{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "\n",
    "# Space elements, kappa function and p_Amemiya norm \n",
    "\n",
    "To use `numerical_function_spaces.orlicz_spaces` in a project:\n"
   ],
   "metadata": {}
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/DyonOylloug/numerical_function_spaces/HEAD?labpath=docs%2Fnorms.ipynb) - link to interactive notebooks session."
  },
  {
   "cell_type": "code",
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import numerical_function_spaces.orlicz_spaces as osm"
   ],
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:40:25.535107Z",
     "start_time": "2024-09-04T07:40:22.713948Z"
    }
   },
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:02.717583Z",
     "start_time": "2024-09-04T07:39:02.713552Z"
    }
   },
   "cell_type": "code",
   "source": "## Points/elements in spaces",
   "outputs": [],
   "execution_count": 38
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Define $x$ as simple function $x(t)=\\sum_{i=0}^{{len\\_t} - 1} a_i \\cdot \\chi_{A_i}(t)$ as two rows numpy array, where first row is for $a_i$ and second is for $\\mu(A_i)$ "
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Define $x_1(t)=1 \\cdot \\chi_{[0,2)}(t)$"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:02.834575Z",
     "start_time": "2024-09-04T07:39:02.828520Z"
    }
   },
   "cell_type": "code",
   "source": [
    "len_t = 1\n",
    "x_1 = np.zeros(shape=(2, len_t))\n",
    "x_1[1, 0] = 2  #  measure of support\n",
    "x_1[0, 0] = 1  # value"
   ],
   "outputs": [],
   "execution_count": 39
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:03.198874Z",
     "start_time": "2024-09-04T07:39:02.873569Z"
    }
   },
   "cell_type": "code",
   "source": [
    "for i in range(0, len_t):\n",
    "    plt.hlines(y=x_1[0, i], xmin=sum([j for j in x_1[1, 0:i]]), xmax=sum([j for j in x_1[1, 0:i + 1]]),\n",
    "               label='$x_1(t)$' if i == 0 else None, )\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 40
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Define $x_2(t)=1 \\cdot \\chi_{[0,\\infty)}(t)$"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:03.243607Z",
     "start_time": "2024-09-04T07:39:03.238132Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# support with infinite measure support\n",
    "len_t = 1\n",
    "x_2 = np.zeros(shape=(2, len_t))\n",
    "x_2[1, 0] = np.inf  #  measure of support\n",
    "x_2[0, 0] = 1  # value"
   ],
   "outputs": [],
   "execution_count": 41
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:03.602881Z",
     "start_time": "2024-09-04T07:39:03.362839Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot([0, 5], [x_2[0, 0], x_2[0, 0]], label='$x_2(t)$')\n",
    "plt.xticks(np.arange(0, 6, step=1), labels=[str(i) if i < 5 else r\"$\\infty$\" for i in range(6)])\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 42
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "Define $x_3(t)=1 \\cdot \\chi_{[0,1)}(t) + \\frac{1}{2} \\cdot \\chi_{[1,3)}(t) +\n",
    " \\frac{1}{3} \\cdot \\chi_{[3,6)}(t) + \\frac{1}{4} \\cdot \\chi_{[6,10)}(t) + \\frac{1}{5} \\cdot \\chi_{[10,15)}(t)$ \\\n",
    "or $x_3(t) = \\sum_{i=0}^{4} \\frac{1}{i+1}\\cdot \\chi_{A_{i}}(t)$ for disjoint $A_i$ sets with $\\mu(A_i)=i+1$."
