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 fmultiple variable f
scalar valued fu is a scalar, y is a scalaru is a vector, y is a scalar
vector valued fu is a scalar, y is a vectoru is a vector, y is a vector

With batching (using BatchIntegralFunction)

single variable fmultiple variable f
scalar valued fu is a vector, y is a vectoru is a matrix, y is a vector
vector valued fu is a vector, y is a matrixu 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.