mirror of
https://gitlab.com/scemama/QCaml.git
synced 2024-12-23 04:43:32 +01:00
204 lines
4.8 KiB
Org Mode
204 lines
4.8 KiB
Org Mode
#+begin_src elisp tangle: no :results none :exports none
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(setq pwd (file-name-directory buffer-file-name))
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(setq name (file-name-nondirectory (substring buffer-file-name 0 -4)))
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(setq lib (concat pwd "lib/"))
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(setq testdir (concat pwd "test/"))
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(setq mli (concat lib name ".mli"))
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(setq ml (concat lib name ".ml"))
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(setq test-ml (concat testdir name ".ml"))
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(org-babel-tangle)
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#+end_src
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* Coordinate
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:PROPERTIES:
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:header-args: :noweb yes :comments both
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:END:
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Coordinates in 3D space.
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All operations on points are done in atomic units. Therefore,
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all coordinates are given in bohr and manipulated with this
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module.
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** Type
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#+NAME: types
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#+begin_src ocaml :tangle (eval mli)
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type bohr
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type angstrom
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type xyz = {
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x : float ;
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y : float ;
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z : float ;
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}
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type 'a point = xyz
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type t = bohr point
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type axis = X | Y | Z
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#+end_src
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#+begin_src ocaml :tangle (eval ml) :exports none
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<<types>>
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#+end_src
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** Creation
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#+begin_src ocaml :tangle (eval mli)
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val make : 'a point -> t
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val make_angstrom : 'a point -> angstrom point
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val zero : bohr point
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#+end_src
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| ~make~ | Creates a point in atomic units |
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| ~make_angstrom~ | Creates a point in angstrom |
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| ~zero~ | $(0., 0., 0.)$ |
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#+begin_src ocaml :tangle (eval ml) :exports none
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external make : 'a point -> t = "%identity"
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external make_angstrom : 'a point -> angstrom point = "%identity"
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let zero =
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make { x = 0. ; y = 0. ; z = 0. }
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#+end_src
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** Conversion
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#+begin_src ocaml :tangle (eval mli)
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val bohr_to_angstrom : bohr point -> angstrom point
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val angstrom_to_bohr : angstrom point -> bohr point
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#+end_src
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| ~bohr_to_angstrom~ | Converts a point in bohr to angstrom |
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| ~angstrom_to_bohr~ | Converts a point in angstrom to bohr |
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#+begin_src ocaml :tangle (eval ml) :exports none
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let b_to_a b = Constants.a0 *. b
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let bohr_to_angstrom { x ; y ; z } =
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make { x = b_to_a x ;
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y = b_to_a y ;
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z = b_to_a z ; }
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let a_to_b a = Constants.a0_inv *. a
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let angstrom_to_bohr { x ; y ; z } =
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make { x = a_to_b x ;
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y = a_to_b y ;
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z = a_to_b z ; }
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#+end_src
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** Vector operations
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#+begin_src ocaml :tangle (eval mli)
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val neg : t -> t
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val get : axis -> bohr point -> float
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val dot : t -> t -> float
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val norm : t -> float
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val ( |. ) : float -> t -> t
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val ( |+ ) : t -> t -> t
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val ( |- ) : t -> t -> t
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#+end_src
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| ~neg~ | Negative of a point |
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| ~get~ | Extracts the projection of the coordinate on an axis |
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| ~dot~ | Dot product |
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| ~norm~ | $\ell{^2}$ norm of the vector |
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| ~¦.~ | Scales the vector by a constant |
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| ~¦+~ | Adds two vectors |
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| ~¦-~ | Subtracts two vectors |
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#+begin_example
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Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
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- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -2.; z = -3.}
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Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
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- : float = 2.
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Coordinate.(
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2. |. { x=1. ; y=2. ; z=3. }
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) ;;
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- : Coordinate.t = {Qcaml.Common.Coordinate.x = 2.; y = 4.; z = 6.}
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Coordinate.(
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{ x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. }
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);;
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- : Coordinate.t = {Qcaml.Common.Coordinate.x = 3.; y = 5.; z = 4.}
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Coordinate.(
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{ x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. }
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);;
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- : Coordinate.t = {Qcaml.Common.Coordinate.x = -1.; y = -1.; z = 2.}
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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let get axis { x ; y ; z } =
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match axis with
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| X -> x
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| Y -> y
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| Z -> z
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let ( |. ) s { x ; y ; z } =
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make { x = s *. x ;
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y = s *. y ;
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z = s *. z ; }
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let ( |+ )
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{ x = x1 ; y = y1 ; z = z1 }
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{ x = x2 ; y = y2 ; z = z2 } =
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make { x = x1 +. x2 ;
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y = y1 +. y2 ;
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z = z1 +. z2 ; }
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let ( |- )
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{ x = x1 ; y = y1 ; z = z1 }
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{ x = x2 ; y = y2 ; z = z2 } =
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make { x = x1 -. x2 ;
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y = y1 -. y2 ;
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z = z1 -. z2 ; }
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let neg a = -1. |. a
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let dot
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{ x = x1 ; y = y1 ; z = z1 }
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{ x = x2 ; y = y2 ; z = z2 } =
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x1 *. x2 +.
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y1 *. y2 +.
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z1 *. z2
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let norm u =
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sqrt ( dot u u )
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#+end_src
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** Printers
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#+begin_src ocaml :tangle (eval mli)
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val pp : Format.formatter -> t -> unit
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val pp_bohr: Format.formatter -> t -> unit
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val pp_angstrom : Format.formatter -> t -> unit
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#+end_src
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Coordinates can be printed in bohr or angstrom.
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#+begin_src ocaml :tangle (eval ml) :exports none
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open Format
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let pp ppf c =
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fprintf ppf "@[@[%8.4f@] @[%8.4f@] @[%8.4f@]@]" c.x c.y c.z
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let pp_bohr ppf c =
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fprintf ppf "@[(@[%10f@], @[%10f@], @[%10f@] Bohr)@]" c.x c.y c.z
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let pp_angstrom ppf c =
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let c = bohr_to_angstrom c in
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fprintf ppf "@[(@[%10f@], @[%10f@], @[%10f@] Angs)@]" c.x c.y c.z
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#+end_src
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