{ "metadata": { "name": "", "signature": "sha256:6ca662affe476e0562d8e59ef277df06e4de12e50f5986043294e272c420b332" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Benchmarking linear N-dimensional interpolators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Rationale*\n", "\n", "A fast and simple interpolation routine is needed in the Stochastic Dynamic Programming algorithm.\n", "The \"fast and simple\" requirement leads to choose the *linear interpolation* method.\n", "\n", "The method needs to be applicable to N-dimensional input, i.e. to interpolate a scalar function :\n", "\n", "$$x\\mapsto f(x)\\in\\mathbb{R} ,\\quad x\\in D \\subset \\mathbb{R}^n$$\n", "\n", "where the dimension $n$ will be *in practice* less than 3 or 4.\n", "\n", "We here try to evaluate what routines can be found \"off-the-shelf\".\n", "\n", "*References*\n", "\n", "* scipy.interpolate doc http://docs.scipy.org/doc/scipy/reference/interpolate.html\n", "* scipy.ndimage doc \n", "* interpolation in the dolo project: https://github.com/EconForge/dolo/tree/master/dolo/numeric/interpolation (Multilinear interpolation removed since then...)\n", "\n", "Update February 2015: add [scipy.interpolate.RegularGridInterpolator](http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.interpolate.RegularGridInterpolator.html) in the benchmark (added in scipy 0.14, released in May 2014)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from numpy import pi\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.interpolate import (\n", " LinearNDInterpolator, RectBivariateSpline,\n", " RegularGridInterpolator)\n", "from scipy.ndimage import map_coordinates\n", "from dolointerpolation import MultilinearInterpolator" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 90 }, { "cell_type": "code", "collapsed": false, "input": [ "# Tweak how images are plotted with imshow\n", "mpl.rcParams['image.interpolation'] = 'none' # no interpolation\n", "mpl.rcParams['image.origin'] = 'lower' # origin at lower left corner\n", "mpl.rcParams['image.cmap'] = 'RdBu_r'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 64 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "1) Define a simple interpolation problem" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def f_2d(x,y):\n", " '''a function with 2D input to interpolate on [0,1]'''\n", " twopi = 2*pi\n", " return np.exp(-x)*np.cos(x*2*pi)*np.sin(y*2*pi)\n", "\n", "# quick check :\n", "f_2d(0,0.25)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "1.0" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "def f_3d(x,y,z):\n", " '''a function with 3D input to interpolate on [0,1]'''\n", " twopi = 2*pi\n", " return np.sin(x*2*pi)*np.sin(y*2*pi)*np.sin(z*2*pi)\n", "\n", "# quick check :\n", "f_3d(0.25,0.25,0.25)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "1.0" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Build the 2D and 3D data grids" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Ndata = 50\n", "xgrid = np.linspace(0,1, Ndata)\n", "ygrid = np.linspace(0,1, Ndata+1) # use a slighly different size to check differences\n", "zgrid = np.linspace(0,1, Ndata+2)\n", "\n", "f_2d_grid = f_2d(xgrid.reshape(-1,1), ygrid)\n", "\n", "plt.imshow(f_2d_grid.T)\n", "plt.title(u'image of a 2D function ({}\u00b2 pts)'.format(Ndata));\n", "\n", "f_2d_grid.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "(50, 51)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 3D case" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_grid = f_3d(xgrid.reshape(-1,1,1), ygrid.reshape(1,-1,1), zgrid)\n", "f_3d_grid.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "(50, 51, 52)" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2) Use interpolators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Try several interpolation routines.\n", "\n", "Notice how each routine has its special way (API) to\n", " \n", "1. build the interpolator (instanciation)\n", "2. call the interpolator (evaluation)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Define the grid to interpolate on :\n", "Ninterp = 1000\n", "xinterp = np.linspace(0,1, Ninterp)\n", "yinterp = np.linspace(0,1, Ninterp+1) # use a slighly different size to check differences\n", "zinterp = np.linspace(0,1, 5) # small dimension to avoid size explosion" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "a) LinearNDInterpolator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LinearNDInterpolator uses an *unstructured data* which is provided as a list of points. There is also a cousin : NearestNDInterpolator\n", "\n", "LinearNDInterpolator(points, values)\n", "([documentation](http://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.LinearNDInterpolator.html))\n", "\n", "**Performance** : \n", "\n", "* instanciation :\n", "\n", " * 18 ms for 50x50 pts,\n", " * but __19.1 s__ for 50x50x50 pts\n", " \n", "* evaluation : 45 ms for 1 Mpts." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Build data for the interpolator\n", "points_x, points_y = np.broadcast_arrays(xgrid.reshape(-1,1), ygrid)\n", "points = np.vstack((points_x.flatten(),\n", " points_y.flatten())).T\n", "values = f_2d_grid.flatten()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "# Build\n", "%timeit f_2d_interp = LinearNDInterpolator(points, values)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "100 loops, best of 3: 17.7 ms per loop\n" ] } ], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": [ "f_2d_interp = LinearNDInterpolator(points, values)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "# Evaluate\n", "%timeit f_2d_interp(xinterp.reshape(-1,1), yinterp)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 loops, best of 3: 44.7 ms per loop\n" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "# Display\n", "plt.imshow(f_2d_interp(xinterp.reshape(-1,1), yinterp).T)\n", "plt.title(u'interpolation of a 2D function ({}\u00b2 pts)'.format(Ninterp));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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OfHOAshZMLqqtHMqODlS25zEBysgIRODAxdVhruACoLhFMY4YhspWgJTINrJo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"text": [ "" ] } ], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 3D case : __terrible performance !__" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Build data for the interpolator\n", "points_x, points_y, points_z = np.broadcast_arrays(xgrid.reshape(-1,1,1), ygrid.reshape(1,-1,1), zgrid)\n", "points = np.vstack((points_x.flatten(),\n", " points_y.flatten(),\n", " points_z.flatten()\n", " )).T\n", "values = f_3d_grid.flatten()\n", "points.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 34, "text": [ "(132600, 3)" ] } ], "prompt_number": 34 }, { "cell_type": "code", "collapsed": false, "input": [ "%time f_3d_interp = LinearNDInterpolator(points, values) " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "CPU times: user 19.1 s, sys: 88 ms, total: 19.2 s\n", "Wall time: 19.2 s\n" ] } ], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_interp = LinearNDInterpolator(points, values)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "# Evaluate:\n", "%time f_3d_interp(xinterp.reshape(-1,1), np.linspace(0,1,5), 0.25);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "CPU times: user 2min 44s, sys: 0 ns, total: 2min 44s\n", "Wall time: 2min 44s\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 37, "text": [ "array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,\n", " 0.00000000e+00, 0.00000000e+00],\n", " [ 0.00000000e+00, 6.23317279e-03, 7.64852773e-19,\n", " -6.23317279e-03, -1.53553034e-18],\n", " [ 0.00000000e+00, 1.24663456e-02, 1.52970555e-18,\n", " -1.24663456e-02, -3.07106068e-18],\n", " ..., \n", " [ 0.00000000e+00, -1.25138148e-02, -1.53553034e-18,\n", " 1.25138148e-02, 3.07106068e-18],\n", " [ 0.00000000e+00, -6.25690738e-03, -7.67765169e-19,\n", " 6.25690738e-03, 1.53553034e-18],\n", " [ 0.00000000e+00, -2.44098405e-16, -2.99525375e-32,\n", " 2.44098405e-16, 5.99050750e-32]])" ] } ], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interpolation on a slice along the x-axis, just to check that it works." ] }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_interp_grid = f_3d_interp(xinterp.reshape(-1,1,1), 0.25, 0.25)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 38 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(f_3d_interp_grid.flatten());" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "b) RectBivariateSpline (scipy.interpolate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*for 2D interpolation only !*\n", "\n", "RectBivariateSpline(x, y, z, bbox=[None, None, None, None], kx=3, ky=3, s=0)\n", "([documentation](http://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.html))\n", "\n", "* x,y : 1-D arrays of coordinates in strictly ascending order.\n", "* z : 2-D array of data with shape (x.size,y.size).