open Lacaml.D (** All utilities which should be included in all source files are defined here *) (** {2 Functions from libm} *) external erf_float : float -> float = "erf_float_bytecode" "erf_float" [@@unboxed] [@@noalloc] (** Error function [erf] from [libm] *) external erfc_float : float -> float = "erfc_float_bytecode" "erfc_float" [@@unboxed] [@@noalloc] (** Complementary error function [erfc] from [libm] *) external gamma_float : float -> float = "gamma_float_bytecode" "gamma_float" [@@unboxed] [@@noalloc] (** Gamma function [gamma] from [libm] *) (** {2 General functions} *) val fact : int -> float (** Factorial function. @raise Invalid_argument for negative arguments or arguments >100. *) val binom : int -> int -> int (** Binomial coefficient. [binom n k] {% $= C_n^k$ %}. *) val pow : float -> int -> float (** Fast implementation of the power function for small integer powers *) val chop : float -> (unit -> float) -> float (** In [chop a f], evaluate [f] only if the absolute value of [a] is larger than {!Constants.epsilon}, and return [a *. f ()]. *) (** {2 Functions related to the Boys function} *) val incomplete_gamma : alpha:float -> float -> float (** {{:https://en.wikipedia.org/wiki/Incomplete_gamma_function} Lower incomplete gamma function} @raise Failure when the calculation doesn't converge. *) val boys_function : maxm:int -> float -> float array (** {{:https://link.springer.com/article/10.1007/s10910-005-9023-3} Generalized Boys function}. @param maxm Maximum total angular momentum. *) (** {2 Extension of the Array module} *) val array_sum : float array -> float (** Returns the sum of all the elements of the array *) val array_product : float array -> float (** Returns the product of all the elements of the array *) (** {2 Extension of the List module} *) val list_some : 'a option list -> 'a list (** Filters out all [None] elements of the list, and returns the elements without the [Some]. *) val list_range : int -> int -> int list (** [list_range first last] returns a list [first; first+1 ; ... ; last-1 ; last ]. *) val list_pack : int -> 'a list -> 'a list list (** Example: {[ list_pack 3 [ 1; 2; 3; ...; 18; 19; 20 ] = [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]; [10; 11; 12]; [13; 14; 15]; [16; 17; 18]; [19; 20]] ]} *) (** {2 Useful streams} *) val stream_range : int -> int -> int Stream.t (** [stream_range first last] returns a stream . *) val stream_to_list : 'a Stream.t -> 'a list (** Read a stream and put items in a list. *) (** {2 Linear algebra } *) val normalize : Vec.t -> Vec.t (** Returns a the vector normalized *) val normalize_mat : Mat.t -> Mat.t (** Returns the matrix with all the column vectors normalized *) val diagonalize_symm : Mat.t -> Mat.t * Vec.t (** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *) val xt_o_x : o:Mat.t -> x:Mat.t -> Mat.t (** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *) val x_o_xt : o:Mat.t -> x:Mat.t -> Mat.t (** Computes {% $\mathbf{X\, O\, X^\dag}$ %} *) val qr_ortho : Mat.t -> Mat.t (** QR orthogonalization of the input matrix *) val canonical_ortho: ?thresh:float -> overlap:Mat.t -> Mat.t -> Mat.t (** Canonical orthogonalization. [overlap] is the overlap matrix {% $\mathbf{S}$ %}, and the last argument contains the vectors {% $\mathbf{C}$ %} to orthogonalize. {% $$ \mathbf{C_\bot} = \mathbf{C\, U\, D^{-1/2}}, \; \mathbf{U\, D\, V^\dag} = \mathbf{S} $$ %} *) val debug_matrix: string -> Mat.t -> unit (** Prints a matrix in stdout for debug *) val matrix_of_file : string -> Mat.t (** Reads a matrix from a file with format "%d %d %f" corresponding to [i, j, A.{i,j}]. *) val sym_matrix_of_file : string -> Mat.t (** Reads a symmetric matrix from a file with format "%d %d %f" corresponding to [i, j, A.{i,j}]. *) (** {2 Bitstring functions} *) val bit_permtutations : int -> int -> Z.t list (** [bit_permtutations m n] generates the list of all possible [n]-bit strings with [m] bits set to 1. Algorithm adapted from {{:https://graphics.stanford.edu/~seander/bithacks.html#NextBitPermutation} Bit twiddling hacks}. Example: {[ bit_permtutations 2 4 = [ 0011 ; 0101 ; 0110 ; 1001 ; 1010 ; 1100 ] ]} *) (** {2 Printers} *) val pp_float_array_size : Format.formatter -> float array -> unit (** Example: {[ [ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] ]} *) val pp_float_array : Format.formatter -> float array -> unit (** Example: {[ [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] ]} *) val pp_float_2darray_size : Format.formatter -> float array array -> unit (** Example: {[ [ 2:[ 6: 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] [ 4: 1.000000 2.000000 3.000000 4.000000 ] ] ]} *) val pp_float_2darray : Format.formatter -> float array array -> unit (** Example: {[ [ [ 1.000000 1.732051 1.732051 1.000000 1.732051 1.000000 ] [ 1.000000 2.000000 3.000000 4.000000 ] ] ]} *) val pp_bitstring : int -> Format.formatter -> Z.t -> unit (** Example: [ pp_bitstring 14 ppf z -> +++++------+-- ] *) val pp_matrix : Format.formatter -> Mat.t -> unit