Source code for kite.covariance

# -*- coding: utf-8 -*-
import numpy as num
import scipy as sp
import time

from kite import covariance_ext
from pyrocko import guts
from pyrocko.guts_array import Array
from kite.util import (Subject, property_cached,  # noqa
                       trimMatrix, derampMatrix, squareMatrix)

__all__ = ['Covariance', 'CovarianceConfig']


noise_regimes = [
    (1./2000, num.inf),
    (1./2000, 1./500),
    (1./500, 1./10),
    (0, num.inf)]

[docs]def modelCovarianceExponential(distance, a, b): """Exponential function model to approximate a positive-definite covariance We assume the following simple covariance model to describe the empirical noise observations: .. math:: cov(d) = c \\cdot e^{\\frac{-d}{b}} :param distance: Distance between :type distance: float or :class:`numpy.ndarray` :param a: Linear model coefficient :type a: float :param b: Exponential model coefficient :type b: float :returns: Covariance at ``distance`` :rtype: :class:`numpy.ndarray` """ return a * num.exp(-distance/b)
[docs]def modelCovarianceExponentialCosine(distance, a, b, c, d): r"""Exponential function model to approximate a positive-definite covariance We assume the following simple covariance model to describe the empirical noise observations: .. math:: cov(d) = c \\cdot e^{\\frac{-d}{b}} \\cdot \cos{\\frac{d-c}{d}} :param distance: Distance between :type distance: float or :class:`numpy.ndarray` :param a: Linear model coefficient :type a: float :param b: Exponential model coefficient :type b: float :param c: Cosinus distance correction :type c: float :param c: Cosinus coefficient :type c: float :returns: Covariance at ``distance`` :rtype: :class:`numpy.ndarray` """ return a * num.exp(-distance/b) * num.cos((distance-c)/d)
[docs]def modelPowerspec(k, beta, D): """Exponential linear model to estimate a log-linear power spectrum We assume the following log-linear model for a measured power spectrum: .. math:: pow(k) = \\frac{k^\\beta}{D} :param k: Wavenumber :type k: float or :class:`numpy.ndarray` :param a: Exponential model factor :type a: float :param b: Fractional model factor :type b: float """ return (k**beta)/D
[docs]class CovarianceConfig(guts.Object): noise_coord = Array.T( shape=(None,), dtype=num.float, serialize_as='list', optional=True, help='Noise patch coordinates and size,') model_coefficients = guts.Tuple.T( optional=True, help='Covariance model coefficients. Either two (exponential) ' 'or three (exponential and cosine term) coefficients.' 'See also :func:`~kite.covariance.modelCovariance`.') model_function = guts.StringChoice.T( choices=['exponential', 'exponential_cosine'], default='exponential', help='Covariance approximation function.') sampling_method = guts.StringChoice.T( choices=['spectral', 'spatial'], default='spatial', help='Method for estimating the covariance and structure function.') spatial_bins = guts.Int.T( default=75, help='Number of distance bins for spatial covariance sampling.') spatial_pairs = guts.Int.T( default=200000, help='Number of random pairs for spatial covariance sampling.') variance = guts.Float.T( optional=True, help='Variance of the model.') adaptive_subsampling = guts.Bool.T( default=True, help='Adaptive subsampling flag for full covariance calculation.') covariance_matrix = Array.T( dtype=num.float, optional=True, serialize_as='base64', help='Cached covariance matrix, ' 'see :attr:`~kite.Covariance.covariance_matrix`.') def __init__(self, *args, **kwargs): if len(kwargs) != 0: if 'a' in kwargs and 'b' in kwargs: kwargs['model_coefficients'] = ( kwargs.pop('a'), kwargs.pop('b')) guts.Object.__init__(self, *args, **kwargs)
[docs]class Covariance(object): """Construct the variance-covariance matrix of quadtree subsampled data. Variance and covariance estimates are used to construct the weighting matrix to be used later in an optimization. Two different methods exist to propagate full-resolution data variances and covariances of :class:`kite.Scene.displacement` to the covariance matrix of the subsampled dataset: 1. The distance between :py:class:`kite.quadtree.QuadNode` leaf focal points, :py:class:`kite.covariance.Covariance.matrix_focal` defines the approximate covariance of the quadtree leaf pair. 2. The _accurate_ propagation of covariances by taking the mean of every node pair pixel covariances. This process is computational very expensive and can take a few minutes. :py:class:`kite.covariance.Covariance.matrix_focal` :param quadtree: Quadtree to work on :type quadtree: :class:`~kite.Quadtree` :param config: Config object :type config: :class:`~kite.covariance.CovarianceConfig` """ def __init__(self, scene, config=CovarianceConfig()): self.evChanged = Subject() self.evConfigChanged = Subject() self.frame = scene.frame self.quadtree = scene.quadtree self.scene = scene self._noise_data = None self._powerspec1d_cached = None self._powerspec2d_cached = None self._powerspec3d_cached = None self._noise_data_grid = None self._initialized = False self._nthreads = 0 self._log = scene._log.getChild('Covariance') self.setConfig(config) self.quadtree.evChanged.subscribe(self._clear) self.scene.evConfigChanged.subscribe(self.setConfig) def __call__(self, *args, **kwargs): return self.getLeafCovariance(*args, **kwargs)
[docs] def setConfig(self, config=None): """ Sets and updated the config of the instance :param config: New config instance, defaults to configuration provided by parent :class:`~kite.Scene` :type config: :class:`~kite.covariance.CovarianceConfig`, optional """ if config is None: config = self.scene.config.covariance if self.scene.config.old_import: self._log.warning('Old format - resetting noise patch coordinates') config.covariance_matrix = None config.noise_coord = None self.config = config if config.noise_coord is None\ and (config.model_coefficients is not None or config.variance is not None): self.noise_data # init data array self.config.model_coefficients = config.model_coefficients self.config.variance = config.variance self._clear(config=False) self.evConfigChanged.notify()
def _clear(self, config=True, spectrum=True): if config: self.config.model_coefficients = None self.config.variance = None self.config.covariance_matrix = None if spectrum: self.structure_spectral = None self._powerspec1d_cached = None self._powerspec2d_cached = None self._noise_data_grid = None self.covariance_matrix = None self.covariance_matrix_focal = None self.covariance_spectral = None self.covariance_spatial = None self.structure_spatial = None self.weight_matrix = None self.weight_matrix_focal = None self._initialized = False self.evChanged.notify() @property def nthreads(self): """ Number of threads (CPU cores) to use for full covariance calculation Setting ``nthreads`` to ``0`` uses all available cores (default). :setter: Sets the number of threads :type: int """ return self._nthreads @nthreads.setter def nthreads(self, value): self._nthreads = int(value) @property def finished_combinations(self): return covariance_ext.get_finished_combinations() @property def noise_coord(self): """ Coordinates of the noise patch in local coordinates. :setter: Set the noise coordinates :getter: Get the noise coordinates :type: :class:`numpy.ndarray`, ``[llE, llN, sizeE, sizeN]`` """ if self.config.noise_coord is None: self.noise_data return self.config.noise_coord @noise_coord.setter def noise_coord(self, values): self.config.noise_coord = num.array(values) @property def noise_patch_size_km2(self): """ :getter: Noise patch size in :math:`km^2`. :type: float """ if self.noise_coord is None: return 0. size = (self.noise_coord[2] * self.noise_coord[3])*1e-6 if self.noise_data.size < self.NOISE_PATCH_MIN_PX: self._log.warning('Defined noise patch is instably small') return size @property def noise_data(self, data): """ Noise data we process to estimate the covariance :setter: Set the noise patch to analyze the