o Yi @s0ddlZddlZddlmZddlmZddlmZddl m Z ddl m Z ddlmZdZed d Zgd d d eDdd eDZgdeedd eDZddZddZddZddZddZddZejdddded ggd!d"Zejdgd#d$d%Z ejdd&d'gd(d)Z!ejd*gd+d,d-Z"d.d/Z#d0d1Z$d2d3Z%ejd4eejd*d5d6d7Z&ejd4eejd*d5d8d9Z'ejd:e(eed;d<Z)ejd:e(eed=d>Z*ejd:e(eed?d@Z+ejdedAdBZ,ejdedCdDZ-dS)EN)assert_array_almost_equal)Rotation)linear_sum_assignment)cdist)golden)cKDTreeg-q= )IOTcCg|]}d|qS)C%d.0nrrY/tmp/pip-target-1s0edx8b/lib/python/scipy/spatial/transform/tests/test_rotation_groups.py rcCr )D%drrrrrrr)< cCsg|]}d|qS)rrrrrrrcCs(t||dd}t|}t||S)zCalculates the root-mean-square distance between the points of P and Q. The distance is taken as the minimum over all possible matchings. It is zero if P and Q are identical and non-zero if not. sqeuclidean)metric)rrnpsqrtsum)PQdistance_matrixmatchingrrr_calculate_rmsdsr$cCshtddtj|ddd}tt|t|t|gj}t|gdgf}tj ||ddS)Nrrrrrraxis) rlinspacepivstackzeroscossinr concatenateroll)rr(thetasr rrr_generate_pyramids $r2cCstddtj|ddd}tt| t|t|gj}tt| t|t|gj}t||f}tj ||ddS)Nrrrr%r') rr)r*r+onesr-r.r r/r0)rr(r1bottomtopr rrr_generate_prism#s &&r6csNtddt gddt gddt gddt ggtfddtdDS)Nrr%rcsg|] }tj|ddqS)rr')rr0)rixrrr0sz)_generate_icosahedron..)rarrayphir/rangerrr8r_generate_icosahedron+s    r>c Cs.tgdgdgdgdgdgdgS)N)r%rrr&)rr%r)rrr)rrr%)rrrrr;rrrr_generate_octahedron3sr@cCs"tgdgdgdgdgS)N)rrr)rr%r%)r%rr%)r%r%rr?rrrr_generate_tetrahedron8s"rAnamer%TC3cC>tjtddt|WddS1swYdS)Nzmust be a stringmatchpytestraises ValueErrorr create_grouprBrrrtest_group_type<  "rM)r! CAzC DAzD I2cCrD)Nz(must be one of 'I', 'O', 'T', 'Dn', 'Cn'rErGrLrrrtest_group_nameCrNrTC0D0cCrD)NzGroup order must be positiverErGrLrrrtest_group_order_positiveJrNrWr()AbrrrFNcCs@tjtddtd|WddS1swYdS)Nz`axis` must be one ofrEC1rGr'rrrtest_axis_validQs "r\cCs@t}tdD]}t|}t|||tksJqdS)zThe icosahedral group fixes the rotations of an icosahedron. Here we test that the icosahedron is invariant after application of the elements of the rotation group.r N)r>rrK from_quatas_quatr$applyTOLr grrrtest_icosahedralXs rccC2t}tdD]}t|||tksJqdS)zRTest that the octahedral group correctly fixes the rotations of an octahedron.r N)r@rrKr$r_r`rarrrtest_octahedralbrecCrd)zSTest that the tetrahedral group correctly fixes the rotations of a tetrahedron.r N)rArrKr$r_r`rarrrtest_tetrahedraljrfrgrXYZcCFt|d|d}tjd||dD]}t|||tks JqdS)zJTest that the dicyclic group correctly fixes the rotations of a prism.rhr'rN)r6indexrrKr$r_r`rr(r rbrrr test_dicyclicrrlcCri)zJTest that the cyclic group correctly fixes the rotations of a pyramid.rhr'rN)r2rjrrKr$r_r`rkrrr test_cyclic|rmrnz name, sizecCstt||ks JdS)N)lenrrK)rBsizerrrtest_group_sizessrqcCs0t|}t|}t|ddksJdS)NgMbP?r)rrKrr^ro query_pairs)rBrprbkdtreerrrtest_group_no_duplicatess  rtcCsbt|}t| |f}tt||}tj|ddtj|dd}|t k s/JdS)Nrr') rrKrr/r^sortrmaxminr`all)rBrprbqdistancedeltasrrrtest_group_symmetrys r|cCs0t|}||}t|tt|dS)zaTest that the elements of the rotation group are correctly mapped onto the identity rotation.N)rrKreducer magnituderr,rorBrbfrrrtest_reductions  rcCs<t|}|d|}t|d|jdksJdS)Nr%r)rZ)rrKr}rr~r^shaperrrrtest_single_reductions r).rHnumpyr numpy.testingrscipy.spatial.transformrscipy.optimizerscipy.spatial.distancerscipy.constantsrr< scipy.spatialrr`r=NSNAMESlistSIZESr$r2r6r>r@rAmark parametrizer;rMrTrWr\rcrergrlrnziprqrtr|rrrrrrsZ       $