Lud

LU decomposition is the first step in a method used to solve a system of linear equations, where a matrix representing one of the known values is split into a lower and upper triangular matrix.

For e.g., a linear equation system A.x = z can be split into L U x = z, where L and U are the lower and upper triangular matrices which can be solved as y = U x = L^-1 z and x = U^-1 y

Source code snippet
int size = 32;
float *a = malloc(size * size * sizeof(float));
float sum;

for (i=0; i < size; i++){
    for (j=i; j < size; j++){
         sum=a[i*size+j];
         for (k=0; k < i; k++) sum -= a[i*size+k]*a[k*size+j];
         a[i*size+j]=sum;
    }

    for (j=i+1;j < size; j++){
         sum=a[j*size+i];
         for (k=0; k < i; k++) sum -=a[j*size+k]*a[k*size+i];
         a[j*size+i]=sum/a[i*size+i];
    }
}

}