Python: Data limit in Plotly frames? - python-3.x

Question

I have recently started to use Plotly to make 3D plots in python and I wanted to create an animation of what is going on in terms of column vectos of a 3 by 3 matrix when applying Gaussain elimination.
I wrote a function to get the row echelon form and the history of the matrix obtained at each step.
Then I wanted to plot the comuns vectors at each step of the algorithm.
At first I was able to get an animation of the the evolution of the three vectors by adpating this code : https://plotly.com/python/visualizing-mri-volume-slices/
But then I wanted to show on each frame the three row vectors of a given step and the three row vectors from the matrix of the previous step with opacity 0.2.
And when I added that part of the code I got a strange behavior from Plotly. It only showed me the three first vectors which are given to the frame and not all of them.
Here the code I have so far :
import numpy as np
import numpy.linalg as la
import plotly.graph_objects as go
v1 = np.array([5,2,1])
v2 = np.array([2,3,2])
v3 = np.array([3,-1,1])
A = np.transpose(np.vstack([v1,v2,v3]))
# G, H = pivot_Gauss(A)
H = [np.array([[ 5, 2, 3],[ 2, 3, -1],[ 1, 2, 1]]), np.array([[ 1, 0, 0],[ 2, 3, -1],[ 1, 2, 1]]),
np.array([[ 1, 0, 0],[ 0, 3, -1],[ 1, 2, 1]]), np.array([[ 1, 0, 0],[ 0, 3, -1],[ 0, 2, 1]]),
np.array([[1, 0, 0],[0, 1, 0],[0, 2, 1]]), np.array([[1, 0, 0],[0, 1, 0],[0, 0, 1]]),
np.array([[1, 0, 0],[0, 1, 0],[0, 0, 1]]) ]
G = np.array([[1,0,0],[0,1,0],[0,0,1]]) # results obtained using the function pivot_Gauss(A)
nb_frames = len(H)
frames = []
v_norm = 5
colors = ["blue","red","green"]
for k in range(nb_frames): # go.Frame(data,name=str(k))
dat = []
for j in range(np.shape(A)[1]):
v = H[k][:,j]
if la.norm(v) != 0 :
d1 = go.Scatter3d( x=[0,v[0]],y=[0,v[1]],z=[0,v[2]],name="v"+str(k+j+1),hoverinfo='name',
marker=dict(size=0), line=dict(color=colors[j], width=10 ))
dat.append(d1)
d2 = go.Cone(x=[v[0]],y=[v[1]],z=[v[2]],
u=[v[0]/v_norm],v=[v[1]/v_norm],w=[v[2]/v_norm],sizeref=1,
sizemode="scaled",anchor="cm",name="v"+str(k+j+1),hoverinfo='x+y+z+name',
colorscale=[[0, colors[j]], [1,colors[j]]],showscale=False)
dat.append(d2)
if k>0 : # add column vectors of previous Gaussain elimination step (causes some troubles,
#if this if section is commented I get an animation of the three clumn vectors of current step)
vk = H[k-1][:,j]
if la.norm(v) != 0 :
d3 = go.Scatter3d( x=[0,vk[0]],y=[0,vk[1]],z=[0,vk[2]],name="v"+str(k+j+1),hoverinfo='name',
marker=dict(size=0), line=dict(color=colors[j], width=10), opacity = 0.2 )
dat.append(d3)
d4 = go.Cone(x=[vk[0]],y=[vk[1]],z=[vk[2]],
u=[vk[0]/v_norm],v=[vk[1]/v_norm],w=[vk[2]/v_norm],sizeref=1,
sizemode="scaled",anchor="cm",name="v"+str(k+j+1),hoverinfo='x+y+z+name',
colorscale=[[0, colors[j]], [1,colors[j]]],showscale=False,opacity=0.2)
dat.append(d4)
frames.append(go.Frame(data=dat,name=str(k)))
fig = go.Figure(frames=frames)
# Add data to be displayed before animation starts
for j in range(A.shape[1]):
v = A[:,j]
if la.norm(v) != 0 :
fig.add_trace( go.Scatter3d( x=[0,v[0]],y=[0,v[1]],z=[0,v[2]],name="v"+str(k+1),hoverinfo='name',
marker=dict(size=0), line=dict(color=colors[j], width=10 )) )
fig.add_trace( go.Cone(x=[v[0]],y=[v[1]],z=[v[2]],
u=[v[0]/v_norm],v=[v[1]/v_norm],w=[v[2]/v_norm],sizeref=1,
sizemode="scaled",anchor="cm",name="v"+str(k+1),hoverinfo='x+y+z+name',
colorscale=[[0, colors[j]], [1,colors[j]]],showscale=False) )
### This remained almost exactly as the Plotly example
def frame_args(duration):
return {
"frame": {"duration": duration},
"mode": "immediate",
"fromcurrent": True,
"transition": {"duration": duration, "easing": "linear"},
}
sliders = [
{
"pad": {"b": 10, "t": 60},
"len": 0.9,
"x": 0.1,
"y": 0,
"steps": [
{
"args": [[f.name], frame_args(0)],
"label": str(k),
"method": "animate",
}
for k, f in enumerate(fig.frames)
],
}
]
matrix_but = [
{"buttons: [{},{},{},{},{},{}]"}
]
# Layout
fig.update_layout(
title='Pivot de Gauss',
width=600,
height=400,
scene=dict(xaxis=dict(autorange=True),
yaxis=dict(autorange=True),
zaxis=dict(autorange=True),
aspectratio=dict(x=1, y=1, z=1),
),
updatemenus = [
{
"buttons": [
{
"args": [None, frame_args(200)],
"label": "▶", # play symbol
"method": "animate",
},
{
"args": [[None], frame_args(0)],
"label": "◼", # pause symbol
"method": "animate",
},
],
"direction": "left",
"pad": {"r": 10, "t": 70},
"type": "buttons",
"x": 0.1,
"y": 0,
}
],
sliders=sliders
)
fig.show()
You will notice that for each vector I first draw a 3D line and then use cone to get the it arrow_shaped. It might not be the best way to do it, but I do not want to use cone alone as the apsect does not fit what I would like.
I stumbled across a (I think) similar question here : https://community.plotly.com/t/only-one-trace-showing-per-frame-in-animated-plot/25803
But I did not undestand the answer nor the example.
It seems from what I get that only the first six elemetns of the data contained in each frame is taken into account, but I do not understand why and I would like to show everything.
If someone has some insight (and a solution) on the subject, it would be warmly welcomed.
I can clarify things if needed.
Image of the two first column vectors of matrix from current step and first column vector of matrix from previous step
Image of the three column vectors of current matrix when part below if k>0 is commented

Answer 1

It seems from what I get that only the first six elemetns of the data contained in each frame is taken into account, but I do not understand why and I would like to show everything.
There's this paragraph under the heading 'Current Animation Limitations and Caveats':
Animations are designed to work well when each row of input is present across all animation frames, and when categorical values mapped to symbol, color and facet are constant across frames. Animations may be misleading or inconsistent if these constraints are not met.
Though in your first frame you have only three vectors (three lines plus three coneheads) to plot, it violates the above constraint when following frames contain six vectors. To overcome this restriction, we could insert the three vectors in the first frame (and also in the data to be displayed before animation starts) twice, i. e. to the
if k>0 : # add column vectors of previous Gaussain elimination step (causes some troubles,
block add an
else:
dat.append(d1)
dat.append(d2)
block, and in the
if la.norm(v) != 0 :
block duplicate the two fig.add_trace calls.