API
DifferentiationInterface — ModuleDifferentiationInterfaceAn interface to various automatic differentiation backends in Julia.
Argument wrappers
DifferentiationInterface.Context — TypeContextAbstract supertype for additional context arguments, which can be passed to differentiation operators after the active input x but are not differentiated.
See also
DifferentiationInterface.Constant — TypeConstantConcrete type of Context argument which is kept constant during differentiation.
Note that an operator can be prepared with an arbitrary value of the constant. However, same-point preparation must occur with the exact value that will be reused later.
Example
julia> using DifferentiationInterface
+
+julia> import ForwardDiff
+
+julia> f(x, c) = c * sum(abs2, x);
+
+julia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(10))
+2-element Vector{Float64}:
+ 20.0
+ 40.0
+
+julia> gradient(f, AutoForwardDiff(), [1.0, 2.0], Constant(100))
+2-element Vector{Float64}:
+ 200.0
+ 400.0DifferentiationInterface.Cache — TypeCacheConcrete type of Context argument which can be mutated with active values during differentiation.
The initial values present inside the cache do not matter.
First order
Pushforward
DifferentiationInterface.prepare_pushforward — Functionprepare_pushforward(f, backend, x, tx, [contexts...]) -> prep
+prepare_pushforward(f!, y, backend, x, tx, [contexts...]) -> prepCreate a prep object that can be given to pushforward and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.prepare_pushforward_same_point — Functionprepare_pushforward_same_point(f, backend, x, tx, [contexts...]) -> prep_same
+prepare_pushforward_same_point(f!, y, backend, x, tx, [contexts...]) -> prep_sameCreate an prep_same object that can be given to pushforward and its variants if they are applied at the same point x and with the same contexts.
If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.pushforward — Functionpushforward(f, [prep,] backend, x, tx, [contexts...]) -> ty
+pushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> tyCompute the pushforward of the function f at point x with a tuple of tangents tx.
To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.
Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp.
DifferentiationInterface.pushforward! — Functionpushforward!(f, dy, [prep,] backend, x, tx, [contexts...]) -> ty
+pushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> tyCompute the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.
To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.
Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named jvp!.
DifferentiationInterface.value_and_pushforward — Functionvalue_and_pushforward(f, [prep,] backend, x, tx, [contexts...]) -> (y, ty)
+value_and_pushforward(f!, y, [prep,] backend, x, tx, [contexts...]) -> (y, ty)Compute the value and the pushforward of the function f at point x with a tuple of tangents tx.
To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.
Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp.
Required primitive for forward mode backends.
DifferentiationInterface.value_and_pushforward! — Functionvalue_and_pushforward!(f, dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)
+value_and_pushforward!(f!, y, dy, [prep,] backend, x, tx, [contexts...]) -> (y, ty)Compute the value and the pushforward of the function f at point x with a tuple of tangents tx, overwriting ty.
To improve performance via operator preparation, refer to prepare_pushforward and prepare_pushforward_same_point.
Pushforwards are also commonly called Jacobian-vector products or JVPs. This function could have been named value_and_jvp!.
Pullback
DifferentiationInterface.prepare_pullback — Functionprepare_pullback(f, backend, x, ty, [contexts...]) -> prep
+prepare_pullback(f!, y, backend, x, ty, [contexts...]) -> prepCreate a prep object that can be given to pullback and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.prepare_pullback_same_point — Functionprepare_pullback_same_point(f, backend, x, ty, [contexts...]) -> prep_same
+prepare_pullback_same_point(f!, y, backend, x, ty, [contexts...]) -> prep_sameCreate an prep_same object that can be given to pullback and its variants if they are applied at the same point x and with the same contexts.
If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.pullback — Functionpullback(f, [prep,] backend, x, ty, [contexts...]) -> tx
+pullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> txCompute the pullback of the function f at point x with a tuple of tangents ty.
To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.
Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp.
DifferentiationInterface.pullback! — Functionpullback!(f, dx, [prep,] backend, x, ty, [contexts...]) -> tx
+pullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> txCompute the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.
To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.
Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named vjp!.
