linear_algebra.rst

Linear Algebra

This module provides support for calculations using arrays containing uncertain numbers.

The shorter name la has been defined as an alias for linear_algebra, to resolve the names of objects defined in this module.

Arrays of Uncertain Numbers

.UncertainArray is a convenient container of uncertain numbers. The preferred way to create arrays is the function ~.linear_algebra.uarray.

An array can contain a mixture of ~.lib.UncertainReal, ~.lib.UncertainComplex and Python numbers (int, float and complex).

The usual mathematical operations can be applied to an array. For instance, if A and B have the same size, they can be added A + B, subtracted A - B, etc; or a function like sqrt(A) can be applied. This vectorisation provides a succinct notation for repetitive operations but it does not offer a significant speed advantage over Python iteration.

Note

To evaluate the product of two-dimensional arrays representing matrices, the function ~linear_algebra.matmul should be used (for Python 3.5 and above the built-in binary operator @ is an alternative). For example:

>>> a = la.uarray([[1.1,.5],[ureal(3,1),.5]])
>>> b = la.uarray([[5.2,ucomplex(4,1)],[.1,.1+3j]])
>>> la.matmul(a,b)
uarray([[5.7700000000000005,
         ucomplex((4.45+1.5j), u=[1.1,1.1], r=0.0, df=inf)],
        [ureal(15.650000000000002,5.2,inf),
         ucomplex((12.05+1.5j), u=[5.0,3.0], r=0.0, df=inf)]])

linear_algebra

uncertain_array.UncertainArray