LU factorization of square matrices. This is an implementation of the algorithm given in Strang's Intro to Linear Algebra textbook

square_lu.c

#include <stdio.h>
#include <math.h>

void square_lu(float A[][3], float L[][3], float U[][3])
{
  int n = 3;
  for (int k = 0; k < n; k++)
    {
      L[k][k] = 1.0f;
      for (int i = k+1; i < n; i++)
        {
          L[i][k] = A[i][k] / A[k][k]; /* load multipliers for column k into L */
          for (int j = k+1; j < n; j++)
            {
              A[i][j] = A[i][j] - (L[i][k] * A[k][j]);
            }
        }
    
      for (int j = k; j < n; j++)
        {
          U[k][j] = A[k][j];
        }
    }
}


int main()
{
  float L[3][3];
  float U[3][3];
  float A[3][3] = {1,2,3, 4,5,6, 7,8,10};
  
  square_lu(A, L, U);
  printf("L:\n");
  for (int i = 0; i < 3; i++)
    {
      for (int j = 0; j < 3; j++)
        {
          printf("%.2f\t", L[i][j]);
        }
      printf("\n");
    }

  printf("\nU:\n");
  for (int i = 0; i < 3; i++)
    {
      for (int j = 0; j < 3; j++)
        {
          printf("%.2f\t", U[i][j]);
        }
      printf("\n");
    }
}