pymor.bindings.scipy

Module Contents

class pymor.bindings.scipy.ScipyBicgStabSolver(check_finite=None, tol=1e-15, maxiter=None)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

class pymor.bindings.scipy.ScipyBicgStabSpILUSolver(check_finite=None, tol=1e-15, maxiter=None, spilu_drop_tol=0.0001, spilu_fill_factor=10, spilu_drop_rule=None, spilu_permc_spec='COLAMD')[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

class pymor.bindings.scipy.ScipyLGMRESSolver(check_finite=None, tol=1e-05, maxiter=1000, inner_m=39, outer_k=3)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

class pymor.bindings.scipy.ScipyLSMRSolver(check_finite=None, damp=0.0, atol=1e-06, btol=1e-06, conlim=100000000.0, maxiter=None, show=False)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

least_squares = True[source]
class pymor.bindings.scipy.ScipyLSQRSolver(check_finite=None, damp=0.0, atol=1e-06, btol=1e-06, conlim=100000000.0, iter_lim=None, show=False)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

least_squares = True[source]
class pymor.bindings.scipy.ScipyLSTSQSolver(check_finite=True)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

least_squares = True[source]
class pymor.bindings.scipy.ScipyLUSolveSolver(check_finite=None, check_cond=True)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

class pymor.bindings.scipy.ScipyLinearSolver(check_finite=True)[source]

Bases: pymor.solvers.interface.Solver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

class pymor.bindings.scipy.ScipySpSolveSolver(check_finite=None, permc_spec='COLAMD', keep_factorization=True, use_umfpack=True)[source]

Bases: ScipyLinearSolver

Equation solver.

Solves operator equations of the form

\[A(U; \mu) = V\]

The operator \(A\) can be linear or non-linear. When \(A\) is linear, a solver can also be used to solve the adjoint equation

\[A^H(V; \mu) = U\]

for \(U\).

When least_squares is True, the equations are solved in a least-squares sense:

\[\operatorname{argmin}_{U} \|A(U; \mu) - V\|^2 \quad\text{or}\quad \operatorname{argmin}_{V} \|A^H(V; \mu) - U\|^2\]

Solvers will typically only work for certain classes of Operators. In most cases, solvers are invoked by the apply_inverse and apply_inverse_adjoint methods of Operators. If an Operator has no associated solver, DefaultSolver is used.

pymor.bindings.scipy.lyap_dense_solver_options()[source]

Return available dense Lyapunov solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.lyap_lrcf_solver_options()[source]

Return available Lyapunov solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.matrix_astype_nocopy(matrix, dtype)[source]
pymor.bindings.scipy.ricc_dense_solver_options()[source]

Return available Riccati solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.ricc_lrcf_solver_options()[source]

Return available Riccati solvers with default options for the SciPy backend.

Returns:

A dict of available solvers with default solver options.

pymor.bindings.scipy.solve_lyap_dense(A, E, B, trans=False, cont_time=True, options=None)[source]

Compute the solution of a Lyapunov equation.

See

for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov or scipy.linalg.solve_discrete_lyapunov, which are dense solvers for Lyapunov equations with E=I.

Note

If E is not None, the problem will be reduced to a standard algebraic Lyapunov equation by inverting E.

Parameters:

  • A – The matrix A as a 2D NumPy array.

  • E – The matrix E as a 2D NumPy array or None.

  • B – The matrix B as a 2D NumPy array.

  • trans – Whether the first operator in the Lyapunov equation is transposed.

  • cont_time – Whether the continuous- or discrete-time Lyapunov equation is solved.

  • options – The solver options to use (see lyap_dense_solver_options).

Returns:

X – Lyapunov equation solution as a NumPy array.

pymor.bindings.scipy.solve_lyap_lrcf(A, E, B, trans=False, cont_time=True, options=None)[source]

Compute an approximate low-rank solution of a Lyapunov equation.

See

for a general description.

This function uses scipy.linalg.solve_continuous_lyapunov or scipy.linalg.solve_discrete_lyapunov, which are dense solvers for Lyapunov equations with E=I. Therefore, we assume A and E can be converted to NumPy arrays using to_matrix and that B.to_numpy is implemented.

Note

If E is not None, the problem will be reduced to a standard algebraic Lyapunov equation by inverting E.

Parameters:

  • A – The non-parametric Operator A.

  • E – The non-parametric Operator E or None.

  • B – The operator B as a VectorArray from A.source.

  • trans – Whether the first Operator in the Lyapunov equation is transposed.

  • cont_time – Whether the continuous- or discrete-time Lyapunov equation is solved.

  • options – The solver options to use (see lyap_lrcf_solver_options).

Returns:

Z – Low-rank Cholesky factor of the Lyapunov equation solution, VectorArray from A.source.

pymor.bindings.scipy.solve_pos_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute the solution of a Riccati equation.

See pymor.algorithms.riccati.solve_pos_ricc_dense for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver.

Parameters:
Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.scipy.solve_pos_ricc_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute an approximate low-rank solution of a positive Riccati equation.

See pymor.algorithms.riccati.solve_pos_ricc_lrcf for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:
Returns:

Z – Low-rank Cholesky factor of the positive Riccati equation solution, VectorArray from A.source.

pymor.bindings.scipy.solve_ricc_dense(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute the solution of a Riccati equation.

See pymor.algorithms.riccati.solve_ricc_dense for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver.

Parameters:
Returns:

X – Riccati equation solution as a NumPy array.

pymor.bindings.scipy.solve_ricc_lrcf(A, E, B, C, R=None, S=None, trans=False, options=None)[source]

Compute an approximate low-rank solution of a Riccati equation.

See pymor.algorithms.riccati.solve_ricc_lrcf for a general description.

This function uses scipy.linalg.solve_continuous_are, which is a dense solver. Therefore, we assume all Operators and VectorArrays can be converted to NumPy arrays using to_matrix and to_numpy.

Parameters:
Returns:

Z – Low-rank Cholesky factor of the Riccati equation solution, VectorArray from A.source.

pymor.bindings.scipy.svd_lapack_driver(driver='gesvd_unless_win_mkl')[source]
pymor.bindings.scipy.SCIPY_1_14_OR_NEWER[source]
pymor.bindings.scipy.sparray[source]