a6d.dZddlZddlZddlZdZdZdS)a)Analytical transformations from raw image moments to central moments. The expressions for the 2D central moments of order <=2 are often given in textbooks. Expressions for higher orders and dimensions were generated in SymPy using ``tools/precompute/moments_sympy.py`` in the GitHub repository. Nc |j}|jddz }|j}|tjd}t j|}|dks|dvrtd|}|dkrT|d |d z }|d |d z }|d |d <|dkrE|d ||d zz |d <|d ||d zz |d <|d||d zz |d<|dkr|dd|z|d zz ||d zz |dz|d zz||z|d zz|d<|dd|z|d zz ||dzz d|z|z|d zz|d<|dd|z|d zz d|dzz|d zz|d<|dd|z|dzz d|dzz|d zz|d<n|d|dz }|d|dz }|d|dz }|d|d<|dkr| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<| |dz|dz|d<|dkr)d|dzz|dzd|z|dzz |dz|d<| |dzd|z||dz|dz zz|dz|d<|dz|dzd|z|dzz |||dz|dz zz|d z|d <d|dzz|dzd|z|dzz |d!z|d!<| |dzd|z||dz|dz zz|d"z|d"<| |dz|||dz|dz zz|||dz|dz zz|d#z|d#<| |dzd|z| |dz|dzzz |d$z|d$<|dz|dzd|z|dzz |||dz|dz zz|d%z|d%<|dz|dzd|z|dzz |||dz|dz zz|d&z|d&<d|dzz|dzd|z|dzz |d'z|d'<||dS)(aOAnalytical formulae for 2D and 3D central moments of order < 4. `moments_raw_to_central` will automatically call this function when ndim < 4 and order < 4. Parameters ---------- moments_raw : ndarray The raw moments. Returns ------- moments_central : ndarray The central moments. rF)copyz:This function only supports 2D or 3D moments of order < 4.r)rr)rr)rr)rr)rr)rr)rr)rr)r rr )rr )rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr )rrr)rrr)rr r)rrr)rrr)rrr)rrr)rrr)r rr)ndimshapedtypeastypenpfloat64 zeros_like ValueError) moments_rawr order float_dtypemoments_centralmcxcyczs Clib/python3.11/site-packages/skimage/measure/_moments_analytical.py_moments_raw_to_central_fastrs0  D  a 1 $E#K$$RZe$<z*moments_raw_to_central..s"'E'E'Ea!e 'E'E'Er)r r rrrtupleeyeintrmathcomb itertoolsproductsumzip)rr rrrcenterspqiterm1jterm2ordersidxsvali_ordercidxs rmoments_raw_to_centralr9qs  D  a 1 $E v~~%!))+K888mK00OAAeBF4s333445$t) DEEG qyyuqy!! E EA519%% E Eq55==q1uEEA IaOOEwqzkq1u55E"1q5\\EE $ !Q71:+1q5!99'1---uQq!tW1DD----EE E #uUQY'7'7&9D&@B + + v;;   %'E'Ef'E'E'EF + +DD'C#&vw#=#= / /Cty#...# .. F # # #s * # # # #  + r)__doc__r(r&numpyrrr9rrr=s^ `;`;`;F,,,,,r