{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "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": [
    "# 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,@ %g)@]@;\" t.indices.{i} t.values.{i}\n",
    "    done\n",
    "  in\n",
    "  Format.fprintf ppf \"@[{@[dim:@ %d@]@;@[%a@]}@]\" t.dim pp_data t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install_printer pp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val make0 : int -> t = <fun>\n"
      ]
     },
     "execution_count": 4,
     "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val of_vec : ?threshold:float -> Lacaml.D.vec -> t = <fun>\n"
      ]
     },
     "execution_count": 5,
     "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 }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val of_array : ?threshold:float -> float array -> t = <fun>\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let of_array ?(threshold=0.) a =\n",
    "  L.Vec.of_array a\n",
    "  |> of_vec ~threshold "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val copy : t -> t = <fun>\n"
      ]
     },
     "execution_count": 7,
     "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": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val map : ?threshold:float -> (float -> float) -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let map ?(threshold=0.) f t =\n",
    "  let indices = \n",
    "    Bigarray.(Array1.create int fortran_layout) t.nnz\n",
    "  in\n",
    "  let check =\n",
    "    if threshold = 0. then\n",
    "      fun x -> x <> 0.\n",
    "    else\n",
    "      fun x -> abs_float x > threshold\n",
    "  in\n",
    "  let values = L.Vec.create t.nnz in\n",
    "  let nnz = ref 0 in\n",
    "  for i=1 to t.nnz do\n",
    "    let w = f t.values.{i} in\n",
    "    if check w then (\n",
    "      incr nnz;\n",
    "      values.{!nnz} <- w ;\n",
    "      indices.{!nnz} <- t.indices.{i}\n",
    "    )\n",
    "  done;\n",
    "  { dim = t.dim ;\n",
    "    nnz = !nnz ;\n",
    "    indices ; values }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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",
       "    6.91705E-310 6.91705E-310  0 ... 6.91705E-310 6.91705E-310 6.91705E-310}\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val dense_a : Lacaml.D.vec = R1 R2 R3     R7 R8 R9\n",
       "                              1 -2  0 ...  0  3  0\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val sparse_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": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = false\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let x = make0 10 \n",
    "\n",
    "let dense_a = \n",
    "   L.Vec.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"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Accessors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val dim : t -> int = <fun>\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val nnz : t -> int = <fun>\n"
      ]
     },
     "execution_count": 10,
     "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": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val values : t -> L.Vec.t = <fun>\n"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val density : t -> float = <fun>\n"
      ]
     },
     "execution_count": 10,
     "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\n",
    "let density t = float_of_int t.nnz /. float_of_int t.dim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val get : t -> int -> float = <fun>\n"
      ]
     },
     "execution_count": 11,
     "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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val iter : (int -> float -> 'a) -> t -> unit = <fun>\n"