covariance. :getter: If the noise data has not been set manually, we grab data through :func:`~kite.Covariance.selectNoiseNode`. :type: :class:`numpy.ndarray` """ return self._noise_data @noise_data.getter def noise_data(self): if self._noise_data is not None: return self._noise_data elif self.config.noise_coord is not None: self._log.debug('Selecting noise_data from config...') llE, llN = self.scene.frame.mapENMatrix( *self.config.noise_coord[:2]) sE, sN = self.scene.frame.mapENMatrix( *self.config.noise_coord[2:]) slice_E = slice(llE, llE + sE) slice_N = slice(llN, llN + sN) covariance_matrix = self.config.covariance_matrix self.noise_data = self.scene.displacement[slice_N, slice_E] self.config.covariance_matrix = covariance_matrix else: self._log.debug('Selecting noise_data from Quadtree...') node = self.selectNoiseNode() self.noise_data = node.displacement self.noise_coord = [node.llE, node.llN, node.sizeE, node.sizeN] return self.noise_data @noise_data.setter def noise_data(self, data): data = data.copy() data = derampMatrix(trimMatrix(data)) data[num.isnan(data)] = 0. self._noise_data = data self._clear() @property def noise_data_gridE(self): return self._get_noise_data_grid()[0] @property def noise_data_gridN(self): return self._get_noise_data_grid()[1] def _get_noise_data_grid(self): if self._noise_data_grid is None: scene = self.scene llE, llN = scene.frame.mapENMatrix(*self.noise_coord[:2]) sE, sN = scene.frame.mapENMatrix(*self.noise_coord[2:]) slice_E = slice(llE, llE + sE + 1) slice_N = slice(llN, llN + sN + 1) gridE = scene.frame.gridEmeter[slice_N, slice_E] gridN = scene.frame.gridNmeter[slice_N, slice_E] gridE = trimMatrix(self.noise_data, data=gridE) gridN = trimMatrix(self.noise_data, data=gridN) self._noise_data_grid = (gridE, gridN) return self._noise_data_grid
[docs] def selectNoiseNode(self): """ Choose noise node from quadtree the biggest :class:`~kite.quadtree.QuadNode` from :class:`~kite.Quadtree`. :returns: A quadnode with the least signal. :rtype: :class:`~kite.quadtree.QuadNode` """ t0 = time.time() node_selection = [n for n in self.quadtree.nodes if n.npixel > NOISE_PATCH_MIN_PX and n.nan_fraction < NOISE_PATCH_MAX_NAN] if not node_selection: node_selection = self.quadtree.leaves stdmax = max([n.std for n in node_selection]) lmax = max([n.std for n in node_selection]) def costFunction(n): nl = num.log2(n.length)/num.log2(lmax) ns = n.std/stdmax return nl*(1.-ns)*(1.-n.nan_fraction) fitness = num.array([costFunction(n) for n in node_selection]) self._log.debug('Fetched noise from Quadtree.nodes [%0.4f s]' % (time.time() - t0)) return node_selection[num.argmin(fitness)]
def _mapLeaves(self, nx, ny): """ Helper function returning appropriate :class:`~kite.quadtree.QuadNode` and for maintaining the internal mapping with the matrices. :param nx: matrix x position :type nx: int :param ny: matrix y position :type ny: int :returns: tuple of :class:`~kite.quadtree.QuadNode` s for ``nx`` and ``ny`` :rtype: tuple """ leaf1 = self.quadtree.leaves[nx] leaf2 = self.quadtree.leaves[ny] self._leaf_mapping[] = nx self._leaf_mapping[] = ny return leaf1, leaf2 def isFullCovarianceCalculated(self): if self.config.covariance_matrix is None: return False return True @property_cached def covariance_matrix(self): """ Covariance matrix calculated from mean of all pixel pairs inside the node pairs (full and accurate propagation). :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves` x :class:`~kite.Quadtree.nleaves`) """ if not isinstance(self.config.covariance_matrix, num.ndarray): self.config.covariance_matrix =\ self._calcCovarianceMatrix(method='full') self.evChanged.notify() elif self.config.covariance_matrix.ndim == 1: try: nl = self.quadtree.nleaves self.config.covariance_matrix =\ self.config.covariance_matrix.reshape(nl, nl) except ValueError: self.config.covariance_matrix = None return self.covariance_matrix return self.config.covariance_matrix @property_cached def