Integral Problems
IntegralProblem is a SciMLBase problem type reexported by Integrals.jl for convenience. Its construction API is documented by SciMLBase; this page describes the integrand shapes accepted by Integrals.jl algorithms.
The correct shape of the variables (inputs) u and the values (outputs) y of the integrand f depends on whether batching is used. Batching is enabled by using BatchIntegralFunction instead of IntegralFunction.
Without batching (using IntegralFunction)
single variable f | multiple variable f | |
|---|---|---|
scalar valued f | u is a scalar, y is a scalar | u is a vector, y is a scalar |
vector valued f | u is a scalar, y is a vector | u is a vector, y is a vector |
With batching (using BatchIntegralFunction)
single variable f | multiple variable f | |
|---|---|---|
scalar valued f | u is a vector, y is a vector | u is a matrix, y is a vector |
vector valued f | u is a vector, y is a matrix | u is a matrix, y is a matrix |
The last dimension is always used as the batching dimension, e.g., if u is a matrix, then u[:,i] is the ith point where the integrand will be evaluated.