o :ήcã@sHddlZddlZddlZdd„Zdd„Zdd„Z   d d d „ZdS)éNcCs|\}}||}|d}|d}||}t gd¢¡d}t t t |¡|¡d¡}t t t |¡|¡d¡} |dt gd¢|¡} | dt gd¢|¡} d| k| |k@d| k@| |k@} || || } | | || }t ||¡| }tj || |ff||f¡}|j}||fS)Né) érrrérrrréé ) éÿÿÿÿrrrrrrrr) rrrrrrrrrr) ÚnpÚfloat64ÚrepeatÚtileÚarangeÚscipyÚsparseÚ csr_matrixÚT)ÚshapeÚhÚwÚnÚh2Úw2Ún2ÚweightsÚx2Úy2ÚxÚyÚmaskÚi_indsÚj_indsÚvaluesÚ downsampleÚupsample©r#úF/tmp/pip-target-vg8gfxp4/lib/python/pymatting/preconditioner/vcycle.pyÚmake_Ps" r%cCs\|dur|dkr|||}|d8}nt |¡}t|ƒD]}|||| |¡|}q|S)Nrr)rÚ zeros_likeÚrangeÚdot)ÚAÚA_diagÚbrÚnum_iterÚomegaÚ_r#r#r$Ú jacobi_step s    r/c Csæ|\}} || } | |krtjj ||¡S||vr3t|ƒ\} } |  |¡ | ¡} | ¡}| | | |f||<n||\} } } }t|||d||ƒ}|| |¡}|  |¡}t| ||d| df|||||ƒ}||  |¡7}t||||||ƒ}|S)Nr) r rÚlinalgÚspsolver%r(Údiagonalr/Ú _vcycle_step)r)r+rÚcacheÚ num_pre_iterÚ num_post_iterr-Údirect_solve_sizerrrr"r!Úcoarse_Ar*rÚresidualÚcoarse_residualÚcoarse_xr#r#r$r3.s4   ø r3rçš™™™™™é?é@cs(ˆduri‰‡‡‡‡‡‡‡fdd„}|S)aæ Implements the V-Cycle preconditioner. The V-Cycle solver was recommended by :cite:`lee2014scalable` to solve the alpha matting problem. Parameters ---------- A: numpy.ndarray Input matrix shape: tuple of ints Describing the height and width of the image num_pre_iter: int Number of Jacobi iterations before each V-Cycle, defaults to 1 num_post_iter: int Number of Jacobi iterations after each V-Cycle, defaults to 1 omega: float Weight parameter for the Jacobi method. If method fails to converge, try different values. Returns ------- precondition: function Function which applies the V-Cycle preconditioner to a vector Example ------- >>> from pymatting import * >>> import numpy as np >>> from scipy.sparse import csc_matrix >>> A = np.array([[2, 3], [3, 5]]) >>> preconditioner = vcycle(A, (2, 2)) >>> preconditioner(np.array([1, 2])) array([-1., 1.]) Nc stˆ|ˆˆˆˆˆˆƒS)N)r3)Úr©r)r4r7r6r5r-rr#r$Ú precondition”sÿzvcycle..preconditionr#)r)rr5r6r-r7r4r@r#r?r$Úvcyclegs*rA)rrr<r=N) ÚnumpyrÚ scipy.sparser Úscipy.sparse.linalgr%r/r3rAr#r#r#r$Ús<ù