DifferentiationInterface.value_and_pullback — Functionvalue_and_pullback(f, [prep,] backend, x, ty, [contexts...]) -> (y, tx)
+value_and_pullback(f!, y, [prep,] backend, x, ty, [contexts...]) -> (y, tx)Compute the value and the pullback of the function f at point x with a tuple of tangents ty.
To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.
Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp.
Required primitive for reverse mode backends.
DifferentiationInterface.value_and_pullback! — Functionvalue_and_pullback!(f, dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)
+value_and_pullback!(f!, y, dx, [prep,] backend, x, ty, [contexts...]) -> (y, tx)Compute the value and the pullback of the function f at point x with a tuple of tangents ty, overwriting dx.
To improve performance via operator preparation, refer to prepare_pullback and prepare_pullback_same_point.
Pullbacks are also commonly called vector-Jacobian products or VJPs. This function could have been named value_and_vjp!.
Derivative
DifferentiationInterface.prepare_derivative — Functionprepare_derivative(f, backend, x, [contexts...]) -> prep
+prepare_derivative(f!, y, backend, x, [contexts...]) -> prepCreate a prep object that can be given to derivative and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.derivative — Functionderivative(f, [prep,] backend, x, [contexts...]) -> der
+derivative(f!, y, [prep,] backend, x, [contexts...]) -> derCompute the derivative of the function f at point x.
To improve performance via operator preparation, refer to prepare_derivative.
DifferentiationInterface.derivative! — Functionderivative!(f, der, [prep,] backend, x, [contexts...]) -> der
+derivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> derCompute the derivative of the function f at point x, overwriting der.
To improve performance via operator preparation, refer to prepare_derivative.
DifferentiationInterface.value_and_derivative — Functionvalue_and_derivative(f, [prep,] backend, x, [contexts...]) -> (y, der)
+value_and_derivative(f!, y, [prep,] backend, x, [contexts...]) -> (y, der)Compute the value and the derivative of the function f at point x.
To improve performance via operator preparation, refer to prepare_derivative.
DifferentiationInterface.value_and_derivative! — Functionvalue_and_derivative!(f, der, [prep,] backend, x, [contexts...]) -> (y, der)
+value_and_derivative!(f!, y, der, [prep,] backend, x, [contexts...]) -> (y, der)Compute the value and the derivative of the function f at point x, overwriting der.
To improve performance via operator preparation, refer to prepare_derivative.
Gradient
DifferentiationInterface.prepare_gradient — Functionprepare_gradient(f, backend, x, [contexts...]) -> prepCreate a prep object that can be given to gradient and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.
DifferentiationInterface.gradient — Functiongradient(f, [prep,] backend, x, [contexts...]) -> gradCompute the gradient of the function f at point x.
To improve performance via operator preparation, refer to prepare_gradient.
DifferentiationInterface.gradient! — Functiongradient!(f, grad, [prep,] backend, x, [contexts...]) -> gradCompute the gradient of the function f at point x, overwriting grad.
To improve performance via operator preparation, refer to prepare_gradient.
DifferentiationInterface.value_and_gradient — Functionvalue_and_gradient(f, [prep,] backend, x, [contexts...]) -> (y, grad)Compute the value and the gradient of the function f at point x.
To improve performance via operator preparation, refer to prepare_gradient.
DifferentiationInterface.value_and_gradient! — Functionvalue_and_gradient!(f, grad, [prep,] backend, x, [contexts...]) -> (y, grad)Compute the value and the gradient of the function f at point x, overwriting grad.
To improve performance via operator preparation, refer to prepare_gradient.
Jacobian
DifferentiationInterface.prepare_jacobian — Functionprepare_jacobian(f, backend, x, [contexts...]) -> prep
+prepare_jacobian(f!, y, backend, x, [contexts...]) -> prepCreate a prep object that can be given to jacobian and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again. For in-place functions, y is mutated by f! during preparation.
DifferentiationInterface.jacobian — Functionjacobian(f, [prep,] backend, x, [contexts...]) -> jac
+jacobian(f!, y, [prep,] backend, x, [contexts...]) -> jacCompute the Jacobian matrix of the function f at point x.
To improve performance via operator preparation, refer to prepare_jacobian.
DifferentiationInterface.jacobian! — Functionjacobian!(f, jac, [prep,] backend, x, [contexts...]) -> jac
+jacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> jacCompute the Jacobian matrix of the function f at point x, overwriting jac.