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:03.661753Z",
     "start_time": "2024-09-04T07:39:03.655851Z"
    }
   },
   "cell_type": "code",
   "source": [
    "len_t = 5  # \n",
    "x_3 = np.zeros(shape=(2, len_t))\n",
    "for i in range(len_t):\n",
    "    x_3[1, i] = i + 1  #  measure of supports\n",
    "    x_3[0, i] = 1 / (i + 1)  # values"
   ],
   "outputs": [],
   "execution_count": 43
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:04.020524Z",
     "start_time": "2024-09-04T07:39:03.726398Z"
    }
   },
   "cell_type": "code",
   "source": [
    "for i in range(0, len(x_3[1, :])):\n",
    "    plt.hlines(y=x_3[0, i], xmin=sum([j for j in x_3[1, 0:i]]), xmax=sum([j for j in x_3[1, 0:i + 1]]),\n",
    "               label='$x_3(t)$' if i == 0 else None)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 44
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "Define \n",
    "\\begin{equation*}\n",
    "x_4(t)=\\sum_{i=0}^{999} \\left\\{ \\begin{array}{lll}\n",
    "                   \\sin\\left(\\frac{2\\cdot \\pi}{1000}\\cdot i\\right) & \\text{if} & \\frac{2\\cdot \\pi}{1000}\\cdot i \\leq 3, \\\\\n",
    "                   0     & \\text{if} & \\text{otherwise}\n",
    "\\end{array}\n",
    "\\right\\}  \\cdot \\chi_{A_{i}}(t)\n",
    "\\end{equation*}\n",
    "for disjoint $A_i$ sets with $\\mu(A_i)=\\frac{2\\cdot \\pi}{1000}$."
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:04.050641Z",
     "start_time": "2024-09-04T07:39:04.040515Z"
    }
   },
   "cell_type": "code",
   "source": [
    "t_max = 2 * np.pi\n",
    "len_t = 1000\n",
    "x_4 = np.zeros(shape=(2, len_t))\n",
    "x_4[1, :] = t_max / len_t  # measure of supports\n",
    "for i in range(len_t):\n",
    "    arg = t_max / len_t * i\n",
    "    if arg <= 3:\n",
    "        x_4[0, i] = np.sin(arg)  # values\n"
   ],
   "outputs": [],
   "execution_count": 45
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:06.900429Z",
     "start_time": "2024-09-04T07:39:04.142884Z"
    }
   },
   "cell_type": "code",
   "source": [
    "for i in range(0, len_t):\n",
    "    plt.hlines(y=x_4[0, i], xmin=sum([j for j in x_4[1, 0:i]]), xmax=sum([j for j in x_4[1, 0:i + 1]]),\n",
    "               label='$x_4(t)$' if i == 0 else None, )\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 46
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:07.190334Z",
     "start_time": "2024-09-04T07:39:06.952400Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(np.linspace(0, t_max, len(x_4[1, :])), x_4[0], label='$x_4(t)$')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 47
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## Orlicz space\n",
    "Given any Orlicz function $\\Phi $ we define on $L_{0}$ the modular $I_{\\Phi\n",
    "} $ by\n",
    "\\begin{equation*}\n",
    "    I_{\\Phi }(x)=\\int_{T}\\Phi \\left( x(t)\\right) d\\mu \\cdot\n",
    "\\end{equation*}\n",
    "Then the set\n",
    "\\begin{equation*}\n",
    "    L_{\\Phi }=\\left\\{ x\\in L^{0}(T):I_{\\Phi }(cx)<\\infty  \\right\\}\n",
    "\\end{equation*}\n",
    "for some $c>0$ depending on $x$ is called an *Orlicz space.* This space is usually equipped with the *Luxemburg norm*\n",
    "\\begin{equation*}\n",
    "    \\left\\Vert x\\right\\Vert _{\\Phi }=\\inf \\left\\{ \\varepsilon >0:I_{\\Phi }\\left(\n",
    "    \\frac{x}{\\varepsilon }\\right) \\leq 1\\right\\}\n",
    "\\end{equation*}\n",
    "or with the equivalent one\n",
    "\\begin{equation*}\n",
    "    \\left\\Vert x\\right\\Vert _{\\Phi }^{0}=\\underset{k>0}{\\inf }\\frac{1}{k}\\left(\n",
    "    1+I_{\\Phi }(kx)\\right)\n",
    "\\end{equation*}\n",
    "called the *Orlicz norm* in the *Amemiya form*."
