o ˷e‹@sdZddlZddlmZgdZddZedd8d d Zd9d d Zd:ddZ d;ddZ ed         ddd Zd!d"Zd#d$Zd?d%d&Zd@d'd(Zd@d)d*Zd9d+d,ZdAd/d0ZdBd2d3ZdCd4d5ZdCd6d7ZdS)Da ****** Layout ****** Node positioning algorithms for graph drawing. For `random_layout()` the possible resulting shape is a square of side [0, scale] (default: [0, 1]) Changing `center` shifts the layout by that amount. For the other layout routines, the extent is [center - scale, center + scale] (default: [-1, 1]). Warning: Most layout routines have only been tested in 2-dimensions. N)np_random_state) bipartite_layoutcircular_layoutkamada_kawai_layout random_layoutrescale_layoutrescale_layout_dict shell_layout spring_layoutspectral_layout planar_layoutfruchterman_reingold_layout spiral_layoutmultipartite_layoutcCshddl}t|tjst}|||}|dur||}n||}t||kr0d}t|||fS)Nrz;length of center coordinates must match dimension of layout) numpy isinstancenxGraphadd_nodes_fromzerosasarraylen ValueError)Gcenterdimnp empty_graphmsgrN/var/www/ideatree/venv/lib/python3.10/site-packages/networkx/drawing/layout.py_process_params&s     r!cCsJddl}t|||\}}|t|||}||j}tt||}|S)aNPosition nodes uniformly at random in the unit square. For every node, a position is generated by choosing each of dim coordinates uniformly at random on the interval [0.0, 1.0). NumPy (http://scipy.org) is required for this function. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. seed : int, RandomState instance or None optional (default=None) Set the random state for deterministic node layouts. If int, `seed` is the seed used by the random number generator, if numpy.random.RandomState instance, `seed` is the random number generator, if None, the random number generator is the RandomState instance used by numpy.random. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.lollipop_graph(4, 3) >>> pos = nx.random_layout(G) rN)rr!randrastypefloat32dictzip)rrrseedrposrrr r;s ' rcCsddl}|dkr tdt|||\}}td|d}t|dkr%i}|St|dkr5tj||i}|S|ddt|dddd|j }| |j }| | ||||t||fg}t||d|}tt||}|S)abPosition nodes on a circle. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. If dim>2, the remaining dimensions are set to zero in the returned positions. If dim<2, a ValueError is raised. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim < 2 Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.circular_layout(G) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. rNr#zcannot handle dimensions < 2r+scale)rrr!maxrrutilsarbitrary_elementlinspacepir%r& column_stackcossinrrr'r()rr.rrrpaddimsr*thetarrr rls&*   ( "rcCsddl}|dkr tdt|||\}}t|dkriSt|dkr*tj||iS|dur3t|g}|t|}t|ddkrDd}n|}|durQ|jt|}|} i} |D]5} |j dd|jt| d|j d| } || | | | | g|} | t| | ||7}| |7} qW| S) aPosition nodes in concentric circles. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. nlist : list of lists List of node lists for each shell. rotate : angle in radians (default=pi/len(nlist)) Angle by which to rotate the starting position of each shell relative to the starting position of the previous shell. To recreate behavior before v2.5 use rotate=0. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout, currently only dim=2 is supported. Other dimension values result in a ValueError. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim != 2 Examples -------- >>> G = nx.path_graph(4) >>> shells = [[0], [1, 2, 3]] >>> pos = nx.shell_layout(G, shells) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. rNr#can only handle 2 dimensionsr+F)endpointdtype)rrr!rrr0r1listr3r2r&r4r5r6updater()rnlistrotater.rrr radius_bumpradius first_thetanposnodesr8r*rrr r s80    " r verticalUUUUUU?cCs4ddl}|dvrd}t|t||dd\}}t|dkriSd}||} | d|df} t|} t|| } t| t| }|dt| } || t| }|d|t| }|d|t| }|| |g| }|||g| }| ||g}t ||d|}|d kr|ddddd f}t t ||}|S) aPosition nodes in two straight lines. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. nodes : list or container Nodes in one node set of the bipartite graph. This set will be placed on left or top. align : string (default='vertical') The alignment of nodes. Vertical or horizontal. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. aspect_ratio : number (default=4/3): The ratio of the width to the height of the layout. Returns ------- pos : dict A dictionary of positions keyed by node. Examples -------- >>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123) >>> top = nx.bipartite.sets(G)[0] >>> pos = nx.bipartite_layout(G, top) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. rNrF horizontal,align must be either vertical or horizontal.r#rrr+r-rIr,) rrr!rsetr=repeatr2r4 concatenaterr'r()rrEalignr.r aspect_ratiorrheightwidthoffsettopbottomleft_xsright_xsleft_ysright_ystop_pos bottom_posr*rrr r s2,  r 2-C6?weightc  sddl} t||| \}}|dur:|durtd|D] } | |vr$tdqddt|D| fdd|D}|durrtdd |D} | dkrOd } | t|| | |}t|D]\}}||vrp| ||||<q_nd}d } t|dkr~iSt|d krt j | |iSz1t|d krtt j ||d d }|dur|dur|j\}}| | |}t||||||| | }Wn/tyt j||d}|dur|dur|j\}}| | |}t||||||| | }Ynw|dur|durt||d|}tt||}|S)au Position nodes using Fruchterman-Reingold force-directed algorithm. The algorithm simulates a force-directed representation of the network treating edges as springs holding nodes close, while treating nodes as repelling objects, sometimes called an anti-gravity force. Simulation continues until the positions are close to an equilibrium. There are some hard-coded values: minimal distance between nodes (0.01) and "temperature" of 0.1 to ensure nodes don't fly away. During the simulation, `k` helps determine the distance between nodes, though `scale` and `center` determine the size and place after rescaling occurs at the end of the simulation. Fixing some nodes doesn't allow them to move in the simulation. It also turns off the rescaling feature at the simulation's end. In addition, setting `scale` to `None` turns off rescaling. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. k : float (default=None) Optimal distance between nodes. If None the distance is set to 1/sqrt(n) where n is the number of nodes. Increase this value to move nodes farther apart. pos : dict or None optional (default=None) Initial positions for nodes as a dictionary with node as keys and values as a coordinate list or tuple. If None, then use random initial positions. fixed : list or None optional (default=None) Nodes to keep fixed at initial position. Nodes not in ``G.nodes`` are ignored. ValueError raised if `fixed` specified and `pos` not. iterations : int optional (default=50) Maximum number of iterations taken threshold: float optional (default = 1e-4) Threshold for relative error in node position changes. The iteration stops if the error is below this threshold. weight : string or None optional (default='weight') The edge attribute that holds the numerical value used for the edge weight. Larger means a stronger attractive force. If None, then all edge weights are 1. scale : number or None (default: 1) Scale factor for positions. Not used