def construct(self):
A = np.random.randn(30, 30)
factors = {'A': A}
fg = factor_graph(factors, 'ij->ij')
fg.nodes['A']['pos'] = (0, 0)
fg.nodes['i']['pos'] = (0, 2)
fg.nodes['j']['pos'] = (0, -2)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
fg = combine_variables('i', 'j', fg)
fg.nodes['A']['pos'] = (-1, 0)
fg.nodes['i']['pos'] = (1, 0)
fg.edges['A', 'i', 0]['points'] = [(0, 1)]
fg.edges['A', 'i', 1]['points'] = [(0, -1)]
self.play(*mnx.transform_graph(mng, fg))
self.wait(1)
eq1 = TexMobject(r"\text{diag}(A)", color=BLACK)
eq2 = TexMobject(r"\text{tr}(A)", color=BLACK)
eq1.move_to(2 * UP)
eq2.move_to(2 * UP)
self.play(FadeIn(eq1))
self.wait(1)
fg.nodes['i']['summed'] = True
self.play(*mnx.transform_graph(mng, fg), Transform(eq1, eq2))
self.wait(1)
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=4.5,
height=3)
# c.move_to(x*RIGHT+y*DOWN)
self.play(FadeIn(c))
self.wait(2)
fg.edges['A', 'i', 0]['points'] = []
fg.edges['A', 'i', 1]['points'] = []
fg = nx.contracted_nodes(fg, 'A', 'i')
fg.nodes['A']['pos'] = (0, 0)
newn = r'\text{tr}(A)'
fg2 = nx.relabel_nodes(fg, {'A': newn})
self.play(*mnx.transform_graph(mng, fg),
Transform(c, get_fg_node(newn, fg2, h=0.8, w=1.5)))
self.wait(2)
def construct(self):
A = np.random.randn(10, 60)
B = np.random.randn(10, 60)
factors = {'A': A, 'B': B}
fg = factor_graph(factors, 'ij,kl->ijkl')
posA = np.zeros((3, 2))
posA[:, 0] = -2
posA[:, 1] = np.array([2, 0, -2])
mnx.map_attr('pos', ['i', 'A', 'j'], posA, fg)
posB = np.zeros((3, 2))
posB[:, 0] = 2
posB[:, 1] = np.array([2, 0, -2])
mnx.map_attr('pos', ['k', 'B', 'l'], posB, fg)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
fg = combine_variables('i', 'k', fg)
fg = combine_variables('j', 'l', fg)
fg.nodes['i']['pos'] = (0, 2)
fg.nodes['j']['pos'] = (0, -2)
fg.edges['A', 'i', 0]['points'] = [(-1.5, 1)]
fg.edges['A', 'j', 0]['points'] = [(-1.5, -1)]
fg.edges['B', 'i', 0]['points'] = [(1.5, 1)]
fg.edges['B', 'j', 0]['points'] = [(1.5, -1)]
self.play(*mnx.transform_graph(mng, fg))
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=6.5,
height=3)
# c.move_to(x*RIGHT+y*DOWN)
self.play(FadeIn(c))
self.wait(2)
fg.edges['A', 'i', 0]['points'] = []
fg.edges['A', 'j', 0]['points'] = []
fg.edges['B', 'i', 0]['points'] = []
fg.edges['B', 'j', 0]['points'] = []
fg = combine_factors('A', 'B', fg, multiedges=False)
fg.nodes['A']['pos'] = (0, 0)
newn = r'A \odot B'
fg2 = nx.relabel_nodes(fg, {'A': newn})
self.play(*mnx.transform_graph(mng, fg),
Transform(c, get_fg_node(newn, fg2, h=0.8, w=1.5)))
self.wait(2)
def construct(self):
A = np.random.randn(30, 60)
B = np.random.randn(60, 10)
factors = {'A': A, 'B': B}
fg = factor_graph(factors, 'ij,kl->ijkl')
h = 2
n = 6
pos = np.zeros((n, 2))
pos[:, 0] = (np.arange(n) - n / 2.0 + 0.5) * h
mnx.map_attr('pos', ['i', 'A', 'j', 'k', 'B', 'l'], pos, fg)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
fg = combine_variables('j', 'k', fg)
