This is a program that helps to visualise methods of numpy arrays.
It is designed to work in 3 dimensions and can also be extended up to 6 dimensions.
git + clone https://github.com/loijord/numpyviz
cd numpyviz
matplotlib == 3.3.0
numpy == 1.19.1
Import these packages at the beginning of file:
import numpy as np
import matplotlib.pyplot as plt
from numpyviz import VisualArray
Every instance of VisualArray has an arr attribute which is numpy array.
It can be visualised after colors attribute is assigned.
This example demonstrates a very basic usage of VisualArray initialisation and color assignment
import numpy as np
import matplotlib.pyplot as plt
from numpyviz import VisualArray
fig = plt.figure()
titles = ['demo1', 'demo2']
for i, title in enumerate(titles):
ax = fig.add_subplot(1, 2, 1 + i, projection='3d')
ax.set_title(title)
arr = np.arange(24).reshape((2, 3, 4))
va = VisualArray(arr, fig=fig, ax=ax)
cells = va.get_indices()[::5] # make some fun pattern
va.set_colors(cells.T, color='yellow', basecolor='lightblue')
ax.dist = 15
va.vizualize(fixview=True)
plt.show()
# va.get_indices()[::5]:
'''
[[0 0 0]
[0 1 1]
[0 2 2]
[1 0 3]
[1 2 0]]'''
arr = np.arange(90).reshape((6,3,5))
va = VisualArray(arr)
coords = va.get_indices() #indices of every cell
cells = coords[np.sum(coords, axis=1) % 3 == 0]
va.set_colors(cells.T, color='yellow', basecolor='lightblue')
va.vizualize(fixview=True)
plt.show()
Alternative way to get indices
arr = np.random.randint(100, size=60).reshape((2,6,5))
coords = np.array(list(np.ndindex(arr.shape)))
cells = coords[np.sum(coords, axis=1) % 3 == 0]
fig = plt.figure()
ax = fig.add_subplot(2, 1, 1, projection='3d')
ax.set_title('top')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(cells.T, color='yellow', basecolor='lightblue')
va.vizualize(fixview=True)
ax = fig.add_subplot(2, 1, 2, projection='3d')
ax.set_title('bottom')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(cells.T, color='yellow', basecolor='lightblue')
va.vizualize(fixview=True)
ax.elev = -30
plt.show()
arr = np.arange(64).reshape((1,8,8))
va = VisualArray(arr)
cells = va.get_indices_chequerwise(window=(1,1,1))
va.set_colors(cells.T, color='white', basecolor='grey')
va.vizualize(fixview=True, axis_labels=(None,None,None))
va.ax.dist = 12.5 #zoom out a little
plt.show()
import matplotlib.gridspec as gridspec
arr = np.random.randint(99, size=24).reshape((3, 4, 2))
fig = plt.figure(constrained_layout=True)
spec = gridspec.GridSpec(ncols=5, nrows=1, figure=fig)
ax = fig.add_subplot(spec[0], projection='3d')
ax.set_title(f'body of shape={arr.shape}')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(va.get_indices().T, color='lawngreen', basecolor='aqua')
va.mix_colors(va.get_indices_chequerwise((1,1,arr.shape[2])).T, 'black')
va.vizualize(fixview=True, axis_labels=('axis=0','axis=1','axis=2'))
ax = fig.add_subplot(spec[1:], projection='3d')
ax.set_title(f'body of shape={arr.flatten().shape}')
va2 = VisualArray(va.arr.flatten(), fig=fig, ax=ax)
va2.set_colors(va2.get_indices().T, color='lawngreen', basecolor='aqua')
va2.mix_colors(va2.get_indices_chequerwise((1,1,arr.shape[2])).T, 'black')
