10
1
mirror of https://gitlab.com/scemama/qmcchem.git synced 2024-11-18 12:03:39 +01:00
qmcchem/ocaml/Random_variable.ml

751 lines
18 KiB
OCaml

open Core.Std
open Qptypes
type t =
{ property : Property.t ;
data : Block.t list;
}
module Average = struct
include Sample
end
module Error = struct
include Sample
end
module Variance = struct
include Sample
end
module Skewness: sig
type t
val to_float : t -> float
val of_float : float -> t
val to_string : t -> string
end = struct
type t = float
let to_string = Float.to_string
let to_float x = x
let of_float x = x
end
module Kurtosis: sig
type t
val to_float : t -> float
val of_float : float -> t
val to_string : t -> string
end = struct
type t = float
let to_string = Float.to_string
let to_float x = x
let of_float x = x
end
module GaussianDist: sig
type t
val create : mu:Average.t -> sigma2:Variance.t -> t
val eval : g:t -> x:float -> float
end = struct
type t = { mu: Average.t ; sigma2: Variance.t }
let create ~mu ~sigma2 =
{ mu ; sigma2 }
let eval ~g ~x =
let { mu ; sigma2 } =
g
in
let mu =
Average.to_float mu
and sigma2 =
Variance.to_float sigma2
in
let x2 =
(x -. mu) *. ( x -. mu) /. sigma2
in
let pi =
acos (-1.)
in
let c =
1. /. (sqrt (sigma2 *. (pi +. pi)))
in
c *. exp ( -0.5 *. x2)
end
(** Build from raw data. Range values are given in percent. *)
let of_raw_data ?(locked=true) ~range property =
let data =
Block.raw_data ~locked ()
|> List.filter ~f:(fun x -> x.Block.property = property)
in
let data_in_range rmin rmax =
let total_weight =
List.fold_left data ~init:0. ~f:(fun accu x ->
(Weight.to_float x.Block.weight) +. accu
)
in
let wmin, wmax =
rmin *. total_weight *. 0.01,
rmax *. total_weight *. 0.01
in
let (_, new_data) =
List.fold_left data ~init:(0.,[]) ~f:(fun (wsum, l) x ->
if (wsum > wmax) then
(wsum,l)
else
begin
let wsum_new =
wsum +. (Weight.to_float x.Block.weight)
in
if (wsum_new > wmin) then
(wsum_new, x::l)
else
(wsum_new, l)
end
)
in
List.rev new_data
in
let result =
match range with
| (0.,100.) -> { property ; data }
| (rmin,rmax) -> { property ; data=data_in_range rmin rmax }
in
result
(** Compute average *)
let average { property ; data } =
if Property.is_scalar property then
let (num,denom) =
List.fold ~init:(0., 0.) ~f:(fun (an, ad) x ->
let num =
(Weight.to_float x.Block.weight) *. (Sample.to_float x.Block.value)
and den =
(Weight.to_float x.Block.weight)
in (an +. num, ad +. den)
) data
in
num /. denom
|> Average.of_float
else
let dim =
match data with
| [] -> 1
| x :: tl -> Sample.dimension x.Block.value
in
let (num,denom) =
List.fold ~init:(Array.create ~len:dim 0. , 0.) ~f:(fun (an, ad) x ->
let num =
Array.map (Sample.to_float_array x.Block.value) ~f:(fun y ->
(Weight.to_float x.Block.weight) *. y)
and den = (Weight.to_float x.Block.weight)
in (
Array.mapi an ~f:(fun i y -> y +. num.(i)) ,
ad +. den)
) data
in
let denom_inv =
1. /. denom
in
Array.map num ~f:(fun x -> x *. denom_inv)
|> Average.of_float_array ~dim
(** Compute sum (for CPU/Wall time) *)
let sum { property ; data } =
List.fold data ~init:0. ~f:(fun accu x ->
let num = (Weight.to_float x.Block.weight) *. (Sample.to_float x.Block.value)
in accu +. num
)
(** Calculation of the average and error bar *)
let ave_error { property ; data } =
let rec loop ~sum ~avsq ~ansum ~avsum ~n ?idx = function
| [] ->
begin
if (n > 0.) then
( Average.of_float (sum /. ansum),
Some (Error.of_float (sqrt ( Float.abs ( avsq /.( ansum *. n)))) ))
else
( Average.of_float (sum /. ansum), None)
end
| (x,w) :: tail ->
begin
let avcu0 =
avsum /. ansum
in
let xw =
x *. w
in
let ansum, avsum, sum =
ansum +. w ,
avsum +. xw ,
sum +. xw
in
loop tail
~sum:sum
~avsq:(avsq +. (1. -. (w /. ansum)) *. (x -. avcu0)
*. (x -. avcu0) *. w)
~avsum:avsum
~ansum:ansum
~n:(n +. 1.)
end
in
let ave_error_scalar = function
| [] -> (Average.of_float 0., None)
| (x,w) :: tail ->
loop tail
~sum:(x *. w)
~avsq:0.
