cairo_draw.py 99.7 KB
Newer Older
1001
    ...               edge_control_points=control, # some curvy edges
1002
1003
1004
    ...               output="graph-draw.pdf")
    <...>

1005
    .. testcleanup::
1006

1007
       conv_png("graph-draw.pdf")
1008

1009
1010
1011
    .. figure:: graph-draw.png
       :align: center
       :width: 80%
1012

1013
1014
1015
       SFDP force-directed layout of a Price network with 1500 nodes. The
       vertex size and color indicate the degree, and the edge color and width
       the edge betweenness centrality.
1016
1017
1018

    """

Tiago Peixoto's avatar
Tiago Peixoto committed
1019
1020
1021
1022
    vprops = vprops.copy() if vprops is not None else {}
    eprops = eprops.copy() if eprops is not None else {}

    props, kwargs = parse_props("vertex", kwargs)
1023
    props = _convert_props(props, "v", g, kwargs.get("vcmap", default_cm))
Tiago Peixoto's avatar
Tiago Peixoto committed
1024
1025
    vprops.update(props)
    props, kwargs = parse_props("edge", kwargs)
1026
    props = _convert_props(props, "e", g, kwargs.get("ecmap", default_cm))
Tiago Peixoto's avatar
Tiago Peixoto committed
1027
1028
1029
    eprops.update(props)

    if pos is None:
1030
        if (g.num_vertices() > 2 and output is None and
1031
1032
            not inline and kwargs.get("update_layout", True) and
            mplfig is None):
Tiago Peixoto's avatar
Tiago Peixoto committed
1033
1034
1035
1036
1037
1038
1039
1040
1041
            L = np.sqrt(g.num_vertices())
            pos = random_layout(g, [L, L])
            if g.num_vertices() > 1000:
                if "multilevel" not in kwargs:
                    kwargs["multilevel"] = True
            if "layout_K" not in kwargs:
                kwargs["layout_K"] = _avg_edge_distance(g, pos) / 10
        else:
            pos = sfdp_layout(g)
1042
1043
    else:
        _check_prop_vector(pos, name="pos", floating=True)
1044
        if output is None and not inline and mplfig is None:
1045
1046
1047
1048
            if "layout_K" not in kwargs:
                kwargs["layout_K"] = _avg_edge_distance(g, pos)
            if "update_layout" not in kwargs:
                kwargs["update_layout"] = False
Tiago Peixoto's avatar
Tiago Peixoto committed
1049

1050
1051
1052
    if "pen_width" in eprops and "marker_size" not in eprops:
        pw = eprops["pen_width"]
        if isinstance(pw, PropertyMap):
1053
            pw = pw.copy("double")
1054
            pw.fa *= 2.75
1055
1056
1057
            eprops["marker_size"] = pw
        else:
            eprops["marker_size"] = pw * 2.75
1058

1059
1060
1061
    if "text" in eprops and "text_distance" not in eprops and "pen_width" in eprops:
        pw = eprops["pen_width"]
        if isinstance(pw, PropertyMap):
1062
            pw = pw.copy("double")
1063
            pw.fa *= 2
1064
1065
1066
1067
            eprops["text_distance"] = pw
        else:
            eprops["text_distance"] = pw * 2

1068
    if "text" in vprops and ("text_color" not in vprops or vprops["text_color"] == "auto"):
1069
        vcmap = kwargs.get("vcmap", default_cm)
1070
1071
1072
1073
        bg = _convert(vertex_attrs.fill_color,
                      vprops.get("fill_color", _vdefaults["fill_color"]),
                      vcmap)
        bg_color = kwargs.get("bg_color", [1., 1., 1., 1.])
1074
1075
1076
1077
1078
        vprops["text_color"] = auto_colors(g, bg,
                                           vprops.get("text_position",
                                                      _vdefaults["text_position"]),
                                           bg_color)

1079
    if mplfig is not None:
1080
1081
1082
1083
1084
1085
1086
1087
        ax = None
        if isinstance(mplfig, matplotlib.figure.Figure):
            ctr = ax = mplfig.gca()
        elif isinstance(mplfig, matplotlib.axes.Axes):
            ctr = ax = mplfig
        else:
            ctr = mplfig

1088
1089
1090
1091
1092
1093
1094
1095
1096
        x, y = ungroup_vector_property(pos, [0, 1])
        l, r = x.a.min(), x.a.max()
        b, t = y.a.min(), y.a.max()

        adjust_default_sizes(g, (r - l, t - b), vprops, eprops)

        artist = GraphArtist(g, pos, vprops, eprops, ax, vorder=vorder,
                             eorder=eorder, nodesfirst=nodesfirst, **kwargs)

1097
1098
        ctr.artists.append(artist)

1099
1100
1101
1102
1103
1104
        if fit_view != False and ax is not None:
            try:
                x, y, w, h = fit_view
            except TypeError:
                w = r - l
                h = t - b
1105
1106
1107
            if fit_view != True:
                w *= float(fit_view)
                h *= float(fit_view)
1108
            ax.set_xlim(l - w * .1, r + w * .1)
1109
            ax.set_ylim(t + h * .1, b - h * .1)
1110
1111

        return pos
1112

1113
1114
    output_file = output
    if inline and output is None:
1115
        if fmt == "auto":
1116
1117
1118
1119
            if output is None:
                fmt = "png"
            else:
                fmt = get_file_fmt(output)
1120
1121
        output = io.BytesIO()

