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Coordinate org
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common/coordinate.org
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273
common/coordinate.org
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#+begin_src elisp tangle: no :results 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 / conversion
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*** ~make~
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Creates a point in atomic units.
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#+begin_src ocaml :tangle (eval mli)
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val make : 'a point -> t
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#+end_src
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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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#+end_src
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*** ~make_angstrom~
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Creates a point in angstrom.
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#+begin_src ocaml :tangle (eval mli)
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val make_angstrom : 'a point -> angstrom point
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#+end_src
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#+begin_src ocaml :tangle (eval ml) :exports none
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external make_angstrom : 'a point -> angstrom point = "%identity"
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#+end_src
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*** ~bohr_to_angstrom~
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Converts a point in bohr to angstrom.
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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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#+end_src
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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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#+end_src
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*** ~angstrom_to_bohr~
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Converts a point in angstrom to bohr.
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#+begin_src ocaml :tangle (eval mli)
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val angstrom_to_bohr : angstrom point -> bohr point
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#+end_src
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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*** ~zero~
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~zero~ = (0., 0., 0.)
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#+begin_src ocaml :tangle (eval mli)
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val zero : bohr point
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#+end_src
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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*** ~get~
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Extracts the projection of the coordinate on an axis.
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#+begin_example
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Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
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- : float = 2.
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#+end_example
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#+begin_src ocaml :tangle (eval mli)
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val get : axis -> bohr point -> float
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#+end_src
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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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#+end_src
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** Vector operations
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*** Scale
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#+begin_src ocaml :tangle (eval mli)
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val ( |. ) : float -> t -> t
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#+end_src
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#+begin_example
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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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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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#+end_src
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*** Add
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#+begin_src ocaml :tangle (eval mli)
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val ( |+ ) : t -> t -> t
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#+end_src
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#+begin_example
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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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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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#+end_src
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*** Subtract
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#+begin_src ocaml :tangle (eval mli)
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val ( |- ) : t -> t -> t
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#+end_src
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#+begin_example
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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 ( |- )
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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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#+end_src
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*** Negative
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#+begin_src ocaml :tangle (eval mli)
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val neg : t -> t
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#+end_src
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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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#+end_example
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#+begin_src ocaml :tangle (eval ml) :exports none
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let neg a = -1. |. a
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#+end_src
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*** Dot product
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#+begin_src ocaml :tangle (eval mli)
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val dot : t -> t -> float
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#+end_src
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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#+end_src
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*** Norm
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#+begin_src ocaml :tangle (eval mli)
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val norm : t -> float
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#+end_src
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$\ell{^2}$ norm of the vector.
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#+begin_src ocaml :tangle (eval ml) :exports none
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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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Coordinates can be printed in bohr or angstrom.
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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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#+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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@ -1,3 +1,4 @@
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(* [[file:../coordinate.org::*Type][Type:2]] *)
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type bohr
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type angstrom
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@ -11,79 +12,135 @@ type 'a point = xyz
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type t = bohr point
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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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type axis = X | Y | Z
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(* Type:2 ends here *)
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(* [[file:../coordinate.org::*~make~][~make~:2]] *)
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external make : 'a point -> t = "%identity"
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(* ~make~:2 ends here *)
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let a_to_b a = Constants.a0_inv *. a
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(* [[file:../coordinate.org::*~make_angstrom~][~make_angstrom~:2]] *)
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external make_angstrom : 'a point -> angstrom point = "%identity"
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(* ~make_angstrom~:2 ends here *)
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(* [[file:../coordinate.org::*~bohr_to_angstrom~][~bohr_to_angstrom~:2]] *)