~ansum:w
~avsum:(x *. w)
~n:0.
in
if (Property.is_scalar property) then
List.map data ~f:(fun x ->
(Sample.to_float x.Block.value,
Weight.to_float x.Block.weight)
)
|> ave_error_scalar
else
match data with
| [] -> (Average.of_float 0., None)
| head::tail as list_of_samples ->
let dim =
head.Block.value
|> Sample.dimension
in
let result =
Array.init dim ~f:(fun idx ->
List.map list_of_samples ~f:(fun x ->
(Sample.to_float ~idx x.Block.value,
Weight.to_float x.Block.weight)
)
|> ave_error_scalar
)
in
( Array.map result ~f:(fun (x,_) -> Average.to_float x)
|> Average.of_float_array ~dim ,
if (Array.length result < 2) then
None
else
Some (Array.map result ~f:(function
| (_,Some y) -> Error.to_float y
| (_,None) -> 0.)
|> Average.of_float_array ~dim)
)
(** Fold function for block values *)
let fold_blocks ~f { property ; data } =
let init = match List.hd data with
| None -> 0.
| Some block -> Sample.to_float block.Block.value
in
List.fold_left data ~init:init ~f:(fun accu block ->
let x = Sample.to_float block.Block.value
in f accu x
)
(** Convergence plot *)
let convergence { property ; data } =
let rec loop ~sum ~avsq ~ansum ~avsum ~n ~accu = function
| [] -> List.rev accu
| head :: tail ->
begin
let x = Sample.to_float head.Block.value
and w = Weight.to_float head.Block.weight
and avcu0 = avsum /. ansum
in
let xw = x *. w
in
let ansum = ansum +. w
and avsum = avsum +. xw
and sum = sum +. xw
in
let accu =
if (n > 0.) then
(sum /. ansum, sqrt ( Float.abs ( avsq /.( ansum *. n))))::accu
else
(sum /. ansum, 0.)::accu
in
loop tail
~sum:sum
~avsq:(avsq +. (1. -. (w /. ansum)) *. (x -. avcu0)
*. (x -. avcu0) *. w)
~avsum:avsum
~ansum:ansum
~n:(n +. 1.)
~accu:accu
end
in
match data with
| [] -> []
| head :: tail ->
begin
let x = Sample.to_float head.Block.value
and w = Weight.to_float head.Block.weight
in
let s = x *. w in
loop tail
~sum:s
~avsq:0.
~ansum:w
~avsum:s
~n:0.
~accu:[ (s /. w, 0.) ]
end
let rev_convergence { property ; data } =
let p = { property=property ; data = List.rev data } in
convergence p
|> List.rev
(** Min and max of block *)
let min_block =
fold_blocks ~f:(fun accu x ->
if (x < accu) then x
else accu
)
let max_block =
fold_blocks ~f:(fun accu x ->
if (x > accu) then x
else accu
)
(** Create a hash table for merging *)
let create_hash ~hashable ~create_key ?(update_block_id=(fun x->x)) t =
let table = Hashtbl.create ~hashable:hashable ()
in
List.iter t.data ~f:(fun block ->
let key = create_key block
in
let open Block in
Hashtbl.change table key (function
| Some current ->
let wc, wb =
Weight.to_float current.weight,
Weight.to_float block.weight
in
let sw =
wc +. wb
in
if (Property.is_scalar current.property) then
let vc, vb =
Sample.to_float current.value,
Sample.to_float block.value
in Some
{ property = current.property ;
weight = Weight.of_float sw ;
value = Sample.of_float ((wc *. vc +. wb *. vb) /. sw);
block_id = update_block_id block.block_id;
pid = block.pid ;
compute_node = block.compute_node;
}
else
let vc, vb =
Sample.to_float_array current.value,
Sample.to_float_array block.value
and dim =
Sample.dimension current.value
in Some
{ property = current.property ;
weight = Weight.of_float sw ;
value =
Array.init dim ~f:(fun i -> ((wc *. vc.(i) +. wb *. vb.(i)) /. sw))
|> Sample.of_float_array ~dim ;
block_id = update_block_id block.block_id;
pid = block.pid ;
compute_node = block.compute_node;
}
| None -> Some
{ property = block.property ;
weight = block.weight;
value = block.value ;
block_id = update_block_id block.block_id;
pid = block.pid ;