1122
    if output is None:
Tiago Peixoto's avatar
Tiago Peixoto committed
1123
        return interactive_window(g, pos, vprops, eprops, vorder, eorder,
1124
                                  nodesfirst, geometry=output_size,
1125
                                  fit_view=fit_view, **kwargs)
Tiago Peixoto's avatar
Tiago Peixoto committed
1126
    else:
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
        adjust_default_sizes(g, output_size, vprops, eprops)

        if ink_scale != 1:
            scale_ink(ink_scale, vprops, eprops)

        if inline and fmt != "svg":
            output_size = [int(x * inline_scale) for x in output_size]
            scale_ink(inline_scale, vprops, eprops)

        if fit_view != False:
            try:
                x, y, w, h = fit_view
                zoom = min(output_size[0] / w, output_size[1] / h)
            except TypeError:
                pad = fit_view if fit_view is not True else 0.9
                output_size = list(output_size)
                x, y, zoom = fit_to_view_ink(g, pos, output_size, vprops,
                                             eprops, adjust_aspect, pad=pad)
        else:
            x, y, zoom = x, y, 1


1149
        if isinstance(output, (str, unicode)):
1150
1151
1152
1153
1154
            out, auto_fmt = open_file(output, mode="wb")
        else:
            out = output
            if fmt == "auto":
                raise ValueError("File format must be specified.")
Tiago Peixoto's avatar
Tiago Peixoto committed
1155
1156

        if fmt == "auto":
1157
            fmt = auto_fmt
Tiago Peixoto's avatar
Tiago Peixoto committed
1158
1159
1160
1161
        if fmt == "pdf":
            srf = cairo.PDFSurface(out, output_size[0], output_size[1])
        elif fmt == "ps":
            srf = cairo.PSSurface(out, output_size[0], output_size[1])
Tiago Peixoto's avatar
Tiago Peixoto committed
1162
1163
1164
        elif fmt == "eps":
            srf = cairo.PSSurface(out, output_size[0], output_size[1])
            srf.set_eps(True)
Tiago Peixoto's avatar
Tiago Peixoto committed
1165
1166
        elif fmt == "svg":
            srf = cairo.SVGSurface(out, output_size[0], output_size[1])
1167
            srf.restrict_to_version(cairo.SVG_VERSION_1_2)
Tiago Peixoto's avatar
Tiago Peixoto committed
1168
1169
1170
1171
1172
1173
1174
1175
1176
        elif fmt == "png":
            srf = cairo.ImageSurface(cairo.FORMAT_ARGB32, output_size[0],
                                     output_size[1])
        else:
            raise ValueError("Invalid format type: " + fmt)

        cr = cairo.Context(srf)

        cr.scale(zoom, zoom)
1177
        cr.translate(-x, -y)
Tiago Peixoto's avatar
Tiago Peixoto committed
1178
1179

        cairo_draw(g, pos, cr, vprops, eprops, vorder, eorder,
1180
                   nodesfirst, **kwargs)
1181

1182
        srf.flush()
1183
        if fmt == "png":
Tiago Peixoto's avatar
Tiago Peixoto committed
1184
            srf.write_to_png(out)
1185
1186
        elif fmt == "svg":
            srf.finish()
1187
1188
1189

        del cr

1190
        if inline and output_file is None:
1191
1192
            img = None
            if fmt == "png":
1193
1194
1195
                img = IPython.display.Image(data=out.getvalue(),
                                            width=int(output_size[0]/inline_scale),
                                            height=int(output_size[1]/inline_scale))
1196
            elif fmt == "svg":
1197
                img = IPython.display.SVG(data=out.getvalue())
1198
            elif img is None:
1199
1200
                inl_out = io.BytesIO()
                inl_srf = cairo.ImageSurface(cairo.FORMAT_ARGB32,
Pietro Battiston's avatar
Pietro Battiston committed
1201
1202
                                             output_size[0],
                                             output_size[1])
1203
1204
1205
1206
1207
                inl_cr = cairo.Context(inl_srf)
                inl_cr.set_source_surface(srf, 0, 0)
                inl_cr.paint()
                inl_srf.write_to_png(inl_out)
                del inl_srf
1208
1209
1210
                img = IPython.display.Image(data=inl_out.getvalue(),
                                            width=int(output_size[0]/inline_scale),
                                            height=int(output_size[1]/inline_scale))
1211
            srf.finish()
1212
            IPython.display.display(img)
1213
        del srf
Tiago Peixoto's avatar
Tiago Peixoto committed
1214
        return pos
1215
1216
1217
1218
1219


def adjust_default_sizes(g, geometry, vprops, eprops, force=False):
    if "size" not in vprops or force:
        A = geometry[0] * geometry[1]
Tiago Peixoto's avatar
Tiago Peixoto committed
1220
1221
        N = max(g.num_vertices(), 1)
        vprops["size"] = np.sqrt(A / N) / 3.5
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232

    if "pen_width" not in vprops or force:
        size = vprops["size"]
        if isinstance(vprops["size"], PropertyMap):
            size = vprops["size"].fa.mean()
        vprops["pen_width"] = size / 10
        if "pen_width" not in eprops or force:
            eprops["pen_width"] = size / 10
        if "marker_size" not in eprops or force:
            eprops["marker_size"] = size * 0.8

1233
1234
1235
1236
1237
    if "font_size" not in vprops or force:
        size = vprops["size"]
        if isinstance(vprops["size"], PropertyMap):
            size = vprops["size"].fa.mean()
        vprops["font_size"] =  size * .6
1238