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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
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{
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x = b_to_a x ;
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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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}
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z = b_to_a z ; }
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(* ~bohr_to_angstrom~:2 ends here *)
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(* [[file:../coordinate.org::*~angstrom_to_bohr~][~angstrom_to_bohr~:2]] *)
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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
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{
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x = a_to_b x ;
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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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}
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z = a_to_b z ; }
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(* ~angstrom_to_bohr~:2 ends here *)
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(* [[file:../coordinate.org::*~zero~][~zero~:2]] *)
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let zero =
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make { x = 0. ; y = 0. ; z = 0. }
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(* ~zero~:2 ends here *)
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(** Linear algebra *)
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let ( |. ) s { x ; y ; z } =
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make {
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x = s *. x ;
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y = s *. y ;
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z = s *. z ;
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}
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let ( |+ ) { x = x1 ; y = y1 ; z = z1 } { x = x2 ; y = y2 ; z = z2 } =
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make {
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x = x1 +. x2 ;
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y = y1 +. y2 ;
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z = z1 +. z2 ;
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}
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let ( |- ) { x = x1 ; y = y1 ; z = z1 } { x = x2 ; y = y2 ; z = z2 } =
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make {
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x = x1 -. x2 ;
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y = y1 -. y2 ;
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z = z1 -. z2 ;
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}
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let neg a = -1. |. a
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let dot { x = x1 ; y = y1 ; z = z1 } { x = x2 ; y = y2 ; z = z2 } =
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x1 *. x2 +. y1 *. y2 +. z1 *. z2
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let norm u =
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sqrt ( dot u u )
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(* [[file:../coordinate.org::*~get~][~get~:2]] *)
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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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(* ~get~:2 ends here *)
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(* #+begin_example
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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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* #+end_example *)
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(* [[file:../coordinate.org::*Scale][Scale:2]] *)
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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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(* Scale:2 ends here *)
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(* #+begin_example
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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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* #+end_example *)
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(* [[file:../coordinate.org::*Add][Add:2]] *)
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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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(* Add:2 ends here *)
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(* #+begin_example
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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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(* [[file:../coordinate.org::*Subtract][Subtract:2]] *)
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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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(* Subtract:2 ends here *)
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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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* #+end_example *)
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(* [[file:../coordinate.org::*Negative][Negative:2]] *)
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let neg a = -1. |. a
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(* Negative:2 ends here *)
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(* [[file:../coordinate.org::*Dot product][Dot product:2]] *)
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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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(* Dot product:2 ends here *)
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(* $\ell{^2}$ norm of the vector. *)
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(* [[file:../coordinate.org::*Norm][Norm:2]] *)
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let norm u =
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sqrt ( dot u u )
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(* Norm:2 ends here *)
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(* [[file:../coordinate.org::*Printers][Printers:2]] *)
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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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@ -94,4 +151,4 @@ let pp_bohr ppf c =
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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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(* Printers:2 ends here *)
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@ -1,10 +1,8 @@
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(** Type for 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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||||
*)
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(* Type
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*
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||||
* #+NAME: types *)
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||||
(* [[file:../coordinate.org::types][types]] *)
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type bohr
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||||
type angstrom
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@ -18,91 +16,117 @@ type 'a point = xyz
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type t = bohr point
|
||||
|
||||
val make : 'a point -> t
|
||||
(** Creates a point in atomic units *)
|
||||
|
||||
val make_angstrom : 'a point -> angstrom point
|
||||
(** Creates a point in Angstrom *)
|
||||
|
||||
type axis = X | Y | Z
|
||||
(* types ends here *)
|
||||
|
||||
(* ~make~
|
||||
*
|
||||
* Creates a point in atomic units. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~make~][~make~:1]] *)
|
||||
val make : 'a point -> t
|
||||
(* ~make~:1 ends here *)
|
||||
|
||||
(* ~make_angstrom~
|
||||
*
|
||||
* Creates a point in angstrom. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~make_angstrom~][~make_angstrom~:1]] *)
|
||||
val make_angstrom : 'a point -> angstrom point
|
||||
(* ~make_angstrom~:1 ends here *)
|
||||
|
||||
(* ~bohr_to_angstrom~
|
||||
*
|
||||
* Converts a point in bohr to angstrom. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~bohr_to_angstrom~][~bohr_to_angstrom~:1]] *)
|
||||
val bohr_to_angstrom : bohr point -> angstrom point
|
||||
(** Converts a point in bohr to angstrom. *)
|
||||
(* ~bohr_to_angstrom~:1 ends here *)
|
||||
|
||||
(* ~angstrom_to_bohr~
|
||||
*
|
||||
* Converts a point in angstrom to bohr. *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~angstrom_to_bohr~][~angstrom_to_bohr~:1]] *)
|
||||
val angstrom_to_bohr : angstrom point -> bohr point
|
||||
(** Converts a point in Angstrom to bohr. *)
|
||||
(* ~angstrom_to_bohr~:1 ends here *)
|
||||
|
||||
(* ~zero~
|
||||
*
|
||||
* ~zero~ = (0., 0., 0.) *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~zero~][~zero~:1]] *)
|
||||
val zero : bohr point
|
||||
(** [zero = { x = 0. ; y=0. ; z=0. }] *)
|
||||
(* ~zero~:1 ends here *)
|
||||
|
||||
(* ~get~
|
||||
*
|
||||
* Extracts the projection of the coordinate on an axis.