compute_node = block.compute_node;
}
)
);
table
(** Genergic merge function *)
let merge ~hashable ~create_key ?update_block_id t =
let table = create_hash ~hashable:hashable ~create_key:create_key
?update_block_id:update_block_id t
in
{ property = t.property ;
data = Hashtbl.to_alist table
|> List.sort ~cmp:(fun x y ->
if (x>y) then 1
else if (x<y) then -1
else 0)
|> List.map ~f:(fun (x,y) -> y)
}
(** Merge per block id *)
let merge_per_block_id =
merge
~hashable:Int.hashable
~create_key:(fun block -> Block_id.to_int block.Block.block_id)
(** Merge per compute_node *)
let merge_per_compute_node =
merge
~hashable:String.hashable
~create_key:(fun block ->
Printf.sprintf "%s"
(Compute_node.to_string block.Block.compute_node) )
(** Merge per Compute_node and PID *)
let merge_per_compute_node_and_pid =
merge
~hashable:String.hashable
~create_key:(fun block ->
Printf.sprintf "%s %10.10d"
(Compute_node.to_string block.Block.compute_node)
(Pid.to_int block.Block.pid) )
(** Merge per Compute_node and BlockId *)
let merge_per_compute_node_and_block_id =
merge
~hashable:String.hashable
~create_key:(fun block ->
Printf.sprintf "%s %10.10d"
(Compute_node.to_string block.Block.compute_node)
(Block_id.to_int block.Block.block_id) )
(** Merge two consecutive blocks *)
let compress =
merge
~hashable:String.hashable
~create_key:(fun block ->
Printf.sprintf "%s %10.10d" (Compute_node.to_string block.Block.compute_node)
(((Block_id.to_int block.Block.block_id)+1)/2))
~update_block_id:(fun block_id ->
((Block_id.to_int block_id)+1)/2
|> Block_id.of_int )
(** Last value on each compute node (for wall_time) *)
let max_value_per_compute_node t =
let table = Hashtbl.create ~hashable:String.hashable ()
in
let create_key block =
Printf.sprintf "%s %10.10d"
(Compute_node.to_string block.Block.compute_node)
(Pid.to_int block.Block.pid)
in
List.iter t.data ~f:(fun block ->
let key = create_key block
in
let open Block in
Hashtbl.change table key (function
| Some current ->
let vc = Sample.to_float current.value
and vb = Sample.to_float block.value
in
if (vc > vb) then
Some current
else
Some block
| None -> Some block
)
);
{ property = t.property ;
data = Hashtbl.to_alist table
|> List.sort ~cmp:(fun x y ->
if (x>y) then 1
else if (x<y) then -1
else 0)
|> List.map ~f:(fun (x,y) -> y)
}
(** String representation *)
let to_string p =
match p.property with
| Property.Cpu -> Printf.sprintf "%s" (Time.Span.to_string (Time.Span.of_sec (sum p)))
| Property.Wall -> Printf.sprintf "%s" (Time.Span.to_string (Time.Span.of_sec (sum (max_value_per_compute_node p))))
| Property.Accep -> Printf.sprintf "%16.10f" (average p |> Average.to_float)
| _ ->
begin
if Property.is_scalar p.property then
match ave_error p with
| (ave, Some error) ->
let (ave, error) =
Average.to_float ave,
Error.to_float error
in
Printf.sprintf "%16.10f +/- %16.10f" ave error
| (ave, None) ->
let ave =
Average.to_float ave
in
Printf.sprintf "%16.10f" ave
else
match ave_error p with
| (ave, Some error) ->
let idxmax =
Average.dimension ave
in
let rec f accu idx =
if (idx < idxmax) then
let (ave, error) =
Average.to_float ~idx ave,
Error.to_float ~idx error
in
let s =
Printf.sprintf "%8d : %16.10f +/- %16.10f ;\n" (idx+1) ave error
in
f (accu ^ s) (idx+1)
else
accu
in
(f "[ \n" 0) ^ " ]"
| (ave, None) ->
Average.to_float ave
|> Printf.sprintf "%16.10f"
end
(** Compress block files : Merge all the blocks computed on the same host *)
let compress_files () =
Block._raw_data := None;
let properties =
Lazy.force Block.properties
in
(* Create temporary file *)