pos = np.zeros((n - 1, 2))
pos[:, 0] = (np.arange(n - 1) - (n - 1) / 2.0 + 0.5) * h
mnx.map_attr('pos', ['i', 'A', 'j', 'B', 'l'], pos, fg)
self.play(*mnx.transform_graph(mng, fg))
fg = fg.copy()
fg.nodes['j']['summed'] = True
self.play(*mnx.transform_graph(mng, fg))
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=6.5,
height=3.5)
x, y = fg.nodes['j']['pos']
c.move_to(x * RIGHT + y * DOWN)
self.play(FadeIn(c))
self.wait(2)
fg = nx.contracted_nodes(fg, 'A', 'j')
fg = nx.contracted_nodes(fg, 'A', 'B')
fg.node['A']['pos'] = (x, y)
fg = nx.relabel_nodes(fg, {'A': 'AB'})
mng.relabel_id(fg, 'A', 'AB')
fg.nodes['i']['pos'] = (-2, y)
fg.nodes['l']['pos'] = (2, y)
self.play(*mnx.transform_graph(mng, fg),
Transform(c, get_fg_node('AB', fg)))
self.wait(2)
def construct(self):
A = np.random.randn(10, 100, 30, 40, 10)
factors = {'A': A}
vars = ['i', 'j', 'k', 'l', 'm']
fg = factor_graph(factors, 'ijklm->ijkl')
fg.nodes['A']['pos'] = (0, -1)
fg.nodes['i']['pos'] = (0, 1)
fg.nodes['j']['pos'] = (-2, 0)
fg.nodes['k']['pos'] = (-2, -2)
fg.nodes['l']['pos'] = (0, -3)
fg.nodes['m']['pos'] = (2, -1)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
sizes = A.shape
texs = [TexMobject(s) for s in sizes]
full = TexMobject(*[_ for t in sizes[:-1] for _ in [t, '\cdot']],
sizes[-1],
f'={np.array(sizes).prod()}' + r'\text{ additions}',
color=BLACK)
# circ = Circle(radius=1, color=ORANGE)
# circ.move_to(DOWN)
full.shift(2.5 * UP)
self.add(mng)
self.wait(2)
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=4.5,
height=3)
c.move_to(DOWN + 1 * RIGHT)
self.play(FadeIn(c))
# self.play(ShowCreation(circ))
# self.wait(0.5)
self.play(
TransformFromCopy(mng.edges[fg.edges['A', vars[0], 0]['mob_id']],
full.submobjects[0]))
for i, v in enumerate(vars[1:]):
self.play(
TransformFromCopy(mng.edges[fg.edges['A', v, 0]['mob_id']],
full.submobjects[2 * (i + 1)]),
FadeIn(full.submobjects[2 * i + 1]))
self.wait(0.5)
self.play(FadeIn(full.submobjects[-1]))
self.wait(1)
fg = nx.contracted_nodes(fg, 'A', 'm')
self.play(*mnx.transform_graph(mng, fg),
Transform(c, get_fg_node('A', fg)))
self.wait(3)
def construct(self):
A = np.random.randn(100)
factors = {'A': A}
fg = factor_graph(factors, 'i->i')
fg.nodes['A']['pos'] = (-1, 0)
fg.nodes['i']['pos'] = (1, 0)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
A = np.random.randn(20, 5)
factors = {'A': A}
fg2 = factor_graph(factors, 'ij->ij')
fg2.nodes['A']['pos'] = (-1, 0)
fg2.nodes['i']['pos'] = (1, 1)
fg2.nodes['j']['pos'] = (1, -1)
fg2.nodes['A']['mob_id'] = fg.nodes['A']['mob_id']
fg2.nodes['i']['mob_id'] = fg.nodes['i']['mob_id']
fg2.nodes['j']['expansion'] = {'i': fg.nodes['i']}
fg2.edges['A', 'i', 0]['mob_id'] = fg.edges['A', 'i', 0]['mob_id']
fg2.edges['A', 'j', 0]['expansion'] = {
('A', 'i', 0): fg.edges['A', 'i', 0]
}
self.play(*mnx.transform_graph(mng, fg2))
self.wait(2)
def construct(self):
A = np.random.randn(30)
B = np.random.randn(30)
