def scalar_product_partial(anchors, indizes_1, indizes_2, start):
q = (anchors[1][0]-anchors[0][0])
z = (start-anchors[1][0]) / q
vector_1 = np.vstack([
anchors[0][1][indizes_1], # a_1
anchors[0][2][indizes_1] * q, # b_1
anchors[1][1][indizes_1], # c_1
anchors[1][2][indizes_1] * q, # d_1
])
vector_2 = np.vstack([
anchors[0][1][indizes_2], # a_2
anchors[0][2][indizes_2] * q, # b_2
anchors[1][1][indizes_2], # c_2
anchors[1][2][indizes_2] * q, # d_2
])
return np.einsum(
vector_1, [0,2],
partial_sp_matrix(z), [0,1],
vector_2, [1,2]
)*q
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