pymoto.solvers.SolverDiagonal

class pymoto.solvers.SolverDiagonal(A=None)

Solver for diagonal matrices

__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])	Solve using the diagonal only, by \(x_i = b_i / A_{ii}\)
update(A)	Extracts the diagonal of the matrix

Attributes

defined

update(A)

Extracts the diagonal of the matrix

solve(rhs, x0=None, trans='N')

Solve using the diagonal only, by \(x_i = b_i / A_{ii}\)

The right-hand-side \(\mathbf{b}\) can be of size (N) or (N, K), where N is the size of matrix \(\mathbf{A}\) and K is the number of right-hand sides.

defined = True

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