Financial Modelling in Python

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38 Financial Modelling in Python

4.5 LINEAR ALGEBRA

The Python NumPy package contains a module that covers most of what is required from

linear algebra from a financial engineering perspective. For the most part, this section provides

some examples of its use for problems common in financial engineering. This section just

touches on the capabilities of NumPy for linear algebra. The interested reader is referred to the

NumPy documentation for further detail. Readers with an interest in the development of linear

algebra routines in Python are encouraged to consult Jaan Kiusalaas’s Numerical Methods in

Engineering with Python [12].

4.5.1 Matrix Multiplication

The ordinary matrix product.

>>> from numpy import *

>>> from numpy.linalg import inv

>>> A = array([ [1, 3, 2], [1, 0, 0], [2, 1, 1]])

>>> M = matrix(A)

>>> print M*M

[[854]

[1 3 2]

[5 7 5]]

Note the use of the matrix construction function in the example above. It is this that gives the

interpretation of the operation as a matrix product. Multiplying two arrays, on the other hand,

gives the product element-wise, e.g.

>>> print A*A

[[194]

[1 0 0]

[4 1 1]]

Matrix multiplication can be performed on arrays by use of the dot function, as illustrated

below.

>>> print dot(A, A)

[[854]

[1 3 2]

[5 7 5]]

4.5.2 Matrix Inversion

Find the inverse of a square non-singular matrix.

>>> from numpy import *

>>> from ...