To improve performance via operator preparation, refer to prepare_jacobian.
DifferentiationInterface.value_and_jacobian — Functionvalue_and_jacobian(f, [prep,] backend, x, [contexts...]) -> (y, jac)
+value_and_jacobian(f!, y, [prep,] backend, x, [contexts...]) -> (y, jac)Compute the value and the Jacobian matrix of the function f at point x.
To improve performance via operator preparation, refer to prepare_jacobian.
DifferentiationInterface.value_and_jacobian! — Functionvalue_and_jacobian!(f, jac, [prep,] backend, x, [contexts...]) -> (y, jac)
+value_and_jacobian!(f!, y, jac, [prep,] backend, x, [contexts...]) -> (y, jac)Compute the value and the Jacobian matrix of the function f at point x, overwriting jac.
To improve performance via operator preparation, refer to prepare_jacobian.
Second order
DifferentiationInterface.SecondOrder — TypeSecondOrderCombination of two backends for second-order differentiation.
SecondOrder backends do not support first-order operators.
Constructor
SecondOrder(outer_backend, inner_backend)Fields
outer::AbstractADType: backend for the outer differentiationinner::AbstractADType: backend for the inner differentiation
Second derivative
DifferentiationInterface.prepare_second_derivative — Functionprepare_second_derivative(f, backend, x, [contexts...]) -> prepCreate a prep object that can be given to second_derivative and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.
DifferentiationInterface.second_derivative — Functionsecond_derivative(f, [prep,] backend, x, [contexts...]) -> der2Compute the second derivative of the function f at point x.
To improve performance via operator preparation, refer to prepare_second_derivative.
DifferentiationInterface.second_derivative! — Functionsecond_derivative!(f, der2, [prep,] backend, x, [contexts...]) -> der2Compute the second derivative of the function f at point x, overwriting der2.
To improve performance via operator preparation, refer to prepare_second_derivative.
DifferentiationInterface.value_derivative_and_second_derivative — Functionvalue_derivative_and_second_derivative(f, [prep,] backend, x, [contexts...]) -> (y, der, der2)Compute the value, first derivative and second derivative of the function f at point x.
To improve performance via operator preparation, refer to prepare_second_derivative.
DifferentiationInterface.value_derivative_and_second_derivative! — Functionvalue_derivative_and_second_derivative!(f, der, der2, [prep,] backend, x, [contexts...]) -> (y, der, der2)Compute the value, first derivative and second derivative of the function f at point x, overwriting der and der2.
To improve performance via operator preparation, refer to prepare_second_derivative.
Hessian-vector product
DifferentiationInterface.prepare_hvp — Functionprepare_hvp(f, backend, x, tx, [contexts...]) -> prepCreate a prep object that can be given to hvp and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.
DifferentiationInterface.prepare_hvp_same_point — Functionprepare_hvp_same_point(f, backend, x, tx, [contexts...]) -> prep_sameCreate an prep_same object that can be given to hvp and its variants if they are applied at the same point x and with the same contexts.
If the function or the point changes in any way, the result of preparation will be invalidated, and you will need to run it again.
DifferentiationInterface.hvp — Functionhvp(f, [prep,] backend, x, tx, [contexts...]) -> tgCompute the Hessian-vector product of f at point x with a tuple of tangents tx.
To improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.
DifferentiationInterface.hvp! — Functionhvp!(f, tg, [prep,] backend, x, tx, [contexts...]) -> tgCompute the Hessian-vector product of f at point x with a tuple of tangents tx, overwriting tg.
To improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.
DifferentiationInterface.gradient_and_hvp — Functiongradient_and_hvp(f, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)Compute the gradient and the Hessian-vector product of f at point x with a tuple of tangents tx.
To improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.
DifferentiationInterface.gradient_and_hvp! — Functiongradient_and_hvp!(f, grad, tg, [prep,] backend, x, tx, [contexts...]) -> (grad, tg)Compute the gradient and the Hessian-vector product of f at point x with a tuple of tangents tx, overwriting grad and tg.
To improve performance via operator preparation, refer to prepare_hvp and prepare_hvp_same_point.