va2.vizualize(fixview=True, axis_labels=(None,None,'axis=0'))
ax.dist = 8
plt.get_current_fig_manager().window.state('zoomed')
plt.show()
arr = np.random.randint(99, size=1260).reshape((10,9,14))
shape = (7,2,3,2,5,3)
fig = plt.figure('dimension')
ax = fig.add_subplot(1, 2, 1, projection='3d')
ax.set_title(f'body of shape={arr.shape}')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(va.get_indices().T, color='lawngreen', basecolor='aqua')
va.vizualize(fixview=False, axis_labels=('axis=0','axis=1','axis=2'))
ax = fig.add_subplot(1, 2, 2, projection='3d')
ax.set_title(f'body of shape={shape}')
va2 = VisualArray(va.arr, va.colors, fig=fig, ax=ax)
va2.permute(shape)
va2.vizualize(fixview=True, axis_labels=('axis=0','axis=1','axis=2'))
plt.get_current_fig_manager().window.state('zoomed')
ax.azim, ax.elev = -115, 24
plt.show()
# After some break, improve visual view of axis labels and upload demo for this problem:
# https://stackoverflow.com/questions/70444407/why-is-4d-realisation-of-max-pooling-in-numpy-misleading
import numpy as np
import matplotlib.pyplot as plt
from numpyviz import VisualArray
arr = np.random.randint(99, size=(1,8,12))
w = (2, 4)
print(arr.reshape(4, 2, 3, 4))
print('-'*50)
print(arr.reshape(4, 2, 3, 4).max(axis=1))
print('-'*50)
print(arr.reshape(4, 2, 3, 4).max(axis=3))
print('-'*50)
print(arr.reshape(4, 2, 3, 4).max(axis=(1,3)))
fig = plt.figure()
ax = fig.add_subplot(1, 3, 1, projection='3d')
ax.set_title('arr')
va = VisualArray(arr, fig=fig, ax=ax) #indices of every cell
cells = va.get_indices_chequerwise(window=(1,)+w)
va.set_colors(cells.T, color='lawngreen', basecolor='aqua')
va.vizualize(fixview=True, axis_labels=(None, 'axis=0', 'axis=1'))
ax = fig.add_subplot(1, 3, 2, projection='3d')
va2 = VisualArray(va.arr, va.colors, fig=fig, ax=ax) #shape: (1, 8, 12)
shape = (va2.arr.shape[1]//w[0], w[0], va2.arr.shape[2]//w[1], w[1])
ax.set_title(f'arr.reshape{shape}')
va2.reshape(shape) #shape: (4, 2, 3, 4)
va2.permute(shape)
va2.vizualize(fixview=True, axis_labels=('axis=0,3','axis=1','axis=2'))
def argmin(arr):
#bug...
a3 = arr.argmin(axis=(1, 3))
a1, a2 = np.indices((arr.shape[0], arr.shape[2]))
x, y, z = zip(*np.broadcast(a1, a2, a3))
return x, y, z
ax = fig.add_subplot(1, 3, 3, projection='3d')
arr3 = arr.reshape(shape).max(axis=(1, 3))[:,:,None]
va3 = VisualArray(arr3, fig=fig, ax=ax) #indices of every cell
cells = va3.get_indices_chequerwise(window=(1,1,1))
va3.set_colors(cells.T, color='lawngreen', basecolor='aqua')
dark_cells = va3.get_indices_chequerwise(window=(1,3,1))
va3.mix_colors(dark_cells.T, 'black', r=0.4)
va3.ax.set_title(f'arr.reshape{shape}.max(axis=(0,2))')
va3.ax.dist = 15
va3.vizualize(fixview=True, axis_labels=('axis=3', 'axis=1', None))
print(f'arr = np.random.randint(99, size=(1,8,12)) =')
print(arr)
print('-'*50)
print(f'arr.reshape{shape}.max(axis=(0, 2)) =')
print(arr.reshape(shape).max(axis=(0, 2)))
print('-'*50)
print(f'arr.reshape{shape}.max(axis=(1, 3)) =')
print(arr.reshape(shape).max(axis=(1, 3)))
plt.show()
def argmin_axis0(arr):
a1 = np.argmin(arr, axis=0)
a2, a3 = np.indices((arr.shape[1], arr.shape[2]))
x, y, z = zip(*np.broadcast(a1, a2, a3))