covariance_matrix_focal(self): """ Approximate Covariance matrix from quadtree leaf pair distance only. Fast, use for intermediate steps only and finallly use approach :attr:`~kite.Covariance.covariance_matrix`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves` x :class:`~kite.Quadtree.nleaves`) """ return self._calcCovarianceMatrix(method='focal') @property_cached def weight_matrix(self): """ Weight matrix from full covariance :math:`cov^{-1}`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves` x :class:`~kite.Quadtree.nleaves`) """ return num.linalg.inv(self.covariance_matrix) @property_cached def weight_matrix_L2(self): """ Weight matrix from full covariance :math:`\\sqrt{cov^{-1}}`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves` x :class:`~kite.Quadtree.nleaves`) """ incov = num.linalg.inv(self.covariance_matrix) return sp.linalg.sqrtm(incov) @property_cached def weight_matrix_focal(self): """ Approximated weight matrix from fast focal method :math:`cov_{focal}^{-1}`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves` x :class:`~kite.Quadtree.nleaves`) """ return num.linalg.inv(self.covariance_matrix_focal) @property_cached def weight_vector(self): """ Weight vector from full covariance :math:`cov^{-1}`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves`) """ return num.sum(self.weight_matrix, axis=1) @property_cached def weight_vector_focal(self): """ Weight vector from fast focal method :math:`\\sqrt{cov_{focal}^{-1}}`. :type: :class:`numpy.ndarray`, size (:class:`~kite.Quadtree.nleaves`) """ return num.sum(self.weight_matrix_focal, axis=1) def _calcCovarianceMatrix(self, method='focal', nthreads=None): """Constructs the covariance matrix. :param method: Either ``focal`` point distances are used - this is quick but only an approximation. Or ``full``, where the full quadtree pixel distances matrices are calculated , defaults to ``focal`` :type method: str, optional :returns: Covariance matrix :rtype: thon:numpy.ndarray """ self._initialized = True if nthreads is None: nthreads = self.nthreads nl = len(self.quadtree.leaves) self._leaf_mapping = {} t0 = time.time() if method == 'focal': model = self.getModelFunction() coords = self.quadtree.leaf_focal_points_meter dist_matrix = num.sqrt( (coords[:, 0] - coords[:, 0, num.newaxis])**2 + (coords[:, 1] - coords[:, 1, num.newaxis])**2) cov_matrix = model(dist_matrix, *self.covariance_model) # adding variance if self.variance < cov_matrix.max(): variance = cov_matrix.max() else: variance = self.variance if self.quadtree.leaf_mean_px_var is not None: self._log.debug( 'Adding variance from scene.displacement_px_var') variance += self.quadtree.leaf_mean_px_var num.fill_diagonal(cov_matrix, variance) for nx, ny in num.nditer(num.triu_indices_from(dist_matrix)): self._mapLeaves(nx, ny) elif method == 'full': leaf_map = num.empty((len(self.quadtree.leaves), 4), dtype=num.uint32) for nl, leaf in enumerate(self.quadtree.leaves): leaf, _ = self._mapLeaves(nl, nl) leaf_map[nl, 0], leaf_map[nl, 1] = (leaf._slice_rows.start, leaf._slice_rows.stop) leaf_map[nl, 2], leaf_map[nl, 3] = (leaf._slice_cols.start, leaf._slice_cols.stop) nleaves = self.quadtree.nleaves cov_matrix = covariance_ext.covariance_matrix( self.scene.frame.gridEmeter.filled(), self.scene.frame.gridNmeter.filled(), leaf_map, self.covariance_model, self.variance, nthreads, self.config.adaptive_subsampling)\ .reshape(nleaves, nleaves) if self.quadtree.leaf_mean_px_var is not None: self._log.debug( 'Adding variance from scene.displacement_px_var') cov_matrix[num.diag_indices_from(cov_matrix)] +=\ self.quadtree.leaf_mean_px_var else: raise TypeError('Covariance calculation %s method not defined!' % method) self._log.debug('Created covariance matrix - %s mode [%0.4f s]' % (method, time.time()-t0)) return cov_matrix def isMatrixPosDefinite(self, full=False): self._log.debug('Checking whether matrix is positive-definite') if full: matrix = self.covariance_matrix