1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
    if "font_size" not in eprops or force:
        size = vprops["size"]
        if isinstance(vprops["size"], PropertyMap):
            size = vprops["size"].fa.mean()
        eprops["font_size"] =  size * .6


def scale_ink(scale, vprops, eprops, copy=False):
    vink_props = ["size", "pen_width", "font_size", "text_out_width"]
    eink_props = ["marker_size", "pen_width", "font_size", "text_distance",
                  "text_out_width"]
    if copy:
        vprops = dict(vprops)
        eprops = dict(eprops)
    for p in vink_props:
        if p not in vprops:
            vprops[p] = _vdefaults[p]
        if isinstance(vprops[p], PropertyMap):
            if copy:
                vprops[p] = vprops[p].copy()
            vprops[p].fa *= scale
1260
        else:
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
            vprops[p] = vprops[p] * scale
    for p in eink_props:
        if p not in eprops:
            eprops[p] = _edefaults[p]
        if isinstance(eprops[p], PropertyMap):
            if copy:
                eprops[p] = eprops[p].copy()
            eprops[p].fa *= scale
        else:
            eprops[p] = eprops[p] * scale
    if copy:
        return vprops, eprops
1273

1274
def get_bb(g, pos):
1275
1276
1277
    pos_x, pos_y = ungroup_vector_property(pos, [0, 1])
    x_range = [pos_x.fa.min(), pos_x.fa.max()]
    y_range = [pos_y.fa.min(), pos_y.fa.max()]
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
    return x_range[0], y_range[1], x_range[1] - x_range[0], y_range[1] - y_range[0]

def fit_to_view(rec, output_size, adjust_aspect=False, pad=.9):
    x, y, w, h = rec
    d = max(w, h)
    if adjust_aspect:
        if h > w:
            output_size[0] = int(round(float(output_size[1] * w / h)))
        else:
            output_size[1] = int(round(float(output_size[0] * h / w)))

1289
1290
1291
1292
1293
1294
    zoom = min(output_size[0] / w, output_size[1] / h)

    x -= (output_size[0] / zoom - w) / 2
    y -= (output_size[1] / zoom - h) / 2

    zoom *= pad
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324

    x -= (1-pad) / 2 * output_size[0] / zoom
    y -= (1-pad) / 2 * output_size[1] / zoom

    return x, y, zoom

def fit_to_view_ink(g, pos, output_size, vprops, eprops, adjust_aspect=False,
                    pad=0.9):
    x, y, zoom = fit_to_view(get_bb(g, pos), output_size, pad=pad)

    srf = cairo.RecordingSurface(cairo.Content.COLOR_ALPHA,
                                 cairo.Rectangle(-output_size[0] * 5,
                                                 -output_size[1] * 5,
                                                 output_size[0] * 10,
                                                 output_size[1] * 10))
    cr = cairo.Context(srf)

    cr.scale(zoom, zoom)
    cr.translate(-x, -y)

    cairo_draw(g, pos, cr, vprops, eprops)

    bb = list(srf.ink_extents())

    bb[0], bb[1] = cr.device_to_user(bb[0], bb[1])
    bb[2], bb[3] = cr.device_to_user_distance(bb[2], bb[3])

    x, y, zoom = fit_to_view(bb, output_size,
                             adjust_aspect=adjust_aspect, pad=pad)
    return x, y, zoom
1325
1326
1327
1328
1329
1330
1331


def transform_scale(M, scale):
    p = M.transform_distance(scale / np.sqrt(2),
                             scale / np.sqrt(2))
    return np.sqrt(p[0] ** 2 + p[1] ** 2)

1332
1333
def get_hierarchy_control_points(g, t, tpos, beta=0.8, cts=None, is_tree=True,
                                 max_depth=None):
Tiago Peixoto's avatar
Tiago Peixoto committed
1334
    r"""Return the Bézier spline control points for the edges in ``g``, given the hierarchical structure encoded in graph `t`.
1335
1336
1337
1338
1339
1340
1341
1342
1343

    Parameters
    ----------
    g : :class:`~graph_tool.Graph`
        Graph to be drawn.
    t : :class:`~graph_tool.Graph`
        Directed graph containing the hierarchy of ``g``. It must be a directed
        tree with a single root. The direction of the edges point from the root
        to the leaves, and the vertices in ``t`` with index in the range
Tiago Peixoto's avatar
Tiago Peixoto committed
1344
        :math:`[0, N-1]`, with :math:`N` being the number of vertices in ``g``,
1345
        must correspond to the respective vertex in ``g``.
1346
    tpos : :class:`~graph_tool.VertexPropertyMap`
1347
1348
        Vector-valued vertex property map containing the x and y coordinates of
        the vertices in graph ``t``.
1349
    beta : ``float`` (optional, default: ``0.8`` or :class:`~graph_tool.EdgePropertyMap`)
1350
        Edge bundling strength. For ``beta == 0`` the edges are straight lines,
1351
1352
1353
        and for ``beta == 1`` they strictly follow the hierarchy. This can be
        optionally an edge property map, which specified a different bundling
        strength for each edge.
1354
    cts : :class:`~graph_tool.EdgePropertyMap` (optional, default: ``None``)
1355
1356
        Edge property map of type ``vector<double>`` where the control points
        will be stored.
1357
1358
1359
    is_tree : ``bool`` (optional, default: ``True``)
        If ``True``, ``t`` must be a directed tree, otherwise it can be any
        connected graph.
1360
1361
1362
    max_depth : ``int`` (optional, default: ``None``)
        If supplied, only the first ``max_depth`` bottom levels of the hierarchy
        will be used.
1363

1364
1365
1366
1367

    Returns
    -------

1368
    cts : :class:`~graph_tool.EdgePropertyMap`
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
        Vector-valued edge property map containing the Bézier spline control
        points for the edges in ``g``.

    Notes
    -----
    This is an implementation of the edge-bundling algorithm described in
    [holten-hierarchical-2006]_.