|
||||
*
|
||||
* #+begin_example
|
||||
* Coordinate.(get Y { x=1. ; y=2. ; z=3. })
|
||||
* - float: 2.
|
||||
* #+end_example *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*~get~][~get~:1]] *)
|
||||
val get : axis -> bohr point -> float
|
||||
(** Extracts the projection of the coordinate on an axis.
|
||||
(* ~get~:1 ends here *)
|
||||
|
||||
Example:
|
||||
|
||||
[Coordinate.(get Y) { x=1. ; y=2. ; z=3. } -> 2.]
|
||||
|
||||
*)
|
||||
|
||||
(** {1 Vector operations} *)
|
||||
(* Scale *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Scale][Scale:1]] *)
|
||||
val ( |. ) : float -> t -> t
|
||||
(** Scale by a float.
|
||||
(* Scale:1 ends here *)
|
||||
|
||||
Example:
|
||||
|
||||
[ 2. |. { x=1. ; y=2. ; z=3. } -> { x=2. ; y=4. ; z=6. } ]
|
||||
|
||||
*)
|
||||
(* Add *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Add][Add:1]] *)
|
||||
val ( |+ ) : t -> t -> t
|
||||
(** Add two vectors.
|
||||
(* Add:1 ends here *)
|
||||
|
||||
Example:
|
||||
|
||||
{[{ x=1. ; y=2. ; z=3. } |+ { x=2. ; y=3. ; z=1. } ->
|
||||
{ x=3. ; y=5. ; z=4. }]}
|
||||
|
||||
*)
|
||||
(* Subtract *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Subtract][Subtract:1]] *)
|
||||
val ( |- ) : t -> t -> t
|
||||
(** Subtract two vectors.
|
||||
(* Subtract:1 ends here *)
|
||||
|
||||
Example:
|
||||
|
||||
{[{ x=1. ; y=2. ; z=3. } |- { x=2. ; y=3. ; z=1. } ->
|
||||
{ x=-1. ; y=-1. ; z=2. }]}
|
||||
|
||||
*)
|
||||
(* Negative *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Negative][Negative:1]] *)
|
||||
val neg : t -> t
|
||||
(** Example:
|
||||
(* Negative:1 ends here *)
|
||||
|
||||
{[Coordinate.neg { x=1. ; y=2. ; z=-3. } ->
|
||||
{ x=-1. ; y=-2. ; z=3. }]}
|
||||
(* Dot product *)
|
||||
|
||||
*)
|
||||
|
||||
(* [[file:../coordinate.org::*Dot product][Dot product:1]] *)
|
||||
val dot : t -> t -> float
|
||||
(** Dot product. *)
|
||||
(* Dot product:1 ends here *)
|
||||
|
||||
(* Norm *)
|
||||
|
||||
|
||||
(* [[file:../coordinate.org::*Norm][Norm:1]] *)
|
||||
val norm : t -> float
|
||||
(** L{^2} norm of the vector. *)
|
||||
(* Norm:1 ends here *)
|
||||
|
||||
(* Printers
|
||||
*
|
||||
* Coordinates can be printed in bohr or angstrom. *)
|
||||
|
||||
|
||||
(** {2 Printers} *)
|
||||
|
||||
(* [[file:../coordinate.org::*Printers][Printers:1]] *)
|
||||
val pp : Format.formatter -> t -> unit
|
||||
|
||||
val pp_bohr: Format.formatter -> t -> unit
|
||||
|
||||
val pp_angstrom : Format.formatter -> t -> unit
|
||||
|
||||
(* Printers:1 ends here *)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user