test.jl

include("rtp.jl")
include("irreps.jl")
using Einsum
using LinearAlgebra


function assert_equivariance()
	irreps_in = "1o"
	_, irreps_out, Q = ReducedTensorProduct.reduced_product_dq("ijkl=jikl=klij", Dict('i' => irreps_in))

	abc = o3.rand_angles(())

	R = o3.D_from_angles_irreps(o3.Irreps(irreps_in), abc...)
	D = o3.D_from_angles_irreps(irreps_out, abc...)

	@einsum Q1[z, a, b, c, d] := Q[z, i, j, k, l] * R[i, a] * R[j, b] * R[k, c] * R[l, d]
	@einsum Q2[w, i, j, k, l] := D[w, z] * Q[z, i, j, k, l]

	@assert isapprox(Q1, Q2, atol = 1e-5)
end


function assert_permutation()
	irreps_in = "1o"
	_, irreps_out, Q = ReducedTensorProduct.reduced_product_dq("ijkl=jikl=klij", Dict('i' => irreps_in))

	@einsum Q1[z, i, j, k, l] := Q[z, j, i, k, l]
	@assert isapprox(Q1, Q, atol = 1e-5)

	@einsum Q2[z, i, j, k, l] := Q[z, k, l, j, i]
	@assert isapprox(Q2, Q, atol = 1e-5)
end


function assert_permutation2()
	irreps_in = "1o"
	_, irreps_out, Q = ReducedTensorProduct.reduced_product_dq("ijk=-jik=jki", Dict('i' => irreps_in))

	@einsum Q1[z, i, j, k] := -Q[z, j, i, k]
	@assert isapprox(Q1, Q, atol = 1e-5)

	@einsum Q2[z, i, j, k] := Q[z, j, k, i]
	@assert isapprox(Q2, Q, atol = 1e-5)
end


function assert_orthogonality()
	irreps_in = "1o"
	_, irreps_out, Q = ReducedTensorProduct.reduced_product_dq("ijkl=jikl=klij", Dict('i' => irreps_in))
	@einsum n2[z, w] := Q[z, i, j, k, l] * Q[w, i, j, k, l]
	@assert isapprox(n2, I(size(Q, 1)), atol = 1e-5)
end


function all_tests()
	assert_equivariance()
	assert_permutation()
	assert_permutation2()
	assert_orthogonality()
end