    Examples
    --------
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
    .. testsetup:: nested_cts

       gt.seed_rng(42)
       np.random.seed(42)

    .. doctest:: nested_cts

       >>> g = gt.collection.data["netscience"]
       >>> g = gt.GraphView(g, vfilt=gt.label_largest_component(g))
       >>> g.purge_vertices()
1390
       >>> state = gt.minimize_nested_blockmodel_dl(g, deg_corr=True)
1391
       >>> t = gt.get_hierarchy_tree(state)[0]
1392
1393
1394
       >>> tpos = pos = gt.radial_tree_layout(t, t.vertex(t.num_vertices() - 1), weighted=True)
       >>> cts = gt.get_hierarchy_control_points(g, t, tpos)
       >>> pos = g.own_property(tpos)
1395
       >>> b = state.levels[0].b
Tiago Peixoto's avatar
Tiago Peixoto committed
1396
1397
1398
       >>> shape = b.copy()
       >>> shape.a %= 14
       >>> gt.graph_draw(g, pos=pos, vertex_fill_color=b, vertex_shape=shape, edge_control_points=cts,
1399
1400
1401
1402
1403
       ...               edge_color=[0, 0, 0, 0.3], vertex_anchor=0, output="netscience_nested_mdl.pdf")
       <...>

    .. testcleanup:: nested_cts

1404
       conv_png("netscience_nested_mdl.pdf")
1405

1406
    .. figure:: netscience_nested_mdl.png
1407
       :align: center
1408
       :width: 80%
1409
1410
1411
1412

       Block partition of a co-authorship network, which minimizes the description
       length of the network according to the nested (degree-corrected) stochastic blockmodel.

1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423


    References
    ----------

    .. [holten-hierarchical-2006] Holten, D. "Hierarchical Edge Bundles:
       Visualization of Adjacency Relations in Hierarchical Data.", IEEE
       Transactions on Visualization and Computer Graphics 12, no. 5, 741–748
       (2006). :doi:`10.1109/TVCG.2006.147`
    """

1424
1425
1426
1427
    if cts is None:
        cts = g.new_edge_property("vector<double>")
    if cts.value_type() != "vector<double>":
        raise ValueError("cts property map must be of type 'vector<double>' not '%s' " % cts.value_type())
1428
1429
1430
1431

    u = GraphView(g, directed=True)
    tu = GraphView(t, directed=True)

1432
1433
1434
1435
1436
    if not isinstance(beta, PropertyMap):
        beta = u.new_edge_property("double", beta)
    else:
        beta = beta.copy("double")

1437
1438
1439
    if max_depth is None:
        max_depth = t.num_vertices()

1440
    tu = GraphView(tu, skip_vfilt=True)
1441
    tpos = tu.own_property(tpos)
1442
1443
    libgraph_tool_draw.get_cts(u._Graph__graph,
                               tu._Graph__graph,
1444
1445
                               _prop("v", tu, tpos),
                               _prop("e", u, beta),
1446
                               _prop("e", u, cts),
1447
                               is_tree, max_depth)
1448
    return cts
1449
1450
1451
1452
1453
1454
1455

#
# The functions and classes below depend on GTK
# =============================================
#

try:
1456
1457
    import gi
    gi.require_version('Gtk', '3.0')
1458
    from gi.repository import Gtk, Gdk, GdkPixbuf
1459
    from gi.repository import GObject as gobject
1460
1461
    from .gtk_draw import *
except (ImportError, RuntimeError) as e:
1462
    msg = "Error importing Gtk module: %s; GTK+ drawing will not work." % str(e)
1463
    warnings.warn(msg, RuntimeWarning)
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477

def gen_surface(name):
    fobj, fmt = open_file(name)
    if fmt in ["png", "PNG"]:
        sfc = cairo.ImageSurface.create_from_png(fobj)
        return sfc
    else:
        pixbuf = GdkPixbuf.Pixbuf.new_from_file(name)
        surface = cairo.ImageSurface(cairo.FORMAT_ARGB32, pixbuf.get_width(),
                                     pixbuf.get_height())
        cr = cairo.Context(surface)
        Gdk.cairo_set_source_pixbuf(cr, pixbuf, 0, 0)
        cr.paint()
        return surface
1478
#
1479
1480
# matplotlib
# ==========
1481
#
1482

1483
1484
1485
1486
1487
1488
class GraphArtist(matplotlib.artist.Artist):
    """:class:`matplotlib.artist.Artist` specialization that draws
       :class:`graph_tool.Graph` instances.

    .. warning::

1489
        Only cairo-based backends are supported.
1490
1491
1492

    """

1493
    def __init__(self, g, pos, vprops, eprops, ax=None, **kwargs):
1494
1495
1496
1497
1498
        matplotlib.artist.Artist.__init__(self)
        self.g = g
        self.pos = pos
        self.vprops = vprops
        self.eprops = eprops
1499
        self.ax = ax
1500
1501
1502
1503
        self.kwargs = kwargs

    def draw(self, renderer):
        if not isinstance(renderer, matplotlib.backends.backend_cairo.RendererCairo):
1504
            raise NotImplementedError("graph plotting is supported only on cairo backends")
1505
1506

        ctx = renderer.gc.ctx
1507
1508
1509
1510

        if not isinstance(ctx, cairo.Context):
            ctx = _UNSAFE_cairocffi_context_to_pycairo(ctx)

1511
1512
        ctx.save()

1513
1514
1515
1516
        pos = self.pos.copy()
        eprops = dict(self.eprops)
        vprops = dict(self.vprops)

1517
        if self.ax is not None:
1518
1519
            transform = (self.ax.transData.get_affine() +
                         matplotlib.transforms.Affine2D().scale(1, -1).translate(0, renderer.height))
1520