unless `fixed is None`. If scale is None, no rescaling is performed. center : array-like or None Coordinate pair around which to center the layout. Not used unless `fixed is None`. dim : int Dimension of layout. seed : int, RandomState instance or None optional (default=None) Set the random state for deterministic node layouts. If int, `seed` is the seed used by the random number generator, if numpy.random.RandomState instance, `seed` is the random number generator, if None, the random number generator is the RandomState instance used by numpy.random. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.spring_layout(G) # The same using longer but equivalent function name >>> pos = nx.fruchterman_reingold_layout(G) rNz'nodes are fixed without positions givencSsi|]\}}||qSrr).0inoderrr z!spring_layout..csg|] }|vr|qSrr)r`rbnfixedrr sz!spring_layout..css|] }|D]}|VqqdS)Nr)r`pos_tupcoordrrr sz spring_layout..r+fr_r<r_r-)rr!r enumeraterr/valuesr$rrr0r1rEto_scipy_sparse_arrayshapesqrt_sparse_fruchterman_reingoldto_numpy_array_fruchterman_reingoldrr'r()rkr*fixed iterations thresholdr_r.rrr)rrbdom_sizepos_arrranAnnodes_rrer r Ysd_       r c Csddl}z|j\} } Wnty} zd} t| | d} ~ ww|dur1|j|| ||jd}n||j}|durB| d| }t t |j dt |j dt |j dt |j dd} | |d}|j |jd|jd|jdf|jd}t|D]u}|dd|jddf||jddddf}|jj|dd}|j|d d|d |d ||||d |||}|jj|dd}||d kd|}|d || |}|durd||<||7}| |8} |j|| |kr|Sq|S)Nr9fruchterman_reingold() takes an adjacency matrix as inputr<?r+皙?r,axis{Gz?)outz ijk,ij->ikr#zij,i->ijr:)rrrAttributeErrorr NetworkXErrorrr$r<r%rsr/Tminrrangenewaxislinalgnormclipeinsumwhere)r~rwr*rxryrzrr)rrrerrrtdtdelta iterationdistance displacementlength delta_posrrr rvsF  > ( 0rvc CsBddl}ddl} ddl} z|j\} } Wnty'} zd}t|| d} ~ wwz|}Wnty?| j |}Ynw|durQ|j | | ||j d}n| |j }|dur]g}|durh|d| }tt|jdt|jdt|jdt|jdd}||d}||| f}t|D]}|d9}t|jdD]G}||vrq|||j}||djdd}||d kd |}||}|dd|f||||d|||jdd7<q||djdd}||d kd|}|||j}||7}||8}|j|| |kr|Sq|S) Nrrrrr+rr#rr)rscipy scipy.sparserrrrrtolilsparse coo_arrayrr$r<r%rsr/rrrrsumr getrowviewtoarrayrr)r~rwr*rxryrzrr)rsprrrrrrrrrrarrAirrrrr rt4s`    >   rtc s@ddl}t|||\}}t|}|dkriS|dur#ttj||d}d|||f} t|D]#\} } | |vr9q0|| } t|D]\} }|| vrJqA| || | | <qAq0dur|dkrct||dn|dkrnt ||dndd t || dd t|D| fd d |D}t | ||t|d |tt |S)aPosition nodes using Kamada-Kawai path-length cost-function. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. dist : dict (default=None) A two-level dictionary of optimal distances between nodes, indexed by source and destination node. If None, the distance is computed using shortest_path_length(). pos : dict or None optional (default=None) Initial positions for nodes as a dictionary with node as keys and values as a coordinate list or tuple. If None, then use circular_layout() for dim >= 2 and a linear layout for dim == 1. weight : string or None optional (default='weight') The edge attribute that holds the numerical value used for the edge weight. If None, then all edge weights are 1. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.kamada_kawai_layout(G) rNrng.Ar")rr#cSsi|]\}}||qSrr)r`r}ptrrr rcrdz'kamada_kawai_layout..r+cg|]}|qSrr)r`r}r*rr rgz'kamada_kawai_layout..r-)rr!rr'rshortest_path_lengthonesrorrr(r2array_kamada_kawai_solver)rdistr*r_r.rrrnNodesdist_mtxrownrrdistcolncr|rrr r~s6+" rc Csjddl}ddl}ddl}d}|d|||jdd||f}|jjt|d|dd}|j d|fS)NrMbP?r+zL-BFGS-BT)methodargsjacr,) rrscipy.optimizeeyerroptimizeminimize_kamada_kawai_costfnravelxreshape) rr|rrrrmeanwtcostargs optresultrrr rs$rc