      ]
     },
     "execution_count": 12,
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 13,
     "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": 13,
     "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val to_assoc_list : t -> (int * float) list = <fun>\n"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val to_vec : t -> Lacaml.D.vec = <fun>\n"
      ]
     },
     "execution_count": 14,
     "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\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : (int * float) list = [(1, 1.); (2, -2.); (5, 0.5); (6, 1e-08); (8, 3.)]\n"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 44,
     "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": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val immutable : (t -> 'a) -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val scale_mut : float -> t -> unit = <fun>\n"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val scale : float -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val neg : t -> t = <fun>\n"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val norm : t -> float = <fun>\n"
      ]
     },
     "execution_count": 45,
     "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",
    "  \n",
    "let norm t =\n",
    "  L.nrm2 t.values\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val sparse_b : t = {dim: 9 (1, 1) (2, -2) (5, 0.5) (6, 1e-08) (8, 3) }\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val dense_b : L.vec = R1 R2 R3     R7 R8 R9\n",
       "                       1 -2  0 ...  0  3  0\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val sparse_c : t = {dim: 9 (1, 0.5) (2, -1) (5, 0.25) (6, 5e-09) (8, 1.5) }\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let sparse_b = copy sparse_a;;\n",
    "scale_mut 0.5 sparse_b;;\n",
    "\n",
    "equal sparse_b @@ map (fun x -> x *. 0.5) sparse_a;;\n",
    "\n",
    "\n",
    "let dense_b = L.copy dense_a;;\n",
    "L.scal 0.5 dense_b;;\n",
    "\n",
    "let sparse_c = scale 0.5 sparse_a;;\n",
    "\n",
    "equal sparse_b sparse_c;;\n",
    "    \n",
    "let _ =\n",
    "    let n1 = neg sparse_a in\n",
    "    neg n1 = sparse_a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two-vector operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val equal : t -> t -> bool = <fun>\n"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let equal x y =\n",
    "  (x.nnz + y.nnz = 0) || (\n",
    "  (x.dim = y.dim) &&\n",
    "  (x.nnz  = y.nnz) &&\n",
    "  Bigarray.Array1.(sub x.indices 1 x.nnz = sub y.indices 1 y.nnz) &&\n",
    "  (Array.sub (L.Vec.to_array x.values) 0 (x.nnz-1) = Array.sub (L.Vec.to_array y.values) 0 (y.nnz-1) )\n",
    "  )"
   ]
  },
  {
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val axpy : ?threshold:float -> ?alpha:float -> t -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 20,
     "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 > threshold\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",
    "              (aux [@tailcall]) (k+1) l (m+1)\n",
    "          ) else (aux [@tailcall]) (k+1) l m\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",
    "              (aux [@tailcall]) k (l+1) (m+1)\n",
    "          ) else (aux [@tailcall]) k (l+1) m\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",
    "              (aux [@tailcall]) (k+1) (l+1) (m+1)\n",
    "          ) else (aux [@tailcall]) (k+1) (l+1) m\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": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val add : ?threshold:float -> t -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val sub : ?threshold:float -> t -> t -> t = <fun>\n"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let add ?(threshold=0.) x y = axpy ~threshold ~alpha:1. x y\n",