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "Let's define another class of norms given by the Amemiya formula -\n",
    "norms generated by the function\n",
    "\\begin{equation*}\n",
    "s_p(u)=\\left\\{ \\begin{array}{lll}\n",
    "                   \\left(1+u^p\\right)^{\\frac{1}{p}} & \\text{if} & 1 \\leq p < \\infty, \\\\\n",
    "                   \\max\\left\\{1,u\\right\\}           & \\text{if} & p = \\infty%\n",
    "\\end{array}%\n",
    "\\right.\n",
    "\\end{equation*}"
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## kappa() function"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "Let $x\\in L_{\\Phi,p}.$ For any $k \\in (0,\\infty) $ define function\n",
    "$\\kappa_{p,x}(k)\\colon (0,\\infty) \\rightarrow (0,\\infty]$ by formula\n",
    "\\begin{equation*}\n",
    "    \\kappa_{p,x}(k) =  \\frac{1}{k}s_p\\left(I_{\\Phi }(kx)\\right).\n",
    "\\end{equation*}"
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:07.216659Z",
     "start_time": "2024-09-04T07:39:07.211121Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def Orlicz_function(u):\n",
    "    return np.where(u <= 1, u, np.inf)"
   ],
   "outputs": [],
   "execution_count": 48
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:07.314412Z",
     "start_time": "2024-09-04T07:39:07.308031Z"
    }
   },
   "cell_type": "code",
   "source": "osm.kappa(Orlicz_function, x=x_1, k=1, p_norm=1)",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(3.0)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 49
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:10.559906Z",
     "start_time": "2024-09-04T07:39:07.411356Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.kappa(Orlicz_function, x=x_1, k=1, p_norm=1)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38.9 μs ± 2.55 μs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "execution_count": 50
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## p_Amemiya_norm() "
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "By the $p-$Amemiya norm of an element $x\\in L_0$ we mean the norm defined by the formula\n",
    "\\begin{equation*}\n",
    "\\left\\Vert x\\right\\Vert _{\\Phi,p }=\\underset{k>0}{\\inf }\\frac{1}{k}s_p\\left(\n",
    "I_{\\Phi }(kx)\\right) \\quad \\text{ for } \\quad 1\\leq p \\leq \\infty.\n",
    "\\end{equation*}"
   ]
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "It is well known that for $p=1$ the $p-$Amemiya norm coincides with the Orlicz norm and\n",
    "    for $p=\\infty$ with the Luxemburg norm {cite}`HudzikMaligranda`. \n",
    "    "
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:10.614128Z",
     "start_time": "2024-09-04T07:39:10.580750Z"
    }
   },
   "cell_type": "code",
   "source": "osm.p_Amemiya_norm(Orlicz_function, x=x_1, p_norm=1)",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(3.0)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 51
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:22.234923Z",
     "start_time": "2024-09-04T07:39:10.682126Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.p_Amemiya_norm(Orlicz_function, x=x_1, p_norm=1)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.1 ms ± 365 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "execution_count": 52
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:40:10.462027Z",
     "start_time": "2024-09-04T07:40:08.443118Z"
    }
   },
   "cell_type": "code",
   "source": [
    "x = np.array([[1], [3]])\n",
    "osm.plot_p_norms(Orlicz_function,\n",
    "                 x=x,\n",
    "                 p_min=1,\n",
    "                 p_max=10,\n",
    "                 dp=.2,\n",
    "                 attach_inf=True,\n",
    "                 figsize=(8, 5))"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 74
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## p_Amemiya_norm_with_stars()"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "Denote $k^*_{p}(x) = \\inf{K_{p}(x)}$ and $k^{**}_{p}(x) = \\sup{K_{p}(x)}$\n",
    "(with convention $\\inf \\emptyset = \\infty$).\n",
    "Then\n",
    "\\begin{equation*}\n",
    "K_{p}(x) =\n",
    "\\left\\{ \\begin{array}{lll}\n",
    "\\left[k^*_{p}(x), k^{**}_{p}(x)\\right] & \\text{if } & k^{**}_{p}(x)<\\infty, \\\\\n",
    "\\left[k^*_{p}(x), \\infty \\right) & \\text{if} & k^*_{p}(x)<\\infty \\text{ and } k^{**}_{p}(x)=\\infty, \\\\\n",
    "\\emptyset & \\text{if } & k^*_{p}(x)=\\infty\n",
    "\\end{array}%\n",
    "\\right.\n",
    "\\end{equation*}\n",
    "and of any $k \\in K_{p}(x) $ holds\n",
    "\\begin{equation*}\n",
    "\\left\\Vert x\\right\\Vert _{\\Phi,p }=\\frac{1}{k}s_p\\left(\n",
    "I_{\\Phi }(kx)\\right)\n",
    "\\end{equation*}\n",