\n", "\n", "**Performance**\n", "\n", "* instanciation : 0.2 ms for 50x50 pts\n", "* evaluation : 21 ms for 1 Mpts" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Build\n", "f_2d_interp = RectBivariateSpline(xgrid, ygrid, f_2d_grid)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10000 loops, best of 3: 192 \u00b5s per loop\n" ] } ], "prompt_number": 58 }, { "cell_type": "code", "collapsed": false, "input": [ "f_2d_interp = RectBivariateSpline(xgrid, ygrid, f_2d_grid)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 59 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Evaluate\n", "f_2d_interp(xinterp, yinterp)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 loops, best of 3: 21.2 ms per loop\n" ] } ], "prompt_number": 60 }, { "cell_type": "code", "collapsed": false, "input": [ "# Display\n", "plt.imshow(f_2d_interp(xinterp, yinterp).T)\n", "plt.title(u'interpolation of a 2D function ({}\u00b2 pts)'.format(Ninterp));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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AbWQMQwAHIMYRQ04DD1mVcC7xB1qwDIGAPHyxT9W7+8jFDbocGQIoq1bGDLGz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"text": [ "" ] } ], "prompt_number": 65 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "c) map_coordinates (scipy.ndimage)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "notice that this method has no separation between _instanciation_ and _evaluation_ !\n", "\n", "map_coordinates(input, coordinates, output=None, order=3, mode='constant', cval=0.0, prefilter=True)\n", "([documentation](http://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.interpolation.map_coordinates.html))\n", "\n", "\n", "**Performance** : \n", "\n", "* 56 ms (instanciation + evaluation 1Mpts)\n", "* 511 ms (5 Mpts in 3D)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y = np.broadcast_arrays(xinterp.reshape(-1,1), yinterp)\n", "coord = np.vstack((points_x.flatten()*(len(xgrid)-1) , # a weird formula !\n", " points_y.flatten()*(len(ygrid)-1)))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 48, "text": [ "(2, 1001000)" ] } ], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Build and Evaluate\n", "f_2d_interp = map_coordinates(f_2d_grid, coord, order=1)\n", "# Reshape\n", "f_2d_interp = f_2d_interp.reshape(len(xinterp), len(yinterp))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 loops, best of 3: 56.4 ms per loop\n" ] } ], "prompt_number": 66 }, { "cell_type": "code", "collapsed": false, "input": [ "# Display \n", "f_2d_interp = map_coordinates(f_2d_grid, coord, order=1).reshape(len(xinterp), len(yinterp))\n", "\n", "plt.imshow(f_2d_interp.T)\n", "plt.title(u'interpolation of a 2D function ({}\u00b2 pts)'.format(Ninterp));" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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AaWwvCj3fAU1dzswbLWe3Z3Znzb3p5jv32eior92S8cT37BQC3v1Rj3hIA7U3ap7707kr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"text": [ "" ] } ], "prompt_number": 67 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 3D case" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y, points_z = np.broadcast_arrays(xinterp.reshape(-1,1,1), yinterp.reshape(1,-1,1), zinterp)\n", "coord = np.vstack((points_x.flatten()*(len(xgrid)-1), # a weird formula !\n", " points_y.flatten()*(len(ygrid)-1),\n", " points_z.flatten()*(len(zgrid)-1)\n", " ))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 68, "text": [ "(3, 5005000)" ] } ], "prompt_number": 68 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Build and Evaluate\n", "f_3d_interp = map_coordinates(f_3d_grid, coord, order=1)\n", "# Reshape\n", "f_3d_interp = f_3d_interp.reshape(len(xinterp), len(yinterp), len(zinterp))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1 loops, best of 3: 511 ms per loop\n" ] } ], "prompt_number": 69 }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_interp = map_coordinates(f_3d_grid, coord, order=1)\n", "f_3d_interp = f_3d_interp.reshape(len(xinterp), len(yinterp), len(zinterp))\n", "f_3d_interp.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 70, "text": [ "(1000, 1001, 5)" ] } ], "prompt_number": 70 }, { "cell_type": "code", "collapsed": false, "input": [ "n_z = 1\n", "plt.imshow(f_3d_interp[:,:,n_z])\n", "plt.title('f_3d(x,y, z={:.2f})'.format(zinterp[n_z]))\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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m+6REBtAHoAWeur5Ds7E+4CTwaWEz76RmLisrCz0FngGbbGvW0+uq80Pj7l4l8WHVoG/g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\nLwBT+AzUWV1Oi23sD2a9b71sb9ubRKB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jYx/3BDz2cU8AYNSHcX1H6g+OsGYZ5FT6twsA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\nfwvAXwDwW9w6P4zcpwF8Xp5/HlrQfRKqANetd29XVF9NcKh7K7ttCzz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VnnDYaiQzAA2I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UAxNRCMAEKo7jDgBkCfj1e79/3t+V5ZPPR6tTdKfBj4tI3v1MT1wmZu1tU4oAdeF9tzUCyZ3hu2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\n", "text": [ "" ] } ], "prompt_number": 72 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "d) MultilinearInterpolator from Pablo Winant" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Performance** : \n", "\n", "* 0.010 ms for instanciation. 