Hessian
DifferentiationInterface.prepare_hessian — Functionprepare_hessian(f, backend, x, [contexts...]) -> prepCreate a prep object that can be given to hessian and its variants.
If the function changes in any way, the result of preparation will be invalidated, and you will need to run it again.
DifferentiationInterface.hessian — Functionhessian(f, [prep,] backend, x, [contexts...]) -> hessCompute the Hessian matrix of the function f at point x.
To improve performance via operator preparation, refer to prepare_hessian.
DifferentiationInterface.hessian! — Functionhessian!(f, hess, [prep,] backend, x, [contexts...]) -> hessCompute the Hessian matrix of the function f at point x, overwriting hess.
To improve performance via operator preparation, refer to prepare_hessian.
DifferentiationInterface.value_gradient_and_hessian — Functionvalue_gradient_and_hessian(f, [prep,] backend, x, [contexts...]) -> (y, grad, hess)Compute the value, gradient vector and Hessian matrix of the function f at point x.
To improve performance via operator preparation, refer to prepare_hessian.
DifferentiationInterface.value_gradient_and_hessian! — Functionvalue_gradient_and_hessian!(f, grad, hess, [prep,] backend, x, [contexts...]) -> (y, grad, hess)Compute the value, gradient vector and Hessian matrix of the function f at point x, overwriting grad and hess.
To improve performance via operator preparation, refer to prepare_hessian.
Utilities
Backend queries
DifferentiationInterface.check_available — Functioncheck_available(backend)Check whether backend is available (i.e. whether the extension is loaded).
DifferentiationInterface.check_inplace — Functioncheck_inplace(backend)Check whether backend supports differentiation of in-place functions.
DifferentiationInterface.outer — Functionouter(backend::SecondOrder)
+outer(backend::AbstractADType)Return the outer backend of a SecondOrder object, tasked with differentiation at the second order.
For any other backend type, this function acts like the identity.
DifferentiationInterface.inner — Functioninner(backend::SecondOrder)
+inner(backend::AbstractADType)Return the inner backend of a SecondOrder object, tasked with differentiation at the first order.
For any other backend type, this function acts like the identity.
Backend switch
DifferentiationInterface.DifferentiateWith — TypeDifferentiateWithFunction wrapper that enforces differentiation with a "substitute" AD backend, possible different from the "true" AD backend that is called.
For instance, suppose a function f is not differentiable with Zygote because it involves mutation, but you know that it is differentiable with Enzyme. Then f2 = DifferentiateWith(f, AutoEnzyme()) is a new function that behaves like f, except that f2 is differentiable with Zygote (thanks to a chain rule which calls Enzyme under the hood). Moreover, any larger algorithm alg that calls f2 instead of f will also be differentiable with Zygote (as long as f was the only Zygote blocker).
This is mainly relevant for package developers who want to produce differentiable code at low cost, without writing the differentiation rules themselves. If you sprinkle a few DifferentiateWith in places where some AD backends may struggle, end users can pick from a wider variety of packages to differentiate your algorithms.
DifferentiateWith only supports out-of-place functions y = f(x) without additional context arguments. It only makes these functions differentiable if the true backend is either ForwardDiff or compatible with ChainRules. For any other true backend, the differentiation behavior is not altered by DifferentiateWith (it becomes a transparent wrapper).
Fields
f: the function in question, with signaturef(x)backend::AbstractADType: the substitute backend to use for differentiation
For the substitute AD backend to be called under the hood, its package needs to be loaded in addition to the package of the true AD backend.
Constructor
DifferentiateWith(f, backend)Example
julia> using DifferentiationInterface
+
+julia> import FiniteDiff, ForwardDiff, Zygote
+
+julia> function f(x::Vector{Float64})
+ a = Vector{Float64}(undef, 1) # type constraint breaks ForwardDiff
+ a[1] = sum(abs2, x) # mutation breaks Zygote
+ return a[1]
+ end;
+
+julia> f2 = DifferentiateWith(f, AutoFiniteDiff());
+
+julia> f([3.0, 5.0]) == f2([3.0, 5.0])
+true
+
+julia> alg(x) = 7 * f2(x);
+
+julia> ForwardDiff.gradient(alg, [3.0, 5.0])
+2-element Vector{Float64}:
+ 42.0
+ 70.0
+
+julia> Zygote.gradient(alg, [3.0, 5.0])[1]
+2-element Vector{Float64}:
+ 42.0
+ 70.0Sparsity detection
DifferentiationInterface.DenseSparsityDetector — TypeDenseSparsityDetectorSparsity pattern detector satisfying the detection API of ADTypes.jl.
