Live Programming and Computing with Python, R, Sage, Octave, Maxima, Singular, Gap, GP, HTML & Macaulay2

[Eli]

Extract/unzip and analyze the Planck chains/MCMC samples from the Planck Legacy Archive:

Code: [Select all] [Expand/Collapse]

1. import zipfile
2. import urllib.request
3.  
4. urllib.request.urlretrieve("http://pla.esac.esa.int/pla/aio/product-action?COSMOLOGY.FILE_ID=COM_CosmoParams_base-plikHM-TTTEEE-lowl-lowE_R3.00.zip", "COM_CosmoParams_base-plikHM-TTTEEE-lowl-lowE_R3.00.zip")
5.  
6. with zipfile.ZipFile('./COM_CosmoParams_base-plikHM-TTTEEE-lowl-lowE_R3.00.zip', 'r') as zip_ref:
7.     zip_ref.extractall() #You can specify the directory inside () to extract to
8.    

[Eli]

Test GetDist with this code, see more examples here:

Code: [Select all] [Expand/Collapse]

1. # Show plots inline, and load main getdist plot module and samples class
2. from __future__ import print_function
3. import sys, os
4. sys.path.insert(0,os.path.realpath(os.path.join(os.getcwd(),'..')))
5. from getdist import plots, MCSamples
6. import getdist
7. # use this *after* importing getdist if you want to use interactive plots
8. # %matplotlib notebook
9. import matplotlib.pyplot as plt
10. import IPython
11. print('GetDist Version: %s, Matplotlib version: %s'%(getdist.__version__, plt.matplotlib.__version__))
12. # matplotlib 2 may not work very well without usetex on, can uncomment
13. # plt.rcParams['text.usetex']=True
14.  
15. #Let test GetDist by getting some random samples for demonstration and then
16. #make some random covariance, then independent samples from Gaussian
17.  
18. import numpy as np
19. ndim = 4
20. nsamp = 10000
21. np.random.seed(10)
22. A = np.random.rand(ndim,ndim)
23. cov = np.dot(A, A.T)
24. samps = np.random.multivariate_normal([0]*ndim, cov, size=nsamp)
25. A = np.random.rand(ndim,ndim)
26. cov = np.dot(A, A.T)
27. samps2 = np.random.multivariate_normal([0]*ndim, cov, size=nsamp)
28.  
29. # Get the getdist MCSamples objects for the samples, specifying same parameter
30. # names and labels; if not specified weights are assumed to all be unity
31. names = ["x%s"%i for i in range(ndim)]
32. labels =  ["x_%s"%i for i in range(ndim)]
33. samples1 = MCSamples(samples=samps,names = names, labels = labels)
34. samples2 = MCSamples(samples=samps2,names = names, labels = labels, label='Second set')
35.  
36. # Triangle plot
37. g = plots.get_subplot_plotter()
38. g.triangle_plot([samples1, samples2], filled=True)
39. plt.show()
40.  
41. # Get 1D marginalized comparison plot
42. g = plots.get_single_plotter(width_inch=3)
43. g.plot_1d([samples1, samples2], 'x1')
44. plt.show()
45.  
46. # Get filled 2D comparison plot with legend
47. g = plots.get_single_plotter(width_inch=4, ratio=1)
48. g.plot_2d([samples1, samples2], 'x1', 'x2', filled=True)
49. g.add_legend(['sim 1', 'sim 2'], colored_text=True);
50. plt.show()

The outputs are:

[Eli]

Test TensorFlow and Keras with Fashion MNIST dataset, take over from the code below:

Code: [Select all] [Expand/Collapse]

1. from __future__ import absolute_import, division, print_function, unicode_literals
2. # TensorFlow and tf.keras
3. import tensorflow as tf
4. from tensorflow import keras
5.  
6. # Helper libraries
7. import numpy as np
8. import matplotlib.pyplot as plt
9.  
10. print(tf.__version__)
11.  
12. fashion_mnist = tf.keras.datasets.fashion_mnist
13.  
14. (train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()
15.  
16. print(test_labels)
17.  
18. class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat',
19.                'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']
20.  
21. print(train_images.shape)
22. print(len(train_labels))
23. print(train_labels)
24. print(test_images.shape)
25. print(len(test_labels))
26.  
27. #Preprocess the data
28. plt.figure()
29. plt.imshow(train_images[0])
30. plt.colorbar()
31. plt.grid(False)
32. plt.show()

[Eli]

Use tikzplotlib to convert matplotlib figures into TikZ/PGF Plots for native inclusion into LaTeX or ConTeXt documents.

The output of tikzplotlib is in PGFPlots, a TeX library that sits on top of PGF/TikZ and describes graphs in terms of axes, data and so on:

Code: [Select all] [Expand/Collapse]

1. import matplotlib.pyplot as plt
2. import numpy as np
3.  
4. plt.style.use("ggplot")
5.  
6. t = np.arange(0.0, 2.0, 0.1)
7. s = np.sin(2 * np.pi * t)
8. s2 = np.cos(2 * np.pi * t)
9. plt.plot(t, s, "o-", lw=4.1)
10. plt.plot(t, s2, "o-", lw=4.1)
11. plt.xlabel("time (s)")
12. plt.ylabel("Voltage (mV)")
13. #plt.title("Simple plot $\\frac{\\alpha}{2}$")
14. plt.grid(True)
15. plt.show()
16.  
17. import tikzplotlib
18.  
19. tikzplotlib.save("test.tex")

[Eli]

Testing NBODYKIT, a massively parallel, large-scale structure toolkit (see this paper):