1521
1522
1523
1524
1525
            m = transform.get_matrix()

            m_s = ctx.get_matrix()
            cm = cairo.Matrix(m[0,0], m[1,0], m[0,1], m[1,1], m[0,2], m[1,2])
            ctx.transform(cm)
1526
1527
            l, r = self.ax.get_xlim()
            b, t = self.ax.get_ylim()
1528
            ctx.new_path()
1529
1530
            ctx.rectangle(l, b, r-l, t-b)
            ctx.clip()
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
            ctx.set_matrix(m_s)

            vprops, eprops = scale_ink(np.mean([m[0,0], m[1,1]]), vprops, eprops,
                                       copy=True)

            x = np.ones(3)
            for v in self.g.vertices():
                x[:2] = pos[v].a
                pos[v].a = np.dot(m, x)[:2]

            cp = eprops.get("control_points", None)
            if isinstance(cp, PropertyMap):
                ctx.save()
                cp = cp.copy()
                for e in self.g.edges():
                    s = self.pos[e.source()].a
                    t = self.pos[e.target()].a
                    a = np.arctan2(t[1] - s[1],
                                   t[0] - s[0])
                    l = np.sqrt((t[1] - s[1]) ** 2 +
                                (t[0] - s[0]) ** 2)
                    c = cp[e]
                    for i in range(len(c) // 2):
                        x[:2] = c.a[i*2:(i+1)*2]
                        ctx.identity_matrix()
                        ctx.translate(s[0], s[1])
                        ctx.rotate(a)
                        ctx.scale(l, 1)
                        x[:2] = ctx.user_to_device(x[0], x[1])
                        x = np.dot(m, x)
                        c.a[i*2:(i+1)*2] = x[:2]

                    s = pos[e.source()].a
                    t = pos[e.target()].a
                    a = np.arctan2(t[1] - s[1],
                                   t[0] - s[0])
                    l = np.sqrt((t[1] - s[1]) ** 2 +
                                (t[0] - s[0]) ** 2)

                    for i in range(len(c) // 2):
                        x[:2] = c.a[i*2:(i+1)*2]
                        ctx.identity_matrix()
                        ctx.scale(1/l, 1)
                        ctx.rotate(-a)
                        ctx.translate(-s[0], -s[1])
                        x[:2] = ctx.user_to_device(x[0], x[1])
                        c.a[i*2:(i+1)*2] = x[:2]
                ctx.restore()
                eprops["control_points"] = cp

        cairo_draw(self.g, pos, ctx, vprops, eprops, **self.kwargs)
1582
1583

        ctx.restore()
1584
1585
1586
1587
1588
1589
1590


#
# Drawing hierarchies
# ===================
#

1591
1592
def draw_hierarchy(state, pos=None, layout="radial", beta=0.8, node_weight=None,
                   vprops=None, eprops=None, hvprops=None, heprops=None,
1593
                   subsample_edges=None, rel_order="degree", deg_size=True,
1594
                   vsize_scale=1, hsize_scale=1, hshortcuts=0, hide=0,
1595
                   bip_aspect=1., empty_branches=False, **kwargs):
1596
1597
1598
1599
1600
    r"""Draw a nested block model state in a circular hierarchy layout with edge
    bundling.