return x,y,z
def argmin_axis1(arr):
a2 = np.argmin(arr, axis=1)
a1, a3 = np.indices((arr.shape[0], arr.shape[2]))
x, y, z = zip(*np.broadcast(a1, a2, a3))
return x, y, z
def argmin_axis2(arr):
a3 = np.argmin(arr, axis=2)
a1, a2 = np.indices((arr.shape[0], arr.shape[1]))
x, y, z = zip(*np.broadcast(a1, a2, a3))
return x, y, z
fig = plt.figure()
arr = np.random.randint(100, size=60).reshape((2,6,5))
titles = ['np.argmin(arr, axis=0)', 'np.argmin(arr, axis=1)', 'np.argmin(arr, axis=2)']
result_titles = ['result along axis=0', 'result along axis=1', 'result along axis=2']
cells = [argmin_axis0(arr), argmin_axis1(arr), argmin_axis2(arr)]
cell_results = [np.argmin(arr, axis=0)[None,:,:], np.argmin(arr, axis=1)[:,None,:], np.argmin(arr, axis=2)[:,:,None]]
axis_names = [(None, 'axis=0', 'axis=1'), ('axis=0', None, 'axis=1'), ('axis=0', 'axis=1', None)]
for i in range(3):
ax = fig.add_subplot(2, 3, 1 + i, projection='3d')
ax.set_title(titles[i])
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(cells[i], color='yellow', basecolor='lightblue')
va.vizualize(fixview=True)
for i in range(3):
ax = fig.add_subplot(2, 3, 4 + i, projection='3d')
ax.set_title(result_titles[i])
va = VisualArray(cell_results[i], fig=fig, ax=ax)
va.set_colors(basecolor='lightgreen')
va.vizualize(fixview=True, axis_labels=axis_names[i])
plt.show()
arr = np.array([[r'$\times$', r'$x^2$', r'$y^2$', r'$z^2$', r'$-xy$', r'$-yz$', r'$-xz$'],
[r'$x$', r'$x^3$', r'$xy^2$', r'$xz^2$', r'$-x^2y$', r'$-xyz$', r'$-x^2z$'],
[r'$y$', r'$x^2y$', r'$y^3$', r'$yz^2$', r'$-xy^2$', r'$-y^2z$', r'$-xyz$'],
[r'$z$', r'$x^2z$', r'$y^2z$', r'$z^3$', r'$-xyz$', r'$-yz^2$', r'$-xz^2$']])
va = VisualArray(arr)
blue = [(0,i,0) for i in range(1,4)] + [(0,0,i) for i in range(1,7)]
lime = [(0,1,1), (0,2,2), (0,3,3), (0,1,-2), (0,2,-1), (0,3,-3)]
va.set_colors(zip(*blue), color='lightblue', basecolor='white')
va.set_colors(zip(*lime), color='lime')
va.set_colors(zip(*[(0,2,-2), (0,-1,2)]), color='#ffff00')
va.set_colors(zip(*[(0,1,2), (0,2,4)]), color='#dddd00')
va.set_colors(zip(*[(0,1,3), (0,-1,-1)]), color='#bbbb00')
va.set_colors(zip(*[(0,1,4), (0,2,1)]), color='#999900')
va.set_colors(zip(*[(0,1,6), (0,-1,1)]), color='#777700')
va.set_colors(zip(*[(0,2,3), (0,-1,-2)]), color='#555500')
va.vizualize(fixview=True,
axis_labels = [None, '$x+y+z$', r'$' + r'\!'*35 + r' x^2+y^2+z^2-xy-yz-zx$'],
scale=0.4)
va.ax.set_title('Why $(x+y+z)(x^2+y^2+z^2-xy-yz-zx) = x^3+y^3+z^3-3xyz$? \n Simplify monochromatic pairs of yellow cubes!')
va.ax.azim, va.ax.elev = -108, 54
plt.show()
"""this is an example that demonstrates how to multiply five polynomials"""
arr = np.array([[[r'$x^2y$', r'$xy^2$'],[r'$xy^2$', r'$y^3$']],
[[r'$x^3$', r'$x^2y$'],[r'$x^2y$', r'$xy^2$']]])
va = VisualArray(arr)
va.set_colors(zip(*[(0,1,1)]), color='#6666ff')
va.set_colors(zip(*[(1,0,0)]), color='#ff66ff')
va.set_colors(zip(*[(0,0,0),(1,1,0),(1,0,1)]), color='#66ff66')
va.set_colors(zip(*[(0,1,0),(0,0,1),(1,1,1)]), color='#66ffff')
va.vizualize(fixview=False,
axis_labels = ['$x+y$', '$x+y$', '$x+y$'],
scale=0.7)
va.ax.set_title('Why $(x+y)^3 = x^3+3x^2y+3xy^2+y^3$?')
