{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Localized Spectral Analysis on the Sphere\n", "\n", "A localised spectral estimate can be seen as the spectrum of a global function multiplied with a window. In a 2D cartesian coordinate system, this multiplication becomes a convolution in Fourier domain: the window *couples* different Fourier coefficients of the global function to each other.\n", "\n", "Windowing on the sphere leads to similar effects: Multiplication with a window function leads to coupling of the spherical harmonic coefficients of the globally defined function. In the case of an isotropic and stationary function, a coupling matrix describes the relation between the input power to the output power. This matrix resembles a convolution at high degrees." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "from __future__ import print_function # only necessary if using Python 2.x\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate a random model using the SHCoeffs class interface\n", "\n", "We first generate a random model using the SHCoeffs class interface to SHTOOLS. This class simplifies coefficient generation and provides a simple access to most SHTOOLS functions. We start by generating coefficients that have a power spectrum that follows a power-law decay." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kBytPoa2LBHsArZvSmbYW1oqctqZ0prXO7dvgWRSdp/VWLSYo11aZPnQVtIxs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NIazbMwk0gj0qcTs0q1SGuuVp9fe2SpZTE/oykVUxz4uD0z/3KBW52jOsgPWykiqwdE9PVSuV+k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\n0i3BI1fRyQPaY3g2v/RAYaTF1EhA65LQ6RL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(,\n", " )" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from pyshtools.shclasses import SHCoeffs, SHWindow, SHGrid\n", "\n", "nl = 100 # l = [0, 199]\n", "lmax = nl - 1\n", "a = 4 # scale length\n", "ls = np.arange(nl, dtype=np.float)\n", "power = 1. / (1. + (ls / a) ** 2) ** 1.5\n", "\n", "# Generate the random coefficients using an input power spectrum.\n", "coeffs_global = SHCoeffs.from_random(power)\n", "\n", "# Plot the power per band spectrum using the class method plot_powerperband().\n", "coeffs_global.plot_powerperband()\n", "\n", "# Get the power per degree spectrum as a numpy array using the class method\n", "# get_powerperdegree().\n", "power_global = coeffs_global.get_powerperdegree()\n", "\n", "# Expand the data on a global grid using the class method expand().\n", "grid_global = coeffs_global.expand('DH2')\n", "\n", "# Plot the raw grid using the class method plot_rawdata().\n", "grid_global.plot_rawdata()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate a box window function\n", "\n", "We now generate a window function that picks a few local regions from the globally defined model. In this example, the window contains sharp boundaries, so the spherical harmonic bandwidth of the function is infinite. In general, this could severely bias the localized power spectrum away from its global value, especially when the power spectrum follows a power law. To combat this negative characteristic, we will later show how to construct windows with a specified spherical harmonic bandwith that are optimally concentrated within the provided region.\n", "\n", "The example makes use of the SHTOOLS class SHGrid, which is the counterpart to SHCoeffs." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Y5LKm929gMXAmcFbi++fTa57Ltd69Yccdw9mt6VxU7LST/QH544/pfU7VujdP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\n4PDDN36uUSPr3qxaLwwDr+n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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make an arbitrary mask.\n", "latgrid, longrid = np.meshgrid(grid_global.get_lats(), grid_global.get_lons(), indexing='ij')\n", "window = (-40 < latgrid) & (latgrid < -30) & (10 < longrid) & (longrid < 30)\n", "window += (0 < latgrid) & (latgrid < 30) & (60 < longrid) & (longrid < 80)\n", "window += (-70 < latgrid) & (latgrid < -40) & (130 < longrid) & (longrid < 150)\n", "window += (20 < latgrid) & (latgrid < 40) & (125 < longrid) & (longrid < 145)\n", "window += (10 < latgrid) & (latgrid < 30) & (220 < longrid) & (longrid < 250)\n", "\n", "# Generate an SHGrid instance from the input array. The first element of the grid corresponds\n", "# to zero longitude and 90 degrees north.\n", "grid_window = SHGrid.from_array(window.astype(np.float64)[::-1]) # DH grid starts at north-pole\n", "\n", "grid_window.plot_rawdata()\n", "\n", "# Expand the grid in spherical harmonics using the class method expand().\n", "coeffs_window = grid_window.expand()\n", "\n", "coeffs_window.plot_powerperband()\n", "power_window = coeffs_window.get_powerperdegree()\n", "norm_window = power_window.