The nonzeros in a Jacobian or Hessian are detected by computing the relevant matrix with dense AD, and thresholding the entries with a given tolerance (which can be numerically inaccurate). This process can be very slow, and should only be used if its output can be exploited multiple times to compute many sparse matrices.
In general, the sparsity pattern you obtain can depend on the provided input x. If you want to reuse the pattern, make sure that it is input-agnostic.
DenseSparsityDetector functionality is now located in a package extension, please load the SparseArrays.jl standard library before you use it.
Fields
backend::AbstractADTypeis the dense AD backend used under the hoodatol::Float64is the minimum magnitude of a matrix entry to be considered nonzero
Constructor
DenseSparsityDetector(backend; atol, method=:iterative)The keyword argument method::Symbol can be either:
:iterative: compute the matrix in a sequence of matrix-vector products (memory-efficient):direct: compute the matrix all at once (memory-hungry but sometimes faster).
Note that the constructor is type-unstable because method ends up being a type parameter of the DenseSparsityDetector object (this is not part of the API and might change).
Examples
using ADTypes, DifferentiationInterface, SparseArrays
+import ForwardDiff
+
+detector = DenseSparsityDetector(AutoForwardDiff(); atol=1e-5, method=:direct)
+
+ADTypes.jacobian_sparsity(diff, rand(5), detector)
+
+# output
+
+4×5 SparseMatrixCSC{Bool, Int64} with 8 stored entries:
+ 1 1 ⋅ ⋅ ⋅
+ ⋅ 1 1 ⋅ ⋅
+ ⋅ ⋅ 1 1 ⋅
+ ⋅ ⋅ ⋅ 1 1Sometimes the sparsity pattern is input-dependent:
ADTypes.jacobian_sparsity(x -> [prod(x)], rand(2), detector)
+
+# output
+
+1×2 SparseMatrixCSC{Bool, Int64} with 2 stored entries:
+ 1 1ADTypes.jacobian_sparsity(x -> [prod(x)], [0, 1], detector)
+
+# output
+
+1×2 SparseMatrixCSC{Bool, Int64} with 1 stored entry:
+ 1 ⋅Internals
The following is not part of the public API.
DifferentiationInterface.AutoZeroForward — TypeAutoZeroForward <: ADTypes.AbstractADTypeTrivial backend that sets all derivatives to zero. Used in testing and benchmarking.
DifferentiationInterface.AutoZeroReverse — TypeAutoZeroReverse <: ADTypes.AbstractADTypeTrivial backend that sets all derivatives to zero. Used in testing and benchmarking.
DifferentiationInterface.BatchSizeSettings — TypeBatchSizeSettings{B,singlebatch,aligned}Configuration for the batch size deduced from a backend and a sample array of length N.
Type parameters
B::Int: batch sizesinglebatch::Bool: whetherB > Naligned::Bool: whetherN % B == 0
Fields
N::Int: array lengthA::Int: number of batchesA = div(N, B, RoundUp)B_last::Int: size of the last batch (ifalignedisfalse)
DifferentiationInterface.DerivativePrep — TypeDerivativePrepAbstract type for additional information needed by derivative and its variants.
DifferentiationInterface.ForwardOverForward — TypeForwardOverForwardTraits identifying second-order backends that compute HVPs in forward over forward mode (inefficient).
DifferentiationInterface.ForwardOverReverse — TypeForwardOverReverseTraits identifying second-order backends that compute HVPs in forward over reverse mode.
DifferentiationInterface.GradientPrep — TypeGradientPrepAbstract type for additional information needed by gradient and its variants.
DifferentiationInterface.HVPPrep — TypeHVPPrepAbstract type for additional information needed by hvp and its variants.
DifferentiationInterface.HessianPrep — TypeHessianPrepAbstract type for additional information needed by hessian and its variants.
DifferentiationInterface.InPlaceNotSupported — TypeInPlaceNotSupportedTrait identifying backends that do not support in-place functions f!(y, x).
