Add ParameterAnalysis

docs/docs/tutorials/tutorial0_basics.ipynb

@@ -23,7 +23,9 @@
     "\n",
     "import easydynamics as edyn\n",
     "import easydynamics.sample_model as sm\n",
-    "from easydynamics.analysis.analysis import Analysis\n",
+    "from easydynamics.analysis import Analysis\n",
+    "from easydynamics.analysis import ParameterAnalysis\n",
+    "from easydynamics.analysis.parameter_analysis import FitBinding\n",
     "\n",
     "# Make the plots interactive\n",
     "%matplotlib widget"
@@ -322,7 +324,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "print(f'The reduced chi-squared value for Q_index=5 is: {fit_result_all_Q[5].reduced_chi}')\n",
+    "print(f'The reduced chi-squared value for Q_index=5 is: {fit_result_all_Q[5].reduced_chi2}')\n",
     "\n",
     "print(f'The minimizer engine is: {fit_result_all_Q[5].minimizer_engine}')"
    ]
@@ -368,7 +370,79 @@
    "id": "842c1f01",
    "metadata": {},
    "source": [
-    "It will soon be possible to use **EasyDynamics** to fit these parameters to e.g. a polynomial."
+    "The final step in this tutorial is to fit the are of the `Gaussian` to a straight line. For this, we use the `ParameterAnalysis` class. We create a `Polynomial` with two coefficients for the fit function. We create a `FitBinding`, telling the class we want to fit the parameter named `Gaussian area` with the fit function that we define."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "75db3d4c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fit_func = sm.Polynomial(coefficients=[3.7, -0.5], display_name='Straight line')\n",
+    "\n",
+    "binding = FitBinding(parameter_name='Gaussian area', model=fit_func)\n",
+    "\n",
+    "parameter_analysis = ParameterAnalysis(\n",
+    "    parameters=analysis,\n",
+    "    bindings=[binding],\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "01f45034",
+   "metadata": {},
+   "source": [
+    "Let us plot the start guess using the `plot()` method:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bd3cf4a6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "634bebdc",
+   "metadata": {},
+   "source": [
+    "It looks decent, so we can fit and plot again:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d5ba8985",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.fit()\n",
+    "parameter_analysis.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dc33728c",
+   "metadata": {},
+   "source": [
+    "To see the parameters we can use the `get_all_parameters()` method:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f18e2944",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.get_all_parameters()"
    ]
   }
  ],

docs/docs/tutorials/tutorial0_more_advanced.ipynb

@@ -292,7 +292,65 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "analysis.plot_parameters(names=['Gaussian area', 'Lorentzian area', 'DHO area'])"
+    "analysis.plot_parameters(names=['Gaussian area', 'DHO area', 'DHO center'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0eadbd91",
+   "metadata": {},
+   "source": [
+    "With apologies for the lack of creativity, these all appear like straight lines. We can fit them individually or all together using `ParameterAnalysis`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bb2f0e06",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "gauss_fit_func = sm.Polynomial(\n",
+    "    coefficients=[3.7, -0.5], unit='1/angstrom', display_name='Gauss area fit'\n",
+    ")\n",
+    "dho_area_fit_func = sm.Polynomial(\n",
+    "    coefficients=[2.0, 0.12], unit='1/angstrom', display_name='DHO area fit'\n",
+    ")\n",
+    "dho_center_fit_func = sm.Polynomial(\n",
+    "    coefficients=[1.1, 0.2], unit='1/angstrom', display_name='DHO center fit'\n",
+    ")\n",
+    "\n",
+    "binding1 = edyn.FitBinding(parameter_name='Gaussian area', model=gauss_fit_func)\n",
+    "\n",
+    "binding2 = edyn.FitBinding(parameter_name='DHO area', model=dho_area_fit_func)\n",
+    "\n",
+    "binding3 = edyn.FitBinding(parameter_name='DHO center', model=dho_center_fit_func)\n",
+    "\n",
+    "parameter_analysis = edyn.ParameterAnalysis(\n",
+    "    parameters=analysis,\n",
+    "    bindings=[binding1, binding2, binding3],\n",
+    ")\n",
+    "\n",
+    "parameter_analysis.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32bc1efc",
+   "metadata": {},
+   "source": [
+    "The start guesses look reasonable, so we fit:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a5548093",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.fit()\n",
+    "parameter_analysis.plot()"
    ]
   }
  ],

docs/docs/tutorials/tutorial1_brownian.ipynb

@@ -24,6 +24,8 @@
     "import pooch\n",
     "\n",
     "from easydynamics.analysis.analysis import Analysis\n",
+    "from easydynamics.analysis.parameter_analysis import FitBinding\n",
+    "from easydynamics.analysis.parameter_analysis import ParameterAnalysis\n",
     "from easydynamics.experiment import Experiment\n",
     "from easydynamics.sample_model import BrownianTranslationalDiffusion\n",
     "from easydynamics.sample_model import ComponentCollection\n",
@@ -460,7 +462,7 @@
    "id": "45daa848",
    "metadata": {},
    "source": [
-    "The fit looks good, so now we want to look at the most interesting fit parameters: the width and area of the Lorentzian. In later versions of EasyDynamics it will be possible to fit them to e.g. a DiffusionModel."
+    "The fit looks good, so now we want to look at the most interesting fit parameters: the width and area of the Lorentzian. "
    ]
   },
   {
@@ -470,7 +472,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "# Let us look at the most interesting fit parameters\n",
     "diffusion_analysis.plot_parameters(names=['Lorentzian width', 'Lorentzian area'])"
    ]
   },
@@ -485,7 +486,105 @@
     "$$\n",
     "where $\\Gamma(Q) = D Q^2$ and $D$ is the diffusion coefficient. $S$ is an overall scale.\n",
     "\n",
-    "In addition to this diffusion model, there is still the elastic incoherent scattering.\n",
+    "To fit the Brownian translational diffusion model to the data, we use the `ParameterAnalysis`. This time, we wish to fit the `Lorentzian`, and we wish to fit both its area (scale, $S$) and width to the diffusion model. We do this by creating a `FitBinding`, saying we want to fit both the area an width of the component called `Lorentzian`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9c1ab6b0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "brownian_diffusion_model = BrownianTranslationalDiffusion(\n",
+    "    display_name='Brownian Translational Diffusion', diffusion_coefficient=2.4e-9, scale=0.5\n",
+    ")\n",
+    "\n",
+    "binding = FitBinding(\n",
+    "    parameter_name='Lorentzian',\n",
+    "    model=brownian_diffusion_model,\n",
+    "    modes=['area', 'width'],\n",
+    ")\n",
+    "\n",
+    "parameter_analysis = ParameterAnalysis(\n",
+    "    parameters=diffusion_analysis,\n",
+    "    bindings=[binding],\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53dc12dc",
+   "metadata": {},
+   "source": [
+    "We first plot the start guess to see if it's reasonable."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c7074c64",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.plot()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "57b76d06",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.plot(names=['Polynomial_c0'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64babb01",
+   "metadata": {},
+   "source": [
+    "This looks pretty good. Let's fit and plot again:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "26c418ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.fit()\n",
+    "parameter_analysis.plot()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "81d30f55",
+   "metadata": {},
+   "source": [
+    "And we can get the parameters of the diffusion model:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7c47bcd4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.get_all_parameters()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc2f8434",
+   "metadata": {},
+   "source": [
+    "This is a good result, but we can do better. Now that we know that the quasielastic scattering is well described by a model of diffusion, we can fit this model directly to the data, fitting all $Q$ simultaneously.\n",
+    "\n",
+    "In addition to this diffusion model, we will still fit the elastic incoherent scattering.\n",
     "\n",
     "We create a new `SampleModel` which as a `DeltaFunction` component for the elastic incoherent scattering and a `BrownianTranslationalDiffusion` diffusion model to describe the rest. We also create a new `BackgroundModel` and `InstrumentModel`."
    ]
@@ -593,7 +692,7 @@
    "id": "bbeec088",
    "metadata": {},
    "source": [
-    "It does not make sense to plot the diffusion parameters, but we can display them (with uncertainties) like this."
+    "It does not make sense to plot the diffusion parameters, as they are just two numbers with uncertainties, but we can display them (with uncertainties) like this."
    ]
   },
   {
@@ -605,6 +704,24 @@
    "source": [
     "diffusion_model.get_all_parameters()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc9bf6b1",
+   "metadata": {},
+   "source": [
+    "For reference, here are the diffusion parameters found from fitting the width and scale of the fitted Lorentzians. Notice that the error bars when fitting everything simultaneously are a lot lower than the two-step fit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0af81fa8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "parameter_analysis.get_all_parameters()"
+   ]
   }
  ],
  "metadata": {