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiply the random model with the window\n", "\n", "Multiplication of the global random model with the window function localizes the data, and its expansion in spherical harmonics gives a *local* power spectrum estimate of the input function. The interaction of the window function with the random model *distorts* the spectrum. In general, the ouput spectrum at degree l is influenced by the input spherical harmonic degrees from l - Lwin to l + Lwin, where Lwin in the spherical harmonic bandwidth of the windowing function." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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J9T8hqJ1lfmMsSJFrbY5ljvAkk5SpUNqYp2/aVziydobck21i79G4rkJvzuhh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\np+eKmFkJ+O/AjyalmpH/vl0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Multiply the data by the window and plot the spatially localized data.\n", "grid_local = SHGrid.from_array(grid_global.data * grid_window.data)\n", "grid_local.plot_rawdata()\n", "\n", "# Next, expand the localized data in spherical harmonics and plot the\n", "# power per band spectrum.\n", "coeffs_local = grid_local.expand()\n", "coeffs_local.plot_powerperband()\n", "power_local = coeffs_local.get_powerperdegree()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compute the coupling matrix\n", "\n", "The expected distortion of the global spectrum due to the windowing operation can be described by a *coupling matrix* under the assumption that the model is isotropic and stationary. This means that the local (expected) spectra are independent of the position and orientation of the windows. In this case, the expected local spectrum depends only on the power spectrum of the window, which is taken as input for the SHMTCouplingMatrix function.\n", "\n", "The coupling matrix describes how input power maps to output power. At high degrees, it is approximately symmetric around the diagonal and resembles a convolution in degree l space. At low degrees, however, input power is spread more unevently into output power. For example, input degree 0 maps preferentially to output degree 4, which is off-diagonal. This is a direct consquence of describing a 2D multiplication with coupling of a single dimension parameter *l*. A similar bias can be seen when describing coupling in 2D Fourier space between coefficients with similar |k|." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mpxRO7Q1M+8TlQr0A1Src/I7ncN1L7+PBv7qM8YkhosKxQ0N23j1ibc8CCgye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\n7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the coupling matrix\n", "from pyshtools.localizedspectralanalysis import SHMTCouplingMatrix\n", "coupling_matrix = SHMTCouplingMatrix(lmax, power_window.reshape(nl, 1))\n", "\n", "# Plot the coupling matrix\n", "fig, (col1, col2) = plt.subplots(1, 2, figsize=(10, 3))\n", "col1.imshow(coupling_matrix, cmap='viridis')\n", "col1.set(xlabel='input degree l', ylabel='output degree l', xlim=(-0.5, 10.5), ylim=(10.5, -0.5),\n", " title='zoomed coupling matrix');\n", "col2.imshow(coupling_matrix, cmap='viridis')\n", "col2.set(xlabel='input degree l', ylabel='output degree l', title='full coupling matrix');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predict the biased spectrum\n", "\n", "Finally, the coupling matrix can be used to predict the spectrum of the windowed function. SHTOOLS provides also the functions SHBiasK and SHBias that can compute directly the biased spectrum without explicitely computing the coupling matrix. Under some assumptions, the coupling matrix can be inverted allowing the global input power spectrum to be estimated from the localized spectrum. This has to be done with care because as a smoothing operation, windowing leads to loss of information (less resolution in degree l space) and has to be regularized to stabilize the inversion." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SFo9dTDdPG5vliTKRa8nlwMUDrI1Zy9yDc2nVsBV/7fFXRgWMsllcf6eeXSaz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\njycj47p33hJCiAornD5812ajp9nMnlatgPyRrh8cDqbGxtb4RfG1N9B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Compute the biased spectrum using two different methods\n", "from pyshtools.localizedspectralanalysis import SHBias\n", "power_local2 = np.dot(coupling_matrix, power)\n", "power_local3 = SHBias(power_window, power)\n", "\n", "# plot the observed and predicted spectra\n", "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n", "ax.plot(ls, power_global, label='measured global')\n", "ax.plot(ls, power_local, label='measured local')\n", "ax.plot(power_local2, label='predicted local (CouplingMatrix)')\n", "ax.plot(power_local3, 'x', label='predicted local (SHBias)')\n", "ax.legend(loc=3)\n", "ax.set_xscale('log', basex=2)\n", "ax.set_yscale('log', basey=2)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }