_-Ph,<dZddlZddlZddlmZeddfdZd d Z dS) z'Discretizations of the Poisson problem.N) stencil_gridFDct|}t|}|dkst|dkrtd||dkrdt jd|z|}t |D]0}d|d|zdzd||z dz zz<d|d|zd zd||z dz zz<1d |z|d|z<|d kr(t jd|z| }d |zdz |d|z<t||| S)aReturn a sparse matrix for the N-dimensional Poisson problem. The matrix represents a finite Difference approximation to the Poisson problem on a regular n-dimensional grid with unit grid spacing and Dirichlet boundary conditions. The last dimension is iterated over first: z, then y, then x. This should be used with np.mgrid() or np.ndenumerate. Parameters ---------- grid : tuple of integers grid dimensions e.g. (100,100) Notes ----- The matrix is symmetric and positive definite (SPD). Examples -------- >>> from pyamg.gallery import poisson >>> # 4 nodes in one dimension >>> poisson((4,)).toarray() array([[ 2., -1., 0., 0.], [-1., 2., -1., 0.], [ 0., -1., 2., -1.], [ 0., 0., -1., 2.]]) >>> # rectangular two dimensional grid >>> poisson((2,3)).toarray() array([[ 4., -1., 0., -1., 0., 0.], [-1., 4., -1., 0., -1., 0.], [ 0., -1., 4., 0., 0., -1.], [-1., 0., 0., 4., -1., 0.], [ 0., -1., 0., -1., 4., -1.], [ 0., 0., -1., 0., -1., 4.]]) rzInvalid grid shape: r))dtype)r)r)r FEr)format) tuplelenmin ValueErrornpzerosrangeonesr)gridrr typeNstencilis W/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/pyamg/gallery/laplacian.pypoissonr s)L ;;D D A1uuD A 666777 t||(4!85111q 7 7A46GDFTMD!A#a%L0 146GDFTMD!A#a%L0 1 1A#Q t||74!851111Q$(Q f 5 5 55?皙?c  |}t||fdt}dtjz|ztj||zz}dtjz|ztj||zz}t |jD]}|j|}|j |} tj || z } t|| } || krd} nd} | dkr(dtj | || zz|j |<| |kr(dtj | || zz|j |<dtjz|ztj||zz}dtjz|ztj||zz}g} g}g}g}t d|D]J}| |||||zz|z ||Kt ||z|z ||zD]J}| |||||zz |z||Kt d||zdz |D]G}| ||||zdz |dHt |dz ||z|D]G}| ||||z dz|dHtt!| |D]\}\}} ||} t|| } || krd} nd} | dkr3|dtj | || zz| |kr3|dtj | || zztj|j tj|f}tj|jtj| f}tj|j tj|f}t&j|||ff||z||zf}d|d zz |zS) aConstruct a Gauge Laplacian from Quantum Chromodynamics for regular 2D grids. Note that this function is not written efficiently, but should be fine for N x N grids where N is in the low hundreds. Parameters ---------- npts : int number of pts in x and y directions spacing : float grid spacing between points beta : float temperature Note that if beta=0, then we get the typical 5pt Laplacian stencil Returns ------- A : csr matrix A is Hermitian positive definite for beta > 0.0 A is Symmetric semi-definite for beta = 0.0 Examples -------- >>> from pyamg.gallery import gauge_laplacian >>> A = gauge_laplacian(10) References ---------- .. [1] MacLachlan, S. and Oosterlee, C., "Algebraic Multigrid Solvers for Complex-Valued Matrices", Vol. 30, SIAM J. Sci. Comp, 2008 coo)r ry@grrr)shaper )rcomplexrpirandomrandnrnnzrowcolabsrexpdataappend enumerateziphstackarrayspsparse coo_matrixtocsr)nptsspacingbetarAalpha_xalpha_yrrcdiffindexsnew_rnew_cnew_datanew_diffr+r'r(s rgauge_laplacianrDFs~L AAuG444A 25 4'")//!A#*>*>>G25 4'")//!A#*>*>>G15\\:: E!H E!Hva!e}}Aq  q55AAA 199rva'%.&8999AF1I 199rva'%.&8999AF1I25 4'")//!A#*>*>>G25 4'")//!A#*>*>>G E EHH 1a[[ Q Q1Wq[!!! 1Q37AaC  Q Q1Wq[!!! 1ac!eQ   Q QUQY 1Q3!Q   Q QUQYs5%0011 ? ? 6Aq{Aq  q55AAA 199 OOD26!gen*<#=#== > > > 199 OOD26!gen*<#=#== > > > 9afbhx001 2 2D )QUBHUOO, - -C )QUBHUOO, - -C dS#J/!QqSzBBHHJJA  NA r)rr) __doc__numpyrscipyr1rrfloatrrDrrrJsy--!!!!!!d96969696xppppppr