Advanced Python on Abel - Universitetet i oslo · 4/4/16 3 NumPy, SciPy, matplotlib Centrally...

Advanced Python on Abel

Dmytro KarpenkoResearch Infrastructure Services groupDepartment for Scientific ComputingUSIT, UiO

4/4/16 2

Support for large, multi-dimensional arrays and matrices, and a large library of high-level mathematical functions to operate on these arrays

Support for scientific computing: optimization, linear algebra, integration, interpolation, statistics, FFT, signal and image processing, etc. Based heavily on NumPy

Plotting library, designed especially for use with NumPy, with MatLab-like interface

4/4/16 3

NumPy, SciPy, matplotlib

● Centrally managed on Abel

● Tight mutual integration

● Powerful set of tools for data analysis and visualization

● Usually available on every scientific resource

● Easy to learn and use

● The 3 pieces used together can replace MATLAB.

4/4/16 4

Getting started on Abel● For interactive use:

However, you'd rather use matplotlib as

>>> import matplotlib.pyplot as plt>>> import matplotlib.pyplot as plt

-bash-4.1$ module load python2

-bash-4.1$ python

Python 2.7.10 (default, Jul 1 2015, 11:02:23)

[GCC Intel(R) C++ gcc 4.4 mode] on linux2

Type "help", "copyright", "credits" or "license" for more information.

>>> import numpy

>>> import scipy

>>> import matplotlib

-bash-4.1$ module load python2

-bash-4.1$ python

Python 2.7.10 (default, Jul 1 2015, 11:02:23)

[GCC Intel(R) C++ gcc 4.4 mode] on linux2

Type "help", "copyright", "credits" or "license" for more information.

>>> import numpy

>>> import scipy

>>> import matplotlib

4/4/16 5

Numpy

http://docs.scipy.org/doc/numpy/

https://docs.scipy.org/doc/numpy/reference/routines.html

Routines index

General documentation

SciPYhttp://docs.scipy.org/doc/scipy/reference/

Matplotlibhttp://matplotlib.org/1.5.1/users/index.html

4/4/16 6

Numpy arrays>>> import numpy as np

>>> cvalues = [25.3, 24.8, 26.9, 23.9]

>>> C = np.array(cvalues)

>>> print(C)

[ 25.3 24.8 26.9 23.9]

>>> print(C * 9 / 5 + 32)

[ 77.54 76.64 80.42 75.02]

# Indexing and slicing similar to python lists

>>> print C[0]

>>> print C[1:3]

>>> import numpy as np

>>> cvalues = [25.3, 24.8, 26.9, 23.9]

>>> C = np.array(cvalues)

>>> print(C)

[ 25.3 24.8 26.9 23.9]

>>> print(C * 9 / 5 + 32)

[ 77.54 76.64 80.42 75.02]

# Indexing and slicing similar to python lists

>>> print C[0]

>>> print C[1:3]

● More straightforward syntax than with lists

● Considerably faster

4/4/16 7

Numpy arrays: advanced addressing and slicing

>>> A = np.array([ [3.4, 8.7, 9.9], [1.1, -7.8, -0.7], [4.1, 12.3, 4.8] ])

>>> print(A[1, 0])

1.1

>>> A = np.array([

... [11,12,13,14,15],

... [21,22,23,24,25],

... [31,32,33,34,35],

... [41,42,43,44,45],

... [51,52,53,54,55] ] )

>>> print(A[:3,2:])

[[13 14 15]

[23 24 25]

[33 34 35]]

>>> A = np.array([ [3.4, 8.7, 9.9], [1.1, -7.8, -0.7], [4.1, 12.3, 4.8] ])

>>> print(A[1, 0])

1.1

>>> A = np.array([

... [11,12,13,14,15],

... [21,22,23,24,25],

... [31,32,33,34,35],

... [41,42,43,44,45],

... [51,52,53,54,55] ] )

>>> print(A[:3,2:])

[[13 14 15]

[23 24 25]

[33 34 35]]

4/4/16 8

Numpy arrays: advanced slicing (using step)

>>> A = np.array([ [ 0 1 2 3 4 5 6]

... [ 7 8 9 10 11 12 13]

... [14 15 16 17 18 19 20]

... [21 22 23 24 25 26 27] ] )

>>> print (A[::2, ::3])

[[ 0 3 6]

[14 17 20]]

>>> print(A[::2, ::3])

[[ 0 3 6]

[14 17 20]]

>>> A = np.array([ [ 0 1 2 3 4 5 6]

... [ 7 8 9 10 11 12 13]

... [14 15 16 17 18 19 20]

... [21 22 23 24 25 26 27] ] )

>>> print (A[::2, ::3])

[[ 0 3 6]

[14 17 20]]

>>> print(A[::2, ::3])

[[ 0 3 6]

[14 17 20]]

[start:stop:step]

4/4/16 9

Numpy arrays: evenly spaced values>>> a = np.arange(1, 10)

>>> print(a)

[1 2 3 4 5 6 7 8 9]

>>> x = np.arange(0.5, 10.4, 0.8)

>>> print(x)

[ 0.5 1.3 2.1 2.9 3.7 4.5 5.3 6.1 6.9 7.7 8.5 9.3 10.1]

>>> print(np.linspace(1, 10))

[ 1. 1.18367347 1.36734694 1.55102041 1.73469388 1.91836735 2.10204082 2.28571429 2.46938776

2.65306122 2.83673469 3.02040816 3.20408163 3.3877551 3.57142857 3.75510204 3.93877551 4.12244898

4.30612245 4.48979592 4.67346939 4.85714286 5.04081633 5.2244898 5.40816327 5.59183673 5.7755102

5.95918367 6.14285714 6.32653061 6.51020408 6.69387755 6.87755102 7.06122449 7.24489796 7.42857143

7.6122449 7.79591837 7.97959184 8.16326531 8.34693878 8.53061224 8.71428571 8.89795918 9.08163265

9.26530612 9.44897959 9.63265306 9.81632653 10. ]

>>> a = np.arange(1, 10)

>>> print(a)

[1 2 3 4 5 6 7 8 9]

>>> x = np.arange(0.5, 10.4, 0.8)

>>> print(x)

[ 0.5 1.3 2.1 2.9 3.7 4.5 5.3 6.1 6.9 7.7 8.5 9.3 10.1]

>>> print(np.linspace(1, 10))

[ 1. 1.18367347 1.36734694 1.55102041 1.73469388 1.91836735 2.10204082 2.28571429 2.46938776

2.65306122 2.83673469 3.02040816 3.20408163 3.3877551 3.57142857 3.75510204 3.93877551 4.12244898

4.30612245 4.48979592 4.67346939 4.85714286 5.04081633 5.2244898 5.40816327 5.59183673 5.7755102

5.95918367 6.14285714 6.32653061 6.51020408 6.69387755 6.87755102 7.06122449 7.24489796 7.42857143

7.6122449 7.79591837 7.97959184 8.16326531 8.34693878 8.53061224 8.71428571 8.89795918 9.08163265

9.26530612 9.44897959 9.63265306 9.81632653 10. ]

4/4/16 10

Numpy arrays: reshaping>>> x = np.array([ [67, 63, 87], [77, 69, 59], [85, 87, 99], [79, 72, 71], [63, 89, 93], [68, 92, 78]])

>>> print(np.shape(x))

(6, 3)

>>> x.shape = (3, 6)

>>> print(x)

[[67 63 87 77 69 59]

[85 87 99 79 72 71]

[63 89 93 68 92 78]]

>>> X = np.arange(28).reshape(4,7)

>>> print(X)

[[ 0 1 2 3 4 5 6]

[ 7 8 9 10 11 12 13]

[14 15 16 17 18 19 20]

[21 22 23 24 25 26 27]]

>>> x = np.array([ [67, 63, 87], [77, 69, 59], [85, 87, 99], [79, 72, 71], [63, 89, 93], [68, 92, 78]])

>>> print(np.shape(x))

(6, 3)

>>> x.shape = (3, 6)

>>> print(x)

[[67 63 87 77 69 59]

[85 87 99 79 72 71]

[63 89 93 68 92 78]]

>>> X = np.arange(28).reshape(4,7)

>>> print(X)

[[ 0 1 2 3 4 5 6]

[ 7 8 9 10 11 12 13]

[14 15 16 17 18 19 20]

[21 22 23 24 25 26 27]]

4/4/16 11

Scipy statistics>>> from scipy import stats

# Probability density function

>>> stats.norm.pdf(0.5)

0.35206532676429952

# Cumulative distribution function

>>> stats.norm.cdf(0.5)

0.69146246127401312

# Typical statistics functions

>>> norm.mean()

0.0

>>> norm.median()

0.0

>>> norm.std()

1.0

>>> from scipy import stats

# Probability density function

>>> stats.norm.pdf(0.5)

0.35206532676429952

# Cumulative distribution function

>>> stats.norm.cdf(0.5)

0.69146246127401312

# Typical statistics functions

>>> norm.mean()

0.0

>>> norm.median()

0.0

>>> norm.std()

1.0

4/4/16 12

Scipy statistics>>> a = np.array([1,2,3,4])

>>> b = np.array([10,9,8,7])

# Pearson correlation coefficient

>>> stats.pearsonr(a, b)

(-1.0, 0.0)

# Measure Kolmogorov-Smirnov distance between two samples

>>> stats.ks_2samp(a,b)

Ks_2sampResult(statistic=1.0, pvalue=0.011065637015803861)

# Maximum Likelihood Estimation

>>> a=np.array([0.1, 0.2, 0.3, 0.4, 0.5])

>>> stat.norm.fit(a)

(0.29999999999999999, 0.1414213562373095)

>>> a = np.array([1,2,3,4])

>>> b = np.array([10,9,8,7])

# Pearson correlation coefficient

>>> stats.pearsonr(a, b)

(-1.0, 0.0)

# Measure Kolmogorov-Smirnov distance between two samples

>>> stats.ks_2samp(a,b)

Ks_2sampResult(statistic=1.0, pvalue=0.011065637015803861)

# Maximum Likelihood Estimation

>>> a=np.array([0.1, 0.2, 0.3, 0.4, 0.5])

>>> stat.norm.fit(a)

(0.29999999999999999, 0.1414213562373095)

4/4/16 13

matplotlibimport matplotlib.pyplot as plt

plt.plot([1,2,3,4])

plt.ylabel('some numbers')

plt.show()

import matplotlib.pyplot as plt

plt.plot([1,2,3,4])

plt.ylabel('some numbers')

plt.show()

4/4/16 14

matplotlibimport matplotlib.pyplot as plt

plt.plot([1,2,3,4], [1,4,9,16])

plt.show()

import matplotlib.pyplot as plt

plt.plot([1,2,3,4], [1,4,9,16])

plt.show()

4/4/16 15

matplotlibimport matplotlib.pyplot as plt

plt.plot([1,2,3,4], [1,4,9,16], 'ro')

plt.axis([0, 6, 0, 20])

plt.show()

import matplotlib.pyplot as plt

plt.plot([1,2,3,4], [1,4,9,16], 'ro')

plt.axis([0, 6, 0, 20])

plt.show()

4/4/16 16

matplotlibimport numpy as np

import matplotlib.pyplot as plt

t = np.arange(0., 5., 0.2)

plt.plot(t, t, 'r--', t, t**2, 'bs', t, t**3, 'g^')

plt.show()

import numpy as np

import matplotlib.pyplot as plt

t = np.arange(0., 5., 0.2)

plt.plot(t, t, 'r--', t, t**2, 'bs', t, t**3, 'g^')

plt.show()

4/4/16 17

matplotlibimport numpy as np

import matplotlib.pyplot as plt

mu, sigma = 100, 15

x = mu + sigma * np.random.randn(10000)

n, bins, patches = plt.hist(x, 50, normed=1, facecolor='g', alpha=0.75)

plt.xlabel('Smarts')

plt.ylabel('Probability')

plt.title('Histogram of IQ')

plt.text(60, .025, r'$\mu=100,\ \sigma=15$')

plt.axis([40, 160, 0, 0.03])

plt.grid(True)

plt.show()

import numpy as np

import matplotlib.pyplot as plt

mu, sigma = 100, 15

x = mu + sigma * np.random.randn(10000)

n, bins, patches = plt.hist(x, 50, normed=1, facecolor='g', alpha=0.75)

plt.xlabel('Smarts')

plt.ylabel('Probability')

plt.title('Histogram of IQ')

plt.text(60, .025, r'$\mu=100,\ \sigma=15$')

plt.axis([40, 160, 0, 0.03])

plt.grid(True)

plt.show()

4/4/16 18

matplotlibplt.scatter([x[0] for x in alldata],[x[1] for x in alldata],s=5,marker='+',c='b')

plt.text(200000,6000,"Pearson coef = %.3f" % stat.pearsonr([x[0] for x in alldata],[x[1] for x in alldata])[0])

plt.show()

plt.scatter([x[0] for x in alldata],[x[1] for x in alldata],s=5,marker='+',c='b')

plt.text(200000,6000,"Pearson coef = %.3f" % stat.pearsonr([x[0] for x in alldata],[x[1] for x in alldata])[0])

plt.show()

4/4/16 19

matplotlib

● For non-interactive use:

import matplotlib as mpl

mpl.use('Agg')

import matplotlib.pyplot as plt

import matplotlib as mpl

mpl.use('Agg')

import matplotlib.pyplot as plt

now use as usual......but don't forget to save the picture instead of showing

x = np.arange(0, 3 * np.pi, 0.1)

y = np.sin(x)

plt.plot(x, y)

plt.savefig("plt_test.png")

x = np.arange(0, 3 * np.pi, 0.1)

y = np.sin(x)

plt.plot(x, y)

plt.savefig("plt_test.png")

4/4/16 20

Exampleimport numpy as np

from scipy.stats import norm

import matplotlib

matplotlib.use('Agg')

import matplotlib.pyplot as plt

a = np.array([1, 2, 3]) # Create a rank 1 array

print type(a) # Prints "<type 'numpy.ndarray'>"

print a.shape # Prints "(3,)"

print a[0], a[1], a[2] # Prints "1 2 3"

a[0] = 5 # Change an element of the array

print a

print "-------------"

print norm.cdf(0)

…............................

import numpy as np

from scipy.stats import norm

import matplotlib

matplotlib.use('Agg')

import matplotlib.pyplot as plt

a = np.array([1, 2, 3]) # Create a rank 1 array

print type(a) # Prints "<type 'numpy.ndarray'>"

print a.shape # Prints "(3,)"

print a[0], a[1], a[2] # Prints "1 2 3"

a[0] = 5 # Change an element of the array

print a

print "-------------"

print norm.cdf(0)

…............................

…......................

print "-----------------"

x = np.arange(0, 3 * np.pi, 0.1)

y = np.sin(x)

# Plot the points using matplotlib

plt.plot(x, y)

plt.savefig("plt_test.png")

print "\nDone"

…......................

print "-----------------"

x = np.arange(0, 3 * np.pi, 0.1)

y = np.sin(x)

# Plot the points using matplotlib

plt.plot(x, y)

plt.savefig("plt_test.png")

print "\nDone"

4/4/16 21

Example#!/bin/bash

#SBATCH --job-name=advanced_python_test

#SBATCH --account=uio

#SBATCH --time=00:03:00

#SBATCH --mem-per-cpu=4G

#SBATCH --mail-type=ALL

## Set up job environment:

source /cluster/bin/jobsetup

module purge # clear any inherited modules

module load python2

set -o errexit # exit on errors

## Copy input files to the work directory:

cp -rf adv_python_test.py $SCRATCH

…...............................................

#!/bin/bash

#SBATCH --job-name=advanced_python_test

#SBATCH --account=uio

#SBATCH --time=00:03:00

#SBATCH --mem-per-cpu=4G

#SBATCH --mail-type=ALL

## Set up job environment:

source /cluster/bin/jobsetup

module purge # clear any inherited modules

module load python2

set -o errexit # exit on errors

## Copy input files to the work directory:

cp -rf adv_python_test.py $SCRATCH

…...............................................

…......................................

## Do some work:

cd $SCRATCH

python pyth.py

cp plt_test.png $SUBMITDIR

…......................................

## Do some work:

cd $SCRATCH

python pyth.py

cp plt_test.png $SUBMITDIR