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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "Finite differencing with xarray and dask\n---------------------------------------"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "\"\"\"xarray/dask-compatible finite differencing functions\"\"\"\nimport dask.array as darray\nimport numpy as np\nimport xarray as xr\n\nfrom scipy.ndimage.filters import correlate1d\nfrom sympy.calculus import finite_diff_weights\nfrom xarray.core import computation\n\n\ndef centered_diff_weights(accuracy, spacing=1.):\n \"\"\"Compute the weights of a central difference approx. to derivative\n\n Does so for an arbitrary even-valued order of accuracy.\n\n Parameters\n ----------\n accuracy : int\n Order of accuracy of approximation (must be even)\n spacing : float\n Uniform spacing between the points (default = 1.)\n\n Returns\n -------\n list of finite difference weights\n \"\"\"\n if accuracy % 2:\n raise ValueError('Can only generate centered difference stencil '\n 'for an even-valued order of accuracy. Got '\n '{}'.format(accuracy))\n domain = np.arange(0., accuracy + 1.) * spacing\n center = (accuracy / 2.) * spacing\n return finite_diff_weights(1, domain, center)[1][-1]\n\n\ndef forward_diff_weights(accuracy, spacing=1.):\n \"\"\"Compute the weights of a forward difference approx. to derivative\n\n Does so for an arbitrary order of accuracy.\n\n Parameters\n ----------\n accuracy : int\n Integer-valued order of accuracy of approximation\n spacing : float\n Uniform spacing between points (default = 1.)\n\n Returns\n -------\n list of finite difference weights\n \"\"\"\n domain = np.arange(0., accuracy + 1.) * spacing\n return finite_diff_weights(1, domain, domain[0])[1][-1]\n\n\ndef backward_diff_weights(accuracy, spacing=1.):\n \"\"\"Compute the weights of a backward difference approx. to derivative\n\n Does so for an arbitrary order of accuracy.\n\n Parameters\n ----------\n accuracy : int\n Integer-valued order of accuracy of approximation\n spacing : float\n Uniform spacing between points (default = 1.)\n\n Returns\n -------\n list of finite difference weights\n \"\"\"\n domain = np.arange(0., accuracy + 1.) * spacing\n return finite_diff_weights(1, domain, domain[-1])[1][-1]\n\n\ndef upwind_weights_right(accuracy, spacing=1.):\n \"\"\"Compute the weights of a right upwind difference approx. to derivative\n\n Does so for an arbitrary order of accuracy. For use when v < 0.\n\n Parameters\n ----------\n accuracy : int\n Integer-valued order of accuracy of approximation\n spacing : float\n Uniform spacing between points (default = 1.)\n\n Returns\n -------\n list of finite difference weights\n \"\"\"\n point = np.ceil((accuracy + 1) / 2.) * spacing\n domain = np.arange(0., accuracy + 1.) * spacing\n return finite_diff_weights(1, domain, point)[1][-1]\n\n\ndef upwind_weights_left(accuracy, spacing=1.):\n \"\"\"Compute the weights of a left upwind difference approx. to derivative\n\n Does so for an arbitrary order of accuracy. For use when v > 0.\n\n Parameters\n ----------\n accuracy : int\n Integer-valued order of accuracy of approximation\n spacing : float\n Uniform spacing between points (default = 1.)\n\n Returns\n -------\n list of finite difference weights\n \"\"\"\n point = ((accuracy + 1) // 2 - 1.) * spacing\n domain = np.arange(0., accuracy + 1.) * spacing\n return finite_diff_weights(1, domain, point)[1][-1]\n\n\ndef xcorrelate1d(da, dim, kernel, **kwargs):\n \"\"\"Apply ``correlate1d`` along a given dimension\n\n Parameters\n ----------\n da : xr.DataArray\n DataArray\n dim : str\n Dimension name\n kernel : array-like\n 1D sequence of numbers (i.e. correlation weights)\n **kwargs\n Keyword arguments to supply to ``scipy.ndimage.filters.correlate1d``\n\n Returns\n -------\n xr.DataArray\n \"\"\"\n def apply_corr(arr, **kwargs):\n if not isinstance(arr, darray.core.Array):\n return correlate1d(arr, **kwargs)\n else:\n origin = kwargs.get('origin', 0)\n depth = int(len(kwargs['weights']) / 2 + np.abs(origin))\n axis = len(arr.shape) - 1\n\n if kwargs['mode'] != 'wrap':\n # TODO: Don't hard-code periodic boundary conditions\n raise NotImplementedError(\n 'xcorrelate1d currently only supports periodic boundary '\n 'conditions on dask arrays')\n \n return darray.ghost.map_overlap(arr, correlate1d,\n depth={axis: depth},\n boundary={axis: 'periodic'},\n **kwargs)\n\n return computation.apply_ufunc(apply_corr, da, input_core_dims=[[dim]],\n output_core_dims=[[dim]],\n kwargs=dict(weights=kernel, **kwargs),\n dask_array='allowed')\n\n\ndef xdiff(da, dim, method='centered', accuracy=2, spacing=1, mode='wrap'):\n \"\"\"Compute the derivative to an arbitrary order of accuracy\n\n Assumes uniform grid spacing.