# LinearSystemBelief¶

class probnum.linalg.solvers.beliefs.LinearSystemBelief(x=None, Ainv=None, A=None, b=None, hyperparams=None)

Bases: object

Belief about quantities of interest of a linear system.

Random variables $$(\mathsf{x}, \mathsf{A}, \mathsf{H}, \mathsf{b})$$ modelling the solution $$x$$, the system matrix $$A$$, its (pseudo-)inverse $$H=A^{-1}$$ and the right hand side $$b$$ of a linear system $$Ax=b$$, as well as any associated hyperparameters.

For instantiation either a belief about the solution or the inverse and right hand side must be provided. Note that if both are specified, their consistency is not checked and depending on the algorithm either may be used.

Parameters

Attributes Summary

 A Belief about the system matrix. Ainv Belief about the (pseudo-)inverse of the system matrix. b Belief about the right hand side. x Belief about the solution.

Methods Summary

 Hyperparameter of the linear system belief.

Attributes Documentation

A

Return type

RandomVariable

Ainv

Belief about the (pseudo-)inverse of the system matrix.

Return type
b

Belief about the right hand side.

Return type

RandomVariable

x

Methods Documentation

hyperparameter(key)[source]

Hyperparameter of the linear system belief.

Parameters

key (str) – Hyperparameter key.

Return type

RandomVariable