    "or (if $K_{p}(x) = \\emptyset$ )\n",
    "\\begin{equation*}\n",
    "\\left\\Vert x\\right\\Vert _{\\Phi,p }= \\lim_{k\\rightarrow \\infty}\\frac{1}{k}s_p\\left(\n",
    "I_{\\Phi }(kx)\\right)\n",
    "\\end{equation*}"
   ]
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:23.701644Z",
     "start_time": "2024-09-04T07:39:23.455874Z"
    }
   },
   "cell_type": "code",
   "source": "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x_1, p_norm=1)",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(3.000110995691083),\n",
       " np.float64(0.9998890166275929),\n",
       " np.float64(0.9998890166275929))"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 55
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "where first result is $||x||$, second is $k_p^*(x)$ and third is $k_p^{**}(x)$"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:25.567962Z",
     "start_time": "2024-09-04T07:39:23.746728Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x_1, p_norm=1)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "226 ms ± 1.89 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "execution_count": 56
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "example of using p_Amemiya_norm_with_stars() function with additional parameters"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:25.668426Z",
     "start_time": "2024-09-04T07:39:25.613706Z"
    }
   },
   "cell_type": "code",
   "source": [
    "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x_1, p_norm=1,\n",
    "                              k_min=0.9,\n",
    "                              k_max=1.1,\n",
    "                              len_domain_k=1000, )\n",
    "# show_progress=True)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(3.000000000000011),\n",
       " np.float64(0.999999999999989),\n",
       " np.float64(0.999999999999989))"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 57
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:29.613296Z",
     "start_time": "2024-09-04T07:39:25.720369Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x_1, p_norm=1, k_min=0.9, k_max=1.1, len_domain_k=1000)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "47.9 ms ± 2.39 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "execution_count": 58
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## p_Amemiya_norm_with_stars_by_decimal()"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Short examples how decimal module works"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:29.637152Z",
     "start_time": "2024-09-04T07:39:29.621628Z"
    }
   },
   "cell_type": "code",
   "source": "import decimal as dc  # for function using decimal precision",
   "outputs": [],
   "execution_count": 59
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:29.719393Z",
     "start_time": "2024-09-04T07:39:29.711021Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(dc.getcontext().prec)\n",
    "print(dc.Decimal(0.2))\n",
    "print(dc.Decimal('0.2'))\n",
    "print(dc.Decimal(1) / 5)\n",
    "print((dc.Decimal(np.sqrt(2))) ** 2)\n",
    "print((dc.Decimal(2).sqrt()) ** 2)\n",
    "\n",
    "dc.getcontext().prec = 50\n",
    "print(dc.Decimal(0.2))\n",
    "print(dc.Decimal('0.2'))\n",
    "print(dc.Decimal(1) / 5)\n",
    "print((dc.Decimal(np.sqrt(2))) ** 2)\n",
    "print((dc.Decimal(2).sqrt()) ** 2)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28\n",
      "0.200000000000000011102230246251565404236316680908203125\n",
      "0.2\n",
      "0.2\n",
      "2.000000000000000273432346306\n",
      "1.999999999999999999999999999\n",
      "0.200000000000000011102230246251565404236316680908203125\n",
      "0.2\n",
      "0.2\n",
      "2.0000000000000002734323463064769280688491650795723\n",
      "1.9999999999999999999999999999999999999999999999999\n"
     ]
    }
   ],
   "execution_count": 60
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Orlicz function and x must be prepared to decimal form"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:29.836175Z",
     "start_time": "2024-09-04T07:39:29.761434Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def Orlicz_function(u):\n",
    "    return np.where(u <= 1, u, dc.Decimal(np.inf))\n",
    "\n",
    "\n",
    "len_t = 1\n",
    "x_5 = np.zeros(shape=(2, len_t), dtype=np.dtype('object'))\n",
    "x_5[1, 0] = dc.Decimal(2)  #  measure of support\n",
    "x_5[0, 0] = dc.Decimal(1)  # value\n",
    "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x_5, p_norm=1)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Decimal('3.1110988766779245797415719566910102134319832100514'),\n",
       " Decimal('0.90000991'),\n",
