Assert that two values are equal

assert np.array_equal(a, b)

Norm of a vector

https://numpy.org/devdocs/reference/generated/numpy.linalg.norm.html

Use np.linalg.norm(v)

• Many different forms of norm possible
• Default norm is Frobenius norm (aka magnitude)
  1. Take absolute values of squares of all elements
  2. Sum it up
  3. Take the square root of the whole value

>>> a
array([1, 2, 3])

>>> np.linalg.norm(a)
np.float64(3.7416573867739413)
# (1+4+9)^½

Kronecker product

• aka tensor product.
• Use np.kron(a, b)
• Make copies of b at every location of a where value is 1. Kinda.

>>> i22 = np.identity(2)

>>> mul = np.array([[1, 1, 1, 0],
                [0, 0, 0, 1]])

>>> np.kron(i22, mul)

array([[1, 1, 1, 0,  0, 0, 0, 0],
       [0, 0, 0, 1,  0, 0, 0, 0],

       [0, 0, 0, 0,  1, 1, 1, 0],
       [0, 0, 0, 0,  0, 0, 0, 1]])

Jargon

• Rank of shape: Number of elements in shape
• C-order: ??

Axis parameter

https://stackoverflow.com/questions/48200911/very-basic-numpy-array-dimension-visualization

• nth axis => nth index
• 'order of indexing into the array'
• In a 2D matrix,
  • axis=0 => rows
  • axis=1 => column

Stacking

• np.vstack: stack two matrices one below the other
• np.hstack: stack two matrices side by side

>>> a = np.array([[1,0],[2,0],[3,0]])
>>> a
array([[1, 0],
       [2, 0],
       [3, 0]])

>>> np.hstack([a,a])
array([[1, 0, 1, 0],
       [2, 0, 2, 0],
       [3, 0, 3, 0]])

Matrix creation

>>> np.zeros(3)
array([0., 0., 0.])

>>> np.zeros(3).shape
(3,)

>>> np.zeros(3).reshape(1,3)
array([[0., 0., 0.]])

>>> np.zeros(3).reshape(1,3).shape
(1, 3)

###

>>> np.zeros((1,3))
array([[0., 0., 0.]])

>>> np.zeros((1,3)).shape
(1, 3)

>>> np.array([[0, 1], [0, 0]])
array([[0, 1],
       [0, 0]])

>>> np.full((2,2), 3)
array([[3, 3],
       [3, 3]])

>>> np.full((2,2), np.inf)
array([[inf, inf],
       [inf, inf]])

>>> np.full((3,2), [1,2])
array([[1, 2],
       [1, 2],
       [1, 2]])

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

Matrix multiplication

• Multipy vector with matrix: np.dot
• Concatenate two vectors: np.concatenate([v1, v2])
  • Arguments must be given as a list

Determinant of a matrix

Remember that determinant is not defined for non-square matrices.

>>> import numpy as np
>>> np.linalg.det(np.array([[1,2],
...                         [3,4]]))
...
-2.0000000000000004

https://numpy.org/doc/stable/reference/generated/numpy.linalg.det.html

Eigen values of a matrix

>>> np.linalg.eigvals(np.array([[1,2],
...                             [3,4]]))
...
array([-0.37228132,  5.37228132])

# Product of Eigen values is determinant
>>> np.prod(np.linalg.eigvals(np.array([[1,2],[3,4]])))
-1.9999999999999998

https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigvals.html

Reading from csv

• np.loadtxt: usable when there are no missing values
• np.genfromtxt: usable even when there are missing values
• https://numpy.org/doc/stable/user/how-to-io.html

Doubts

• np.resize vs np.pad
• np.broadcast_to

Misc

• Pacakges for type hints:
  • https://github.com/ramonhagenaars/nptyping
  • https://pypi.org/project/numpy-typing/
  • https://numpy.org/doc/stable/reference/typing.html

Theory

• Matrix addition is commutative, but multiplication isn't

Merge two Series to make a DataFrame

>>> pd.concat([s1, s2], axis=1)

>>> pd.concat([s1, s2], axis=1).columns
RangeIndex(start=0, stop=2, step=1)

Examples

# Read from a csv file
>>> df = pd.read_csv("name.csv")

# Columns
>>> df.columns
Index(['Site Type', 'Used', 'Fixed', 'Prohibited', 'Available', 'Util%'], dtype='object')

# Number of rows
>>> a.index
RangeIndex(start=0, stop=16, step=1)

Sparse matrix

https://docs.scipy.org/doc/scipy/reference/sparse.html

>>> import scipy
>>> import numpy as np
>>> X = scipy.sparse.csr_matrix(1./2.*np.array([[0.,1.],[1.,0.]]))

>>> X
<2x2 sparse matrix of type '<class 'numpy.float64'>'
        with 2 stored elements in Compressed Sparse Row format>

>>> print(X)
  (0, 1)        0.5
  (1, 0)        0.5

Curve fitting

Find an equation corresponding a function made from a set of data points.

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html

Graph attributes

• Adjacency matrix: nx.adjacency_matrix(G)
• Attribute matrix: nx.attr_matrix(G, <attr-name>)
  • Eg: nx.attr_matrix(G, "weight")

Add nodes

• Insert single node: G.add_node()
• Insert nodes from a list: G.add_nodesfrom()

Add edges

Adding edges implicitly adds nodes.

• Edges from/to on a node in undirected graphs: G.edges(<node>)

• Edges incident on a node in directed graphs: G.in_edges(<node>)

• Edges outgoing from a node in directed graphs: G.out_edges(<node>)

• Check if an edge exists: DiGraph.has_edge(n1, n2)

• Add edge with weight: G.add_edge(from, to, weight=<weight>)

• Node attributes: G[<node>] or G.nodes[<node>]

• Edge attributes: G[n1][n2]['<attr-name>'] = <attr-val>

• Get edge data: G.get_edge_data(n1, n2)

Finding

• Find all elements matching class: soup.find_all("tagname", class_="classname")
• Find by id: soup.find(id='content-container')

Children

• tag.contents: immediate sub-tags as a list
• tag.children: immediate sub-tags as an iterator
• tag.descendants: all sub-tags as generator