Differentiating multiple polynomials

This may be an unexpected behavior. As we know, the polynomials in minterpy may be defined using multiple sets of coefficients denoting multiple polynomials (sharing the same basis).

mi = mp.MultiIndexSet.from_degree(2, 3, 1)
newton_coeffs = np.random.rand(len(mi),5)
newton_poly = mp.NewtonPolynomial(mi, newton_coeffs)
xx = -1 + 2 * np.random.rand(100,2)
newton_poly(xx).shape
# (100, 5)

However, differentiating such polynomials (partial or otherwise) gives a cryptic error message:

newton_poly.partial_diff(1)

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [11], in <cell line: 1>()
----> 1 newton_poly.partial_diff(1)

File ~\Anaconda3\envs\mp-opt-temp\lib\site-packages\minterpy\core\ABC\multivariate_polynomial_abstract.py:798, in MultivariatePolynomialSingleABC.partial_diff(self, dim, order)
    795 if order < 0:
    796     raise ValueError(f"order <{order}> must be a non-negative integer")
--> 798 return self._partial_diff(self, dim, order)

File ~\Anaconda3\envs\mp-opt-temp\lib\site-packages\minterpy\polynomials\newton_polynomial.py:67, in _newton_partial_diff(poly, dim, order)
     65 deriv_order_along = [0]*spatial_dim
     66 deriv_order_along[dim] = order
---> 67 return _newton_diff(poly, deriv_order_along)

File ~\Anaconda3\envs\mp-opt-temp\lib\site-packages\minterpy\polynomials\newton_polynomial.py:79, in _newton_diff(poly, order)
     70 """ Partial differentiation in Newton basis.
     71 
     72 Notes
     73 -----
     74 Performs a transformation from Lagrange to Newton using DDS.
     75 """
     77 # When you evaluate the derivatives on the unisolvent nodes, you get the coefficients for
     78 # the derivative polynomial in Lagrange basis.
---> 79 lag_coeffs = deriv_newt_eval(poly.grid.unisolvent_nodes, poly.coeffs,
     80                              poly.grid.multi_index.exponents,
     81                              poly.grid.generating_points, order)
     83 # DDS returns a 2D array, converting it to 1d
     84 newt_coeffs = dds(lag_coeffs, poly.grid.tree).reshape(-1)

File ~\Anaconda3\envs\mp-opt-temp\lib\site-packages\minterpy\polynomials\utils.py:110, in deriv_newt_eval(x, coefficients, exponents, generating_points, derivative_order_along)
    107                     newt_mon_val = 0.0
    108         monomial_vals[j] = newt_mon_val
--> 110     results[point_nr] = np.dot(coefficients, monomial_vals)
    112 return results

File <__array_function__ internals>:180, in dot(*args, **kwargs)

ValueError: shapes (10,5) and (10,) not aligned: 5 (dim 1) != 10 (dim 0)

Is there a more gracious way of raising an error message, or perhaps even parameterizing the differentiation to choose which polynomial when there are multiple of them? What do you think @thekke48?