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QCaml/Notebooks/SpVec.ipynb

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Added SpVec notebook
2019-11-25 18:44:46 +01:00
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"- : unit = ()\n",
"Findlib has been successfully loaded. Additional directives:\n",
" #require \"package\";; to load a package\n",
" #list;; to list the available packages\n",
" #camlp4o;; to load camlp4 (standard syntax)\n",
" #camlp4r;; to load camlp4 (revised syntax)\n",
" #predicates \"p,q,...\";; to set these predicates\n",
" Topfind.reset();; to force that packages will be reloaded\n",
" #thread;; to enable threads\n",
"\n",
"- : unit = ()\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/scemama/qp2/external/opam/default/lib/bytes: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/base64: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/base64/base64.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/result: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/result/result.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ppx_deriving/runtime: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ppx_deriving_yojson/runtime: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/unix.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/uuidm: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/uuidm/uuidm.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/easy-format: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/easy-format/easy_format.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/biniou: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/biniou/biniou.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/yojson: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/yojson/yojson.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/jupyter: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/jupyter/jupyter.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/jupyter/notebook: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamlbytecomp.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamltoplevel.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/ocaml/bigarray.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/lacaml: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/lacaml/lacaml.cma: loaded\n",
"/home/scemama/qp2/external/opam/default/lib/lacaml/top: added to search path\n",
"/home/scemama/qp2/external/opam/default/lib/lacaml/top/lacaml_top.cma: loaded\n"
]
}
],
"source": [
"#use \"topfind\";;\n",
"#require \"jupyter.notebook\";;\n",
"#require \"lacaml.top\" ;;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sparse Vector module\n",
"----------------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A sparse vector is a structure made of:\n",
"* The dimension of the vector space\n",
"* The number of non-zeros\n",
"* An array of indices\n",
"* An array of values\n",
"\n",
"The indices are stored in an ``int Bigarray`` and the values are stored in a ``Lacaml.Vec.t``\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Types"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"module L = Lacaml.D\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"type t = {\n",
" dim : int;\n",
" nnz : int;\n",
" indices :\n",
" (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t;\n",
" values : L.Vec.t;\n",
"}\n"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"module L = Lacaml.D\n",
"\n",
"type t =\n",
" {\n",
" dim: int ;\n",
" nnz: int ;\n",
" indices: (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t ; (* Indices *)\n",
" values: L.Vec.t\n",
" }\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Printers"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val pp : Format.formatter -> t -> unit = <fun>\n"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let pp ppf t =\n",
" let pp_data ppf t =\n",
" for i=1 to t.nnz do\n",
" Format.fprintf ppf \"@[(%d,@ %f)@]@;\" t.indices.{i} t.values.{i}\n",
" done\n",
" in\n",
" Format.fprintf ppf \"@[{@[dim:@ %d@]@;@[%a@]}@]\" t.dim pp_data t"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Creators"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val of_vec : ?threshold:float -> Lacaml.D.vec -> t = <fun>\n"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let of_vec ?(threshold=0.) v =\n",
