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142 lines
4.0 KiB
OCaml
142 lines
4.0 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 Extension of the List module} *)
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val list_some : 'a option list -> 'a list
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(** Filters out all [None] elements of the list, and returns the elements without
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the [Some]. *)
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val list_range : ?start:int -> int -> int list
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(** Returns a list [start ; start+1 ; ... ; start+n]. Default is [start=0]. *)
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(** {2 Useful streams} *)
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val stream_range : ?start:int -> int -> int Stream.t
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(** Returns a stream <start ; start+1 ; ... ; start+n>. Default is [start=0]. *)
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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 {% $\mathbf{X^\dag\, O\, X}$ %} *)
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val canonical_ortho: ?thresh:float -> overlap:Lacaml.D.mat -> Lacaml.D.mat -> Lacaml.D.mat
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(** Canonical orthogonalization. [overlap] is the overlap matrix {% $\mathbf{S}$ %},
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and the last argument contains the vectors {% $\mathbf{C}$ %} to orthogonalize.
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{%
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$$
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\mathbf{C_\bot} = \mathbf{C\, U\, D^{-1/2}}, \;
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\mathbf{U\, D\, V^\dag} = \mathbf{S}
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$$
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%}
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*)
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val debug_matrix: string -> Lacaml.D.mat -> unit
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(** Prints a matrix in stdout for debug *)
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val matrix_of_file : string -> Lacaml.D.mat
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(** Reads a matrix from a file with format "%d %d %f" corresponding to
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[i, j, A.{i,j}]. *)
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val sym_matrix_of_file : string -> Lacaml.D.mat
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(** Reads a symmetric matrix from a file with format "%d %d %f" corresponding to
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[i, j, A.{i,j}]. *)
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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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val pp_matrix : Format.formatter -> Lacaml.D.mat -> unit
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