Code: [Select all] [Expand/Collapse]

1. from nbodykit.lab import *
2. import numpy as np
3. import matplotlib.pyplot as plt
4. #Below, we create a very simple catalog of uniformly distributed
5. #particles in a box of side length L=1 h^−1 Mpc
6. catalog = UniformCatalog(nbar=100, BoxSize=1.0)
7. BoxSize = 2500.
8. """Catalogs have a fixed size and a set of columns describing the particle data.
9. In this case, our catalog has “Position” and “Velocity” columns.
10. Users can easily manipulate the existing column data or add new columns"""
11. catalog['Position'] *= BoxSize # re-normalize units of Position
12. #catalog['Mass'] = 10**(np.random(12, 15, size=len(catalog))) # add some random mass values
13. mesh = catalog.to_mesh(Nmesh=64, BoxSize=BoxSize)# Interpolate the particles onto a mesh of size 64^3
14. #We can save our mesh to disk to later re-load using nbodykit
15. mesh.save('mesh.bigfile')
16. #or preview a low-resolution, 2D projection of the mesh to make sure everythings looks as expected
17. plt.imshow(mesh.preview(axes=[0,1], Nmesh=32))
18. plt.show()
19. #Use the FFTPower algorithm to compute the power spectrum P(k,μ)
20. #of the density mesh using a fast Fourier transform via
21.  
22. result = FFTPower(mesh,mode="2d", Nmu=5)
23.  
24. #with the measured power stored as the power attribute of the result variable.
25. #The algorithm result and meta-data, input parameters, etc. can then be saved to disk as a JSON file
26. result.save("power-result.json")

[Admin]

NLTK - the Natural Language Toolkit is installed, test it:

Code: [Select all] [Expand/Collapse]

1. import nltk
2.  
3. #Simple nltk demo, Tokenize and tag some text
4.  
5. sentence = """At eight o'clock on Thursday morning Arthur didn't feel very good."""
6. print(sentence)
7. nltk.download('punkt')
8. tokens = nltk.word_tokenize(sentence)
9. print(tokens)
10.  
11. nltk.download('averaged_perceptron_tagger')
12. tagged = nltk.pos_tag(tokens)
13. print(tagged[0:6])
14.  
15. #Identify named entities
16. nltk.download('maxent_ne_chunker')
17. nltk.download('words')
18. entities = nltk.chunk.ne_chunk(tagged)
19. print(entities)
20.  
21. #Display a parse tree:
22.  
23. from nltk.corpus import treebank
24. nltk.download('treebank')
25. t = treebank.parsed_sents('wsj_0001.mrg')[0]
26. print(t)

[Eli]

Test SymPy:

Code: [Select all] [Expand/Collapse]

1. from sympy.plotting import plot
2. from sympy import *
3. plot( sin(x),cos(x), (x, -pi, pi))

Code: [Select all] [Expand/Collapse]

1. from sympy.plotting import plot
2. from sympy import *
3. x=Symbol('x')
4. plot(x**2, line_color='red')

[Eli]

3-D plotting with SymPy:

Code: [Select all] [Expand/Collapse]

1. from sympy import symbols
2. from sympy.plotting import plot3d
3.  
4. x, y = symbols('x y')
5. #Fig 1
6. plot3d(x*y, (x, -5, 5), (y, -5, 5))
7. #Fig 2
8. plot3d(x*y, -x*y, (x, -5, 5), (y, -5, 5))
9. #Fig 3
10. plot3d((x**2 + y**2, (x, -5, 5), (y, -5, 5)), (x*y, (x, -3, 3), (y, -3, 3)))
11. #Fig 4
12. from sympy import symbols, cos, sin
13. from sympy.plotting import plot3d_parametric_surface
14. u, v = symbols('u v')
15. plot3d_parametric_surface(cos(u + v), sin(u - v), u - v, (u, -5, 5), (v, -5, 5))

[Eli]

Further examples with SymPy:

Code: [Select all] [Expand/Collapse]

1. from sympy import plot_implicit, symbols, Eq, And
2. x, y = symbols('x y')
3. #Fig 1
4. plot_implicit(y > x**2)
5.  
6. #PlotGrid Class
7. from sympy import symbols
8. from sympy.plotting import plot, plot3d, PlotGrid
9.  
10. p1 = plot(x, x**2, x**3, (x, -5, 5))
11. p2 = plot((x**2, (x, -6, 6)), (x, (x, -5, 5)))
12. p3 = plot(x**3, (x, -5, 5))
13. p4 = plot3d(x*y, (x, -5, 5), (y, -5, 5))

[Eli]

Plotting options with SymPy:

Code: [Select all] [Expand/Collapse]

1. from sympy import plot_implicit, symbols, Eq, And
2. x, y = symbols('x y')
3.  
4. #PlotGrid Class
5. from sympy import symbols
6. from sympy.plotting import plot, plot3d, PlotGrid
7.  
8. p1 = plot(x, x**2, x**3, (x, -5, 5))
9. p2 = plot((x**2, (x, -6, 6)), (x, (x, -5, 5)))
10. p3 = plot(x**3, (x, -5, 5))
11. p4 = plot3d(x*y, (x, -5, 5), (y, -5, 5))
12.  
13. #Plotting vertically in a single line:
14. PlotGrid(2, 1 , p1, p2)
15.  
16. #Plotting horizontally in a single line:
17. PlotGrid(1, 3 , p2, p3, p4)
18.  
19. #Plotting in a grid form:
20. PlotGrid(2, 2, p1, p2 ,p3, p4)