    "\n",
    "let sub ?(threshold=0.) x y = axpy ~threshold ~alpha:(-1.) y x\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "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": 22,
     "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_As : t = {dim: 10 (1, 1 (2, 2 (5, 0.01 (6, -2 (8, -0.001 }\n"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_Bs : t = {dim: 10 (2, 1 (3, 2 (6, 0.01 (7, -2 (9, -0.001 (10, 2 }\n"
      ]
     },
     "execution_count": 22,
     "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 22,
     "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": 22,
     "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 22,
     "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": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_Cs : t =\n",
       "  {dim: 10\n",
       "  (1, 2 (2, 5 (3, 2 (5, 0.02 (6, -3.99 (7, -2 (8, -0.002 (9, -0.001 (10, 2 }\n"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val m_Ds : t =\n",
       "  {dim: 10\n",
       "  (1, 1 (2, 4 (3, 4 (5, 0.01 (6, -1.98 (7, -4 (8, -0.001 (9, -0.002 (10, 4 }\n"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 22,
     "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 _ =  equal (of_vec m_C) m_Cs;;\n",
    "\n",
    "let m_Ds = axpy ~alpha:2. m_Bs m_As\n",
    "\n",
    "let _ = equal (of_vec m_D) m_Ds;;\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dot product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val dot : t -> t -> float = <fun>\n"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let dot x y =\n",
    "\n",
    "  let rec aux accu k l =\n",
    "    if k <= x.nnz && l <= y.nnz then\n",
    "      begin\n",
    "        if x.indices.{k} < y.indices.{l} then \n",
    "          (aux [@tailcall]) accu (k+1) l\n",
    "        else if x.indices.{k} > y.indices.{l} then (\n",
    "          (aux [@tailcall]) accu k (l+1)\n",
    "        )\n",
    "        else (\n",
    "          (aux [@tailcall]) (accu +. x.values.{k} *. y.values.{l}) (k+1) (l+1)\n",
    "        )\n",
    "      end\n",
    "    else\n",
    "      accu\n",
    "  in\n",
    "  aux 0. 1 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot sparse_a sparse_b = L.dot dense_a dense_b;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/scemama/qp2/external/opam/default/lib/astring: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/astring/astring.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/cmdliner: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/cmdliner/cmdliner.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/seq: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/stdlib-shims: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/stdlib-shims/stdlib_shims.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/fmt: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/fmt/fmt.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/fmt/fmt_cli.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/fmt/fmt_tty.cma: loaded\n",
      "/home/scemama/qp2/external/opam/default/lib/alcotest: added to search path\n",
      "/home/scemama/qp2/external/opam/default/lib/alcotest/alcotest.cma: loaded\n"
     ]
    }
   ],
   "source": [
    "#require \"alcotest\";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val x1 : Lacaml.D.vec =\n",
       "        R1 R2 R3     R98      R99 R100\n",
       "  0.852078  0  0 ...   0 0.656419    0\n",
       "val x2 : Lacaml.D.vec =\n",
       "         R1       R2 R3           R98 R99   R100\n",