DifferentiationInterface.InPlaceSupported — TypeInPlaceSupportedTrait identifying backends that support in-place functions f!(y, x).
DifferentiationInterface.JacobianPrep — TypeJacobianPrepAbstract type for additional information needed by jacobian and its variants.
DifferentiationInterface.PullbackFast — TypePullbackFastTrait identifying backends that support efficient pullbacks.
DifferentiationInterface.PullbackPrep — TypePullbackPrepAbstract type for additional information needed by pullback and its variants.
DifferentiationInterface.PullbackSlow — TypePullbackSlowTrait identifying backends that do not support efficient pullbacks.
DifferentiationInterface.PushforwardFast — TypePushforwardFastTrait identifying backends that support efficient pushforwards.
DifferentiationInterface.PushforwardPrep — TypePushforwardPrepAbstract type for additional information needed by pushforward and its variants.
DifferentiationInterface.PushforwardSlow — TypePushforwardSlowTrait identifying backends that do not support efficient pushforwards.
DifferentiationInterface.ReverseOverForward — TypeReverseOverForwardTraits identifying second-order backends that compute HVPs in reverse over forward mode.
DifferentiationInterface.ReverseOverReverse — TypeReverseOverReverseTraits identifying second-order backends that compute HVPs in reverse over reverse mode.
DifferentiationInterface.SecondDerivativePrep — TypeSecondDerivativePrepAbstract type for additional information needed by second_derivative and its variants.
ADTypes.mode — Methodmode(backend::SecondOrder)Return the outer mode of the second-order backend.
DifferentiationInterface.basis — Methodbasis(backend, a::AbstractArray, i)Construct the i-th standard basis array in the vector space of a with element type eltype(a).
Note
If an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.
DifferentiationInterface.inplace_support — Methodinplace_support(backend)Return InPlaceSupported or InPlaceNotSupported in a statically predictable way.
DifferentiationInterface.multibasis — Methodmultibasis(backend, a::AbstractArray, inds::AbstractVector)Construct the sum of the i-th standard basis arrays in the vector space of a with element type eltype(a), for all i ∈ inds.
Note
If an AD backend benefits from a more specialized basis array implementation, this function can be extended on the backend type.
DifferentiationInterface.prepare!_derivative — Functionprepare!_derivative(f, prep, backend, x, [contexts...]) -> new_prep
+prepare!_derivative(f!, y, prep, backend, x, [contexts...]) -> new_prepSame behavior as prepare_derivative but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_gradient — Functionprepare!_gradient(f, prep, backend, x, [contexts...]) -> new_prepSame behavior as prepare_gradient but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_hessian — Functionprepare!_hessian(f, backend, x, [contexts...]) -> new_prepSame behavior as prepare_hessian but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_hvp — Functionprepare!_hvp(f, backend, x, tx, [contexts...]) -> new_prepSame behavior as prepare_hvp but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_jacobian — Functionprepare!_jacobian(f, prep, backend, x, [contexts...]) -> new_prep
+prepare!_jacobian(f!, y, prep, backend, x, [contexts...]) -> new_prepSame behavior as prepare_jacobian but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_pullback — Functionprepare!_pullback(f, prep, backend, x, ty, [contexts...]) -> new_prep
+prepare!_pullback(f!, y, prep, backend, x, ty, [contexts...]) -> new_prepSame behavior as prepare_pullback but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.prepare!_pushforward — Functionprepare!_pushforward(f, prep, backend, x, tx, [contexts...]) -> new_prep
+prepare!_pushforward(f!, y, prep, backend, x, tx, [contexts...]) -> new_prepSame behavior as prepare_pushforward but can modify an existing prep object to avoid some allocations.
There is no guarantee that prep will be mutated, or that performance will be improved compared to preparation from scratch.
For efficiency, this function needs to rely on backend package internals, therefore it not protected by semantic versioning.
DifferentiationInterface.pullback_performance — Methodpullback_performance(backend)Return PullbackFast or PullbackSlow in a statically predictable way.
DifferentiationInterface.pushforward_performance — Methodpushforward_performance(backend)Return PushforwardFast or PushforwardSlow in a statically predictable way.