" let dim = L.Vec.dim v in\n",
" let buffer_idx = Bigarray.(Array1.create int fortran_layout) dim in\n",
" let buffer_val = Bigarray.(Array1.create float64 fortran_layout) dim in\n",
" let check = \n",
" if threshold = 0. then\n",
" fun x -> x <> 0.\n",
" else\n",
" fun x -> (abs_float x) > 0.\n",
" in\n",
" let rec aux k i =\n",
" if i > dim then\n",
" k-1\n",
" else if check v.{i} then\n",
" ( buffer_idx.{k} <- i ;\n",
" buffer_val.{k} <- v.{i} ;\n",
" aux (k+1) (i+1)\n",
" )\n",
" else\n",
" aux k (i+1)\n",
" in\n",
" let nnz = aux 1 1 in\n",
" let indices = Bigarray.(Array1.create int fortran_layout) nnz in\n",
" let values = L.Vec.create nnz in\n",
" for i=1 to nnz do\n",
" indices.{i} <- buffer_idx.{i};\n",
" values.{i} <- buffer_val.{i};\n",
" done ;\n",
" { dim ; nnz ; indices ; values }\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val make0 : int -> t = <fun>\n"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let make0 dim =\n",
" { dim ;\n",
" nnz = 0;\n",
" indices = Bigarray.(Array1.create int fortran_layout) 32 ;\n",
" values = L.Vec.create 32;\n",
" }"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val of_vec : ?threshold:float -> Lacaml.D.vec -> t = <fun>\n"
]
},
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val of_array : ?threshold:float -> float array -> t = <fun>\n"
]
},
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let of_vec ?(threshold=0.) v =\n",
" let dim = L.Vec.dim v in\n",
" let buffer_idx = Bigarray.(Array1.create int fortran_layout) dim in\n",
" let buffer_val = Bigarray.(Array1.create float64 fortran_layout) dim in\n",
" let check = \n",
" if threshold = 0. then\n",
" fun x -> x <> 0.\n",
" else\n",
" fun x -> (abs_float x) > 0.\n",
" in\n",
" let rec aux k i =\n",
" if i > dim then\n",
" k-1\n",
" else if check v.{i} then\n",
" ( buffer_idx.{k} <- i ;\n",
" buffer_val.{k} <- v.{i} ;\n",
" aux (k+1) (i+1)\n",
" )\n",
" else\n",
" aux k (i+1)\n",
" in\n",
" let nnz = aux 1 1 in\n",
" let indices = Bigarray.(Array1.create int fortran_layout) nnz in\n",
" let values = L.Vec.create nnz in\n",
" for i=1 to nnz do\n",
" indices.{i} <- buffer_idx.{i};\n",
" values.{i} <- buffer_val.{i};\n",
" done ;\n",
" { dim ; nnz ; indices ; values }\n",
"\n",
"\n",
"let of_array ?(threshold=0.) a =\n",
" L.Vec.of_array a\n",
" |> of_vec ~threshold "
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val copy : t -> t = <fun>\n"
]
},
"execution_count": 78,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let copy t =\n",
" let indices = \n",
" Bigarray.(Array1.create int fortran_layout) t.nnz\n",
" in\n",
" Bigarray.Array1.blit t.indices indices ;\n",
" let values = L.copy t.values in\n",
" { dim = t.dim ;\n",
" nnz = t.nnz ;\n",
" indices ; values }"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val x : t =\n",
" {dim = 10; nnz = 0; indices = <abstr>;\n",
" values =\n",
" R1 R2 R3 R30 R31 R32\n",
" 6.9331E-310 6.9331E-310 0 ... 6.9331E-310 6.9331E-310 6.9331E-310}\n"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val dense_a : t =\n",
" {dim = 9; nnz = 5; indices = <abstr>;\n",
" values = R1 R2 R3 R4 R5\n",
" 1 -2 0.5 1E-08 3}\n"
]
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
},
{
"ename": "error",
"evalue": "compile_error",
"output_type": "error",
"traceback": [
"\u001b[32mFile \"[79]\", line 6, characters 22-29:\n\u001b[31mError: This expression has type t but an expression was expected of type\n Lacaml.D.vec =\n (float, Bigarray.float64_elt, Bigarray.fortran_layout)\n Bigarray.Array1.t\n\u001b[36m 5: \u001b[30m \n\u001b[36m 6: \u001b[30mlet sparse_a = of_vec \u001b[4mdense_a\u001b[0m\u001b[30m \n\u001b[36m 7: \u001b[30m\u001b[0m\n"
]
}
],
"source": [
"let x = make0 10 \n",
"\n",
"let dense_a = \n",
" of_array [| 1. ; -2. ; 0. ; 0. ; 0.5 ; 1.e-8 ; 0. ; 3. ; 0. |]\n",
" \n",
"let sparse_a = of_vec dense_a \n",
"\n",
"let _ =\n",
" copy sparse_a = sparse_a\n",
" \n",
"let _ =\n",
" copy sparse_a == sparse_a\n",
"\n",
"let () = \n",
" Format.printf \"@.@[%a@]@.\" pp sparse_a"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# aX + Y\n",
"\n",
"Run along all the entries of `X` and `Y` simultaneously with indices `k` and `l`. `m` is the index of the new array.\n",
"\n",
"if `k<l`, update using `a*x[k]`.\n",
"\n",
"if `k>l`, update using `y[l]`.\n",
"\n",
"if `k=l`, update using `a*x[k] + y[l]`."
