Parameter Make.Algodiff

Type definition
type t =
  1. | F of A.elt
  2. | Arr of A.arr
  3. | DF of t * t * int
  4. | DR of t * t ref * op * int ref * int * int ref
and adjoint = t -> t ref -> (t * t) list -> (t * t) list
and register = t list -> t list
and label = string * t list
and op = adjoint * register * label

Abstract number type

Supported Maths functions
module Maths : sig ... end
module Linalg : sig ... end
module NN : sig ... end
module Mat : sig ... end
module Arr : sig ... end
Core functions
val diff : (t -> t) -> t -> t

``diff f x`` returns the exat derivative of a function ``f : scalar -> scalar`` at point ``x``. Simply calling ``diff f`` will return its derivative function ``g`` of the same type, i.e. ``g : scalar -> scalar``.

Keep calling this function will give you higher-order derivatives of ``f``, i.e. ``f |> diff |> diff |> diff |> ...``

val diff' : (t -> t) -> t -> t * t

similar to ``diff``, but return ``(f x, diff f x)``.

val grad : (t -> t) -> t -> t

gradient of ``f`` : (vector -> scalar) at ``x``, reverse ad.

val grad' : (t -> t) -> t -> t * t

similar to ``grad``, but return ``(f x, grad f x)``.

val jacobian : (t -> t) -> t -> t

jacobian of ``f`` : (vector -> vector) at ``x``, both ``x`` and ``y`` are row vectors.

val jacobian' : (t -> t) -> t -> t * t

similar to ``jacobian``, but return ``(f x, jacobian f x)``

val jacobianv : (t -> t) -> t -> t -> t

jacobian vector product of ``f`` : (vector -> vector) at ``x`` along ``v``, forward ad. Namely, it calcultes ``(jacobian x) v``

val jacobianv' : (t -> t) -> t -> t -> t * t

similar to ``jacobianv'``, but return ``(f x, jacobianv f x v)``

val jacobianTv : (t -> t) -> t -> t -> t

transposed jacobian vector product of ``f : (vector -> vector)`` at ``x`` along ``v``, backward ad. Namely, it calculates ``transpose ((jacobianv f x v))``.

val jacobianTv' : (t -> t) -> t -> t -> t * t

similar to ``jacobianTv``, but return ``(f x, transpose (jacobianv f x v))``

val hessian : (t -> t) -> t -> t

hessian of ``f`` : (scalar -> scalar) at ``x``.

val hessian' : (t -> t) -> t -> t * t

simiarl to ``hessian``, but return ``(f x, hessian f x)``

val hessianv : (t -> t) -> t -> t -> t

hessian vector product of ``f`` : (scalar -> scalar) at ``x`` along ``v``. Namely, it calculates ``(hessian x) v``.

val hessianv' : (t -> t) -> t -> t -> t * t

similar to ``hessianv``, but return ``(f x, hessianv f x v)``.

val laplacian : (t -> t) -> t -> t

laplacian of ``f : (scalar -> scalar)`` at ``x``.

val laplacian' : (t -> t) -> t -> t * t

simiar to ``laplacian``, but return ``(f x, laplacian f x)``.

val gradhessian : (t -> t) -> t -> t * t

return ``(grad f x, hessian f x)``, ``f : (scalar -> scalar)``

val gradhessian' : (t -> t) -> t -> t * t * t

return ``(f x, grad f x, hessian f x)``

val gradhessianv : (t -> t) -> t -> t -> t * t

return ``(grad f x v, hessian f x v)``

val gradhessianv' : (t -> t) -> t -> t -> t * t * t

return ``(f x, grad f x v, hessian f x v)``

Low-level functions
val pack_elt : A.elt -> t

convert from ``elt`` type to ``t`` type.

val unpack_elt : t -> A.elt

convert from ``t`` type to ``elt`` type.

val pack_flt : float -> t

convert from ``float`` type to ``t`` type.

val unpack_flt : t -> float

convert from ``t`` type to ``float`` type.

val pack_arr : A.arr -> t

convert from ``arr`` type to ``t`` type.

val unpack_arr : t -> A.arr

convert from ``t`` type to ``arr`` type.

val tag : unit -> int

TODO

val primal : t -> t

TODO

val primal' : t -> t

TODO

val adjval : t -> t

TODO

val adjref : t -> t ref

TODO

val tangent : t -> t

TODO

val make_forward : t -> t -> int -> t

TODO

val make_reverse : t -> int -> t

TODO

val reverse_prop : t -> t -> unit

TODO

val type_info : t -> string

TODO

val shape : t -> int array

TODO

val copy_primal' : t -> t

TODO

val _f : float -> t

A shortcut function for ``F A.(float_to_elt x)``.

val clip_by_value : amin:A.elt -> amax:A.elt -> t -> t

other functions, without tracking gradient

val clip_by_l2norm : A.elt -> t -> t

other functions, without tracking gradient

Helper functions
val to_trace : t list -> string

``to_trace t0; t1; ...`` outputs the trace of computation graph on the terminal in a human-readable format.

val to_dot : t list -> string

``to_dot t0; t1; ...`` outputs the trace of computation graph in the dot file format which you can use other tools further visualisation, such as Graphviz.

val pp_num : Format.formatter -> t -> unit

``pp_num t`` pretty prints the abstract number used in ``Algodiff``.