       "  -0.606197 0.411059  0 ... -0.368989   0 0.9001\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val x3 : Lacaml.D.vec =\n",
       "       R1 R2 R3     R98     R99 R100\n",
       "  1.70416  0  0 ...   0 1.31284    0\n",
       "val x4 : Lacaml.D.vec =\n",
       "        R1       R2 R3           R98      R99   R100\n",
       "  0.245881 0.411059  0 ... -0.368989 0.656419 0.9001\n",
       "val x5 : Lacaml.D.vec =\n",
       "       R1        R2 R3          R98      R99    R100\n",
       "  1.45827 -0.411059  0 ... 0.368989 0.656419 -0.9001\n",
       "val x6 : L.vec =\n",
       "       R1       R2 R3           R98     R99   R100\n",
       "  1.95004 0.411059  0 ... -0.368989 1.96926 0.9001\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val v1 : Lacaml.D.vec =\n",
       "        R1 R2 R3     R98      R99 R100\n",
       "  0.852078  0  0 ...   0 0.656419    0\n",
       "val v2 : Lacaml.D.vec =\n",
       "         R1       R2 R3           R98 R99   R100\n",
       "  -0.606197 0.411059  0 ... -0.368989   0 0.9001\n",
       "val v3 : Lacaml.D.vec =\n",
       "       R1 R2 R3     R98     R99 R100\n",
       "  1.70416  0  0 ...   0 1.31284    0\n",
       "val v4 : Lacaml.D.vec =\n",
       "        R1       R2 R3           R98      R99   R100\n",
       "  0.245881 0.411059  0 ... -0.368989 0.656419 0.9001\n",
       "val v5 : Lacaml.D.vec =\n",
       "       R1        R2 R3          R98      R99    R100\n",
       "  1.45827 -0.411059  0 ... 0.368989 0.656419 -0.9001\n",
       "val v6 : L.vec =\n",
       "       R1       R2 R3           R98     R99   R100\n",
       "  1.95004 0.411059  0 ... -0.368989 1.96926 0.9001\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val v1_s : t =\n",
       "  {dim: 100\n",
       "  (1, 0.852078 (4, 0.733763 (7, -0.818022 (10, -0.692304 (11, -0.980468\n",
       "  (15, 0.974355 (16, -0.665109 (24, 0.889086 (27, 0.736393 (30, -0.843748\n",
       "  (31, -0.750514 (34, 0.778919 (38, -0.790597 (40, 0.720996 (41, 0.978861\n",
       "  (42, -0.679388 (43, -0.853596 (46, 0.977185 (47, -0.811648 (49, -0.702925\n",
       "  (50, 0.89789 (54, -0.675687 (56, 0.752085 (57, -0.626277 (66, 0.664662\n",
       "  (67, 0.855765 (69, 0.673572 (71, -0.764248 (72, 0.61481 (73, -0.849851\n",
       "  (74, -0.983965 (84, -0.764701 (87, -0.834976 (92, -0.851806 (94, 0.696202\n",
       "  (95, 0.844479 (99, 0.656419 }\n",
       "val v2_s : t =\n",
       "  {dim: 100\n",
       "  (1, -0.606197 (2, 0.411059 (4, 0.329122 (5, -0.740514 (7, 0.387312\n",
       "  (8, 0.977894 (9, -0.43281 (11, -0.971917 (15, -0.471397 (16, 0.863036\n",
       "  (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705 (23, -0.568959\n",
       "  (24, 0.643522 (25, 0.697603 (26, -0.706857 (29, -0.874151 (30, 0.559791\n",
       "  (32, -0.392582 (34, -0.488787 (36, -0.988593 (38, -0.817274 (39, -0.78555\n",
       "  (42, 0.505945 (43, 0.370838 (44, -0.734224 (45, -0.634506 (46, 0.304503\n",
       "  (47, -0.330526 (48, -0.800156 (49, -0.570671 (50, -0.514998 (51, -0.47082\n",
       "  (52, 0.731985 (53, -0.501758 (54, -0.856375 (55, 0.422431 (56, 0.819669\n",
       "  (57, 0.847078 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n",
       "  (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 0.945573\n",
       "  (67, -0.584689 (68, 0.312286 (69, 0.840451 (72, 0.980958 (73, 0.383844\n",
       "  (77, 0.509676 (79, 0.86618 (80, -0.767171 (82, -0.955884 (83, -0.326832\n",
       "  (88, 0.846553 (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, 0.975437\n",
       "  (95, -0.816165 (96, -0.999559 (97, 0.738769 (98, -0.368989 (100, 0.9001 }\n",