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val axpy : ?threshold:float -> ?alpha:float -> t -> t -> t = <fun>\n"
]
},
"execution_count": 105,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let axpy ?(threshold=0.) ?(alpha=1.) x y =\n",
"\n",
" if dim x <> dim y then \n",
" invalid_arg \"Inconsistent dimensions\";\n",
"\n",
" let check = (* Test if value should be added wrt threshold *)\n",
" if threshold = 0. then\n",
" fun x -> x <> 0.\n",
" else\n",
" fun x -> abs_float x > 0.\n",
" in\n",
" \n",
" let f = (* if a=1 in ax+y, then do x+y. If a=0 then do y *)\n",
" if alpha = 1. then\n",
" fun x y -> x +. y\n",
" else if alpha = 0. then\n",
" fun _ y -> y\n",
" else\n",
" fun x y -> alpha *. x +. y\n",
" in\n",
" \n",
" let dim = dim x in\n",
" let nnz = x.nnz + y.nnz in\n",
" let new_indices = Bigarray.(Array1.create int fortran_layout) nnz in\n",
" let new_values = L.Vec.create nnz in\n",
" \n",
" let rec aux k l m =\n",
" match k <= x.nnz, l <= y.nnz with\n",
" | true , true -> (* Both arrays are running *)\n",
" begin\n",
" if x.indices.{k} < y.indices.{l} then (\n",
" let w = f x.values.{k} 0. in\n",
" if check w then (\n",
" new_indices.{m} <- x.indices.{k};\n",
" new_values.{m} <- w\n",
" );\n",
" (aux [@tailcall]) (k+1) l (m+1)\n",
" )\n",
" else if x.indices.{k} > y.indices.{l} then (\n",
" let w = y.values.{l} in\n",
" if check w then (\n",
" new_indices.{m} <- y.indices.{l};\n",
" new_values.{m} <- w\n",
" );\n",
" (aux [@tailcall]) k (l+1) (m+1)\n",
" )\n",
" else (\n",
" let w = f x.values.{k} y.values.{l} in\n",
" if check w then (\n",
" new_indices.{m} <- x.indices.{k};\n",
" new_values.{m} <- w\n",
" );\n",
" (aux [@tailcall]) (k+1) (l+1) (m+1)\n",
" )\n",
" end\n",
" | false, true -> (* Array x is done running *)\n",
" begin\n",
" let m = ref m in\n",
" for i=l to y.nnz do\n",
" let w = y.values.{i} in\n",
" if check w then (\n",
" new_indices.{!m} <- y.indices.{i};\n",
" new_values.{!m} <- w;\n",
" incr m;\n",
" )\n",
" done; !m\n",
" end\n",
" | true, false -> (* Array y is done running *)\n",
" begin\n",
" let m = ref m in\n",
" for i=k to x.nnz do\n",
" let w = alpha *. x.values.{i} in\n",
" if check w then (\n",
" new_indices.{!m} <- x.indices.{i};\n",
" new_values.{!m} <- w;\n",
" incr m;\n",
" )\n",
" done; !m\n",
" end\n",
" | false, false -> (* Both arrays are done *)\n",
" m\n",
" in\n",
" let nnz = (aux 1 1 1) - 1 in\n",
" { dim ; nnz ;\n",
" indices = new_indices ; values = new_values }\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
"val m_A : Lacaml.D.vec = R1 R2 R3 R8 R9 R10\n",
" 1 2 0 ... -0.001 0 0\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_B : Lacaml.D.vec = R1 R2 R3 R8 R9 R10\n",
" 0 1 2 ... 0 -0.001 2\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_As : t =\n",
" {dim = 10; nnz = 5; indices = <abstr>;\n",
" values = R1 R2 R3 R4 R5\n",
" 1 2 0.01 -2 -0.001}\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_Bs : t =\n",
" {dim = 10; nnz = 6; indices = <abstr>;\n",
" values = R1 R2 R3 R4 R5 R6\n",
" 1 2 0.01 -2 -0.001 2}\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_C : L.vec = R1 R2 R3 R8 R9 R10\n",
" 0 1 2 ... 0 -0.001 2\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : L.vec = R1 R2 R3 R8 R9 R10\n",
" 2 5 2 ... -0.002 -0.001 2\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_D : L.vec = R1 R2 R3 R8 R9 R10\n",
" 1 2 0 ... -0.001 0 0\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : L.vec = R1 R2 R3 R8 R9 R10\n",
" 1 4 4 ... -0.001 -0.002 4\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_Cs : t =\n",
" {dim = 10; nnz = 9; indices = <abstr>;\n",
" values =\n",
" R1 R2 R3 R9 R10 R11\n",
" 2 5 2 ... 2 1.04136E-71 8.95166E+271}\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : bool = false\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val m_Ds : t =\n",