13 ms for evaluation 1Mpts\n", "* 105 ms (5 Mpts in 3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "References :\n", "\n", "* Pablo Winant homepage : http://www.mosphere.fr\n", "* on GitHub https://github.com/albop/dolo/tree/master/dolo/numeric/interpolation\n", "* documentation : http://albop.github.io/dolo/interpolation.html\n", "* related thread on Scipy-dev http://mail.scipy.org/pipermail/scipy-dev/2013-February/018389.html http://mail.scipy.org/pipermail/scipy-dev/2013-May/018776.html" ] }, { "cell_type": "code", "collapsed": false, "input": [ "smin = [xgrid[0], ygrid[0]]\n", "smax = [xgrid[-1], ygrid[-1]]\n", "orders = [len(xgrid), len(ygrid)]\n", "\n", "print(smin, smax, orders)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "([0.0, 0.0], [1.0, 1.0], [50, 51])\n" ] } ], "prompt_number": 73 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit\n", "minterp = MultilinearInterpolator(smin,smax,orders)\n", "minterp.set_values(np.atleast_2d(f_2d_grid.flatten()))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "100000 loops, best of 3: 9.47 \u00b5s per loop\n" ] } ], "prompt_number": 75 }, { "cell_type": "code", "collapsed": false, "input": [ "minterp.grid.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 76, "text": [ "(2, 2550)" ] } ], "prompt_number": 76 }, { "cell_type": "code", "collapsed": false, "input": [ "f_2d_grid.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 77, "text": [ "(50, 51)" ] } ], "prompt_number": 77 }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y = np.broadcast_arrays(xinterp.reshape(-1,1), yinterp)\n", "coord = np.vstack((points_x.flatten(),\n", " points_y.flatten()))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 78, "text": [ "(2, 1001000)" ] } ], "prompt_number": 78 }, { "cell_type": "code", "collapsed": false, "input": [ "%timeit f_2d_interp = minterp(coord).reshape(len(xinterp), len(yinterp))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "100 loops, best of 3: 12.6 ms per loop\n" ] } ], "prompt_number": 79 }, { "cell_type": "code", "collapsed": false, "input": [ "# Display \n", "f_2d_interp = minterp(coord).reshape(len(xinterp), len(yinterp))\n", "\n", "plt.imshow(f_2d_interp.T)\n", "plt.title(u'interpolation of a 2D function ({}\u00b2 pts)'.format(Ninterp));\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 80, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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IQHQY4n0+xP8G1Veqv5bpjO+ksc+Lnov+u7nqYwu2KcW3CmmcKgT7vgo7r5Te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"text": [ "" ] } ], "prompt_number": 80 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The 3D case" ] }, { "cell_type": "code", "collapsed": false, "input": [ "smin = [xgrid[0], ygrid[0], zgrid[0]]\n", "smax = [xgrid[-1], ygrid[-1], zgrid[-1]]\n", "orders = [len(xgrid), len(ygrid), len(zgrid)]\n", "\n", "print(smin, smax, orders)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "([0.0, 0.0, 0.0], [1.0, 1.0, 1.0], [50, 51, 52])\n" ] } ], "prompt_number": 81 }, { "cell_type": "code", "collapsed": false, "input": [ "minterp = MultilinearInterpolator(smin,smax,orders)\n", "minterp.set_values(np.atleast_2d(f_3d_grid.flatten()))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 82 }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y, points_z = np.broadcast_arrays(xinterp.reshape(-1,1,1), yinterp.reshape(1,-1,1), zinterp)\n", "coord = np.vstack((points_x.flatten(), # a weird formula !\n", " points_y.flatten(),\n", " points_z.flatten()\n", " ))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 83, "text": [ "(3, 5005000)" ] } ], "prompt_number": 83 }, { "cell_type": "markdown", "metadata": {}, "source": [ "*A very nice interpolation performance !*" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%timeit minterp(coord)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 loops, best of 3: 105 ms per loop\n" ] } ], "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_interp = minterp(coord)\n", "f_3d_interp = f_3d_interp.reshape(len(xinterp), len(yinterp), len(zinterp))\n", "f_3d_interp.