       " Decimal('0.90000991'))"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 61
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:35.706165Z",
     "start_time": "2024-09-04T07:39:29.893695Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x_5, p_norm=1)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71.9 ms ± 20.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "execution_count": 62
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "example of using p_Amemiya_norm_with_stars_by_decimal() function with additional parameters"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:35.840418Z",
     "start_time": "2024-09-04T07:39:35.748100Z"
    }
   },
   "cell_type": "code",
   "source": [
    "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x_5, p_norm=dc.Decimal(1),\n",
    "                                         k_min=dc.Decimal('0.9'),\n",
    "                                         k_max=dc.Decimal('1.1'),\n",
    "                                         len_domain_k=1000, )\n",
    "# show_progress=True)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Decimal('3.0000'), Decimal('1.0000'), Decimal('1.0000'))"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 63
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:40.704964Z",
     "start_time": "2024-09-04T07:39:35.893267Z"
    }
   },
   "cell_type": "code",
   "source": [
    "%%timeit\n",
    "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x_5, p_norm=dc.Decimal(1),\n",
    "                                         k_min=dc.Decimal('0.9'),\n",
    "                                         k_max=dc.Decimal('1.1'),\n",
    "                                         len_domain_k=1000\n",
    "                                         )"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "59.2 ms ± 3.34 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
     ]
    }
   ],
   "execution_count": 64
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "In the next example there is false $k_p^{*}(x)$ less than $k_p^{**}(x)$"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:40.733220Z",
     "start_time": "2024-09-04T07:39:40.714049Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def Orlicz_function(u):\n",
    "    return np.where(u <= 1, u, 2 * u - 1)\n",
    "\n",
    "\n",
    "x = np.array([[1], [3]])\n"
   ],
   "outputs": [],
   "execution_count": 65
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:41.092045Z",
     "start_time": "2024-09-04T07:39:40.793725Z"
    }
   },
   "cell_type": "code",
   "source": "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x, p_norm=20)",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(3.0000000000430616),\n",
       " np.float64(0.64823266269593),\n",
       " np.float64(0.9999516967001615))"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 66
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:41.417566Z",
     "start_time": "2024-09-04T07:39:41.092045Z"
    }
   },
   "cell_type": "code",
   "source": "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x, p_norm=dc.Decimal(10))",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Decimal('3.0000145688845555222000227125563249652936039015189'),\n",
       " Decimal('0.90000991'),\n",
       " Decimal('0.90000991'))"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 67
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "For better accuracy we may reduce domain by"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:41.532664Z",
     "start_time": "2024-09-04T07:39:41.459077Z"
    }
   },
   "cell_type": "code",
   "source": [
    "osm.p_Amemiya_norm_with_stars(Orlicz_function, x=x, p_norm=20,\n",
    "                              k_min=0.45,\n",
    "                              k_max=1.05)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(3.0000000000433653),\n",
       " np.float64(0.6671999999999962),\n",
       " np.float64(0.9995999999999903))"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 68
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-09-04T07:39:41.899951Z",
     "start_time": "2024-09-04T07:39:41.579242Z"
    }
   },
   "cell_type": "code",
   "source": [
    "osm.p_Amemiya_norm_with_stars_by_decimal(Orlicz_function, x=x, p_norm=dc.Decimal(10),\n",
    "                                         k_min=dc.Decimal(45) / 100,\n",
    "                                         k_max=dc.Decimal(105) / 100)"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Decimal('3.0000051008541999106151967575520682494068505040605'),\n",
       " Decimal('0.9996'),\n",
       " Decimal('0.9996'))"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 69
  }
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