let dir_name =
Block.dir_name
in
let dir_name =
Lazy.force dir_name
in
let files =
Sys.ls_dir dir_name
|> List.filter ~f:(fun x ->
match String.substr_index ~pattern:"locked" x with
| Some x -> false
| None -> true
)
|> List.map ~f:(fun x -> dir_name^x)
in
let out_channel_dir =
Filename.temp_dir ~in_dir:(!Ezfio.ezfio_filename ^ "/blocks/") "qmc" ""
in
let out_channel_name =
let hostname =
Lazy.force Qmcchem_config.hostname
and suffix =
Unix.getpid ()
|> Pid.to_string
in
String.concat [ hostname ; "." ; suffix ]
in
let block_channel =
Out_channel.create (out_channel_dir ^ out_channel_name)
in
List.iter properties ~f:(fun p ->
let l =
match p with
| Property.Cpu
| Property.Accep ->
of_raw_data ~locked:false ~range:(0.,100.) p
|> merge_per_compute_node
| Property.Wall ->
of_raw_data ~locked:false ~range:(0.,100.) p
|> max_value_per_compute_node
| _ ->
of_raw_data ~locked:false ~range:(0.,100.) p
|> merge_per_compute_node_and_block_id
in
List.iter l.data ~f:(fun x ->
Out_channel.output_string block_channel (Block.to_string x);
Out_channel.output_char block_channel '\n';
);
);
Out_channel.close block_channel;
List.iter files ~f:Unix.remove ;
Unix.rename ~src:(out_channel_dir^out_channel_name) ~dst:(dir_name^out_channel_name);
Unix.rmdir out_channel_dir
(** Autocovariance function (not weighted) *)
let autocovariance { property ; data } =
let ave =
average { property ; data }
|> Average.to_float
and data =
match (merge_per_block_id { property ; data })
with { property ; data } -> Array.of_list data
in
let x_t =
Array.map ~f:(fun x -> (Sample.to_float x.Block.value) -. ave) data
in
let f i =
let denom =
if (i > 1) then (Float.of_int i) else 1.
in
let r =
Array.sub ~pos:0 ~len:i x_t
|> Array.fold ~init:0. ~f:(fun accu x ->
accu +. x *. x_t.(i))
in
r /. denom
in
Array.init ~f (Array.length data)
|> Array.to_list
(** Computes the first 4 centered cumulants (zero mean) *)
let centered_cumulants { property ; data } =
let ave =
average { property ; data }
|> Average.to_float
in
let centered_data =
List.map ~f:(fun x ->
( (Weight.to_float x.Block.weight),
(Sample.to_float x.Block.value) -. ave )
)
data
in
let var =
let (num, denom) =
List.fold ~init:(0., 0.) ~f:(fun (a2, ad) (w,x) ->
let x2 = x *. x
in
let var = w *. x2
and den = w
in (a2 +. var, ad +. den)
) centered_data
in num /. denom
in
let centered_data =
let sigma_inv =
1. /. (sqrt var)
in
List.map ~f:(fun x ->
( (Weight.to_float x.Block.weight),
( (Sample.to_float x.Block.value) -. ave ) *. sigma_inv )
)
data
in
let (cum3,cum4) =
let (cum3, cum4, denom) =
List.fold ~init:(0., 0., 0.) ~f:(fun (a3, a4, ad) (w,x) ->
let x2 = x *. x
in
let cum3 = w *. x2 *. x
and cum4 = w *. x2 *. x2
and den = w
in (a3 +. cum3, a4 +. cum4, ad +. den)
) centered_data
in
( cum3 /. denom, cum4 /. denom -. 3. )
in
[| ave ; var ; cum3 ; cum4 |]
(** Computes a histogram *)
let histogram { property ; data } =
let min, max =
(min_block { property ; data }),
(max_block { property ; data })
in
let length =
max -. min
and n =
List.length data
|> Float.of_int
|> sqrt
in
let delta_x =
length /. (n-.1.)
and result =
Array.init ~f:(fun _ -> 0.) (Int.of_float (n +. 1.))
in
List.iter ~f:(fun x ->
let w =
(Weight.to_float x.Block.weight)
and x =
(Sample.to_float x.Block.value)
in
let i =
(x -. min) /. delta_x +. 0.5
|> Float.to_int
in
result.(i) <- result.(i) +. w
) data
;
let norm =
1. /. ( delta_x *. (
Array.fold ~init:0. ~f:(fun accu x -> accu +. x) result
) )
in
Array.mapi ~f:(fun i x -> (min +. (Float.of_int i)*.delta_x, x *. norm) ) result
|> Array.to_list