else: matrix = self.covariance_matrix_focal try: chol_decomp = num.linalg.cholesky(matrix) except num.linalg.linalg.LinAlgError: pos_def = False else: pos_def = ~num.all(num.iscomplex(chol_decomp)) finally: if not pos_def: self._log.warning('Covariance matrix is not positiv definite!') return pos_def @staticmethod def _leafFocalDistance(leaf1, leaf2): return num.sqrt((leaf1.focal_point[0] - leaf2.focal_point[0])**2 + (leaf1.focal_point[1] - leaf2.focal_point[1])**2) def _leafMapping(self, leaf1, leaf2): if not isinstance(leaf1, str): leaf1 = if not isinstance(leaf2, str): leaf2 = if not self._initialized: self.covariance_matrix_focal try: return self._leaf_mapping[leaf1], self._leaf_mapping[leaf2] except KeyError as e: raise KeyError('Unknown quadtree leaf with id %s' % e)
[docs] def getLeafCovariance(self, leaf1, leaf2): """Get the covariance between ``leaf1`` and ``leaf2`` from distances. :param leaf1: Leaf one :type leaf1: str of `` or :class:`~kite.quadtree.QuadNode` :param leaf2: Leaf two :type leaf2: str of `` or :class:`~kite.quadtree.QuadNode` :returns: Covariance between ``leaf1`` and ``leaf2`` :rtype: float """ return self.covariance_matrix[self._leafMapping(leaf1, leaf2)]
[docs] def getLeafWeight(self, leaf, model='focal'): """ Get the total weight of ``leaf``, which is the summation of all single pair weights of :attr:`kite.Covariance.weight_matrix`. .. math :: w_{x} = \\sum_i W_{x,i} :param model: ``Focal`` or ``full``, default ``focal`` :type model: str :param leaf: A leaf from :class:`~kite.Quadtree` :type leaf: :class:`~kite.quadtree.QuadNode` :returns: Weight of the leaf :rtype: float """ (nl, _) = self._leafMapping(leaf, leaf) weight_mat = self.weight_matrix_focal return num.mean(weight_mat, axis=0)[nl]
[docs] def syntheticNoise(self, shape=(1024, 1024), dEdN=None, anisotropic=False, rstate=None): """Create random synthetic noise from data noise power spectrum. This function uses the power spectrum of the data noise (:attr:`noise_data`) (:func:`powerspecNoise`) to create synthetic noise, e.g. to use it for data pertubation in optinmizations. The default sampling distances are taken from :attr:`kite.scene.Frame.dE` and :attr:`kite.scene.Frame.dN`. They can be overwritten. :param shape: shape of the desired noise patch. Pixels in northing and easting (`nE`, `nN`), defaults to `(1024, 1024)`. :type shape: tuple, optional :param dEdN: The sampling distance in easting, defaults to (:attr:`kite.scene.Frame.dE`, :attr:`kite.scene.Frame.dN`). :type dE: tuple, floats :returns: synthetic noise patch :rtype: :class:`numpy.ndarray` """ if (shape[0] + shape[1]) % 2 != 0: # self._log.warning('Patch dimensions must be even, ' # 'ceiling dimensions!') pass nE = shape[1] + (shape[1] % 2) nN = shape[0] + (shape[0] % 2) if rstate is None: rstate = num.random.RandomState() rfield = rstate.rand(nN, nE) spec = num.fft.fft2(rfield) if not dEdN: dE, dN = (self.scene.frame.dE, self.scene.frame.dN) kE = num.fft.fftfreq(nE, dE) kN = num.fft.fftfreq(nN, dN) k_rad = num.sqrt(kN[:, num.newaxis]**2 + kE[num.newaxis, :]**2) amp = num.zeros_like(k_rad) if not anisotropic: noise_pspec, k, _, _, _, _ = self.powerspecNoise2D() k_bin = num.insert(k + k[0]/2, 0, 0) for i in range(k.size): k_min = k_bin[i] k_max = k_bin[i+1] r = num.logical_and(k_rad > k_min, k_rad <= k_max) if i == (k.size-1): r = k_rad > k_min if not num.any(r): continue amp[r] = noise_pspec[i] amp[k_rad == 0.] = self.variance amp[k_rad > k.max()] = noise_pspec[num.argmax(k)] amp = num.sqrt(amp * self.noise_data.size * num.pi * 4) elif anisotropic: interp_pspec, _, _, _, skE, skN = self.powerspecNoise3D() kE = num.fft.fftshift(kE) kN = num.fft.fftshift(kN) mkE = num.logical_and(kE >= skE.min(), kE <= skE.max()) mkN = num.logical_and(kN >= skN.min(), kN <= skN.max()) mkRad = num.where( # noqa k_rad < num.sqrt(kN[mkN].max()**2 + kE[mkE].max()**2)) res = interp_pspec(kN[mkN, num.newaxis], kE[num.newaxis, mkE], grid=True) print((amp.shape, res.shape)) print((kN.size, kE.size)) amp = res amp = num.fft.fftshift(amp) print((amp.min(), amp.max())) spec *= amp noise = num.abs(num.fft.ifft2(spec)) noise -= num.mean(noise) # remove shape % 2 padding return noise[:shape[0], :shape[1]]
