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103 lines
2.7 KiB
OCaml
103 lines
2.7 KiB
OCaml
(** All utilities which should be included in all source files are defined here *)
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(** {2 Functions from libm} *)
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external erf_float : float -> float = "erf_float_bytecode" "erf_float"
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[@@unboxed] [@@noalloc]
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(** Error function [erf] from [libm] *)
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external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float"
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[@@unboxed] [@@noalloc]
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(** Complementary error function [erfc] from [libm] *)
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external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float"
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[@@unboxed] [@@noalloc]
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(** Gamma function [gamma] from [libm] *)
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(** {2 General functions} *)
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val fact : int -> float
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(** Factorial function.
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@raise Invalid_argument for negative arguments or arguments >100.
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*)
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val pow : float -> int -> float
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(** Fast implementation of the power function for small integer powers *)
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val chop : float -> (unit -> float) -> float
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(** In [chop a f], evaluate [f] only if the absolute value of [a] is larger
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than {!Constants.epsilon}, and return [a *. f ()].
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*)
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(** {2 Functions related to the Boys function} *)
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val incomplete_gamma : alpha:float -> float -> float
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(** {{:https://en.wikipedia.org/wiki/Incomplete_gamma_function}
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Lower incomplete gamma function}
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@raise Failure when the calculation doesn't converge.
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*)
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val boys_function : maxm:int -> float -> float array
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(** {{:https://link.springer.com/article/10.1007/s10910-005-9023-3}
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Generalized Boys function}.
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@param maxm Maximum total angular momentum.
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*)
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(** {2 Extension of the Array module} *)
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val array_sum : float array -> float
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(** Returns the sum of all the elements of the array *)
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val array_product : float array -> float
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(** Returns the product of all the elements of the array *)
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(** {2 Linear algebra } *)
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val diagonalize_symm : Lacaml.D.mat -> Lacaml.D.mat * Lacaml.D.vec
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(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *)
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val xt_o_x : o:Lacaml.D.mat -> x:Lacaml.D.mat -> Lacaml.D.mat
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(** Computes X{^T}.O.X *)
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(** {2 Printers} *)
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val pp_float_array_size : Format.formatter -> float array -> unit
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(** Example:
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{[
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[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000
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]
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]}
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*)
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val pp_float_array : Format.formatter -> float array -> unit
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(** Example:
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{[
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[ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000
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]
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]}
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*)
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val pp_float_2darray_size : Format.formatter -> float array array -> unit
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(** Example:
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{[
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[
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2:[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
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[ 4: 1.000000 2.000000 3.000000 4.000000 ] ]
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]}
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*)
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val pp_float_2darray : Format.formatter -> float array array -> unit
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(** Example:
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{[
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[ [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ]
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[ 1.000000 2.000000 3.000000 4.000000 ] ]
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]}
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*)
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