" {dim = 10; nnz = 9; indices = <abstr>;\n",
" values =\n",
" R1 R2 R3 R9 R10 R11\n",
" 1 4 4 ... 4 6.82475E-38 8.26993E-72}\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : bool = false\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 2.000000 2.000000\n",
"2 5.000000 5.000000\n",
"3 2.000000 2.000000\n",
"4 0.000000 0.000000\n",
"5 0.020000 0.020000\n",
"6 -3.990000 -3.990000\n",
"7 -2.000000 -2.000000\n",
"8 -0.002000 -0.002000\n",
"9 -0.001000 -0.001000\n",
"10 2.000000 2.000000\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 1.000000 1.000000\n",
"2 4.000000 4.000000\n",
"3 4.000000 4.000000\n",
"4 0.000000 0.000000\n",
"5 0.010000 0.010000\n",
"6 -1.980000 -1.980000\n",
"7 -4.000000 -4.000000\n",
"8 -0.001000 -0.001000\n",
"9 -0.002000 -0.002000\n",
"10 4.000000 4.000000\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 108,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let m_A = L.Vec.of_array [| 1. ; 2. ; 0. ; 0. ; 0.01 ; -2. ; 0. ; -1.e-3 ; 0. ; 0.|]\n",
"let m_B = L.Vec.of_array [| 0. ; 1. ; 2. ; 0. ; 0. ; 0.01 ; -2. ; 0. ; -1.e-3 ; 2. |]\n",
"\n",
"let m_As = of_vec m_A\n",
"let m_Bs = of_vec m_B\n",
"\n",
"let m_C = L.copy m_B ;;\n",
"L.axpy ~alpha:2. m_A m_C;;\n",
"m_C;;\n",
"\n",
"let m_D = L.copy m_A;;\n",
"L.axpy ~alpha:2. m_B m_D;;\n",
"m_D;;\n",
"\n",
"let m_Cs = axpy ~alpha:2. m_As m_Bs\n",
"\n",
"\n",
"let _ = of_vec m_C = m_Cs;;\n",
"\n",
"let m_Ds = axpy ~alpha:2. m_Bs m_As\n",
"\n",
"let _ = of_vec m_D = m_Ds;;\n",
"\n",
"L.Vec.iteri (fun i x -> Format.printf \"%d %f %f\\n%!\" i x (get m_Cs i)) m_C;;\n",
"L.Vec.iteri (fun i x -> Format.printf \"%d %f %f\\n%!\" i x (get m_Ds i)) m_D;;\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Accessors"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
"val dim : t -> int = <fun>\n"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val nnz : t -> int = <fun>\n"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val indices :\n",
" t -> (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t =\n",
" <fun>\n"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val values : t -> L.Vec.t = <fun>\n"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let dim t = t.dim\n",
"let nnz t = t.nnz\n",
"let indices t = t.indices\n",
"let values t = t.values"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val get : t -> int -> float = <fun>\n"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let get t i =\n",
" if i < 1 || i > dim t then invalid_arg \"index out of bounds\";\n",
" \n",
" let rec binary_search index value low high =\n",
" if high = low then\n",
" if index.{low} = value then\n",
" low\n",
" else\n",
" raise Not_found\n",
" else let mid = (low + high) / 2 in\n",
" if index.{mid} > value then\n",
" binary_search index value low (mid - 1)\n",
" else if index.{mid} < value then\n",
" binary_search index value (mid + 1) high\n",
" else\n",
" mid\n",
" in\n",
" try\n",
" let k = \n",
" let id = indices t in\n",
" binary_search id i id.{1} (nnz t)\n",
" in\n",
" t.values.{k}\n",
" with Not_found -> 0."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val iter : (int -> float -> 'a) -> t -> unit = <fun>\n"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let iter f t =\n",
" for k=1 to nnz t do\n",
" f t.indices.{k} t.values.{k}\n",
" done"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test "
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
"- : bool = true\n"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 1.000000\n",
"2 -2.000000\n",
"5 0.500000\n",
"6 0.000000\n",
"8 3.000000\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dense_a = L.Vec.init (dim sparse_a) (get sparse_a);;\n",
