Comment on 5_practice.c for pull request

5_practice.c

@@ -1,40 +1,85 @@
-#include <stdio.h>	// for printf function
-#include <stdlib.h>	// for memory allocation
-#include <time.h>	// for time calculation
-#include <math.h>	// for sine and cosine functions
-int main() {
-	// Declare all the variables
-	int k, n, N;
-	double *x, *yr, *yi;
-	time_t t;
+//
+//  DFT
+//
+//  Created by Liu Yuting on 2022/3/9.
+//
 
-	// Input the number N
-	
-	
-	// Locate the memory for x, yr, yi;
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
 
-	// Initial setting for x, for example, x[k] = k
-
-
-
-
-	t = clock();	
-	// yr[n]+i*yi[n] = sum(exp(-i 2 Pi k n / N)*x[k], k=0..N-1), n=0..N-1 
+int main(int argc, const char * argv[]) {
+    // Declare variables.
+    int N=7;
+    int n, k;
+    int index;
+
+    double *x, *yr, *yi, *cos_array, *sin_array;
+    x=(double *) malloc(N*sizeof(double));
+    yr=(double *) malloc(N*sizeof(double));
+    yi=(double *) malloc(N*sizeof(double));
+    cos_array=(double *) malloc(N*sizeof(double));
+    sin_array=(double *) malloc(N*sizeof(double));
+    for(n=0; n<N; n++) {
+        //Initialize x.
+        x[n]=n;
+    }
+    time_t t;
+
+    t=clock();
+
+    cos_array[0]=1.0;
+    sin_array[0]=0.0;
+    cos_array[1]=cos(2*M_PI/N);
+    sin_array[1]=sin(2*M_PI/N);
+
+    for(n=2; n<N; n++) {
+        //Compute table of cos and sin.
+        cos_array[n]=cos_array[1]*cos_array[n-1]-sin_array[1]*sin_array[n-1];
+        sin_array[n]=cos_array[1]*sin_array[n-1]+sin_array[1]*cos_array[n-1];
+    }
+
+    for(k=0; k<N; k++) {
+        //Compute DFT.
+        yr[k]=0.0;
+        yi[k]=0.0;
+        for(n=0; n<N; n++) {
+            //Compute yr[k], yi[k].
+            index=(n*k)%N;
+            yr[k]+=x[n]*cos_array[index];
+            yi[k]+=x[n]*sin_array[index];
+        }
+    }
+
+    t=clock()-t;
+
+    printf("x:");
+    for(n=0; n<N; n++) {
+        //Print values of x.
+        printf(" %f", x[n]);
+    }
+    printf("\n");
+
+    printf("yr:");
+    for(k=0; k<N; k++) {
+        //Print values of yr.
+        printf(" %f", yr[k]);
+    }
+    printf("\n");
+
+    printf("yi:");
+    for(k=0; k<N; k++) {
+        //Print values of yi.
+        printf(" %f", yi[k]);
+    }
+    printf("\n");
+
+    printf("Time: %f s\n", 1.0*t/CLOCKS_PER_SEC);
+
+    free(yi);
+    free(yr);
+    free(x);
 
-
-
-
-
-
-
-	// output the results
-	t = clock() - t;
-	printf("%d ms for discrete Fourier Transform of %d elements\n", t, N);
-
-	// free the memory located by x, yr, yi
-
-
-
-	return 100;
+    return 0;
 }
-