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152 lines
3.5 KiB
OCaml
152 lines
3.5 KiB
OCaml
(* [[file:~/QCaml/common/coordinate.org::*Type][Type:2]] *)
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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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(* Type:2 ends here *)
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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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(* [[file:~/QCaml/common/coordinate.org::*Creation][Creation:2]] *)
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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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(* Creation:2 ends here *)
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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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(* [[file:~/QCaml/common/coordinate.org::*Conversion][Conversion: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 { 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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(* Conversion:2 ends here *)
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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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* | $\vert .$ | Scales the vector by a constant |
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* | $\vert +$ | Adds two vectors |
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* | $\vert -$ | Subtracts two vectors |
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*
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* Example:
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* #+begin_example
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* Coordinate.neg { x=1. ; y=2. ; z=3. } ;;
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* - : Coordinate.t = -1.0000 -2.0000 -3.0000
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*
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* Coordinate.(get Y { x=1. ; y=2. ; z=3. }) ;;
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* - : float = 2.
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*
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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 = 2.0000 4.0000 6.0000
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*
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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 = 3.0000 5.0000 4.0000
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*
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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 = -1.0000 -1.0000 2.0000
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* #+end_example *)
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(* [[file:~/QCaml/common/coordinate.org::*Vector%20operations][Vector operations: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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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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(* Vector operations:2 ends here *)
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(* Coordinates can be printed in bohr or angstrom. *)
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(* [[file:~/QCaml/common/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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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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(* Printers:2 ends here *)
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