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 85, "text": [ "(1000, 1001, 5)" ] } ], "prompt_number": 85 }, { "cell_type": "code", "collapsed": false, "input": [ "n_z = 1\n", "plt.imshow(f_3d_interp[:,:,n_z])\n", "plt.title('f_3d(x,y, z={:.2f})'.format(zinterp[n_z]))\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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m+6REBtAHoAWeur5Ds7E+4CTwaWEz76RmLisrCz0FngGbbGvW0+uq80Pj7l4l8WHVoG/g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\n6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"text": [ "" ] } ], "prompt_number": 87 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interpolation throuput:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print('{:.1f} Mpts/s'.format(5e6 / 0.105 /1e6) )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "47.6 Mpts/s\n" ] } ], "prompt_number": 88 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "e) RegularGridInterpolator (scipy.interpolate, starting v0.14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[documentation](http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.interpolate.RegularGridInterpolator.html)\n", "\n", "actual interpolation code: https://github.com/scipy/scipy/blob/master/scipy/interpolate/interpolate.py#L1577 (pure Python, no Cython involved!)\n", "\n", "API:\n", "\n", "RegularGridInterpolator(points, values, [...])\n", " \n", "* points: tuple of ndarray of float, with shapes *(m1, ), ..., (mn, )*. \n", " \u2192 The points defining the regular grid in n dimensions.\n", "* value: array_like, shape *(m1, ..., mn, ...)*. \n", " \u2192 The data on the regular grid in n dimensions.\n", "\n", "\n", "**Performance**\n", "\n", "* 0.022 ms for instanciation, 116 ms for evaluation (1Mpts)\n", "* in 1.8 s in 3D (5 Mpts)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Instanciate the interpolator\n", "f_2d_interp = RegularGridInterpolator((xgrid, ygrid), f_2d_grid)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10000 loops, best of 3: 21.6 \u00b5s per loop\n" ] } ], "prompt_number": 93 }, { "cell_type": "code", "collapsed": false, "input": [ "f_2d_interp = RegularGridInterpolator((xgrid, ygrid), f_2d_grid)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 110 }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y = np.broadcast_arrays(xinterp.reshape(-1,1), yinterp)\n", "coord = np.vstack((points_x.flatten(),\n", " points_y.flatten()))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 111, "text": [ "(2, 1001000)" ] } ], "prompt_number": 111 }, { "cell_type": "code", "collapsed": false, "input": [ "f_2d_interp" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 113, "text": [ "" ] } ], "prompt_number": 113 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Interpolate\n", "f_2d_interp_res = f_2d_interp(coord.T).reshape(len(xinterp), len(yinterp))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "10 loops, best of 3: 112 ms per loop\n" ] } ], "prompt_number": 112 }, { "cell_type": "code", "collapsed": false, "input": [ "# Display \n", "\n", "f_2d_interp_res = f_2d_interp(coord.T).reshape(len(xinterp), len(yinterp))\n", "\n", "plt.imshow(f_2d_interp_res.T)\n", "plt.title(u'interpolation of a 2D function ({}\u00b2 pts)'.format(Ninterp));\n", "plt.colorbar();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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bUm/X0bAuxfXC/NDI67ax3QMf9OBM7VkVWAVgC3zqfQE8Px+WYf3KeWSP87/y/iBvfy7G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"text": [ "" ] } ], "prompt_number": 108 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "The 3D case" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f_3d_interp = RegularGridInterpolator((xgrid, ygrid, zgrid), f_3d_grid)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 116 }, { "cell_type": "code", "collapsed": false, "input": [ "# Prepare the coordinates to evaluate the array on :\n", "points_x, points_y, points_z = np.broadcast_arrays(xinterp.reshape(-1,1,1), yinterp.reshape(1,-1,1), zinterp)\n", "coord = np.vstack((points_x.flatten(), # a weird formula !\n", " points_y.flatten(),\n", " points_z.flatten()\n", " ))\n", "coord.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 117, "text": [ "(3, 5005000)" ] } ], "prompt_number": 117 }, { "cell_type": "code", "collapsed": false, "input": [ "%%timeit # Interpolate\n", "f_3d_interp_res = f_3d_interp(coord.T).reshape(len(xinterp), len(yinterp), len(zinterp))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "1 loops, best of 3: 1.8 s per loop\n" ] } ], "prompt_number": 118 }, { "cell_type": "markdown", "metadata": {}, "source": [ "table\n", "\n", "Method | Instanciation | Evaluation (1Mpts 2D) | (5 Mpts, 3D)\n", "------ | ------------- | -------------------- ---\n", "dolo | 0.010 ms | 13 ms | 105 ms\n", "RegularGridInterpolator | 0.022 ms | 116 ms | 1.8 s\n", "\n", "\n", "\n", "Conclusion: Dolo's Multilinear interpolation (for an *even grid* only) is still the best!" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }