# probnum.problems¶

Definitions and collection of problems solved by probabilistic numerical methods.

## Classes¶

 RegressionProblem(observations, locations[, …]) Regression problem. InitialValueProblem(f, t0, tmax, y0[, df, …]) First order ODE initial value problem. LinearSystem(A, b[, solution]) Linear system of equations. QuadratureProblem(integrand, lower_bd, upper_bd) Numerical computation of an integral.

## probnum.problems.zoo¶

Subpackage offering implementations of standard example problems or convenient interfaces to benchmark problems for probabilistic numerical methods. These test problems are meant for rapid experimentation and prototyping.

### probnum.problems.zoo.diffeq¶

Test problems involving ordinary differential equations.

#### Functions¶

 threebody([t0, tmax, y0]) Initial value problem (IVP) based on a three-body problem. vanderpol([t0, tmax, y0, params]) Initial value problem (IVP) based on the Van der Pol Oscillator, implemented in jax. rigidbody([t0, tmax, y0, params]) Initial value problem (IVP) for rigid body dynamics without external forces threebody_jax([tmax]) Initial value problem (IVP) based on a three-body problem. vanderpol_jax([t0, tmax, y0, params]) Initial value problem (IVP) based on the Van der Pol Oscillator, implemented in jax.

### probnum.problems.zoo.filtsmooth¶

Exemplary state space model setups for Bayesian Filtering and Smoothing.

#### Functions¶

 benes_daum([measurement_variance, …]) Filtering/smoothing setup based on the Beneš SDE. car_tracking([measurement_variance, …]) Filtering/smoothing setup for a simple car-tracking scenario. logistic_ode([y0, timespan, step, params, …]) Filtering/smoothing setup for a probabilistic ODE solver for the logistic ODE. ornstein_uhlenbeck([measurement_variance, …]) Filtering/smoothing setup based on an Ornstein Uhlenbeck process. pendulum([measurement_variance, timespan, …]) Filtering/smoothing setup for a (noisy) pendulum.

### probnum.problems.zoo.linalg¶

Test problems from linear algebra.

#### Functions¶

 random_spd_matrix(dim[, spectrum, random_state]) Random symmetric positive definite matrix. random_sparse_spd_matrix(dim, density[, …]) Random sparse symmetric positive definite matrix. suitesparse_matrix(name, group[, verbose]) Sparse matrix from the SuiteSparse Matrix Collection.

#### Classes¶

 SuiteSparseMatrix(matid, group, name, nnz, …) SuiteSparse Matrix.