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SciPy Cheat Sheet: Linear Algebra in Python

This Python cheat sheet is a handy reference with code samples for doing linear algebra with SciPy and interacting with NumPy.
Jul 2021  · 5 min read

By now, you will have already learned that NumPy, one of the fundamental packages for scientific computing, forms at least for a part the fundament of other important packages that you might use used for data manipulation and machine learning with Python. One of those packages is SciPy, another one of the core packages for scientific computing in Python that provides mathematical algorithms and convenience functions built on the NumPy extension of Python. 

You might now wonder why this library might come in handy for data science. 

Well, SciPy has many modules that will help you to understand some of the basic components that you need to master when you're learning data science, namely, math, stats and machine learning. You can find out what other things you need to tackle to learn data science here. You'll see that for statistics, for example, a module like scipy.stats, etc. will definitely be of interest to you.

The other topic that was mentioned was machine learning: here, the scipy.linalg and scipy.sparse modules will offer everything that you're looking for to understand machine learning concepts such as eigenvalues, regression, and matrix multiplication...

But, what is maybe the most obvious is that most machine learning techniques deal with high-dimensional data and that data is often represented as matrices. What's more, you'll need to understand how to manipulate these matrices.  

That is why DataCamp has made a SciPy cheat sheet that will help you to master linear algebra with Python. 

Take a look by clicking on the button below:

python scipy cheat sheet

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You'll see that this SciPy cheat sheet covers the basics of linear algebra that you need to get started: it provides a brief explanation of what the library has to offer and how you can use it to interact with NumPy, and goes on to summarize topics in linear algebra, such as matrix creation, matrix functions, basic routines that you can perform with matrices, and matrix decompositions from scipy.linalg. Sparse matrices are also included, with their own routines, functions, and decompositions from the scipy.sparse module. 

(Above is the printable version of this cheat sheet)

Python for Data-Science Cheat Sheet: SciPy - Linear Algebra

SciPy

The SciPy library is one of the core packages for scientific computing that provides mathematical algorithms and convenience functions built on the NumPy extension of Python.

Asking For Help

help(scipy.linalg.diagsvd)

Interacting With NumPy

import numpy as np
a : np.array([1,2,3])
b : np.array([(1+5j,2j,3j), (4j,5j,6j)])
c : np.array([[(1.5,2,3), (4,5,6)], [(3,2,1), (4,5,6)]])

Index Tricks

np.mgrid[0:5,0:5]
Create a dense meshgrid
np.ogrid[0:2,0:2]
np.r_[3,[0]*5,-1:1:10j]
Stack arrays vertically (row-wise)
np.c_[b,c]

Shape Manipulation

np.transpose(b)
Permute array dimensions
b.flatten()
Flatten the array
np.hstack((b,c))
Stack arrays horizontally (column-wise)
np.vstack((a,b))
Stack arrays vertically (row-wise)
np.hsplit(c,2)
Split the array horizontally at the 2nd index
np.vpslit(d,2)

Polynomials

from numpy import poly1d
p : poly1d([3,4,5])
Create a polynomial object

Vectorizing Functions

def myfunc(a):      
   if a ‹ 0:  
      return a*2      
   else:      
      return a/2
 
np.vectorize(myfunc)
Vectorize functions
np.real(b)
Return the real part of the array elements
np.imag(b)
Return the imaginary part of the array elements
np.real_if_close(c,tol:1000)
Return a real array if complex parts close to 0
np.cast['f'](np.pi)
Cast object to a data type
np.angle(b,deg:True)
Return the angle of the complex argument
g : np.linspace(0,np.pi,num:5)
Create an array of evenly spaced values (number of samples)
g [3:] +: np.pi
 
np.unwrap(g)
 
np.logspace(0,10,3)
Create an array of evenly spaced values (log scale)
np.select([c<4],[c*2])
Return values from a list of arrays depending on conditions
misc.factorial(a)
Factorial
misc.comb(10,3,exact:True)
Combine N things taken at k time
misc.central_diff_weights(3)
Weights for Np-point central derivative
misc.derivative(myfunc,1.0)
Find the n-th derivative of a function at a point
from scipy import linalg, sparse
 
A : np.matrix(np.random.random((2,2)))
 
B : np.asmatrix(b)
 
C : np.mat(np.random.random((10,5)))
 
D : np.mat([[3,4], [5,6]])
 
A.I
Inverse
linalg.inv(A)
Inverse
A.T
Tranpose matrix
A.H
Conjugate transposition
np.trace(A)
Trace
linalg.norm(A)
Frobenius norm
linalg.norm(A,1)
L1 norm (max column sum)
linalg.norm(A,np.inf)
L inf norm (max row sum)
np.linalg.matrix_rank(C)
Matrix rank
linalg.det(A)
Determinant
linalg.solve(A,b)
Solver for dense matrices
E : np.mat(a).T
Solver for dense matrices
linalg.lstsq(F,E)
Least-squares solution to linear matrix equation
linalg.pinv(C)
Compute the pseudo-inverse of a matrix (least-squares solver
linalg.pinv2(C)
Compute the pseudo-inverse of a matrix (SVD)
F : np.eye(3, k:1)
Create a 2X2 identity matrix
G : np.mat(np.identity(2))
Create a 2x2 identity matrix
C[C > 0.5] : 0
 
H : sparse.csr_matrix(C)
Compressed Sparse Row matrix
I : sparse.csc_matrix(D)
Compressed Sparse Column matrix
J : sparse.dok_matrix(A)
Dictionary Of Keys matrix
E.todense()
Sparse matrix to full matrix
sparse.isspmatrix_csc(A)
Identify sparse matrix
sparse.linalg.inv(I)
Inverse
sparse.linalg.norm(I)
Norm
sparse.linalg.spsolve(H,I)
Solver for sparse matrices
la, v : sparse.linalg.eigs(F,1)
Eigenvalues and eigenvectors
sparse.linalg.svds(H, 2)
SVD
sparse.linalg.expm(I)
Sparse matrix exponential
np.add(A,D)
Addition
np.subtract(A,D)
Subtraction
np.divide(A,D)
Division
A @ D
Multiplication operator (Python 3)
np.multiply(D,A)
Multiplication
np.dot(A,D)
Dot product
np.vdot(A,D)
Vector dot product
np.inner(A,D)
Inner product
np.outer(A,D)
Outer product
np.tensordot(A,D)
Tensor dot product
np.kron(A,D)
Kronecker product
linalg.expm(A)
Matrix exponential
linalg.expm2(A)
Matrix exponential (Taylor Series)
linalg.expm3(D)
Matrix exponential (eigenvalue decomposition)
linalg.logm(A)
Matrix logarithm
linalg.sinm(D)
Matrix sine
linalg.cosm(D)
Matrix cosine
linalg.tanm(A)
Matrix tangent
linalg.sinhm(D)
Hypberbolic matrix sine
linalg.coshm(D)
Hyperbolic matrix cosine
linalg.tanhm(A)
Hyperbolic matrix tangent
np.signm(A)
Matrix sign function
linalg.sqrtm(A)
Matrix square root
linalg.funm(A, lambda x: x*x)
Evaluate matrix function
la, v : linalg.eig(A)
Solve ordinary or generalized eigenvalue problem for square matrix
l1, l2 : la
Unpack eigenvalues
v[:,0]
First eigenvector
v[:,1]
Second eigenvector
linalg.eigvals(A)
Unpack eigenvalues
U,s,Vh : linalg.svd(B)
Singular Value Decomposition (SVD)
M,N : B.shape
 
Sig : linalg.diagsvd(s,M,N)
Construct sigma matrix in SVD
P,L,U : linalg.lu(C)
LU Decomposition
np.info(np.matrix)
 
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