Cs|jd}|||f}|dd|jddf||jddddf}|jj|dd}|d|d|||d} ||d} d| ||<d|| d } |d || | |d || | } |j|dd} | d||| d 7} | || 7} | | fS) Nrr,rz ijk,ij->ijkr+rr?r#z ij,ij,ijk->ikz ij,ij,ijk->jk) rrrrrrrr diag_indicesrr)pos_vecrinvdist meanweightrrr|rnodesep directionrScostgradsumposrrr rs 0    rc Cs*ddl}t|||\}}t|dkrAt|dkr|g}nt|dkr+||g}n|||||dg}tt||Sz"t|dkrJttj ||dd}| r]|| |}t ||}Wn t tfytj||d }| r|||j7}t||}Ynwt||d |}tt||}|S) aPosition nodes using the eigenvectors of the graph Laplacian. Using the unnormalized Laplacian, the layout shows possible clusters of nodes which are an approximation of the ratio cut. If dim is the number of dimensions then the positions are the entries of the dim eigenvectors corresponding to the ascending eigenvalues starting from the second one. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. weight : string or None optional (default='weight') The edge attribute that holds the numerical value used for the edge weight. If None, then all edge weights are 1. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.spectral_layout(G) Notes ----- Directed graphs will be considered as undirected graphs when positioning the nodes. For larger graphs (>500 nodes) this will use the SciPy sparse eigenvalue solver (ARPACK). rNr#r+g@rkdrmrnr-)rr!rrrr'r(rrrq is_directed transpose_sparse_spectral ImportErrorrur _spectralr)rr_r.rrrr*r~rrr r s2-      r c Csddl}z|j\}}Wnty}zd}t||d}~ww|j||jd|j|dd}||}|j |\} } | | d|d} | | dd| fS)Nrz-spectral() takes an adjacency matrix as inputrr+r) rrrrrridentityr<rreigargsortreal) r~rrrrrrDL eigenvalues eigenvectorsindexrrr rJs rc Csddl}ddl}ddl}ddl}z|j\}}Wnty+}zd}t||d}~ww|j |j |j ddd||} | |} |d} t d| dt ||} |jjj| | d| d\} }|| d| }||dd|fS)Nrz4sparse_spectral() takes an adjacency matrix as inputr+rr#SM)whichncv)rrrscipy.sparse.linalgrrrrrr csr_arrayspdiagsrr/intrsreigshrr)r~rrrrrrrrrrrwrrrrrrr r_s$ "rcsddl}|dkr tdt|||\}}t|dkriSt|tjr%|}nt|\}}|s3tdt |t |}| fdd|D |j t|d|tt|S) aPosition nodes without edge intersections. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. If G is of type nx.PlanarEmbedding, the positions are selected accordingly. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int Dimension of layout. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ NetworkXException If G is not planar Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.planar_layout(G) rNr#r9zG is not planar.crrr)r`rrrr rgrz!planar_layout..r-)rrr!rrrPlanarEmbeddingcheck_planarityNetworkXExceptioncombinatorial_embedding_to_posr= row_stackr%float64rr'r()rr.rrr embedding is_planar node_listrrr r |s"!     r ffffff?Fc Cs(ddl}|dkr tdt|||\}}t|dkriSt|dkr*tj||iSg}|rad}d} |} | || | 7} tt|D]} | | } | || 7} || | | | | | gqBn|j t|t d} || }| | || || |g}t|||d|}tt||}|S) aPosition nodes in a spiral layout. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. dim : int, default=2 Dimension of layout, currently only dim=2 is supported. Other dimension values result in a ValueError. resolution : float, default=0.35 The compactness of the spiral layout returned. Lower values result in more compressed spiral layouts. equidistant : bool, default=False If True, nodes will be positioned equidistant from each other by decreasing angle further from center. If False, nodes will be positioned at equal angles from each other by increasing separation further from center. Returns ------- pos : dict A dictionary of positions keyed by node Raises ------ ValueError If dim != 2 Examples -------- >>> G = nx.path_graph(4) >>> pos = nx.spiral_layout(G) >>> nx.draw(G, pos=pos) Notes ----- This algorithm currently only works in two dimensions. rNr#r9r+rrr-)rrr!rrr0r1rappendr5r6arangefloatrrrr'r()rr.rr resolution equidistantrr*chordstepr8rrranglerrr rs2,   $$rsubsetc Csddl}|dvrd}t|t||dd\}}t|dkriSi}|jddD]#\}} z| |} Wn ty>d }t|w|g|| g|| <q'zt|}Wnt ybt |}Ynwd} g} t|} t |D]@\}\}} t| }| ||}|j d|td }| d d|d df}|||g|}| dur|} n|| |g} | | qot| |d |} |d kr| dddddf} tt| | } | S)aPosition nodes in layers of straight lines. Parameters ---------- G : NetworkX graph or list of nodes A position will be assigned to every node in G. subset_key : string (default='subset') Key of node data to be used as layer subset. align : string (default='vertical') The alignment of nodes. Vertical or horizontal. scale : number (default: 1) Scale factor for positions. center : array-like or None Coordinate pair around which to center the layout. Returns ------- pos : dict A dictionary of positions keyed by node. Examples -------- >>> G = nx.complete_multipartite_graph(28, 16, 10) >>> pos = nx.multipartite_layout(G) Notes ----- This algorithm currently only works in two dimensions and does not try to minimize edge crossings. Network does not need to be a complete multipartite graph. As long as nodes have subset_key data, they will be placed in the corresponding layers. rNrHrJr#rKT)dataz9all nodes must have subset_key (default='subset') as datarr+r-rIr,)rrr!rrEKeyErrorgetsorteditems TypeErrorr=rorMrrr4rNextendrr'r()r subset_keyrOr.rrrlayersvrlayerr*rErRrarrQxsysrS layer_posrrr rsN'      rcCsd}t|jdD]%}|dd|f|dd|f8<tt|dd|f|}q |dkrKt|jdD]}|dd|f||9<q:|S)aReturns scaled position array to (-scale, scale) in all axes. The function acts on NumPy arrays which hold position information. Each position is one row of the array. The dimension of the space equals the number of columns. Each coordinate in one column. To rescale, the mean (center) is subtracted from each axis separately. Then all values are scaled so that the largest magnitude value from all axes equals `scale` (thus, the aspect ratio is preserved). The resulting NumPy Array is returned (order of rows unchanged). Parameters ---------- pos : numpy array positions to be scaled. Each row is a position. scale : number (default: 1) The size of the resulting extent in all directions. Returns ------- pos : numpy array scaled positions. Each row is a position. See Also -------- rescale_layout_dict rr+N)rrrmeanr/abs)r*r.limrarrr rYs( rcCs<ddl}|siS|t|}t||d}tt||S)aReturn a dictionary of scaled positions keyed by node Parameters ---------- pos : A dictionary of positions keyed by node scale : number (default: 1) The size of the resulting extent in all directions. Returns ------- pos : A dictionary of positions keyed by node Examples -------- >>> import numpy as np >>> pos = {0: np.array((0, 0)), 1: np.array((1, 1)), 2: np.array((0.5, 0.5))} >>> nx.rescale_layout_dict(pos) {0: array([-1., -1.]), 1: array([1., 1.]), 2: array([0., 0.])} >>> pos = {0: np.array((0, 0)), 1: np.array((-1, 1)), 2: np.array((-0.5, 0.5))} >>> nx.rescale_layout_dict(pos, scale=2) {0: array([ 2., -2.]), 1: array([-2., 2.]), 2: array([0., 0.])} See Also -------- rescale_layout rNr-)rrr=rprr'r()r*r.rpos_vrrr rs  r)Nr#N)r+Nr#)NNr+Nr#)rFr+NrG) NNNr]r^r_r+Nr#N)NNNr]r^r#N)NNr_r+Nr#)r_r+Nr#)r#)r+Nr#rF)rrFr+N)r+)__doc__networkxrnetworkx.utilsr__all__r!rrr rr r rvrtrrrr rrr rrrrrrrr sV   0 D\ N  = J M  O   9 O U)