DATA SCIENCE TOOL SET

NUMPY & SCIPY

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Toolsets for Python

NumPy SciPy

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Prepared from:https://docs.scipy.org/doc/numpy/user/quickstart.html

NumPy’s main object is the homogeneous multidimensionalarray.

It is a table of elements (usually numbers), all of the sametype, indexed by a tuple of positive integers.

In NumPy dimensions are called axes.

NumPy’s array class is called ndarray.

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BASICS

ndarray.ndim ndarray.shape ndarray.size ndarray.dtype ndarray.itemsize ndarray.data

import numpy as npndarray = np.arange(15).reshape(3, 5)ndarray

print (ndarray.ndim)print (ndarray.shape)print (ndarray.size)print (ndarray.dtype)print (ndarray.itemsize)print (ndarray.data)

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ARRAY CREATION

import numpy as npa = np.array([2,3,4])print (a)b = np.array([(1.5,2,3), (4,5,6)])print (b)c = np.array( [ [1,2], [3,4] ], dtype=complex )print(c)

import numpy as npnp.zeros( (3,4) )np.ones( (2,3,4), dtype=np.int16 ) np.empty( (2,3) ) b = np.random.random((2,3))

np.arange( 10, 30, 5 )

np.arange( 0, 2, 0.3 )

np.linspace( 0, 2, 9)

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ARRAY CREATION

import numpy as npndarray = np.arange(15).reshape(3, 5)x=np.zeros_like(ndarray)x

np.ones_like

np.empty_like

np.random.rand(3,2): Random values in a given shapefrom a uniform distribution over [0, 1)

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BASICS OPERATIONS

Unary operations a.sum() a.min() a.max()

Binary operations A * B # elementwise product A @ B # matrix product A.dot(B) # another matrix product

A = np.array( [[1,1],[0,1]] )B = np.array( [[2,0],[3,4]] )A*BA@B

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BASICS OPERATIONS

Axis parameter b.sum(axis=0) # sum of each column b.min(axis=1) # min of each row b.cumsum(axis=1) # cumulative sum along each row

b = np.arange(12).reshape(3,4)b

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UNIVERSAL FUNCTIONS

add average round sort sqrt ceil exp floor

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UNIVERSAL FUNCTIONS

max: Return the largest item in an iterable orthe largest of two or more arguments.

maximum: Element-wise maximum of arrayelements.

Min

Minimum

nonzero: Return the indices of the elementsthat are non-zero.

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UNIVERSAL FUNCTIONS

Mean

median

corrcoef: Return Pearson product-moment correlation coefficients.

cov: Estimate a covariance matrix, given data and weights.

std: Compute the standard deviation along the specified axis.

var: Compute the variance along the specified axis.

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UNIVERSAL FUNCTIONS

all: Test whether all array elements along a given axis evaluate to True. any argmax: Returns the indices of the maximum values along an axis. argmin argsort sum: Sum of array elements over a given axis. trace: Return the sum along diagonals of the array. transpose where: Return elements chosen from x or y depending on condition. re: Regular expression operations

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INDEXING, SLICING AND ITERATING

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INDEXING, SLICING AND ITERATING

def f(x,y): return 10*x+y

b = np.fromfunction(f,(5,4),dtype=int)b

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INDEXING, SLICING AND ITERATING

List to Array

from numpy import array# list of datadata = [11, 22, 33, 44, 55]# array of datadata = array(data)print(data)print(type(data))

a = np.arange(10, 1, -2)

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

a[np.array([1, 3, -2])]

a[slice(1,4,2)]

a[1:4 :2]

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INDEXING, SLICING AND ITERATING

x[1,2,...] is equivalent to x[1,2,:,:,:], x[...,3] to x[:,:,:,:,3] x[4,...,5,:] to x[4,:,:,5,:]

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

for row in a:print(row)

for element in a.flat:print(element)

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SHAPE MANIPULATION

reshape resize

a = np.floor(10*np.random.random((3,2)))a

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STACKING

vstack hstack

a = np.floor(10*np.random.random((2,2)))a

b = np.floor(10*np.random.random((2,2)))b

np.vstack((a,b))

np.hstack((a,b))

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COPIES AND VIEWS

No Copy at All: Simple assignments make no copy of array objects or of their data.

View or Shallow Copy: The view method creates a new array object that looks at the same data.

Deep Copy: The copy method makes a complete copy of the array and its data.

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COPIES AND VIEWSNo Copy at All

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COPIES AND VIEWSView or Shallow Copy

a = np.arange(12).reshape(3,4)c = a.view()c is a

c.base is a # c is a view of the data owned by a

c.shape = 2,6 # a's shape doesn't change

a.shape

c[0,4] = 1234 # a's data changes

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COPIES AND VIEWSDeep Copy

a = np.arange(12).reshape(3,4)d = a.copy() # a new array object with new data is createdd is a

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Toolsets for Python

NumPy SciPy

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INTRODUCTION

Prepared From:https://docs.scipy.org/doc/scipy/reference/tutorial/index.html

SciPy is a collection of mathematical algorithms andconvenience functions built on the Numpy extension ofPython.

SciPy is organized into subpackages covering differentscientific computing domains.

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SCIPY ORGANIZATION

Sub-package Description

cluster Clustering algorithms

constants Physical and mathematical constants

fftpack Fast Fourier Transform routines

integrate Integration and ordinary differential equation solvers

interpolate Interpolation and smoothing splines

io Input and Output

linalg Linear algebra

ndimage N-dimensional image processing

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SCIPY ORGANIZATION

Sub-package Description

odr Orthogonal distance regression

optimize Optimization and root-finding routines

signal Signal processing

sparse Sparse matrices and associated routines

spatial Spatial data structures and algorithms

special Special functions

stats Statistical distributions and functions

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FUNCTIONS

Scipy sub-packages need to be imported separately.

The top level of scipy also contains functions from numpy and numpy.lib.scimath.

from scipy import linalg, optimize

import numpy as npnp.some_function()

from scipy import some_modulesome_module.some_function()

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BASIC FUNCTIONS

np.cast['f'](np.pi) np.r_ np.c_ np.select

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POLYNOMIALS

poly1d class Accepts coefficients or polynomial roots to initialize a

polynomial Operations

Algebraic expressions Integration Differentiation Evaluaation

from numpy import poly1dp = poly1d([3,4,5])print(p)

print(p*p)

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LINEAR ALGEBRA

scipy.linalg contains all the functions in numpy.linalg. plus some other advanced functions.

very fast

import numpy as npfrom scipy import linalgA = np.array([[1,2],[3,4]])A

linalg.inv(A)

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LINEAR ALGEBRA

Finding Inverse Solving linear system

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LINEAR ALGEBRA

Solving linear system

import numpy as npfrom scipy import linalgA = np.array([[1, 3,5], [2,5,1],[2, 3, 8]])A

b = np.array([[10], [8],[3]])b

linalg.inv(A).dot(b) #Slow

np.linalg.solve(A, b)

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LINEAR ALGEBRA

Finding Determinant: linalg.det Matrix Exponential: linalg.expm Matrix Logarithm: linalg.logm Trigonometric functions: linalg.sinm, linalg.cosm, and linalg.tanm Hyperbolic trigonometric functions: linalg.sinhm, linalg.coshm , and linalg.tanhm

Special matrices: block diagonal scipy.linalg.block_diag circulant scipy.linalg.circulant Pascal scipy.linalg.pascal …

from scipy.linalg import pascalpascal(4)

pascal(4, kind='lower')

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EXPLORE PACKAGES

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15 17 15SCIPY.STATS

SCIPY.NDIMAGE

SCIPY.SPATIAL

SCIPY.SIGNAL

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