"iter (fun i v -> Printf.printf \"%d %f\\n%!\" i v) sparse_a;;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Converters"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val to_assoc_list : t -> (int * float) list = <fun>\n"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val to_vec : t -> Lacaml.D.vec = <fun>\n"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let to_assoc_list t = \n",
" let rec aux k accu =\n",
" if k = 0 then\n",
" accu\n",
" else\n",
" aux (k-1) ( (t.indices.{k}, t.values.{k})::accu )\n",
" in\n",
" aux (nnz t) []\n",
" \n",
" \n",
"let to_vec t =\n",
" let result = L.Vec.make0 (dim t) in\n",
" iter (fun k v -> result.{k} <- v) t;\n",
" result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [
{
"data": {
"text/plain": [
"- : (int * float) list = [(1, 1.); (2, -2.); (5, 0.5); (6, 1e-08); (8, 3.)]\n"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : bool = true\n"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"to_assoc_list sparse_a;;\n",
"to_vec sparse_a = dense_a;;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Operations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## One-vector operations"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val immutable : (t -> 'a) -> t -> t = <fun>\n"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val scale_mut : float -> t -> unit = <fun>\n"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val scale : float -> t -> t = <fun>\n"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val neg : t -> t = <fun>\n"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let immutable f t =\n",
" let result = copy t in\n",
" f result;\n",
" result\n",
" \n",
"let scale_mut x t = \n",
" L.scal x t.values \n",
"\n",
"let scale x = immutable @@ scale_mut x\n",
" \n",
"let neg t =\n",
" { t with values = L.Vec.neg t.values }\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Test"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"val sparse_b : t =\n",
" {dim = 9; nnz = 5; indices = <abstr>;\n",
" values = R1 R2 R3 R4 R5\n",
" 1 -2 0.5 1E-08 3}\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"val sparse_c : t =\n",
" {dim = 9; nnz = 5; indices = <abstr>;\n",
" values = R1 R2 R3 R4 R5\n",
" 0.5 -1 0.25 5E-09 1.5}\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"{dim: 9\n",
"(1, 1.000000) (2, -2.000000) (5, 0.500000) (6, 0.000000) (8, 3.000000) }\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"{dim: 9\n",
"(1, 0.500000) (2, -1.000000) (5, 0.250000) (6, 0.000000) (8, 1.500000) }\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"{dim: 9\n",
"(1, 0.500000) (2, -1.000000) (5, 0.250000) (6, 0.000000) (8, 1.500000) }\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"{dim: 9\n",
"(1, -1.000000) (2, 2.000000) (5, -0.500000) (6, -0.000000) (8, -3.000000) }\n"
]
},
{
"data": {
"text/plain": [
"- : unit = ()\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/plain": [
"- : bool = true\n"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"let sparse_b = copy sparse_a;;\n",
"scale_mut 0.5 sparse_b;;\n",
"let sparse_c = scale 0.5 sparse_a;;\n",
"Format.printf \"%a@.\" pp sparse_a;;\n",
"Format.printf \"%a@.\" pp sparse_b;;\n",
"Format.printf \"%a@.\" pp sparse_c;;\n",
"Format.printf \"%a@.\" pp (neg sparse_a);;\n",
" \n",
"let _ =\n",
" let n1 = neg sparse_a in\n",
" neg n1 = sparse_a"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Raw Cell Format",
"kernelspec": {
"display_name": "OCaml default",
"language": "OCaml",
"name": "ocaml-jupyter"
},
"language_info": {
"codemirror_mode": "text/x-ocaml",
"file_extension": ".ml",
"mimetype": "text/x-ocaml",
"name": "OCaml",
"nbconverter_exporter": null,
"pygments_lexer": "OCaml",
"version": "4.07.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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