\n\n Parameters\n ----------\n da : xr.DataArray\n DataArray\n dim : str\n Dimension name to perform derivative along\n method : str\n Options are 'centered', 'backward', 'forward', 'upwind_left', 'upwind_right'\n accuracy : int\n Order of accuracy of approximation\n spacing : float\n Grid spacing\n mode : str\n How to handle boundary; options are same as those that can be passed to\n correlate1d\n\n Returns\n -------\n xr.DataArray\n \"\"\"\n if method == 'centered':\n weights = centered_diff_weights(accuracy, spacing)\n origin = 0\n elif method == 'forward':\n weights = forward_diff_weights(accuracy, spacing)\n origin = -(len(weights) // 2)\n elif method == 'backward':\n weights = backward_diff_weights(accuracy, spacing)\n origin = len(weights) // 2\n elif method == 'upwind_left':\n weights = upwind_weights_left(accuracy, spacing)\n origin = -1 # Regardless of whether len(weights) is even or odd, origin = -1 in this case.\n elif method == 'upwind_right':\n weights = upwind_weights_right(accuracy, spacing)\n origin = len(weights) % 2\n else:\n raise ValueError('Invalid differencing method '\n 'specified: {}'.format(method))\n return xcorrelate1d(da, dim, weights, origin=origin, mode=mode)\n\n\ndef xdiff_upwind(da, v, dim, accuracy=2, spacing=1, mode='wrap'):\n \"\"\"Compute the upwind approximation to the derivative\n \n Parameters\n ----------\n da : xr.DataArray\n DataArray to take derivative on\n v : xr.DataArray\n DataArray of the velocity field\n dim : str\n Name of dimension\n accuracy : int\n Even order of accuracy of differencing approximation\n spacing : float\n Distance between points (must be uniform)\n \n Returns\n -------\n xr.DataArray\n \"\"\"\n neg = v < 0.\n pos = ~neg\n left = xdiff(da, dim, method='upwind_left', accuracy=accuracy, spacing=spacing, mode=mode)\n right = xdiff(da, dim, method='upwind_right', accuracy=accuracy, spacing=spacing, mode=mode)\n return neg * right + pos * left\n\n\ndef xgradient(da, dim, accuracy=2, spacing=1.):\n \"\"\"Arbitrary even-order extension of np.gradient for DataArrays.\n\n Meant for computing approximations for derivatives in a non-peridiodic\n setting. Uses centered differencing in the interior, and forward and\n backward differencing on the left and right edges respectively. Currently\n only supports operations along a single axis (though operations along\n multiple axes can be done with repeated calls to ``xgradient``).\n\n Parameters\n ----------\n da : xr.DataArray\n DataArray\n dim : str\n Name of dimension\n accuracy : int\n Even order of accuracy of differencing approximation\n spacing : float\n Distance between points (must be uniform)\n\n Returns\n -------\n xr.DataArray\n \"\"\"\n interior = xdiff(\n da, dim, method='centered',\n accuracy=accuracy, spacing=spacing).isel(\n **{dim: slice(accuracy // 2, -accuracy // 2)})\n \n left = da.isel(**{dim: slice(None, 2 * accuracy)})\n \n if isinstance(left.data, darray.core.Array):\n left = left.chunk({dim: left.sizes[dim]})\n \n left = xdiff(\n left, dim, method='forward',\n accuracy=accuracy, spacing=spacing).isel(\n **{dim: slice(None, accuracy // 2)})\n \n right = da.isel(**{dim: slice(-2 * accuracy, None)})\n \n if isinstance(right.data, darray.core.Array):\n right = right.chunk({dim: right.sizes[dim]})\n \n right = xdiff(\n right, dim, method='backward',\n accuracy=accuracy, spacing=spacing).isel(\n **{dim: slice(-accuracy // 2, None)})\n\n return xr.concat([left, interior, right], dim=dim)",
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": "//anaconda/envs/xdiff-dev/lib/python3.6/site-packages/xarray/core/formatting.py:16: FutureWarning: The pandas.tslib module is deprecated and will be removed in a future version.\n from pandas.tslib import OutOfBoundsDatetime\n",
"name": "stderr"
}
]
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\n%matplotlib inline",
"execution_count": 2,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Simple 1D case without dask\n--------------------------"
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., 2. * np.pi, 100, endpoint=False)\ndx = x[1] - x[0]\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x'])",
