From 20ba5aa802e7249459076d1ac92b35e95fd6f134 Mon Sep 17 00:00:00 2001
From: Julian Weigt <juw@posteo.de>
Date: Sun, 21 Dec 2025 14:47:17 +0000
Subject: Add numerical experiment c source.

---
 charf.c | 132 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 132 insertions(+)
 create mode 100644 charf.c

(limited to 'charf.c')

diff --git a/charf.c b/charf.c
new file mode 100644
index 0000000..64dd540
--- /dev/null
+++ b/charf.c
@@ -0,0 +1,132 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+
+void differentiate(double* f, double** df, int D, int K){
+	df[0] = f;
+	int i;
+	for(int k=1; k<=K; k++){
+		for(i=0; i<D-k; i++){
+			df[k][i] = df[k-1][i+1] - df[k-1][i];
+		}
+	}
+}
+
+double integrate(double* f, double p, int D){
+	double sum = 0.0;
+	for(int i=0;i<D;i++){
+		sum += pow(fabs(f[i]),p);
+	}
+	return pow(sum,1/p);
+}
+
+double compute_derivatives(int* f, int** Sf, double** Af, double* Mf, double** df, double** dMf, double p, double* intdf, double* intdMf, int N, int D, int K){
+
+for(int i=0;i<D;i++) df[0][i] = (double) f[i];
+
+int r=0;
+for(int i=0;i<D;i++) {
+	Sf[i][i] = f[i];
+	Af[i][i] = 1.0*Sf[i][i];
+}
+for(int n=1;n<D;n++){
+	for(int i=0;i+n<D;i++){
+		Sf[i][i+n] = Sf[i][i+n-1]+f[i+n];
+		Sf[i+n][i] = Sf[i][i+n];
+
+		Af[i][i+n] = 1.0*Sf[i][i+n]/(n+1);
+		Af[i+n][i] = Af[i][i+n];
+	}
+}
+
+for(int i=0;i<D;i++){
+	Mf[i] = Af[i][i];
+	for(int j=0;j<D;j++){
+		if(Af[i][j] > Mf[i]) Mf[i] = Af[i][j];
+	}
+}
+
+//printf("Mf    ");
+//for(int i=0;i<D;i++) printf("%+0.1f ",Mf[i]);
+//printf("\n");
+for(int i=0;i<D;i++){
+	//for(int j=0;j<D;j++) printf("%0.1f ",Af[i][j]);
+	//printf("\n");
+}
+
+differentiate(df[0],df,D,K);
+differentiate(dMf[0],dMf,D,K);
+
+//for(int k=0;k<=K;k++){
+	//printf("f  %d: ",k);
+	//for(int i=0;i<D;i++) printf("%+0.1f ",df[k][i]);
+	//printf("\n");
+	//printf("Mf %d: ",k);
+	//for(int i=0;i<D;i++) printf("%+0.1f ",dMf[k][i]);
+	//printf("\n");
+//}
+
+//for(int k=0;k<=K;k++){
+int k=K;
+	intdf[k] = integrate(df[k],p,D);
+	intdMf[k] = integrate(dMf[k],p,D);
+	//printf("%d: %f / %f = %f\n",k,intdMf[k],intdf[k],intdMf[k]/intdf[k]);
+
+return intdMf[k]/intdf[k];
+//}
+
+}
+
+int main() {
+
+int N=16;
+int D=5*N;
+int K=3;
+double p = 1.0;
+
+int* f = malloc(D*sizeof(int));
+int** Sf = malloc(D*sizeof(int*));
+double** Af = malloc(D*sizeof(double*));
+double* Mf = malloc(D*sizeof(double));
+for(int i=0;i<D;i++){
+	Sf[i] = malloc(D*sizeof(int));
+	Af[i] = malloc(D*sizeof(double));
+}
+
+double** df = malloc(D*sizeof(double*));
+double** dMf = malloc(D*sizeof(double*));
+
+for(int k=0;k<=K;k++){
+	df[k] = malloc(D*sizeof(double));
+	dMf[k] = malloc(D*sizeof(double));
+	for(int i=0;i<D;i++){
+		df[k][i] = 0;
+		dMf[k][i] = 0;
+	}
+}
+dMf[0] = Mf;
+
+double* intdf = malloc(sizeof(double)*K);
+double* intdMf = malloc(sizeof(double)*K);
+double r = 0.0;
+
+for(int t=1; t<=(1 << N)-1; t++){
+	for(int i=0;i<D;i++) f[i]=0;
+	//for(int i=0;i<N;i++) f[N+i] = rand() %2;
+	for(int i=0;i<N;i++){
+		f[2*N+i+K/2] = (t >> i) & 1;
+		//if(i%3==0) f[2*N+i+K/2] = 1;
+	}
+	r = compute_derivatives(f, Sf, Af, Mf, df, dMf, p, intdf, intdMf, N, D, K);
+	//printf("%.3d: %.3f  \n",t,r);
+	if(r>.4997){
+		printf("f: ");
+		for(int i=0;i<D;i++) printf("%.1d ",f[i]);
+		printf("\n");
+		printf("%.4f\n",r);
+	}
+}
+
+return 0;
+}
-- 
cgit v1.2.3