tomotok.inversions.solvers package

2.1.1. tomotok.inversions.solvers package#

class tomotok.inversions.solvers.CholeskySolver(check_finite: bool = False)#

Bases: Solver

Scipy based engine using Cholesky decomposition to solve linear systems.

Implementation based on dense matrices, sparse ones are converted to dense.

Methods

solve(a, b)

Sparse matrices are converted to dense arrays before decomposition.
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray | sparray#

Sparse matrices are converted to dense arrays before decomposition.

class tomotok.inversions.solvers.NNLSSolver#

Bases: Solver

Scipy based engine using non-negative least squares to solve linear systems.

Methods

solve(a, b)

Sparse matrices are converted to dense arrays before decomposition.
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray | sparray#

Sparse matrices are converted to dense arrays before decomposition.

class tomotok.inversions.solvers.Solver(sparse: bool = False)#

Bases: object

Base class for solving a system of linear equations.

Methods

__call__(a, b)

Call self as a function.

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ArrayLike | sparray, b: ArrayLike | sparray) → ndarray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

__call__(a: ArrayLike | sparray, b: ArrayLike | sparray) → ndarray#

Call self as a function.

2.1.1.1. Submodules#

2.1.1.2. tomotok.inversions.solvers.base module#

class tomotok.inversions.solvers.base.Solver(sparse: bool = False)#

Bases: object

Base class for solving a system of linear equations.

Methods

__call__(a, b)

Call self as a function.

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ArrayLike | sparray, b: ArrayLike | sparray) → ndarray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

__call__(a: ArrayLike | sparray, b: ArrayLike | sparray) → ndarray#

Call self as a function.

2.1.1.3. tomotok.inversions.solvers.cvxpy module#

class tomotok.inversions.solvers.cvxpy.CvxpyNNLS(verbose: bool = False, cvxpy_solver=cvxpy.CLARABEL)#

Bases: Solver

Implements non-negative least squares solver using cvxpy.

The cvxpy solver accepts sparse matrices. The solver can be configured to use different cvxpy solvers and verbosity levels.

Attributes:
verbose

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
property verbose#
solve(a: ndarray | csc_array, b: ndarray)#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

2.1.1.4. tomotok.inversions.solvers.jax module#

class tomotok.inversions.solvers.jax.JaxCholesky(enable_x64: bool = True)#

Bases: Solver

Uses JAX’s Cholesky decomposition for solving linear systems.

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | spmatrix | sparray, b: ndarray | spmatrix | sparray) → ndarray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

class tomotok.inversions.solvers.jax.JaxSolver(sparse: bool = False)#

Bases: Solver

Uses JAX’s linear solver for solving linear systems.

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | spmatrix | sparray, b: ndarray | spmatrix | sparray) → ndarray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

class tomotok.inversions.solvers.jax.JaxNNLS(parametrization: str = 'quadratic', init_values: float = 1.0)#

Bases: Solver

Non-negative least squares solver using JAX.

The solver supports different parametrizations for enforcing non-negativity, including quadratic, exponential and softplus functions.

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | sparray, b: ndarray | sparray)#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

2.1.1.5. tomotok.inversions.solvers.optax module#

class tomotok.inversions.solvers.optax.OptaxNNLS(iterations: int = 5000)#

Bases: Solver

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | sparray, b: ndarray | sparray)#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

class tomotok.inversions.solvers.optax.OptaxNN(max_iter_num: int = 10000, learning_rate: float = 0.1, tolerance: float = 1e-08)#

Bases: Solver

Dense matrices only, requires reasonable estimate on learning rate and parameters.

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

step
step(x, opt_state)#
solve(a: ndarray | sparray, b: ndarray | sparray)#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

2.1.1.6. tomotok.inversions.solvers.scipy module#

class tomotok.inversions.solvers.scipy.CholeskySolver(check_finite: bool = False)#

Bases: Solver

Scipy based engine using Cholesky decomposition to solve linear systems.

Implementation based on dense matrices, sparse ones are converted to dense.

Methods

solve(a, b)

Sparse matrices are converted to dense arrays before decomposition.
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray | sparray#

Sparse matrices are converted to dense arrays before decomposition.

class tomotok.inversions.solvers.scipy.NNLSSolver#

Bases: Solver

Scipy based engine using non-negative least squares to solve linear systems.

Methods

solve(a, b)

Sparse matrices are converted to dense arrays before decomposition.
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray | sparray#

Sparse matrices are converted to dense arrays before decomposition.

class tomotok.inversions.solvers.scipy.LSQSolver(bounds: tuple[float, float] | None = (0, inf))#

Bases: Solver

Scipy based engine using bounded least squares to solve linear systems.

This engine works with sparse matrices, converting dense matrices to sparse format.

It uses lsa_linear from scipy.optimize to solve the problem with bounds. The default bounds are set to (0, inf) to ensure non-negativity of the solution.

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray | sparray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.

2.1.1.7. tomotok.inversions.solvers.sksparse module#

class tomotok.inversions.solvers.sksparse.SksparseCholesky(sparse: bool = False)#

Bases: Solver

Methods

solve(a, b)

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).
solve(a: ndarray | sparray, b: ndarray | sparray) → ndarray#

Solves the linear system \(\mathbf{Ax}=\mathbf{b}\).

Parameters:
aarray_like or sparse array

System of equations matrix to be solved

barray_like

right hand side vector or matrix (in case of multiple time slices)

Returns:
numpy.ndarray

The solution of the linear system.