    Parameters
    ----------
1601
    state : :class:`~graph_tool.inference.nested_blockmodel.NestedBlockState`
1602
        Nested block state to be drawn.
1603
    pos : :class:`~graph_tool.VertexPropertyMap` (optional, default: ``None``)
1604
1605
        If supplied, this specifies a vertex property map with the positions of
        the vertices in the layout.
1606
    layout : ``str`` or :class:`~graph_tool.VertexPropertyMap` (optional, default: ``"radial"``)
1607
1608
        If ``layout == "radial"`` :func:`~graph_tool.draw.radial_tree_layout`
        will be used. If ``layout == "sfdp"``, the hierarchy tree will be
1609
1610
        positioned using :func:`~graph_tool.draw.sfdp_layout`. If ``layout ==
        "bipartite"`` a bipartite layout will be used. If instead a
1611
        :class:`~graph_tool.VertexPropertyMap` is provided, it must correspond to the
1612
1613
1614
        position of the hierarchy tree.
    beta : ``float`` (optional, default: ``.8``)
        Edge bundling strength.
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
    vprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties. Individual properties may also be
        given via the ``vertex_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property. See :func:`~graph_tool.draw.graph_draw` for
        details.
    eprops : dict (optional, default: ``None``)
        Dictionary with the edge properties. Individual properties may also be
        given via the ``edge_<prop-name>`` parameters, where ``<prop-name>`` is
        the name of the property. See :func:`~graph_tool.draw.graph_draw` for
        details.
    hvprops : dict (optional, default: ``None``)
        Dictionary with the vertex properties for the *hierarchy tree*.
        Individual properties may also be given via the ``hvertex_<prop-name>``
        parameters, where ``<prop-name>`` is the name of the property. See
        :func:`~graph_tool.draw.graph_draw` for details.
    heprops : dict (optional, default: ``None``)
        Dictionary with the edge properties for the *hierarchy tree*. Individual
        properties may also be given via the ``hedge_<prop-name>`` parameters,
        where ``<prop-name>`` is the name of the property. See
        :func:`~graph_tool.draw.graph_draw` for details.
1635
1636
1637
    subsample_edges : ``int`` or list of :class:`~graph_tool.Edge` instances (optional, default: ``None``)
        If provided, only this number of random edges will be drawn. If the
        value is a list, it should include the edges that are to be drawn.
1638
    rel_order : ``str`` or ``None`` or :class:`~graph_tool.VertexPropertyMap` (optional, default: ``"degree"``)
1639
1640
        If ``degree``, the vertices will be ordered according to degree inside
        each group, and the relative ordering of the hierarchy branches. If
1641
        instead a :class:`~graph_tool.VertexPropertyMap` is provided, its value will
1642
        be used for the relative ordering.
1643
1644
1645
    deg_size : ``bool`` (optional, default: ``True``)
        If ``True``, the (total) node degrees will be used for the default
        vertex sizes..
1646
    vsize_scale : ``float`` (optional, default: ``1.``)
1647
        Multiplicative factor for the default vertex sizes.
1648
    hsize_scale : ``float`` (optional, default: ``1.``)
1649
        Multiplicative factor for the default sizes of the hierarchy nodes.
1650
1651
1652
1653
1654
    hshortcuts : ``int`` (optional, default: ``0``)
        Include shortcuts to the number of upper layers in the hierarchy
        determined by this parameter.
    hide : ``int`` (optional, default: ``0``)
        Hide upper levels of the hierarchy.
1655
1656
    bip_aspect : ``float`` (optional, default: ``1.``)
        If ``layout == "bipartite"``, this will define the aspect ratio of layout.
1657
    empty_branches : ``bool`` (optional, default: ``False``)
1658
1659
        If ``empty_branches == False``, dangling branches at the upper layers
        will be pruned.
1660
    vertex_* : :class:`~graph_tool.VertexPropertyMap` or arbitrary types (optional, default: ``None``)
1661
1662
1663
1664
        Parameters following the pattern ``vertex_<prop-name>`` specify the
        vertex property with name ``<prop-name>``, as an alternative to the
        ``vprops`` parameter. See :func:`~graph_tool.draw.graph_draw` for
        details.
1665
    edge_* : :class:`~graph_tool.EdgePropertyMap` or arbitrary types (optional, default: ``None``)
1666
1667
1668
        Parameters following the pattern ``edge_<prop-name>`` specify the edge
        property with name ``<prop-name>``, as an alternative to the ``eprops``
        parameter. See :func:`~graph_tool.draw.graph_draw` for details.
1669
    hvertex_* : :class:`~graph_tool.VertexPropertyMap` or arbitrary types (optional, default: ``None``)
1670
1671
1672
1673
        Parameters following the pattern ``hvertex_<prop-name>`` specify the
        vertex property with name ``<prop-name>``, as an alternative to the
        ``hvprops`` parameter. See :func:`~graph_tool.draw.graph_draw` for
        details.
1674
    hedge_* : :class:`~graph_tool.EdgePropertyMap` or arbitrary types (optional, default: ``None``)
1675
1676
1677
        Parameters following the pattern ``hedge_<prop-name>`` specify the edge
        property with name ``<prop-name>``, as an alternative to the ``heprops``
        parameter. See :func:`~graph_tool.draw.graph_draw` for details.
1678
    **kwargs :
1679
1680
        All remaining keyword arguments will be passed to the
        :func:`~graph_tool.draw.graph_draw` function.
1681
1682
1683

    Returns
    -------
1684
    pos : :class:`~graph_tool.VertexPropertyMap`
1685
1686
1687
1688
        This is a vertex property map with the positions of
        the vertices in the layout.
    t : :class:`~graph_tool.Graph`
        This is a the hierarchy tree used in the layout.
1689
    tpos : :class:`~graph_tool.VertexPropertyMap`
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
        This is a vertex property map with the positions of
        the hierarchy tree in the layout.

    Examples
    --------
    .. testsetup:: draw_hierarchy

       gt.seed_rng(42)
       np.random.seed(42)

    .. doctest:: draw_hierarchy

       >>> g = gt.collection.data["celegansneural"]
       >>> state = gt.minimize_nested_blockmodel_dl(g, deg_corr=True)
       >>> gt.draw_hierarchy(state, output="celegansneural_nested_mdl.pdf")
       (...)

    .. testcleanup:: draw_hierarchy

1709
       conv_png("celegansneural_nested_mdl.pdf")
1710

1711
    .. figure:: celegansneural_nested_mdl.png
1712
       :align: center
1713
       :width: 80%
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725

       Hierarchical block partition of the C. elegans neural network, which
       minimizes the description length of the network according to the nested
       (degree-corrected) stochastic blockmodel.


    References
    ----------
    .. [holten-hierarchical-2006] Holten, D. "Hierarchical Edge Bundles:
       Visualization of Adjacency Relations in Hierarchical Data.", IEEE
       Transactions on Visualization and Computer Graphics 12, no. 5, 741–748
       (2006). :doi:`10.1109/TVCG.2006.147`
1726

1727
1728
1729
1730
    """

    g = state.g

1731
1732
    overlap = state.levels[0].overlap
    if overlap:
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
        ostate = state.levels[0]
        bv, bcin, bcout, bc = ostate.get_overlap_blocks()
        be = ostate.get_edge_blocks()
        orig_state = state
        state = state.copy()
        b = ostate.get_majority_blocks()
        state.levels[0] = BlockState(g, b=b)
    else:
        b = state.levels[0].b

    if subsample_edges is not None:
        emask = g.new_edge_property("bool", False)
        if isinstance(subsample_edges, int):
            eidx = g.edge_index.copy("int").fa.copy()
            numpy.random.shuffle(eidx)
            emask = g.new_edge_property("bool")
            emask.a[eidx[:subsample_edges]] = True
        else:
            for e in subsample_edges:
                emask[e] = True
        g = GraphView(g, efilt=emask)

