Basic Operations¶

The core TransitionMatrix object implements a typical (one period) transition matrix. It supports a variety of operations (more details are documented in the API section)

Initialize a matrix (from data, predefined matrices etc)
Validate a matrix
Attempt to fix a matrix
Compute generators, powers etc.
Print a matrix
Output to json/csv/xlsx formats
Output to html format

Simple Operation Examples¶

Note

The script examples/python/matrix_operations.py contains the below and plenty more simple single matrix examples

Initialize a matrix with values¶

There is a growing list of ways to initialize a transition matrix

Initialize a generic matrix of dimension n
Any list can be used for initialization (but not all shapes are valid transition matrices!)
Any numpy array can be used for initialization (but not all are valid transition matrices!)
Values can be loaded from json or csv files
The transitionMatrix.creditratings.predefined module includes a number of predefined matrices

A = tm.TransitionMatrix(values=[[0.6, 0.2, 0.2], [0.2, 0.6, 0.2], [0.2, 0.2, 0.6]])
print(A)
A.print_matrix(format_type='Standard', accuracy=2)

[[0.6 0.2 0.2]
 [0.2 0.6 0.2]
 [0.2 0.2 0.6]]

0.60 0.20 0.20
0.20 0.60 0.20
0.20 0.20 0.60

A.print_matrix(format_type='Standard', accuracy=2)

60.0% 20.0% 20.0%
20.0% 60.0% 20.0%
20.0% 20.0% 60.0%

Both the intrinsic print function and the specific print_matrix will print you the matrix, but the print_matrix method clearly aims to present the values in a more legible formats.

General Matrix Algebra¶

Note

All standard numerical matrix operations are available as per the numpy API.

Some example operations that leverage the underlying numpy API:

E = tm.TransitionMatrix(values=[[0.75, 0.25], [0.0, 1.0]])
print(E.validate())
# ATTRIBUTES
# Getting matrix info (dimensions, shape)
print(E.ndim)
print(E.shape)
# Obtain the matrix transpose
print(E.T)
# Obtain the matrix inverse
print(E.I)
# Summation methods:
# - along columns
print(E.sum(0))
# - along rows
print(E.sum(1))
# Multiplying all elements of a matrix by a scalar
print(0.01 * A)
# Transition Matrix algebra is very intuitive
print(A * A)
print(A ** 2)
print(A ** 10)

Validating, Fixing and Characterizing a matrix¶

Validate a Matrix¶

The validate() method of the object checks for required properties of a valid transition matrix:

check squareness

check that all values are probabilities (between 0 and 1)

check that all rows sum to one

C = tm.TransitionMatrix(values=[1.0, 3.0])
print(C.validate())

[('Matrix Dimensions Differ: ', (1, 2))]

Characterise a Matrix¶

The characterise() method attempts to characterise a matrix

diagonal dominance