factors = {'A': A, 'B': B}
fg = factor_graph(factors, 'i,j->ij')
tex = r"""
\begin{bmatrix}
& & \\
& C & \\
& &
\end{bmatrix}=
\begin{bmatrix}
\\
A \\
\\
\end{bmatrix}
\begin{bmatrix}
& B^T & \\
\end{bmatrix}
"""
fullatex = TexMobject(tex, color=BLACK)
fullatex.shift(1.5 * UP)
h = 2.5
d = -1
pos = np.zeros((4, 2))
pos[:, 1] = d
pos[:, 0] = (np.arange(4) - 1.5) * h
mnx.map_attr('pos', ['i', 'A', 'B', 'j'], pos, fg)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
fg = combine_factors('A', 'B', fg)
pos = np.zeros((3, 2))
pos[:, 1] = d
pos[:, 0] = (np.arange(3) - 1) * h
mnx.map_attr('pos', ['i', 'A', 'j'], pos, fg)
fg = nx.relabel_nodes(fg, {'A': 'C'})
mng.id_to_node[fg.node['C']['mob_id']] = 'C'
self.play(*mnx.transform_graph(mng, fg))
self.wait(0.5)
self.play(FadeIn(fullatex))
self.wait(4)
def construct(self):
import time
# list of colors to choose from
COLORS = [RED, BLUE, GREEN, ORANGE, YELLOW]
np.random.seed(int(time.time()))
# make a random graph
G1 = nx.erdos_renyi_graph(10, 0.5)
# choose random colors for the nodes
for node in G1.nodes.values():
node['color'] = random.choice(COLORS)
# make the manim graph
mng = mnx.ManimGraph(G1)
self.play(*[ShowCreation(m) for m in mng]) # create G1
self.wait(1)
# lets get a new graph
G2 = G1.copy()
mnx.assign_positions(G2) # assign new node positions
# add and remove random edges
new_G = nx.erdos_renyi_graph(10, 0.5)
G2.add_edges_from(new_G.edges)
for edge in G1.edges:
if edge not in new_G.edges:
G2.remove_edge(*edge)
# recolor nodes randomly
for node in G2.nodes.values():
node['color'] = random.choice(COLORS)
# the transform_graph function neatly moves nodes to their new
# positions along with edges that remain. New edges are faded in and
# removed ones are faded out. Try to replace this with a vanilla
# Transform and notice the difference.
self.play(*mnx.transform_graph(mng, G2)) # transform G1 to G2
# vanilla transform mixes up all mobjects, and doesn't look as good
# self.play(Transform(mng, mnx.ManimGraph(G2)))
self.wait(1)
def construct(self):
A = np.random.randn(20, 5)
factors = {'A': A}
fg = factor_graph(factors, 'ij->ij')
fg.nodes['A']['pos'] = (-1, 0)
fg.nodes['i']['pos'] = (1, 1)
fg.nodes['j']['pos'] = (1, -1)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(mng)
self.wait(2)
fg2 = fg.copy()
fg2.nodes['i']['pos'] = (1, 0.3)
fg2.nodes['j']['pos'] = (1, -0.3)
fg2.edges['A', 'i', 0]['points'] = [(0.7, 0)]
fg2.edges['A', 'j', 0]['points'] = [(0.7, 0)]
self.play(*mnx.transform_graph(mng, fg2))
self.wait(2)
def construct(self):
A = np.random.randn(10, 20)
B = np.random.randn(30, 50)
factors = {'A': A, 'B': B}
vars = ['i', 'j', 'k', 'l']
d = -1
fg = factor_graph(factors, 'ij,kl->ijkl')
fg.nodes['A']['pos'] = (-1.5, d)
fg.nodes['B']['pos'] = (1.5, d)
fg.nodes['i']['pos'] = (-1.5, d + 1.5)
fg.nodes['j']['pos'] = (-1.5, d - 1.5)
fg.nodes['k']['pos'] = (1.5, d + 1.5)
fg.nodes['l']['pos'] = (1.5, d - 1.5)
sizes = A.shape + B.shape
