how to create some linear functions

linear functions.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit"
   ]
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    "\n",
    "def linear_gaus1(x, a0, aslope, b, x0, sigma, per):\n",
    "    '''\n",
    "    here is a simple Gaussian function, but where the\n",
    "    amplitude changes linearly with time.\n",
    "    \n",
    "    note: curve fit will try to fit period in this case!\n",
    "    use very tight boundaries!!\n",
    "    '''\n",
    "    phase = (x % per) / per\n",
    "    ampl = a0 + (x * aslope)\n",
    "    return ampl * np.exp(-(phase - x0)**2 / (2 * sigma**2)) + b\n",
    "\n",
    "\n",
    "def linear_gaus2(x, a0, aslope, b, x0, xslope, sigma, per):\n",
    "    '''\n",
    "    here is a simple Gaussian function, but where the\n",
    "    amplitude AND phase center changes linearly with time\n",
    "    \n",
    "    note: curve fit will try to fit period in this case!\n",
    "    use very tight boundaries!!\n",
    "    '''\n",
    "    phase = (x % per) / per\n",
    "    ampl = a0 + (x * aslope)\n",
    "    xcent = x0 + (phase * xslope)\n",
    "    return ampl * np.exp(-(phase - xcent)**2 / (2 * sigma**2)) + b\n",
    "\n",
    "\n",
    "def linear_gaus_P(x, a0, aslope, b, x0, xslope, sigma, per = 1.234):\n",
    "    '''\n",
    "    here is a simple Gaussian function, but where the\n",
    "    amplitude AND phase center changes linearly with time\n",
    "    \n",
    "    here period is hard coded and does not need to be passed\n",
    "    note: you'd need to make this function for every system.\n",
    "    '''\n",
    "    phase = (x % per) / per\n",
    "    ampl = a0 + (x * aslope)\n",
    "    xcent = x0 + (phase * xslope)\n",
    "    return ampl * np.exp(-(phase - xcent)**2 / (2 * sigma**2)) + b\n",
    "\n",
    "\n",
    "# here's one possible hack... which *might* work. I dont know! :D\n",
    "for k in range(len(systems)):\n",
    "    # define a function INSIDE the loop!\n",
    "    def myfunc(x, a0, aslope, b, x0, xslope, sigma):\n",
    "        return linear_gaus_P(x, a0, aslope, b, x0, xslope, sigma, per=periods[k])\n",
    "    \n",
    "    popt,pcov = curve_fit(myfunc xdata, ydata, p0=[some initial parameters])"
   ]
  }
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