pymoto.solvers.LinearSolver

class pymoto.solvers.LinearSolver(A=None)

Base class of all linear solvers

defined

Flag if the solver is able to run, e.g. false if some dependent library is not available

__init__(A=None)

Initialize the solver

Parameters:: A (matrix, optional) – Optionally provide a matrix, which is used in :method:`update` right away.

Methods

`__init__`([A])	Initialize the solver
`residual`(A, x, b[, trans])	Calculates the (relative) residual of the linear system of equations
`solve`(rhs[, x0, trans])	Solves the linear system of equations \(\mathbf{A} \mathbf{x} = \mathbf{b}\)
`update`(A)	Updates with a new matrix of the same structure

Attributes

update(A)

Updates with a new matrix of the same structure

solve(rhs, x0=None, trans='N')

Solves the linear system of equations \(\mathbf{A} \mathbf{x} = \mathbf{b}\)

Parameters:

rhs – Right hand side \(\mathbf{b}\) of shape (N) or (N, K) for multiple right-hand-sides
x0 (optional) – Initial guess for the solution
trans (optional) – Option to transpose matrix ‘N’: A @ x == rhs (default) Normal matrix ‘T’: A^T @ x == rhs Transposed matrix ‘H’: A^H @ x == rhs Hermitian transposed matrix (conjugate transposed)

Returns:

Solution vector \(\mathbf{x}\) of same shape as \(\mathbf{b}\)

static residual(A, x, b, trans='N')

Calculates the (relative) residual of the linear system of equations

The residual is calculated as \(r = \frac{\left| \mathbf{A} \mathbf{x} - \mathbf{b} \right|}{\left| \mathbf{b} \right|}\)

Parameters:

A – The matrix
x – Solution vector
b – Right-hand side
trans (optional) – Matrix tranformation (N is normal, T is transposed, H is hermitian transposed)

Returns:

Residual value