Module `Tadiff.OrderedTTypeName`Source

Extends TTypeName with comparison operators.

parameter T
module of operators over the underlying type on which we perform automatic differentiation

Parameters

module T : sig ... end

Signature

Sourcetype t

Sourcetype elt = T.elt

Type of values: this is the type that the user should use with make and that will be returned by get

Sourcetype scalar = T.scalar

Type of scalars

Sourceval copy : t -> t

Sourceval deepcopy : t -> t

Constructors

Sourceval create : unit -> t

Sourceval make : elt -> t

Wrap a user-provided value

Sourceval integer : int -> t

Wrap an integer

Sourceval zero : unit -> t

Construct a fresh value corresponding to 0

Sourceval one : unit -> t

Construct a fresh value corresponding to 1

Sourceval two : unit -> t

Construct a fresh value corresponding to 2

Destructors

Sourceval get : t -> elt

Unwrap a value

Sourceval (!!) : t -> elt

Alias for get

Sourceval to_string : t -> string

Sourceval string_of_scalar : scalar -> string

Sourceval string_of_elt : elt -> string

Arithmetic operators

Sourceval (~+) : t -> t

unary plus (with copy)

Sourceval (~-) : t -> t

unary minus (with copy)

Sourceval (+) : t -> t -> t

Sourceval (+=) : t -> t -> t

Sourceval (-) : t -> t -> t

Sourceval (-=) : t -> t -> t

Sourceval (*) : t -> t -> t

Sourceval (*=) : t -> t -> t

Sourceval (/) : t -> t -> t

Sourceval (/=) : t -> t -> t

Sourceval (**) : t -> t -> t

Sourceval inv : t -> t

Sourceval sqr : t -> t

Sourceval sqrt : t -> t

Sourceval log : t -> t

Sourceval exp : t -> t

Sourceval sin : t -> t

Sourceval cos : t -> t

Sourceval tan : t -> t

Sourceval asin : t -> t

Sourceval acos : t -> t

Sourceval atan : t -> t

Scalar operators

Sourceval scale : t -> scalar -> t

Multiplication between a value and a scalar

Sourceval translate : t -> scalar -> t

Addition between a value and a scalar

Comparison operators

Sourceval (=) : t -> t -> bool

Sourceval (<>) : t -> t -> bool

Sourceval (<) : t -> t -> bool

Sourceval (<=) : t -> t -> bool

Sourceval (>) : t -> t -> bool

Sourceval (>=) : t -> t -> bool

Sourceval min : t -> t -> t

Sourceval max : t -> t -> t

Operators

Sourcetype op = ..

Sourcetype op +=

| CONST
| SCALE of scalar
| TRANS of scalar
| SIN of T.t array
| COS of T.t array
| ADD
| SUB
| MUL
| DIV
| POW
| POS
| NEG
| INV
| SQR
| SQRT
| EXP
| LOG
| TAN
| ASIN
| ACOS
| ATAN

Sourceval string_of_op : op -> string

Additionnal constructors

Sourceval lift : T.t -> t

Accessors

Sourceval value : t -> T.t

Same as get but returns an T.t instead of an elt

Sourceval operator : t -> op

operator f retrieves the operator represented by f

Sourceval order : t -> int

Current number of coefficients that have been computed

Constructors

Sourceval un_op : op -> t -> t

un_op op f builds a node that represents the expression op(f) where op is a unary operator. This is useful to write custom operators

Sourceval bin_op : op -> t -> t -> t

bin_op op f1 f2 builds a node that represents the expression op(f1,f2) where op is a binary operator. This is useful to write custom operators

Automatic Taylor Expansion

Sourceval set : t -> int -> T.t -> unit

set f i v sets the i-th coefficient of f to v, this is used to set the direction of the expansion. For example, to expand wrt. a variable x, one would call set x 1 1.. This can also be used to change the value of a variable: eg. set x 0 5..

Sourceval d : t -> int -> elt

d f i retrieves the coefficient of order i in computation f as an elt. Must be called after eval.

Sourceval deriv : t -> int -> T.t

deriv f i retrieves the coefficient of order i in computation f. Must be called after eval.

Sourceval get_tvalues : t -> elt array

get_tvalues f retrieves the array of taylor coefficients of f. Must be called after eval.

Sourceval get_derivatives : t -> elt array

get_derivatives f retrieves the array of derivatives of f. Must be called after eval.

Sourceval eval : t -> int -> int

eval f i propagates the first i taylor coefficients of f. The direction of the expansion should have been set using set.

Sourceval reset : t -> unit

reset f resets all the arrays of coefficients. It is used to compute a new expansion on the same expression without building a new graph.

package fadbadml

Module Tadiff.OrderedTTypeNameSource

Parameters

Signature

Constructors

Destructors

Arithmetic operators

Scalar operators

Comparison operators

Operators

Additionnal constructors

Accessors

Constructors

Automatic Taylor Expansion

Module `Tadiff.OrderedTTypeName`Source