{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "807b592c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from smpl import plot\n",
    "from smpl import functions as fff\n",
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8bcbe1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "from scipy.misc import derivative\n",
    "\n",
    "def trim_domain(f,    \n",
    "    fmin = np.finfo(np.float32).min/2,\n",
    "    fmax = np.finfo(np.float32).max/2,\n",
    "    steps=100000,\n",
    "    min_ch=0.001\n",
    "               ):\n",
    "    test = np.linspace(fmin,fmax,steps)\n",
    "    dr = derivative(f,test,dx=1e-06)\n",
    "    m1 = np.abs(dr)>min_ch\n",
    "    bmin=np.argmax(m1)\n",
    "    m2=(np.abs(dr)>min_ch)[::-1]\n",
    "    tbmax=np.argmax(m2)\n",
    "    xmin = test[bmin]\n",
    "    xmax=test[::-1][tbmax]\n",
    "    if bmin == 0 and tbmax ==0 and not m1[0] and not m2[0]:\n",
    "        # trisect\n",
    "        tmin = xmin\n",
    "        tmax = xmax\n",
    "        t1a,t1b = trim_domain(f,tmin+ (tmax-tmin)/3,tmax -(tmax-tmin)/3,min_ch=min_ch)\n",
    "        if np.isclose(t1a,t1b):\n",
    "            t2a,t2b = trim_domain(f,tmin + (tmax-tmin)/3,tmax,min_ch=min_ch)\n",
    "            if np.isclose(t2a,t2b):\n",
    "                t3a,t3b = trim_domain(f,tmin ,tmax- (tmax-tmin)/3,min_ch=min_ch)\n",
    "                if np.isclose(t3a,t3b):\n",
    "                    return 0.,0. \n",
    "                else:\n",
    "                    return t3a,t3b    \n",
    "            else:\n",
    "                return t2a,t2b\n",
    "        else:\n",
    "            return t1a,t1b\n",
    "    return xmin,xmax\n",
    " \n",
    "def get_domain(f,\n",
    "    fmin = np.finfo(np.float32).min/2,\n",
    "    fmax = np.finfo(np.float32).max/2,\n",
    "    steps=100000,\n",
    "):\n",
    "    \"\"\"\n",
    "    Return the domain of the function ``f``.\n",
    "    \"\"\"\n",
    "    \n",
    "    test = np.linspace(fmin,fmax,steps)\n",
    "    \n",
    "    r = f(test)\n",
    "    mask = np.isfinite(r)        \n",
    "    tr = test[mask]\n",
    "    if len(tr)>0:\n",
    "        tmin = np.amin(tr)\n",
    "        tmax = np.amax(tr)\n",
    "        test_r = np.linspace(tmin,tmax,steps)\n",
    "        if np.equal(tr.shape , test_r.shape) and np.allclose(test_r,tr):\n",
    "            return tmin,tmax\n",
    "    \n",
    "    # trisect\n",
    "    tmin = fmin\n",
    "    tmax = fmax\n",
    "    t1a,t1b = get_domain(f,tmin+ (tmax-tmin)/3,tmax -(tmax-tmin)/3)\n",
    "    if np.isclose(t1a,t1b):\n",
    "        t2a,t2b = get_domain(f,tmin + (tmax-tmin)/3,tmax)\n",
    "        if np.isclose(t2a,t2b):\n",
    "            t3a,t3b = get_domain(f,tmin ,tmax- (tmax-tmin)/3)\n",
    "            if np.isclose(t3a,t3b):\n",
    "                return 0.,0. \n",
    "            else:\n",
    "                return t3a,t3b    \n",
    "        else:\n",
    "            return t2a,t2b\n",
    "    else:\n",
    "        return t1a,t1b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ec7a5d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_monotone(f,tmin=None,tmax=None,):\n",
    "    \"\"\"\n",
    "    Test if function ``f`` is monotone.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    f : function\n",
    "        Function to be tested.\n",
    "    test : array_like\n",
    "        Test points.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    bool\n",
    "        True if function is monotone.\n",
    "    \"\"\"\n",
    "    if tmax is None and tmin is None:\n",
    "        tmin,tmax = get_domain(f)\n",
    "    test = np.linspace(tmin,tmax,1000)\n",
    "    return np.all(f(test[1:])>=f(test[:-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2aaad85d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_interesting_region(f,min_ch = 1e-4):\n",
    "    \"\"\"\n",
    "    Return interesting xmin and xmax of function ``f``.\n",
    "    \"\"\"\n",
    "    omin_x,omax_x = get_domain(f)\n",
    "    if is_monotone(f,omin_x,omax_x):\n",
    "        min_x,max_x=trim_domain(f,omin_x,omax_x,min_ch = min_ch)\n",
    "        #min_x,max_x=omin_x,omax_x\n",
    "    else:\n",
    "        tmax_x= scipy.optimize.minimize(lambda x: -f(x),0.,method='Nelder-Mead',bounds=[(omin_x,omax_x)])\n",
    "        tmin_x= scipy.optimize.minimize(f,0.,method='Nelder-Mead',bounds=[(omin_x,omax_x)])\n",
    "        if tmax_x.success:\n",
    "            tmax_x = tmax_x.x[0]\n",
    "        else:\n",
    "            tmax_x =0.\n",
    "        if tmin_x.success:\n",
    "            tmin_x = tmin_x.x[0]\n",
    "        else:\n",
    "            tmin_x =0.\n",
    "        \n",
    "        if abs(tmax_x) > np.finfo(np.float32).max/10:\n",
    "            tmax_x = 0.\n",
    "        if abs(tmin_x) > np.finfo(np.float32).max/10:\n",
    "            tmin_x = 0.\n",
    "        x_min = min(tmax_x,tmin_x)\n",
    "        x_max = max(tmax_x,tmin_x)\n",
    "        min_x = ((x_max+x_min)/2-(x_max-x_min))\n",
    "        max_x = ((x_max+x_min)/2+(x_max-x_min))\n",
    "        if np.isclose(min_x,max_x):\n",
    "            min_x,max_x=trim_domain(f,omin_x,omax_x,min_ch = min_ch)\n",
    "            \n",
    "            \n",
    "    return min_x,max_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f10d3b27",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = np.exp\n",
    "print(np.finfo(np.float64).min,np.finfo(np.float64).max)\n",
    "print(get_domain(f))\n",
    "print(np.isclose(*get_domain(f)))\n",
    "print(is_monotone(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "febd4179",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return np.exp(x)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d361b19",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return np.sin(x)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07894d8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return x**2\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77db85a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return x\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09d1b27a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return np.cos(x)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a65bf46d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return np.arctan(x)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ddb43496",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    return np.tan(x)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7b66cf0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ff(x):\n",
    "    \"\"\"Lorentz\"\"\"\n",
    "    return fff.lorentz(x,0,5,3,0)\n",
    "xmin,xmax =get_interesting_region(ff)\n",
    "plot.function(ff,xmin=xmin,xmax = xmax,logy=False)"
   ]
  },
  {
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