       "val v3_s : t =\n",
       "  {dim: 100\n",
       "  (1, 1.70416 (4, 1.46753 (7, -1.63604 (10, -1.38461 (11, -1.96094\n",
       "  (15, 1.94871 (16, -1.33022 (24, 1.77817 (27, 1.47279 (30, -1.6875\n",
       "  (31, -1.50103 (34, 1.55784 (38, -1.58119 (40, 1.44199 (41, 1.95772\n",
       "  (42, -1.35878 (43, -1.70719 (46, 1.95437 (47, -1.6233 (49, -1.40585\n",
       "  (50, 1.79578 (54, -1.35137 (56, 1.50417 (57, -1.25255 (66, 1.32932\n",
       "  (67, 1.71153 (69, 1.34714 (71, -1.5285 (72, 1.22962 (73, -1.6997\n",
       "  (74, -1.96793 (84, -1.5294 (87, -1.66995 (92, -1.70361 (94, 1.3924\n",
       "  (95, 1.68896 (99, 1.31284 }\n",
       "val v4_s : t =\n",
       "  {dim: 100\n",
       "  (1, 0.245881 (2, 0.411059 (4, 1.06289 (5, -0.740514 (7, -0.43071\n",
       "  (8, 0.977894 (9, -0.43281 (10, -0.692304 (11, -1.95238 (15, 0.502957\n",
       "  (16, 0.197927 (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705\n",
       "  (23, -0.568959 (24, 1.53261 (25, 0.697603 (26, -0.706857 (27, 0.736393\n",
       "  (29, -0.874151 (30, -0.283957 (31, -0.750514 (32, -0.392582 (34, 0.290132\n",
       "  (36, -0.988593 (38, -1.60787 (39, -0.78555 (40, 0.720996 (41, 0.978861\n",
       "  (42, -0.173443 (43, -0.482758 (44, -0.734224 (45, -0.634506 (46, 1.28169\n",
       "  (47, -1.14217 (48, -0.800156 (49, -1.2736 (50, 0.382892 (51, -0.47082\n",
       "  (52, 0.731985 (53, -0.501758 (54, -1.53206 (55, 0.422431 (56, 1.57175\n",
       "  (57, 0.220801 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n",
       "  (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 1.61024\n",
       "  (67, 0.271076 (68, 0.312286 (69, 1.51402 (71, -0.764248 (72, 1.59577\n",
       "  (73, -0.466006 (74, -0.983965 (77, 0.509676 (79, 0.86618 (80, -0.767171\n",
       "  (82, -0.955884 (83, -0.326832 (84, -0.764701 (87, -0.834976 (88, 0.846553\n",
       "  (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, 0.123631 (94, 0.696202\n",
       "  (95, 0.0283147 (96, -0.999559 (97, 0.738769 (98, -0.368989 (99, 0.656419\n",
       "  (100, 0.9001 }\n",
       "val v5_s : t =\n",
       "  {dim: 100\n",
       "  (1, 1.45827 (2, -0.411059 (4, 0.404641 (5, 0.740514 (7, -1.20533\n",
       "  (8, -0.977894 (9, 0.43281 (10, -0.692304 (11, -0.00855015 (15, 1.44575\n",
       "  (16, -1.52814 (17, 0.497091 (19, -0.8659 (20, -0.572763 (21, -0.963705\n",
       "  (23, 0.568959 (24, 0.245564 (25, -0.697603 (26, 0.706857 (27, 0.736393\n",
       "  (29, 0.874151 (30, -1.40354 (31, -0.750514 (32, 0.392582 (34, 1.26771\n",
       "  (36, 0.988593 (38, 0.0266769 (39, 0.78555 (40, 0.720996 (41, 0.978861\n",
       "  (42, -1.18533 (43, -1.22443 (44, 0.734224 (45, 0.634506 (46, 0.672682\n",
       "  (47, -0.481123 (48, 0.800156 (49, -0.132254 (50, 1.41289 (51, 0.47082\n",
       "  (52, -0.731985 (53, 0.501758 (54, 0.180688 (55, -0.422431 (56, -0.067584\n",
       "  (57, -1.47335 (58, -0.301306 (59, 0.917181 (60, -0.391153 (61, 0.936169\n",
       "  (62, -0.855439 (63, -0.730839 (64, -0.763087 (65, -0.777606 (66, -0.280911\n",
       "  (67, 1.44045 (68, -0.312286 (69, -0.166879 (71, -0.764248 (72, -0.366148\n",
       "  (73, -1.2337 (74, -0.983965 (77, -0.509676 (79, -0.86618 (80, 0.767171\n",
       "  (82, 0.955884 (83, 0.326832 (84, -0.764701 (87, -0.834976 (88, -0.846553\n",
       "  (89, 0.578475 (90, 0.522823 (91, -0.802248 (92, -1.82724 (94, 0.696202\n",
       "  (95, 1.66064 (96, 0.999559 (97, -0.738769 (98, 0.368989 (99, 0.656419\n",
       "  (100, -0.9001 }\n",
       "val v6_s : t =\n",
       "  {dim: 100\n",
       "  (1, 1.95004 (2, 0.411059 (4, 2.53041 (5, -0.740514 (7, -2.06675\n",
