{
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    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Fit data\n\nThis demo shows how data fitting can be performed using the ``itom.dataObject`` and ``itom.algorithms``.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\nfrom itom import dataObject\nfrom itom import algorithms"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Polynomial of order 2 in x- and y-direction\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def polyFuncOrder2x2(x: float, y:float) -> float:\n    return 2.5 * x ** 2 + -1.7 * y ** 2 + 1.3 * x * y + 0.7 * x - 0.3 * y + 3.2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Vectorize this function to be evaluated over an array of x and y-coordinates\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "f = np.vectorize(polyFuncOrder2x2)\n\n[X, Y] = np.meshgrid(np.arange(-10, 10.5, 0.5), np.arange(-10, 10.5, 0.5))\nZ = f(X, Y)\ntotal = np.prod(Z.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "First create a 2d polynomial fit with order x = 2 and order y = 2.\nZ_ must be a regular grid where the x- and y- values are\ndefined by its axisScales and axisOffsets attributes. \n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "Z_ = dataObject(Z)\nZ_.axisScales = (0.5, 0.5)\nZ_.axisOffsets = (20, 20)\n\ncoeffs = algorithms.polyfitWeighted2D(Z_, 2, 2)\nprint(\"coefficients: \", coeffs)\n\n# Reconstruct the fitted sphere using the determined coefficients.\n# First, create a ``dataObject`` with the desired size, scaling and offset for the\n# the grid of x- and y- values. The z-values are then calculated.\nZ_reconstruction = Z_.copy()\nZ_reconstruction[:, :] = float(\"nan\")\n\nalgorithms.polyval2D(Z_reconstruction, coeffs, 2, 2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Randomly select a number of samples unique values in the range ``[0,total)``.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "samples = 100\nrandomUniqueValues = np.random.choice(total, samples)\nX2 = dataObject([1, samples], \"float64\")\nY2 = dataObject([1, samples], \"float64\")\nZ2 = dataObject([1, samples], \"float64\")\nc = Z.shape[1]\n\nfor i in range(samples):\n    idx = randomUniqueValues[i]\n    X2[0, i] = X[int(idx / c), idx % c]\n    Y2[0, i] = Y[int(idx / c), idx % c]\n    Z2[0, i] = Z[int(idx / c), idx % c]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Determine the polyonimal coefficients only using the random samples.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "coeffs2 = algorithms.polyfitWeighted2DSinglePoints( X2, Y2, Z2, 2, 2)\n# coeffs and coeffs2 must be the same!\nprint(\"fitted coefficient: \", coeffs2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "And reconstruct the entire surface for X and Y values.\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "Z2_reconstruction = dataObject()\nalgorithms.polyval2DSinglePoints(\n    dataObject(X),\n    dataObject(Y),\n    Z2_reconstruction,\n    coeffs2,\n    2,\n    2,\n)\n\nsample_reconstruction = dataObject()\nalgorithms.polyval2DSinglePoints(X2, Y2, sample_reconstruction, coeffs2, 2, 2)"
      ]
    }
  ],
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