Tutorials/tuto3_Compare.ipynb

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    "# How to compare several fields in one plot\n",
    "\n",
    "The SciDataTool python module has been created to **ease the handling of scientific data**, and considerately simplify plot commands. It unifies the extraction of relevant data (e.g. slices), whether they are stored in the time/space or in the frequency domain. The call to Fourier Transform functions is **transparent**, although it still can be parameterized through the use of a dictionary.\n",
    "\n",
    "This tutorial explains the how to **compare** several fields, even if they are not defined with the same bases, or even if they were stored in different time/frequency domains.\n",
    "\n",
    "After learning [how to create `Data` objects](https://nbviewer.jupyter.org/github/Eomys/SciDataTool/blob/master/Tutorials/tuto1_Create.ipynb) and [how to extract slices](https://nbviewer.jupyter.org/github/Eomys/SciDataTool/blob/master/Tutorials/tuto2_Slices.ipynb), you may want to **compare on a same graph** several fields. The `compare_along` methods will provide you a very practical tool to do so, as you can see in this first example:"
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      "Loading xls file...\n",
      "Done\n"
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   ],
   "source": [
    "# Add SciDataTool to the Python path\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "\n",
    "# Import useful packages\n",
    "from os.path import join\n",
    "from numpy import pi, squeeze, linspace, sin\n",
    "from pandas import ExcelFile, read_excel\n",
    "import plotly.graph_objects as go\n",
    "import plotly.io as pio\n",
    "pio.renderers.default = 'notebook_connected'\n",
    "\n",
    "# Import SciDataTool modules\n",
    "from SciDataTool import Data1D, DataTime, DataLinspace\n",
    "\n",
    "# Import scientific data\n",
    "print(\"Loading xls file...\")\n",
    "from Tests import DATA_DIR\n",
    "xls_file = ExcelFile(join(DATA_DIR, \"tutorials_data.xlsx\"))\n",
    "time = squeeze(read_excel(xls_file, sheet_name=\"time\", header=None, nrows=1, squeeze=True).to_numpy())\n",
    "angle = squeeze(read_excel(xls_file, sheet_name=\"angle\", header=None, nrows=1, squeeze=True).to_numpy())\n",
    "field = squeeze(read_excel(xls_file, sheet_name=\"Br\", header=None, nrows=1008, squeeze=True).to_numpy())\n",
    "print(\"Done\")\n",
    "\n",
    "# Create analytic field for comparison\n",
    "t0 = 0.01\n",
    "tf = 0.04\n",
    "Nt = 3000\n",
    "time2 = linspace(0.01, 0.04, 3000, endpoint=True)\n",
    "sine_function = 0.2 * sin(375 * time2 - 1.5)\n",
    "\n",
    "# Create Data objects\n",
    "Time = Data1D(name=\"time\", unit=\"s\", values=time)\n",
    "Angle = Data1D(name=\"angle\", unit=\"rad\", values=angle)\n",
    "Br = DataTime(\n",
    "            name=\"Airgap radial flux density\",\n",
    "            unit=\"T\",\n",
    "            symbol=\"B_r\",\n",
    "            axes=[Time, Angle],\n",
    "            values=field,\n",
    "        )\n",
    "Time2 = DataLinspace(\n",
    "            name=\"time\",\n",
    "            unit=\"s\",\n",
    "            symmetries={},\n",
    "            initial=t0,\n",
    "            final=tf,\n",
    "            number=Nt,\n",
    "            include_endpoint=True,\n",
    "        )\n",
    "Analytic = DataTime(\n",
    "            symbol=\"0.2\\sin(375t-1.5)\",\n",
    "            name=\"Sine function\",\n",
    "            unit=\"T\",\n",
    "            symmetries={},\n",
    "            axes=[Time2],\n",
    "            normalizations={},\n",
    "            values=sine_function,\n",
    "        )\n",
    "\n",
    "#---------------------------------------------------------------\n",
    "# Compare the fields\n",
    "results = Br.compare_along(\"time\", data_list=[Analytic])\n",
    "#---------------------------------------------------------------\n",
    "\n",
    "# Plot\n",
    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter(\n",
    "    x=results[\"time\"],\n",
    "    y=results[Br.symbol],\n",
    "    name=r\"$\"+Br.symbol+\"$\"\n",
    "))\n",
    "fig.add_trace(go.Scatter(\n",
    "    x=results[\"time\"],\n",
    "    y=results[Analytic.symbol + \"_0\"],\n",
    "    name=r\"$\"+Analytic.symbol+\"$\"\n",
    "))\n",
    "fig.update_layout(\n",
    "    title={\n",
    "        'text': Br.name + \" comparison with analytical expression\",\n",
    "        'y':0.9,\n",
    "        'x':0.5,\n",
    "        'xanchor': 'center',\n",
    "        'yanchor': 'top'},\n",
    "    xaxis_title=\"Angle [°]\",\n",
    "    yaxis_title=r\"$\"+Br.symbol+\" [\"+Br.unit+\"]$\",\n",
    ")\n",
    "fig.show(config = {\"displaylogo\":False})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Data` classes allow to easily compare several fields in the same graph, even if they don't have the same basis or are stored in different time/frequency domains. To do so, the `compare_along` methods find a common basis for the axes requested, and interpolate the fields on this common basis. The syntax for requesting axes, unit and normalization, is the same as in a slice with the `get_along` methods.\n",
    "\n",
    "An additional argument appears: the `data_list` is a **list** that contains the `Data` objects to compare to the original field.\n",
    "\n",
    "Note that if `data_list` is not specified, the `get_along` method will simply be called, so that this method can be used **by default** (which can be useful to define **generic** plot methods). Note also that `compare_FT_along`, `compare_magnitude_along` and `compare_phase_along` are available for **comparisons of spectra**."
   ]
  }
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