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
full = TexMobject(*[_ for t in sizes[:-1] for _ in [t, '\cdot']],
sizes[-1],
f'={np.array(sizes).prod()}' +
r'\text{ multiplications}',
color=BLACK)
full.shift(2.5 * UP)
self.add(mng)
self.wait(2)
fg = combine_factors('A', 'B', fg)
fg.node['A']['pos'] = (0, d)
fg = nx.relabel_nodes(fg, {'A': 'C'})
mng.relabel_id(fg, 'A', 'C')
self.play(*mnx.transform_graph(mng, fg))
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=2,
height=2)
c.move_to(UP * d)
self.play(FadeIn(c))
self.wait(1)
self.play(
TransformFromCopy(mng.edges[fg.edges['C', 'i', 0]['mob_id']],
full.submobjects[0]))
self.play(
TransformFromCopy(mng.edges[fg.edges['C', 'j', 0]['mob_id']],
full.submobjects[2]),
FadeIn(full.submobjects[1]))
self.play(
TransformFromCopy(mng.edges[fg.edges['C', 'k', 0]['mob_id']],
full.submobjects[4]),
FadeIn(full.submobjects[2 + 1]))
self.play(
TransformFromCopy(mng.edges[fg.edges['C', 'l', 0]['mob_id']],
full.submobjects[6]),
FadeIn(full.submobjects[4 + 1]))
self.play(FadeIn(full.submobjects[-1]))
self.play(Transform(c, get_fg_node('C', fg)))
self.wait(2)
def construct(self):
A = np.random.randn(30, 60)
B = np.random.randn(60, 10)
C = np.random.randn(10, 30)
factors = {'A': A, 'B': B, 'C': C}
fg = factor_graph(factors, 'ij,kl,mn->ijklmn')
tA = TexMobject('A', color=BLACK)
tC = TexMobject('C', color=BLACK)
eq = TexMobject(r"\text{tr}(", 'A', 'B', 'C', ')', color=BLACK)
eq.to_edge(UP)
dfact = 0.6
eq.shift(dfact * DOWN)
tB = eq.submobjects[2]
tA.to_edge(UP)
tA.shift(4.5 * LEFT + dfact * DOWN)
tC.to_edge(UP)
tC.shift(4.5 * RIGHT + dfact * DOWN)
self.add(tA, tB, tC)
h = 1.5
n = 9
pos = np.zeros((n, 2))
pos[:, 1] = 1
pos[:, 0] = (np.arange(n) - n / 2.0 + 0.5) * h
mnx.map_attr('pos', ['i', 'A', 'j', 'k', 'B', 'l', 'm', 'C', 'n'], pos,
fg)
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
delta = tB.get_center()[0] - fg.nodes['B']['pos'][0]
eq.shift(delta * LEFT)
self.add(mng)
self.wait(2)
fg = combine_variables('j', 'k', fg)
mnx.shift_nodes(['A', 'i', 'j'], np.array([h, 0]), fg)
self.play(*mnx.transform_graph(mng, fg),
ReplacementTransform(tA, eq.submobjects[1]))
fg = fg.copy()
fg.nodes['j']['summed'] = True
self.play(*mnx.transform_graph(mng, fg))
self.wait(1)
fg = combine_variables('m', 'l', fg)
mnx.shift_nodes(['C', 'm', 'n'], np.array([-h, 0]), fg)
self.play(*mnx.transform_graph(mng, fg),
ReplacementTransform(tC, eq.submobjects[3]))
fg = fg.copy()
fg.nodes['m']['summed'] = True
self.play(*mnx.transform_graph(mng, fg))
self.wait(1)
fg = combine_variables('i', 'n', fg)
fg.nodes['i']['pos'] = (0, -1)
fg.edges['A', 'i', 0]['points'] = [(pos[0][0], 0.7), (pos[0][0], -0.6)]
fg.edges['C', 'i', 0]['points'] = [(pos[-1][0], 0.7),
(pos[-1][0], -0.6)]
self.play(*mnx.transform_graph(mng, fg))
print(
fg.edges['A', 'i', 0]['points'],
fg.edges['C', 'i', 0]['points'],
fg.nodes['A']['pos'],
fg.nodes['C']['pos'],
)
fg = fg.copy()
