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  {
   "cell_type": "markdown",
   "id": "449cb409-2af4-4caa-a3e0-c80828e9da47",
   "metadata": {},
   "source": [
    "## Appendix I: Generating the synthetic data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8a62cde-00cd-4a60-ad8b-49af53992c52",
   "metadata": {},
   "source": [
    "<a id='two_peaks'></a>\n",
    "### Two peaks\n",
    "<a href='#top'>[back to top]</a> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6410dd9d-ffe1-4333-9140-1d6db9607a2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import hyperspy.api as hs\n",
    "\n",
    "domain = 32 #size of the square domain\n",
    "hfactor = 600\n",
    "cent = (domain//2, domain//2)\n",
    "y,x = np.ogrid[-cent[0]:domain-cent[0], -cent[1]:domain-cent[1]]\n",
    "\n",
    "def gaussian2d(x, y, A=1, x0=0, y0=0, sigmax=20, sigmay=10):\n",
    "    return A * np.exp(-((x-x0)**2 / 2 / sigmax ** 2 + (y-y0)**2 / 2 / sigmay ** 2))\n",
    "\n",
    "center_narrow = 50 + 10 * np.sin(3 * np.pi * x / domain) * np.cos(4 * np.pi * y / domain)\n",
    "center_wide = 50 + 10 * (-0.1 * np.sin(3 * np.pi * x / domain) * np.cos(4 * np.pi * y / domain))\n",
    "\n",
    "r = np.sqrt(x**2 + y**2)\n",
    "h_narrow = .5 * (.5 + np.sin(r)**2) * gaussian2d(x, y) *  hfactor\n",
    "h_wide = (.5 + np.cos(r)**2) * gaussian2d(x, y) *  hfactor\n",
    "\n",
    "s = hs.signals.Signal1D(np.ones((domain,domain, 1024)))\n",
    "s.metadata.General.title = 'Two gaussians'\n",
    "s.axes_manager[0].name = \"x\"\n",
    "s.axes_manager[0].units = \"nm\"\n",
    "s.axes_manager[1].name = \"y\"\n",
    "s.axes_manager[1].units = \"nm\"\n",
    "\n",
    "s.axes_manager[2].name = \"Energy\"\n",
    "s.axes_manager[2].name = \"eV\"\n",
    "s.axes_manager[2].scale = 0.1\n",
    "m0 = s.create_model()\n",
    "\n",
    "gs01 = hs.model.components1D.GaussianHF()\n",
    "gs01.name = \"wide\"\n",
    "m0.append(gs01)\n",
    "gs01.fwhm.value = 60\n",
    "gs01.centre.map['values'][:] = center_wide\n",
    "gs01.centre.map['is_set'][:] = True\n",
    "gs01.height.map['values'][:] = h_wide\n",
    "gs01.height.map['is_set'][:] = True\n",
    "\n",
    "gs02 = hs.model.components1D.GaussianHF()\n",
    "gs02.name = \"narrow\"\n",
    "m0.append(gs02)\n",
    "gs02.fwhm.value = 6\n",
    "gs02.centre.map['values'][:] = center_narrow\n",
    "gs02.centre.map['is_set'][:] = True\n",
    "gs02.height.map['values'][:] = h_narrow\n",
    "gs02.height.map['is_set'][:] = True\n",
    "s.data = m0.as_signal().data\n",
    "s.add_poissonian_noise(random_state=0)\n",
    "m0.store(\"ground truth\")\n",
    "s.save(\"two_peaks.hspy\", overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5af2ac12-ec43-4fba-9a63-ae3a43ceb360",
   "metadata": {},
   "source": [
    "<a id='wobbly_peak'></a>\n",
    "### Wobbly peak\n",
    "<a href='#top'>[back to top]</a> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "630dcc09-01ec-4e33-a073-ea0352f5541b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import hyperspy.api as hs\n",
    "\n",
    "k = 1\n",
    "alpha = 15\n",
    "amp = 3\n",
    "\n",
    "gaus_position = 15\n",
    "gaus_width = 5\n",
    "gaus_A = 300\n",
    "\n",
    "gradient = 0.6\n",
    "offset= 3\n",
    "\n",
    "sin_component = hs.model.components1D.Expression('A * sin(k*x + alpha)', name='sin', k=k,\n",
    "                                               alpha=alpha, A=amp)\n",
    "gaus = hs.model.components1D.Gaussian(A=gaus_A, sigma=gaus_width, centre=gaus_position)\n",
    "\n",
    "poly = hs.model.components1D.Polynomial(1)\n",
    "\n",
    "poly.coefficients.value = (gradient, offset)\n",
    "\n",
    "axis = np.linspace(0, 30, 3000, dtype='double')\n",
    "\n",
    "result = sin_component.function(axis)+ gaus.function(axis) + poly.function(axis)\n",
    "s = hs.signals.Signal1D(result)\n",
    "s.axes_manager[0].name = 'x'\n",
    "s.axes_manager[0].scale = 0.1\n",
    "s.axes_manager[0].offset = 0\n",
    "\n",
    "s.metadata.General.author = 'Tomas Ostasevicius'\n",
    "s.metadata.General.title = 'Sin + poly(2) + Gaussian'\n",
    "s.save('wobbly_peak', overwrite=True)"
   ]
  }
 ],
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