
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return out; |
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} |
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} |
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vector<complex<double>> makeS(fft_param *fp){ |
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double h=fp->h; //Variabeln aus struct holen
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double tmax=fp->tmax; |
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double tmin=fp->tmin;; |
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double t; |
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double tl=fp->tl; |
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double alpha=fp->alpha; |
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int n=fp->n; |
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vector<complex<double>> s(n); //Vektor zum speichern von s
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for(int k=0;k<n;k++){ |
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t=tmin+k*h; |
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if (t-tl >= 0 && t-tl <= tmax){ |
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s[k]=sin(2*M_PI*alpha*(t-tl)); //s berechnen
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} |
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else{ |
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s[k]=0; |
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} |
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} |
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return s; |
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} |
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vector<complex<double>> makeE(fft_param *fp){ |
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double h=fp->h; //Variabeln aus struct holen
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double tmax=fp->tmax; |
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double tmin=fp->tmin; |
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double t; |
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double beta=fp->beta; |
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double tl=fp->tl; |
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double a=fp->a; |
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double b=fp->b; |
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int n=fp->n; |
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vector<complex<double>> e(n); //Vektor zum speichern von e
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vector<complex<double>> s=makeS(fp); //Vektor s wird benötigt
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//FILE *fp3 = fopen("H10_2_30.txt" ,"w");
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for(int k=0;k<n;k++){ |
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t=tmin+k*h; |
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e[k]=b*sin(2*M_PI*beta*t)+ 2*a*(genrand_res53()-0.5)+s[k]; //e berechnen
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//fprintf(fp3,"%f\t%f\n",t,pow(e[k].real(),2));
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//printf("%f\t%f\n",t,pow(e[k].real(),2));
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//printf("%f\t%f\t%f\n",t,e[k].real(),e[k].imag());
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} |
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//fclose(fp3);
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return e; |
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} |
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vector<complex<double>> aufgabe3 (fft_param *fp){ |
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double h=fp->h; //Varabeln aus Struct holen
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double tmin=fp->tmin; |
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double tmax=fp->tmax; |
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double t=tmin; |
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int n=fp->n; |
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vector<complex<double>> e=makeE(fp); //e und s berechnen
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vector<complex<double>> s=makeS(fp); |
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vector<complex<double>> Fe=fourierTrafo(fp,e); //e Fouriertransformieren
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vector<complex<double>> Fs=fourierTrafo(fp,s); //s Fouriertransformieren
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vector<complex<double>> FFes(n); //Vektor machen zum speichern
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for(int k=0;k<n;k++){ |
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//Hier Fouriertransformation von e mal Fouriertransformation von s komplex konjugiert berechnen
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FFes[k]=Fe[k]*conj(Fs[k]); |
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} |
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fft_param fps=*fp; //Sign im struct ändern
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fps.sign=-1; |
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vector<complex<double>> FFFes=fourierTrafo(&fps, FFes); //Rücktransformation des Produkts
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return FFFes; |
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//init_genrand((long)seed);
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} |
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void plotAufgabe3(fft_param *fp){ |
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int n = fp->n; |
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double tmin=fp->tmin; |
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double h=fp->h; |
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vector<complex<double>> es = aufgabe3(fp); |
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FILE *fp4 =fopen("es4.csv","w"); |
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for (int k=0;k<n;k++){ |
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printf("%f\n", norm(es[k])); |
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fprintf(fp4,"%f\t%f\n", tmin+k*h, norm(es[k])); |
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} |
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} |
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int main(){ |
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long seed = 57291; // beliebigen Wert gewählt
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init_genrand(seed); //rufe am Anfang mit einem festen Wert auf für reproduzierbare Ergebnise
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fft_param fp; |
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fp.n= pow(2,13); |
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fp.tmin=0; |
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fp.tmax = 100; |
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fp.h=(fp.tmax-fp.tmin)/fp.n; |
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fp.sign=1; |
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fp.alpha=10; |
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fp.beta=1; |
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fp.a=0.5; |
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fp.b=0.50; |
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fp.tl=5; |
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//test(&fp);
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plotAufgabe3(&fp); |
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//printf("%f\n",genrand_res53());
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//H10.2
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fp.h=0.001; //Schrittweite der Zeit für Plot
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fp.n=100/0.001; // plotte e(t) bis für die Zeit tmin bis tmin + 100
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//makeE(&fp);
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} |
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