       "  (8, 0.977894 (9, -0.43281 (10, -2.07691 (11, -3.91332 (15, 2.45167\n",
       "  (16, -1.13229 (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705\n",
       "  (23, -0.568959 (24, 3.31078 (25, 0.697603 (26, -0.706857 (27, 2.20918\n",
       "  (29, -0.874151 (30, -1.97145 (31, -2.25154 (32, -0.392582 (34, 1.84797\n",
       "  (36, -0.988593 (38, -3.18907 (39, -0.78555 (40, 2.16299 (41, 2.93658\n",
       "  (42, -1.53222 (43, -2.18995 (44, -0.734224 (45, -0.634506 (46, 3.23606\n",
       "  (47, -2.76547 (48, -0.800156 (49, -2.67945 (50, 2.17867 (51, -0.47082\n",
       "  (52, 0.731985 (53, -0.501758 (54, -2.88344 (55, 0.422431 (56, 3.07592\n",
       "  (57, -1.03175 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n",
       "  (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 2.93956\n",
       "  (67, 1.98261 (68, 0.312286 (69, 2.86117 (71, -2.29274 (72, 2.82539\n",
       "  (73, -2.16571 (74, -2.9519 (77, 0.509676 (79, 0.86618 (80, -0.767171\n",
       "  (82, -0.955884 (83, -0.326832 (84, -2.2941 (87, -2.50493 (88, 0.846553\n",
       "  (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, -1.57998 (94, 2.0886\n",
       "  (95, 1.71727 (96, -0.999559 (97, 0.738769 (98, -0.368989 (99, 1.96926\n",
       "  (100, 0.9001 }\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val zero : Lacaml.D.vec = R1 R2 R3     R98 R99 R100\n",
       "                           0  0  0 ...   0   0    0\n",
       "val zero_s : t = {dim: 100 }\n"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let x1 = L.Vec.map (fun x -> if abs_float x < 0.6 then 0. else x) (L.Vec.random 100)\n",
    "and x2 = L.Vec.map (fun x -> if abs_float x < 0.3 then 0. else x) (L.Vec.random 100)                                                                                                            \n",
    "\n",
    "let x3 = L.Vec.map (fun x -> 2. *. x) x1\n",
    "and x4 = L.Vec.add x1 x2\n",
    "and x5 = L.Vec.sub x1 x2\n",
    "and x6 = \n",
    "  let v = L.copy x2 in\n",
    "  L.axpy ~alpha:3. x1 v;\n",
    "  v \n",
    "\n",
    "  \n",
    "let v1 = x1\n",
    "and v2 = x2\n",
    "and v3 = x3 \n",
    "and v4 = x4 \n",
    "and v5 = x5 \n",
    "and v6 = x6 \n",
    "\n",
    "  \n",
    "let v1_s = of_vec x1\n",
    "and v2_s = of_vec x2\n",
    "and v3_s = of_vec x3\n",
    "and v4_s = of_vec x4\n",
    "and v5_s = of_vec x5\n",
    "and v6_s = of_vec x6\n",
    "\n",
    "    \n",
    "let zero   = L.Vec.make0 100\n",
    "and zero_s = of_vec (L.Vec.make0 100)\n",
    "\n",
    "  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val test_conversion : unit -> unit = <fun>\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val test_operations : unit -> unit = <fun>\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val test_dot : unit -> unit = <fun>\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list = <fun>\n"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "  let test_conversion () =\n",
    "    Alcotest.(check bool) \"sparse -> dense  1\" true (to_vec v1_s = v1  );\n",
    "    Alcotest.(check bool) \"sparse -> dense  2\" true (to_vec v2_s = v2  );\n",
    "    Alcotest.(check bool) \"dense  -> sparse 1\" true (of_vec v1   = v1_s);\n",
    "    Alcotest.(check bool) \"dense  -> sparse 2\" true (of_vec v2   = v2_s)\n",
    " \n",
    "  \n",
    "  let test_operations () =\n",
    "    Alcotest.(check  bool)  \"dense   scale\"        true  (let w = L.copy v1 in L.scal 2. w ; w  =  v3);\n",
    "    Alcotest.(check  bool)  \"sparse  scale\"        true  (scale  2.    v1_s  =  v3_s);\n",
    "    \n",
    "    Alcotest.(check  bool)  \"dense   dense   add\"  true  (L.Vec.add  v1  v2    =  v4);\n",
    "    (*\n",