plt.show()
"""this is an example that demonstrates how to multiply five polynomials"""
fig = plt.figure()
arr = np.array([[[r'$x^3y^2$', r'$x^2y^3$'],[r'$x^2y^3$', r'$xy^4$']],
[[r'$x^2y^3$', r'$xy^4$'],[r'$xy^4$', r'$y^5$']],
[[r'$x^4y$', r'$x^3y^2$'],[r'$x^3y^2$', r'$x^2y^3$']],
[[r'$x^3y^2$', r'$x^2y^3$'],[r'$x^2y^3$', r'$xy^4$']],
[[r'$x^4y$', r'$x^3y^2$'], [r'$x^3y^2$', r'$x^2y^3$']],
[[r'$x^3y^2$', r'$x^2y^3$'], [r'$x^2y^3$', r'$xy^4$']],
[[r'$x^5$', r'$x^4y$'], [r'$x^4y$', r'$x^3y^2$']],
[[r'$x^4y$', r'$x^3y^2$'], [r'$x^3y^2$', r'$x^2y^3$']]])
ax = fig.add_subplot(1, 2, 1, projection='3d')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(np.where(arr=='$x^5$'), color='#6666ff')
va.set_colors(np.where(arr=='$x^4y$'), color='#66ff66')
va.set_colors(np.where(arr=='$x^3y^2$'), color='#ff6666')
va.set_colors(np.where(arr=='$x^2y^3$'), color='#ffff66')
va.set_colors(np.where(arr=='$xy^4$'), color='#ff66ff')
va.set_colors(np.where(arr=='$y^5$'), color='#66ffff')
va.permute(shape=(2,2,2,2,2))
va.vizualize(fixview=True,
axis_labels = [r'$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!'+'x(x+y)\!\!+\!\!y(x+y)$',
r'$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!'+'x(x+y)\!\!+\!\!y(x+y)$',
r'$\!\!x+y$'],
scale=0.6)
va.ax.set_title(r'Why $(x+y)^5 = x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$?' +'\n' +
r'Multiply each $2\times 2 \times 2$ subcube by $x^2$, $xy$, $xy$, $y^2$' +
'\n' + r'Then reduce monochromatic terms')
va.ax.dist = 11.5
ax = fig.add_subplot(1, 2, 2, projection='3d')
va = VisualArray(arr, fig=fig, ax=ax)
va.set_colors(np.where(arr=='$x^5$'), color='#6666ff')
va.set_colors(np.where(arr=='$x^4y$'), color='#66ff66')
va.set_colors(np.where(arr=='$x^3y^2$'), color='#ff6666')
va.set_colors(np.where(arr=='$x^2y^3$'), color='#ffff66')
va.set_colors(np.where(arr=='$xy^4$'), color='#ff66ff')
va.set_colors(np.where(arr=='$y^5$'), color='#66ffff')
va.permute(shape=(2,2,2,2,2))
va.vizualize(fixview=True,
axis_labels = [r'$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!'+'x(x+y)\!\!+\!\!y(x+y)$',
r'$\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!'+'x(x+y)\!\!+\!\!y(x+y)$',
r'$\!\!x+y$'],
scale=0.6)
va.ax.set_title(r'BACKSIDE CAMERA')
va.ax.azim, va.ax.elev, va.ax.dist = -55, 35, 11.5
plt.get_current_fig_manager().window.state('zoomed')
plt.show()
Warning: this might be quite slow to render visual array of shape (32, 32, 3)
def tohex(arr):
#shape of array: (X,Y,3)
#this is a vectorized version of arr of rgb -> arr of hex color codes
def tohexarr(x):
form = list('#000000')
c = np.base_repr(x, base=16)
form[-len(c):] = list(c)
return ''.join(form)
arr = np.asarray(arr, dtype='uint32')
hexarr = np.vectorize(tohexarr)
return hexarr((arr[:, :, 0]<<16) + (arr[:, :, 1]<<8) + arr[:, :, 2])\
from PIL import Image
test_image = Image.open('cat.jpg')
test_image = test_image.resize((32,32), Image.ANTIALIAS)
test_image = np.array(test_image).astype(int)