"execution_count": 3,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.plot(label='input')\nxdiff(test, 'x', accuracy=2, method='centered', spacing=dx).plot(label='result (centered)')\nxdiff(test, 'x', accuracy=2, method='forward', spacing=dx).plot(label='result (forward)')\nxdiff(test, 'x', accuracy=2, method='backward', spacing=dx).plot(label='result (backward)')\nplt.gca().legend(loc='lower left')",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x113081c88>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x113081e10>",
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PNkKIMCHEbiHEHVfaSQgx2bBdWGpqavUSG+nzHTGk5xbxZB2ZVrs6dHo97uPv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\nFEVRlBJUYlAURVFK+H/t7DaCa9b1+gAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Derivatives can be computed to arbitrary order of accuracy. E.g.\n# if we plot the absolute value of the error at each point with the \n# three differencing methods we can see the error decreasing as we \n# include more points in the stencil.\nfig, axes = plt.subplots(1, 3, sharey=True)\nfig.set_size_inches(10, 2)\nexpected = xr.DataArray(np.cos(x), coords=[x], dims=['x'])\n\nfor ax, method in zip(axes, ['centered', 'forward', 'backward']):\n for order in [2, 4, 6, 8]:\n result = xdiff(test, 'x', accuracy=order, method=method, spacing=dx)\n np.abs((result - expected)).plot(ax=ax, label=order)\n ax.set_title(method)\n ax.set_yscale('log')\n ax.legend(loc='lower center', ncol=2)",
"execution_count": 5,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1151d3390>",
"image/png": 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jYOaPI1f+gyXghXd/Ju+/s+NGGMFg1OXEosuJbfdzj4qFKP3ZO5LAngTGQZrC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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Simple 1D case with dask\n------------------------"
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., 2. * np.pi, 100, endpoint=False)\ndx = x[1] - x[0]\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x']).chunk({'x': 10})",
"execution_count": 6,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.data",
"execution_count": 7,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 7,
"data": {
"text/plain": "dask.array<xarray-<this-array>, shape=(100,), dtype=float64, chunksize=(10,)>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.plot(label='input')\nxdiff(test, 'x', accuracy=2, method='centered', spacing=dx).plot(label='result (centered)')\nxdiff(test, 'x', accuracy=2, method='forward', spacing=dx).plot(label='result (forward)')\nxdiff(test, 'x', accuracy=2, method='backward', spacing=dx).plot(label='result (backward)')\nplt.gca().legend(loc='lower left')",
"execution_count": 8,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 8,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x11552fd68>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1155b7860>",
"image/png": 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PNkKIMCHEbiHEHVfaSQgx2bBdWGpqavUSG+nzHTGk5xbxZB2ZVrs6dHo97uPv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\nFEVRlBJUYlAURVFK+H/t7DaCa9b1+gAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Derivatives can be computed to arbitrary order of accuracy. E.g.\n# if we plot the absolute value of the error at each point with the \n# three differencing methods we can see the error decreasing as we \n# include more points in the stencil.\nfig, axes = plt.subplots(1, 3, sharey=True)\nfig.set_size_inches(10, 2)\nexpected = xr.DataArray(np.cos(x), coords=[x], dims=['x'])\n\nfor ax, method in zip(axes, ['centered', 'forward', 'backward']):\n for order in [2, 4, 6, 8]:\n result = xdiff(test, 'x', accuracy=order, method=method, spacing=dx)\n np.abs((result - expected)).plot(ax=ax, label=order)\n ax.set_title(method)\n ax.set_yscale('log')\n ax.legend(loc='lower center', ncol=2)",
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x11577ff28>",
"image/png": 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jYOaPI1f+gyXghXd/Ju+/s+NGGMFg1OXEosuJbfdzj4qFKP3ZO5LAngTGQZrC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\nRAQJe5P+nJrDfww/3T9AYscbxLdtZ2jrFmIvvkTHnXfS8dO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},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "What about non-periodic datasets without dask?\n--------------------------------------------\n\nTo estimate these derivatives we will use `xgradient` instead of `xdiff`"
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., np.pi, 50, endpoint=False) # Halt at np.pi (rather than 2 * np.pi)\ndx = x[1] - x[0]\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x'])",