    "    Alcotest.(check  bool)  \"dense   sparse  add\"  true  (add    v1    v2_s  =  v4_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   add\"  true  (add    v1_s  v2    =  v4_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   add\"  true  (add    v1    v2_s  =  v4_s);\n",
    "    *)\n",
    "    Alcotest.(check  bool)  \"sparse  sparse  add\"  true  (equal (add    v1_s  v2_s)  v4_s);\n",
    "    \n",
    "    Alcotest.(check  bool)  \"dense   dense   sub\"  true  (L.Vec.sub    v1    v2    =  v5);\n",
    "    (*\n",
    "    Alcotest.(check  bool)  \"dense   sparse  sub\"  true  (sub    v1    v2_s  =  v5_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   sub\"  true  (sub    v1_s  v2    =  v5_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   sub\"  true  (sub    v1    v2_s  =  v5_s);\n",
    "    *)\n",
    "    Alcotest.(check  bool)  \"sparse  sparse  sub\"  true  (equal (sub v1_s v2_s) v5_s);\n",
    "    \n",
    "    Alcotest.(check  bool)  \"dense   dense   sub\"  true  (L.Vec.sub  v1 v1   =  zero);\n",
    "    (*\n",
    "    Alcotest.(check  bool)  \"dense   sparse  sub\"  true  (sub    v1    v1_s  =  zero_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   sub\"  true  (sub    v1_s  v1    =  zero_s);\n",
    "    *)\n",
    "    Alcotest.(check  bool)  \"sparse  sparse  sub\"  true  (equal (sub v1_s v1_s) zero_s);\n",
    "    \n",
    "    Alcotest.(check  bool)  \"dense   dense   axpy\"  true  (let w = L.copy v2 in L.axpy ~alpha:3. v1  w ;  w  =  v6);\n",
    "    (*\n",
    "    Alcotest.(check  bool)  \"dense   sparse  axpy\"  true  (sub ~threshold:1.e-12 (axpy ~alpha:3.  v1    v2_s) v6_s = zero_s);\n",
    "    Alcotest.(check  bool)  \"sparse  dense   axpy\"  true  (sub ~threshold:1.e-12 (axpy ~alpha:3.  v1_s  v2) v6_s = zero_s);\n",
    "    *)\n",
    "    Alcotest.(check  bool)  \"sparse  sparse  axpy\"  true  (equal (sub ~threshold:1.e-12 (axpy ~alpha:3.  v1_s  v2_s) v6_s) zero_s)\n",
    "  \n",
    "let test_dot () =  \n",
    "    let d1d2 = L.dot x1 x2\n",
    "    and d1d1 = L.dot x1 x1\n",
    "    and d2d2 = L.dot x2 x2 \n",
    "    in\n",
    "    (*\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x dense  1\" (dot v1_s v2  )  d1d2;\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x dense  2\" (dot v1_s v1  )  d1d1;\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x dense  3\" (dot v2_s v2  )  d2d2;\n",
    "    Alcotest.(check (float 1.e-10)) \"dense  x sparse 1\" (dot v1   v2_s)  d1d2;\n",
    "    Alcotest.(check (float 1.e-10)) \"dense  x sparse 2\" (dot v1   v1_s)  d1d1;\n",
    "    Alcotest.(check (float 1.e-10)) \"dense  x sparse 3\" (dot v2   v2_s)  d2d2;\n",
    "    *)\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x sparse 1\" (dot v1_s v2_s)  d1d2;\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x sparse 2\" (dot v1_s v1_s)  d1d1;\n",
    "    Alcotest.(check (float 1.e-10)) \"sparse x sparse 3\" (dot v2_s v2_s)  d2d2\n",
    "    \n",
    "    \n",
    "let test_case () = \n",
    "  [ \n",
    "    \"Conversion\", `Quick, test_conversion;\n",
    "    \"Operations\", `Quick, test_operations;\n",
    "    \"Dot product\", `Quick, test_dot;\n",
    "  ] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "File \"[28]\", line 1, characters 0-3:\n",
      "Warning 1: this `(*' is the start of a comment.\n",
      "Hint: Did you forget spaces when writing the infix operator `( * )'?\n"
     ]
    }
   ],
   "source": [
    "(*)\n",
    "Alcotest.run ~argv:[|\"ignored\"|] \"Unit tests\" [\n",
    "    \"SpVec\", test_case ();\n",
    "];;\n",
    "Printf.printf \"%!\";;\n",
    "*)"
   ]
  }
 ],
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