Task: Cholesky decomposition
C: #include <stdio.h>
#include <stdlib.h>
#include <math.h>

double *cholesky(double *A, int n) {
    double *L = (double*)calloc(n * n, sizeof(double));
    if (L == NULL)
        exit(EXIT_FAILURE);

    for (int i = 0; i < n; i++)
        for (int j = 0; j < (i+1); j++) {
            double s = 0;
            for (int k = 0; k < j; k++)
                s += L[i * n + k] * L[j * n + k];
            L[i * n + j] = (i == j) ?
                           sqrt(A[i * n + i] - s) :
                           (1.0 / L[j * n + j] * (A[i * n + j] - s));
        }

    return L;
}

void show_matrix(double *A, int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            printf("%2.5f ", A[i * n + j]);
        printf("\n");
    }
}

int main() {
    int n = 3;
    double m1[] = {25, 15, -5,
                   15, 18,  0,
                   -5,  0, 11};
    double *c1 = cholesky(m1, n);
    show_matrix(c1, n);
    printf("\n");
    free(c1);

    n = 4;
    double m2[] = {18, 22,  54,  42,
                   22, 70,  86,  62,
                   54, 86, 174, 134,
                   42, 62, 134, 106};
    double *c2 = cholesky(m2, n);
    show_matrix(c2, n);
    free(c2);

    return 0;
}

C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Cholesky
{
    class Program
    {
        
        
        
        
        static void Main(string[] args)
        {
            double[,] test1 = new double[,]
            {
                {25, 15, -5},
                {15, 18, 0},
                {-5, 0, 11},
            };

            double[,] test2 = new double[,]
            {
                {18, 22, 54, 42},
                {22, 70, 86, 62},
                {54, 86, 174, 134},
                {42, 62, 134, 106},
            };

            double[,] chol1 = Cholesky(test1);
            double[,] chol2 = Cholesky(test2);

            Console.WriteLine("Test 1: ");
            Print(test1);
            Console.WriteLine("");
            Console.WriteLine("Lower Cholesky 1: ");
            Print(chol1);
            Console.WriteLine("");
            Console.WriteLine("Test 2: ");
            Print(test2);
            Console.WriteLine("");
            Console.WriteLine("Lower Cholesky 2: ");
            Print(chol2);

        }

        public static void Print(double[,] a)
        {
            int n = (int)Math.Sqrt(a.Length);

            StringBuilder sb = new StringBuilder();
            for (int r = 0; r < n; r++)
            {
                string s = "";
                for (int c = 0; c < n; c++)
                {
                    s += a[r, c].ToString("f5").PadLeft(9) + ",";
                }
                sb.AppendLine(s);
            }

            Console.WriteLine(sb.ToString());
        }

        
        
        
        
        
        
        
        
        public static double[,] Cholesky(double[,] a)
        {
            int n = (int)Math.Sqrt(a.Length);

            double[,] ret = new double[n, n];
            for (int r = 0; r < n; r++)
                for (int c = 0; c <= r; c++)
                {
                    if (c == r)
                    {
                        double sum = 0;
                        for (int j = 0; j < c; j++)
                        {
                            sum += ret[c, j] * ret[c, j];
                        }
                        ret[c, c] = Math.Sqrt(a[c, c] - sum);
                    }
                    else
                    {
                        double sum = 0;
                        for (int j = 0; j < c; j++)
                            sum += ret[r, j] * ret[c, j];
                        ret[r, c] = 1.0 / ret[c, c] * (a[r, c] - sum);
                    }
                }

            return ret;
        }
    }
}