o h@s0dZddlZddlZddlZddZddZdS)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 Cs|j}|jdd}|j}|jtjdd}t|}|dks"|dvr&td|}|dkr|d |d }|d |d }|d |d <|dkrj|d ||d |d <|d ||d |d <|d||d |d<|dkr|dd||d ||d |d|d |||d |d<|dd||d ||dd|||d |d<|dd||d d|d|d |d<|dd||dd|d|d |d<n|d|d}|d|d}|d|d}|d|d<|dkrS| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<| |d|d|d<|dkr}d|d|dd||d|d|d<| |dd|||d|d|d|d<|d|dd||d|||d|d|d |d <d|d|dd||d|d!|d!<| |dd|||d|d|d"|d"<| |d|||d|d|||d|d|d#|d#<| |dd|| |d|d|d$|d$<|d|dd||d|||d|d|d%|d%<|d|dd||d|||d|d|d&|d&<d|d|dd||d|d'|d'<|j|ddS)(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)rrr)rr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)rrr)ndimshapedtypeastypenpfloat64 zeros_like ValueError) moments_rawrorder float_dtypemoments_centralmcxcyczr^/var/www/html/scripts/venv/lib/python3.10/site-packages/skimage/measure/_moments_analytical.py_moments_raw_to_central_fasts  ""00       rc Cs|j}|jdd}|dvr|dkrt|St|}|}t|ttj|td|d|}|dkrt|dD]X}t|dD]O}|||krKqBt|dD]?}t ||} | |d ||9} t|dD]%} t || } | |d || 9} |||f| | ||| f7<qjqQqBq:|St j t|df|D]?} t | |krqt j dd | DD]+} || }t| || D]\}}}|t ||9}|| ||9}q|| |7<qq|S) Nrrrr)r )rrcSsg|]}t|dqS)r)range).0orrr sz*moments_raw_to_central..)rr rr rtupleeyeintrmathcomb itertoolsproductsumzip)rrrrrcenterspqiterm1jterm2ordersidxsvali_ordercidxrrrmoments_raw_to_centralqsD &   &  r5)__doc__r$r"numpyr rr5rrrrs  c