"execution_count": 10,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.plot(label='input')\nxgradient(test, 'x', accuracy=8, spacing=dx).plot(label='result')\nplt.gca().legend(loc='lower left')",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x115b81208>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x115b815f8>",
"image/png": 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UFZEAYDCQ7+wiEWkJfIwVCqfyzK8sIoGO++FAR8CtOrnZ8PNZhk5aT1hIAHPH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\nUiqf/w/lryBpF7/towAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Again this can be done for arbitrary order of accuracy\nax = plt.axes()\nexpected = xr.DataArray(np.cos(x), coords=[x], dims=['x'])\nfor order in [2, 4, 6, 8]:\n result = xgradient(test, 'x', accuracy=order, spacing=dx)\n np.abs((result - expected)).plot(ax=ax, label=order)\nax.set_yscale('log')\nax.legend(loc='lower center', ncol=2)",
"execution_count": 12,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x1159a0ac8>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x115c88c18>",
"image/png": 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KKRO4HfdCvwy4zisFnKGUerjXUg38GLhWKfUNoHIUaRlXp5WfxpzoHOltJHry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\nAAAAAElFTkSuQmCC\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Finally non-periodic datasets with dask\n-------------------------------------"
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., np.pi, 50, endpoint=False) # Halt at np.pi (rather than 2 * np.pi)\ndx = x[1] - x[0]\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x']).chunk({'x': 10})",
"execution_count": 13,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.data",
"execution_count": 14,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": "dask.array<xarray-<this-array>, shape=(50,), dtype=float64, chunksize=(10,)>"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.plot(label='input')\nxgradient(test, 'x', accuracy=8, spacing=dx).plot(label='result')\nplt.gca().legend(loc='lower left')",
"execution_count": 15,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x1159cbb38>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x115387b70>",
"image/png": 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UFZEAYDCQ7+wiEWkJfIwVCqfyzK8sIoGO++FAR8CtOrnZ8PNZhk5aT1hIAHPH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\nUiqf/w/lryBpF7/towAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Again this can be done for arbitrary order of accuracy\nax = plt.axes()\nexpected = xr.DataArray(np.cos(x), coords=[x], dims=['x'])\nfor order in [2, 4, 6, 8]:\n result = xgradient(test, 'x', accuracy=order, spacing=dx)\n np.abs((result - expected)).plot(ax=ax, label=order)\nax.set_yscale('log')\nax.legend(loc='lower center', ncol=2)",
"execution_count": 16,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x115a06e10>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1154d3b00>",
"image/png": 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KKRO4HfdCvwy4zisFnKGUerjXUg38GLhWKfUNoHIUaRlXp5WfxpzoHOltJHry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\nAAAAAElFTkSuQmCC\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "These work on multi-dimensional datasets just as well\n--------------------------------------------------\nThis is a 3D example with dask:"
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., 2. * np.pi, 100, endpoint=False)\ndx = x[1] - x[0]\ny = xr.DataArray(np.arange(10), coords=[np.arange(10)], dims=['y'])\nz = xr.DataArray(np.arange(12, 20), coords=[np.arange(12, 20)], dims=['z'])\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x'])",
"execution_count": 17,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test3d, _ = xr.broadcast(test, y * z)\ntest3d = test3d.transpose('y', 'x', 'z').chunk({'x': 10, 'y': 1})\nresult = xdiff(test3d, 'x', accuracy=6, method='backward', spacing=dx).isel(z=5).plot()",
"execution_count": 18,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x115a0d438>",
"image/png": 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DkjZLuqxN/mJJny/y75Z0Qinv8iL9IUmvmevHSmCPiIYqeuxVtpmuJA0DnwBeC5wMXCzp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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Upwind derivatives\n-----------------\nThese also work with dask; the upwind stencils generated are consistent with Wikipedia for 2nd and 3rd order differences; I'm not 100% sure how to handle higher order cases, but I made the assumption that upwind stencils always are shifted one place from their center (I'm not sure if that's the correct assumption). I've implemented a differencing function that takes into account the velocity direction in `xdiff_upwind` which is demonstrated here. As before, this is dask compatible (as it relies on the previously defined and now extended `xdiff` method)."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "upwind_weights_left(3)",