1755
1756
    t, tb, tvorder = get_hierarchy_tree(state,
                                        empty_branches=empty_branches)
1757
1758

    if layout == "radial":
1759
1760
1761
        if rel_order == "degree":
            rel_order = g.degree_property_map("total")
        vorder = t.own_property(rel_order.copy())
1762
1763
        if pos is not None:
            x, y = ungroup_vector_property(pos, [0, 1])
1764
1765
            x.fa -= x.fa.mean()
            y.fa -= y.fa.mean()
1766
            angle = g.new_vertex_property("double")
1767
            angle.fa = (numpy.arctan2(y.fa, x.fa) + 2 * numpy.pi) % (2 * numpy.pi)
1768
            vorder = t.own_property(angle)
1769
1770
1771
        if node_weight is not None:
            node_weight = t.own_property(node_weight.copy())
            node_weight.a[node_weight.a == 0] = 1
1772
        tpos = radial_tree_layout(t, root=t.vertex(t.num_vertices() - 1,
1773
                                                   use_index=False),
1774
                                  node_weight=node_weight,
1775
1776
                                  rel_order=vorder,
                                  rel_order_leaf=True)
1777
    elif layout == "bipartite":
1778
        tpos = get_bip_hierachy_pos(state, aspect=bip_aspect,
1779
1780
                                    node_weight=node_weight)
        tpos = t.own_property(tpos)
1781
1782
1783
1784
1785
    elif layout == "sfdp":
        if pos is None:
            tpos = sfdp_layout(t)
        else:
            x, y = ungroup_vector_property(pos, [0, 1])
1786
1787
1788
            x.fa -= x.fa.mean()
            y.fa -= y.fa.mean()
            K = numpy.sqrt(x.fa.std() + y.fa.std()) / 10
1789
1790
            tpos = t.new_vertex_property("vector<double>")
            for v in t.vertices():
1791
                if int(v) < g.num_vertices(True):
1792
1793
1794
1795
                    tpos[v] = [x[v], y[v]]
                else:
                    tpos[v] = [0, 0]
            pin = t.new_vertex_property("bool")
1796
            pin.a[:g.num_vertices(True)] = True
1797
1798
1799
1800
            tpos = sfdp_layout(t, K=K, pos=tpos, pin=pin, multilevel=False)
    else:
        tpos = t.own_property(layout)

1801
    hvvisible = t.new_vertex_property("bool", True)
1802
1803
1804
1805
    if hide is None:
        L = len([s for s in state.levels if s.get_nonempty_B() > 0])
        hide = len(state.levels) - L

1806
    if hide > 0:
1807
        root = t.vertex(t.num_vertices(True) - 1)
1808
1809
1810
        dist = shortest_distance(t, source=root)
        hvvisible.fa = dist.fa >= hide

1811
1812
    pos = g.own_property(tpos.copy())

1813
    cts = get_hierarchy_control_points(g, t, tpos, beta,
1814
                                       max_depth=len(state.levels) - hshortcuts)
1815

1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
    vprops_orig = vprops
    eprops_orig = eprops
    hvprops_orig = vprops
    heprops_orig = eprops
    kwargs_orig = kwargs

    vprops = vprops.copy() if vprops is not None else {}
    eprops = eprops.copy() if eprops is not None else {}

    props, kwargs = parse_props("vertex", kwargs)
    vprops.update(props)
    vprops.setdefault("fill_color", b)
    vprops.setdefault("color", b)
1829
    vprops.setdefault("shape", _vdefaults["shape"] if not overlap else "pie")
1830
1831
1832
1833
1834
1835
1836
1837

    output_size = kwargs.get("output_size", (600, 600))
    if kwargs.get("mplfig", None) is not None:
        x, y = ungroup_vector_property(pos, [0, 1])
        w = x.a.max() - x.a.min()
        h = y.a.max() - y.a.min()
        output_size = (w, h)
    s = numpy.mean(output_size) / (4 * numpy.sqrt(g.num_vertices()))
1838
    vprops.setdefault("size", prop_to_size(g.degree_property_map("total"), s/5, s))
1839

1840
1841
    adjust_default_sizes(g, output_size, vprops, eprops)

1842
1843
1844
1845
    if vprops.get("text_position", None) == "centered":
        angle, text_pos = centered_rotation(g, pos, text_pos=True)
        vprops["text_position"] = text_pos
        vprops["text_rotation"] = angle
1846
1847
1848
1849
1850
1851
1852
1853
        toffset = vprops.get("text_offset", None)
        if toffset is not None:
            if not isinstance(toffset, PropertyMap):
                toffset = g.new_vp("vector<double>", val=toffset)
            xo, yo = ungroup_vector_property(toffset, [0, 1])
            xo.a[text_pos.a == numpy.pi] *= -1
            toffset = group_vector_property([xo, yo])
            vprops["text_offset"] = toffset
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866

    self_loops = label_self_loops(g, mark_only=True)
    if self_loops.fa.max() > 0:
        parallel_distance = vprops.get("size", _vdefaults["size"])
        if isinstance(parallel_distance, PropertyMap):
            parallel_distance = parallel_distance.fa.mean()
        cts_p = position_parallel_edges(g, pos, numpy.nan,
                                        parallel_distance)
        gu = GraphView(g, efilt=self_loops)
        for e in gu.edges():
            cts[e] = cts_p[e]


1867
1868
1869
1870
1871
1872
1873
    vprops = _convert_props(vprops, "v", g, kwargs.get("vcmap", default_cm),
                            pmap_default=True)

    props, kwargs = parse_props("edge", kwargs)
    eprops.update(props)
    eprops.setdefault("control_points", cts)
    eprops.setdefault("pen_width", _edefaults["pen_width"])
1874
    eprops.setdefault("color", list(_edefaults["color"][:-1]) + [.6])
1875
    eprops.setdefault("end_marker", "arrow" if g.is_directed() else "none")
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
    eprops = _convert_props(eprops, "e", g, kwargs.get("ecmap", default_cm),
                            pmap_default=True)

    hvprops = hvprops.copy() if hvprops is not None else {}
    heprops = heprops.copy() if heprops is not None else {}

    props, kwargs = parse_props("hvertex", kwargs)
    hvprops.update(props)

    blue = list(color_converter.to_rgba("#729fcf"))
    blue[-1] = .6
    hvprops.setdefault("fill_color", blue)
    hvprops.setdefault("color", [1, 1, 1, 0])
    hvprops.setdefault("shape", "square")
1890
    hvprops.setdefault("size", s)
1891

