public double [,] generate_linear_matrix(Vector3 [] new_positions, double beta)
{
double [,] r = generate_rotation_matrix(new_positions);
double [,] a = MatrixFunctions.matrixMultiply3x3(apq, aqq);
//Rotation_test.print_matrix(aqq);
double determinant = alglib.rmatrixdet(a);
determinant = Mathf.Pow((float)determinant, 1.0f / 3.0f);
MatrixFunctions.scalar_multiply(ref a, beta / determinant);
MatrixFunctions.scalar_multiply(ref r, 1 - beta);
MatrixFunctions.matrix_add_3x3(ref a, r);
return(a);
}