"execution_count": 19,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 19,
"data": {
"text/plain": "[-0.333333333333333, -0.500000000000000, 1.00000000000000, -0.166666666666667]"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "upwind_weights_right(3)",
"execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 20,
"data": {
"text/plain": "[0.166666666666667, -1.00000000000000, 0.500000000000000, 0.333333333333333]"
},
"metadata": {}
}
]
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "x = np.linspace(0., 2. * np.pi, 100, endpoint=False)\nv = np.random.rand(100) - 0.5\ndx = x[1] - x[0]\ntest = xr.DataArray(np.sin(x), coords=[x], dims=['x'])\ntest_v = xr.DataArray(v, coords=[x], dims=['x'])",
"execution_count": 21,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "fig, ax = plt.subplots(1, 1)\nfig.set_size_inches(6, 4)\nexpected = xr.DataArray(np.cos(x), coords=[x], dims=['x'])\n\nfor order in [1, 2, 3, 4, 5, 6, 7, 8]:\n result = xdiff_upwind(test, test_v, 'x', accuracy=order, spacing=dx)\n np.abs((result - expected)).plot(ax=ax, label=order)\nax.set_title(method)\nax.set_yscale('log')\nax.legend(loc='lower center', ncol=4)\nax.set_title('Upwind')",
"execution_count": 22,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 22,
"data": {
"text/plain": "<matplotlib.text.Text at 0x115ea4278>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x115948630>",
"image/png": 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MjngHnclOOuOdNMeaaYw00hhpJJKOYEoTS1pE01E6E+qalJUaNHltwobH7sFj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\nSgiKoijKMJUQFEVRFEAlBEVRFGXY/wdF+4AI7IHjWgAAAABJRU5ErkJggg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "test.plot(label='input')\nxdiff_upwind(test, test_v, 'x', accuracy=2, spacing=dx).plot(label='2')\nxdiff_upwind(test, test_v, 'x', accuracy=3, spacing=dx).plot(label='3')\nplt.gca().legend(loc='lower left')",
"execution_count": 23,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 23,
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x116023048>"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1160236d8>",
"image/png": 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het5rJyHEQNN24bGxhbNK2fwdkdxIzWJUEZlWuyCETsfwoKFc1wuWbxmndRyb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\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "NCL Example Test Case\n---------------------\nSee https://www.ncl.ucar.edu/Document/Functions/Built-in/center_finite_diff_n.shtml"
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "ncl_case = xr.DataArray([30., 33., 39., 36., 41., 37.], dims=['x'])",
"execution_count": 37,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "xdiff(ncl_case, 'x', spacing=2., method='centered')",
"execution_count": 38,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 38,
"data": {
"text/plain": "<xarray.DataArray (x: 6)>\narray([-1. , 2.25, 0.75, 0.5 , 0.25, -2.75])\nDimensions without coordinates: x"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Interior matches NCL's example\nxgradient(ncl_case, 'x', spacing=2., accuracy=2)",
"execution_count": 42,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 42,
"data": {
"text/plain": "<xarray.DataArray (x: 6)>\narray([ 0.75, 2.25, 0.75, 0.5 , 0.25, -4.25])\nDimensions without coordinates: x"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Left boundary is computed via a second-order forward difference\n(-39 + 4 * 33. - 3 * 30.) / (4.)",
"execution_count": 40,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 40,
"data": {
"text/plain": "0.75"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "# Right boundary is computed via a second-order backward difference\n(3. * 37 - 4 * 41. + 36) / 4.",
"execution_count": 41,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 41,
"data": {
"text/plain": "-4.25"
},
"metadata": {}
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.6.1",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"gist_id": "299d5e4a929c416e52b7d748b48bf834"
},
"nbformat": 4,
"nbformat_minor": 1
}
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