1892
1893
1894
1895
    if hvprops.get("text_position", None) == "centered":
        angle, text_pos = centered_rotation(t, tpos, text_pos=True)
        hvprops["text_position"] = text_pos
        hvprops["text_rotation"] = angle
1896
1897
1898
1899
1900
1901
1902
1903
        toffset = hvprops.get("text_offset", None)
        if toffset is not None:
            if not isinstance(toffset, PropertyMap):
                toffset = t.new_vp("vector<double>", val=toffset)
            xo, yo = ungroup_vector_property(toffset, [0, 1])
            xo.a[text_pos.a == numpy.pi] *= -1
            toffset = group_vector_property([xo, yo])
            hvprops["text_offset"] = toffset
1904

1905
1906
1907
1908
1909
1910
1911
1912
    hvprops = _convert_props(hvprops, "v", t, kwargs.get("vcmap", default_cm),
                             pmap_default=True)

    props, kwargs = parse_props("hedge", kwargs)
    heprops.update(props)

    heprops.setdefault("color", blue)
    heprops.setdefault("end_marker", "arrow")
1913
1914
    heprops.setdefault("marker_size", s * .8)
    heprops.setdefault("pen_width", s / 10)
1915
1916
1917

    heprops = _convert_props(heprops, "e", t, kwargs.get("ecmap", default_cm),
                             pmap_default=True)
1918

1919
1920
    vcmap = kwargs.get("vcmap", default_cm)
    ecmap = kwargs.get("ecmap", vcmap)
1921
1922
1923

    B = state.levels[0].B

1924
    if overlap and "pie_fractions" not in vprops:
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
        vprops["pie_fractions"] = bc.copy("vector<double>")
        if "pie_colors" not in vprops:
            vertex_pie_colors = g.new_vertex_property("vector<double>")
            nodes = defaultdict(list)
            def conv(k):
                clrs = [vcmap(r / (B - 1) if B > 1 else 0) for r in k]
                return [item for l in clrs for item in l]
            map_property_values(bv, vertex_pie_colors, conv)
            vprops["pie_colors"] = vertex_pie_colors

    gradient = eprops.get("gradient", None)
1936
1937
    if gradient is None:
        gradient = g.new_edge_property("double")
1938
        gradient = group_vector_property([gradient])
1939
1940
        ecolor = eprops.get("ecolor", _edefaults["color"])
        eprops["gradient"] = gradient
1941
        if overlap:
1942
            for e in g.edges():                       # ******** SLOW *******
1943
                r, s = be[e]
1944
                if not g.is_directed() and e.source() > e.target():
1945
1946
1947
                    r, s = s, r
                gradient[e] = [0] + list(vcmap(r / (B - 1))) + \
                              [1] + list(vcmap(s / (B - 1)))
1948
1949
1950
1951
                if isinstance(ecolor, PropertyMap):
                    gradient[e][4] = gradient[e][9] = ecolor[e][3]
                else:
                    gradient[e][4] = gradient[e][9] = ecolor[3]
1952
1953
1954


    t_orig = t
1955
    t = GraphView(t,
1956
                  vfilt=lambda v: int(v) >= g.num_vertices(True) and hvvisible[v])
1957

1958
1959
    t_vprops = {}
    t_eprops = {}
1960

1961
1962
1963
1964
1965
1966
1967
    props = []
    for k in set(list(vprops.keys()) + list(hvprops.keys())):
        t_vprops[k] = (vprops.get(k, None), hvprops.get(k, None))
        props.append(t_vprops[k])
    for k in set(list(eprops.keys()) + list(heprops.keys())):
        t_eprops[k] = (eprops.get(k, None), heprops.get(k, None))
        props.append(t_eprops[k])
1968

1969
1970
1971
    props.append((pos, tpos))
    props.append((g.vertex_index, tb))
    props.append((b, None))
1972
1973
1974
1975
1976
    if "eorder" in kwargs:
        eorder = kwargs["eorder"]
        props.append((eorder,
                      t.new_ep(eorder.value_type(),
                               eorder.fa.max() + 1)))
1977

1978
    u, props = graph_union(g, t, props=props)
1979

1980
1981
1982
1983
1984
1985
1986
    for k in set(list(vprops.keys()) + list(hvprops.keys())):
        t_vprops[k] = props.pop(0)
    for k in set(list(eprops.keys()) + list(heprops.keys())):
        t_eprops[k] = props.pop(0)
    pos = props.pop(0)
    tb = props.pop(0)
    b = props.pop(0)
1987
1988
    if "eorder" in kwargs:
        eorder = props.pop(0)
1989
1990
1991

    def update_cts(widget, gg, picked, pos, vprops, eprops):
        vmask = gg.vertex_index.copy("int")
1992
        u = GraphView(gg, directed=False, vfilt=vmask.fa < g.num_vertices(True))
1993
        cts = eprops["control_points"]
1994
        get_hierarchy_control_points(u, t_orig, pos, beta, cts=cts,
1995
                                     max_depth=len(state.levels) - hshortcuts)
1996
1997
1998

    def draw_branch(widget, gg, key_id, picked, pos, vprops, eprops):
        if key_id == ord('b'):
1999
2000
            if picked is not None and not isinstance(picked, PropertyMap) and int(picked) > g.num_vertices(True):
                p = shortest_path(t_orig, source=t_orig.vertex(t_orig.num_vertices(True) - 1),