fg.nodes['i']['summed'] = True
self.play(*mnx.transform_graph(mng, fg), FadeIn(eq.submobjects[0]),
FadeIn(eq.submobjects[-1]))
self.wait(1)
eq2 = TexMobject(r"\text{tr}(ABC)", r"= \text{tr}(CAB)", color=BLACK)
eq2.to_edge(UP)
eq2.shift(dfact * DOWN)
eq3 = TexMobject(r"\text{tr}(ABC) = \text{tr}(CAB)",
r"= \text{tr}(BCA)",
color=BLACK)
eq3.to_edge(UP)
eq3.shift(dfact * DOWN)
nodes = ['m', 'B', 'j', 'A', 'i', 'C']
edges = [
('B', 'm', 0),
('B', 'j', 0),
('A', 'j', 0),
('A', 'i', 0),
('C', 'i', 0),
('C', 'm', 0),
]
hex = sp.RegularPolygon(sp.Point2D(0, -1), r=2.5, n=12)
poses = [np.array(p.evalf()).astype(np.float64) for p in hex.vertices]
mnx.map_attr('pos', nodes, poses[::2], fg)
mnx.map_attr('points', edges, [[p * 0.95] for p in poses[1::2]], fg)
self.play(*mnx.transform_graph(mng, fg))
self.wait(2)
def rotate(l, n):
return l[-n:] + l[:-n]
poses = rotate(poses, 4)
mnx.map_attr('pos', nodes, poses[::2], fg)
mnx.map_attr('points', edges, [[p * 0.95] for p in poses[1::2]], fg)
self.play(*mnx.transform_graph(
mng,
fg,
node_transform=HexTransform,
edge_transform=HexTransform,
))
self.play(ApplyMethod(eq.move_to, eq2.submobjects[0].get_center()),
FadeIn(eq2.submobjects[1]))
self.add(eq2.submobjects[0])
self.remove(eq)
self.wait(1)
poses = rotate(poses, 4)
mnx.map_attr('pos', nodes, poses[::2], fg)
mnx.map_attr('points', edges, [[p * 0.95] for p in poses[1::2]], fg)
self.play(*mnx.transform_graph(
mng,
fg,
node_transform=HexTransform,
edge_transform=HexTransform,
))
self.play(ApplyMethod(eq2.move_to, eq3.submobjects[0].get_center()),
FadeIn(eq3.submobjects[1]))
self.wait(4)
def construct(self):
# add shapes in the first
A = np.random.randn(10, 20, 100)
B = np.random.randn(20, 10)
C = np.random.randn(50, 20)
factors = {'A': A, 'B': B, 'C': C}
fg = factor_graph(factors, 'ijk,ji,lj->ijkl')
h = 3
y = -1
pos = np.zeros((3, 2))
pos[:, 1] = y
pos[:, 0] = (np.arange(3) - 1) * h
mnx.map_attr('pos', ['A', 'B', 'C'], pos, fg)
fg.nodes['i']['pos'] = (-1.5, y - 2)
fg.nodes['j']['pos'] = (0, y + 2)
fg.nodes['k']['pos'] = (-5.5, y)
fg.nodes['l']['pos'] = (5.5, y)
# poses = nx.spring_layout(fg, center=np.array([0, -0.5]))
# scale = np.array([6.5, 2])
# for node, pos in poses.items():
# fg.nodes[node]['pos'] = pos*scale
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
Ashape = TexMobject(r'A \in ',
r'\mathbb{R}^{10 \times 20 \times 100}',
color=BLACK)
Bshape = TexMobject(r'B \in ',
r'\mathbb{R}^{20 \times 10}',
color=BLACK)
Cshape = TexMobject(r'C \in ',
r'\mathbb{R}^{50 \times 20}',
color=BLACK)
Ashape.shift(UP)
Cshape.shift(DOWN)
self.add(Ashape, Bshape, Cshape)
self.wait(3)
einsum = TexMobject('D_{',
'k',
'l',
'}',
'=',
'A_{',
'i',
'j',
'k',
'}',
'B_{',
'j',
'i',
'}',
'C_{',
'l',
'j',
'}',
color=BLACK)
einsum.move_to(2.5 * UP)
self.play(Transform(Ashape, VGroup(*einsum.submobjects[5:9])))
self.wait(1)
self.play(Transform(Bshape, VGroup(*einsum.submobjects[9:13])))
self.wait(1)