va = VisualArray(test_image)
coords = va.get_indices()
eye = np.eye(3, dtype=int)
# input of set_colors can be another array of len(cellsT)
for i in range(3):
color = np.expand_dims(test_image[:,:,i], axis=2) * eye[i]
cellsT = coords[coords[:, 2] == i].T #list of coords where z = i
va.set_colors(cellsT, color=tohex(color)[cellsT[0], cellsT[1]])
va.vizualize(fixview=True, scale=0.7, axis_labels=(None,None,None))
va.ax.azim = -140 #change to 40 to see another back side
va.ax.elev = 20
va.ax.dist = 8 #zoom in a little
plt.get_current_fig_manager().window.state('zoomed')
plt.show()
Warning: this might be quite slow to render visual array of shape (32, 32, 1). If you need to convert single color code to rgb, use:
(np.array(matplotlib.colors.to_rgb('#EFF1DE'))*255).astype(int)
def tohex(arr):
def tohexarr(x):
form = list('#000000')
c = np.base_repr(x, base=16)
form[-len(c):] = list(c)
return ''.join(form)
arr = np.asarray(arr, dtype='uint32')
hexarr = np.vectorize(tohexarr)
return hexarr((arr[:, :, 0]<<16) + (arr[:, :, 1]<<8) + arr[:, :, 2])
def tolabels(arr):
def tolabelarr(x):
return r'\begin{array}{l}\,\,\sharp ' + x[1:4] + r'\\ \,\,\,\, ' + x[4:7] + r'\\ ' + r'\\ ' + r'\\ ' + r'\end{array}'
labelarr = np.vectorize(tolabelarr)
return labelarr(arr)
from PIL import Image
test_image = Image.open('cat.jpg')
test_image = test_image.resize((32, 32), Image.ANTIALIAS)
test_image = np.array(test_image).astype(int)
arr = tohex(test_image)
va = VisualArray(arr)
cells = va.get_indices()
x,y,z = cells.T
va.set_colors(cells.T, color=va.arr[x,y,z])
va.arr = tolabels(va.arr)
va.vizualize(fixview=True, scale=0.35, axis_labels=(None,None,None))
va.ax.dist = 11.5 #zoom out a little; change to 3.5 for higher zoom
plt.get_current_fig_manager().window.state('zoomed')
plt.show()
I've used to call it Sputnik1 because it helped to visualise a first quite hard problem on StackOverflow
import numpy as np
import matplotlib.pyplot as plt
from numpyviz import VisualArray
v = np.array([[2,5, 3,5, 1,8],
[4,6, 2,7, 5,9],
[1,8, 2,3, 1,4],
[2,8, 1,4, 3,5],
[5,7, 2,3, 7,8],
[1,2, 4,6, 3,5],
[3,5, 2,8, 1,4]])
s = np.sort(v, axis=1)
arr1 = v[(s[:,:-1] != s[:,1:]).all(1)]
arr2 = arr1.reshape(-1, 3, 2)
fig = plt.figure()
ax = fig.add_subplot(1, 2, 1, projection='3d')
ax.set_title('Initial array')
va = VisualArray(arr1, fig=fig, ax=ax)
va.set_colors(va.get_indices().T, color='yellow', basecolor='lightblue')
va.vizualize(fixview=True, axis_labels=(None, 'axis=0', 'axis=1'))
ax.dist = 12
ax = fig.add_subplot(1, 2, 2, projection='3d')
ax.set_title('Reshaped array')
va = VisualArray(arr2, fig=fig, ax=ax)
va.set_colors(va.get_indices().T, color='yellow', basecolor='lightblue')
va.vizualize(fixview=True)
ax.dist = 12
plt.show()
All the illustrations of Sputniks have its home at sputnik_gallery.
As well as their scripts sputnik_scripts.
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