self.play(Transform(Cshape, VGroup(*einsum.submobjects[13:])))
self.wait(1)
self.play(FadeIn(einsum))
self.clear()
self.add(einsum)
self.wait(1)
fcol = GREEN
indic = Indicate
rt = 2
# self.play(
# indic(einsum.submobjects[0], color=fcol, run_time=rt),
# indic(einsum.submobjects[5], color=fcol, run_time=rt),
# indic(einsum.submobjects[9], color=fcol, run_time=rt),
# *[FadeIn(mng.nodes[fg.nodes[n]['mob_id']])
# for n in fg.nodes.keys() if fg.nodes[n]['type'] == 'factor']
# )
self.play(
TransformFromCopy(einsum.submobjects[5],
mng.nodes[fg.nodes['A']['mob_id']]),
TransformFromCopy(einsum.submobjects[10],
mng.nodes[fg.nodes['B']['mob_id']]),
TransformFromCopy(einsum.submobjects[14],
mng.nodes[fg.nodes['C']['mob_id']]),
)
self.wait(2)
vcol = RED
# self.play(
# indic(einsum.submobjects[1], color=vcol, run_time=rt),
# indic(einsum.submobjects[2], color=vcol, run_time=rt),
# indic(einsum.submobjects[3], color=vcol, run_time=rt),
# indic(einsum.submobjects[10], color=vcol, run_time=rt),
# *[FadeIn(mng.nodes[fg.nodes[n]['mob_id']])
# for n in fg.nodes.keys() if fg.nodes[n]['type'] == 'variable']
# )
self.play(
TransformFromCopy(einsum.submobjects[6],
mng.nodes[fg.nodes['i']['mob_id']]),
TransformFromCopy(einsum.submobjects[7],
mng.nodes[fg.nodes['j']['mob_id']]),
TransformFromCopy(einsum.submobjects[8],
mng.nodes[fg.nodes['k']['mob_id']]),
TransformFromCopy(einsum.submobjects[15],
mng.nodes[fg.nodes['l']['mob_id']]),
)
self.add_foreground_mobjects(*mng.nodes.values())
self.wait(2)
creation = ShowCreation
self.play(
*[
creation(mng.edges[fg.edges[e]['mob_id']])
for e in fg.edges('A', keys=True)
], *[indic(m, color=RED) for m in einsum.submobjects[5:10]])
self.wait(1)
self.play(
*[
creation(mng.edges[fg.edges[e]['mob_id']])
for e in fg.edges('B', keys=True)
], *[indic(m, color=RED) for m in einsum.submobjects[10:14]])
self.wait(1)
self.play(
*[
creation(mng.edges[fg.edges[e]['mob_id']])
for e in fg.edges('C', keys=True)
], *[indic(m, color=RED) for m in einsum.submobjects[14:]])
self.wait(1)
self.clear()
mng = mnx.ManimGraph(fg, get_fg_node, get_fg_edge_curve)
self.add(einsum, mng)
fg = fg.copy()
fg.nodes['i']['summed'] = True
fg.nodes['j']['summed'] = True
self.play(*mnx.transform_graph(mng, fg),
*[indic(m, color=RED) for m in einsum.submobjects[0:4]])
self.wait(2)
# self.bring_to_back(*[mng.edges[fg.edges[e]['mob_id']]
# for e in fg.edges('A', keys=True)])
c = Ellipse(color=GREEN,
fill_color=GREEN,
fill_opacity=0.3,
width=9,
height=5.5)
c.shift(y * UP)
self.play(FadeIn(c))
self.wait(2)
fg = nx.contracted_nodes(fg, 'B', 'A')
fg = nx.contracted_nodes(fg, 'B', 'i')
fg = nx.contracted_nodes(fg, 'B', 'j')
fg = nx.contracted_nodes(fg, 'B', 'C')
fg2 = nx.relabel_nodes(fg, {'B': 'D'})
fg.nodes['k']['pos'] = (-2, y)
fg.nodes['l']['pos'] = (2, y)
self.play(
*mnx.transform_graph(mng, fg),
Transform(mng.nodes[fg.node['B']['mob_id']], get_fg_node('D',
fg2)),
Transform(c, get_fg_node('D', fg2)))
self.wait(4)