[docs] def getQuadtreeNoise(self, rstate=None, gather=num.nanmedian): '''Create noise for a :class:`~kite.quadtree.Quadtree` Use :meth:`~kite.covariance.Covariance.getSyntheticNoise` to create data-driven noise on each quadtree leaf, summarized by :param gather: Function gathering leaf's noise realisation, defaults to num.median. :type normalisation: callable, optional :returns: Array of noise level at each quadtree leaf. :rtype: :class:`numpy.ndarray` ''' qt = self.quadtree syn_noise = self.syntheticNoise( shape=self.scene.displacement.shape, rstate=rstate) syn_noise[self.scene.displacement_mask] = num.nan noise_quadtree_arr = num.full(qt.nleaves, num.nan) for il, lv in enumerate(qt.leaves): noise_quadtree_arr[il] = gather( syn_noise[lv._slice_rows, lv._slice_cols]) return noise_quadtree_arr
def powerspecNoise1D(self, data=None, ndeg=512, nk=512): if self._powerspec1d_cached is None: self._powerspec1d_cached = self._powerspecNoise( data, norm='1d', ndeg=ndeg, nk=nk) return self._powerspec1d_cached def powerspecNoise2D(self, data=None, ndeg=512, nk=512): if self._powerspec2d_cached is None: self._powerspec2d_cached = self._powerspecNoise( data, norm='2d', ndeg=ndeg, nk=nk) return self._powerspec2d_cached def powerspecNoise3D(self, data=None): if self._powerspec3d_cached is None: self._powerspec3d_cached = self._powerspecNoise( data, norm='3d') return self._powerspec3d_cached def _powerspecNoise(self, data=None, norm='1d', ndeg=512, nk=512): """Get the noise power spectrum from :attr:`kite.Covariance.noise_data`. :param data: Overwrite Covariance.noise_data, defaults to `None` :type data: :class:`numpy.ndarray`, optional :returns: `(power_spec, k, f_spectrum, kN, kE)` :rtype: tuple """ if data is None: noise = self.noise_data else: noise = data.copy() if norm not in ['1d', '2d', '3d']: raise AttributeError('norm must be either 1d, 2d or 3d') # noise = squareMatrix(noise) shift = num.fft.fftshift spectrum = shift(num.fft.fft2(noise, axes=(0, 1), norm=None)) power_spec = (num.abs(spectrum)/spectrum.size)**2 kE = shift(num.fft.fftfreq(power_spec.shape[1], d=self.quadtree.frame.dE)) kN = shift(num.fft.fftfreq(power_spec.shape[0], d=self.quadtree.frame.dN)) k_rad = num.sqrt(kN[:, num.newaxis]**2 + kE[num.newaxis, :]**2) power_spec[k_rad == 0.] = 0. power_interp = sp.interpolate.RectBivariateSpline(kN, kE, power_spec) # def power1d(k): # theta = num.linspace(-num.pi, num.pi, ndeg, False) # power = num.empty_like(k) # for i in range(k.size): # kE = num.cos(theta) * k[i] # kN = num.sin(theta) * k[i] # power[i] = num.median(power_interp.ev(kN, kE)) * k[i]\ # * num.pi * 4 # return power def power1d(k): theta = num.linspace(-num.pi, num.pi, ndeg, False) power = num.empty_like(k) for i in range(k.size): kE = num.cos(theta) * k[i] kN = num.sin(theta) * k[i] power[i] = num.median(power_interp.ev(kN, kE)) return power def power2d(k): """ Mean 2D Power works! """ theta = num.linspace(-num.pi, num.pi, ndeg, False) power = num.empty_like(k) for i in range(k.size): kE = num.sin(theta) * k[i] kN = num.cos(theta) * k[i] power[i] = num.median(power_interp.ev(kN, kE)) # Median is more stable than the mean here return power def power3d(k): return power_interp power = power1d if norm == '2d': power = power2d elif norm == '3d': power = power3d k_rad = num.sqrt(kN[:, num.newaxis]**2 + kE[num.newaxis, :]**2) k = num.linspace(k_rad[k_rad > 0].min(), k_rad.max(), nk) dk = 1./k.min() / (2. * nk) return power(k), k, dk, spectrum, kE, kN def _powerCosineTransform(self, p_spec): """Calculating the cosine transform of the power spectrum. The cosine transform of the power spectrum is an estimate of the data covariance (see Hanssen, 2001).""" cos = sp.fftpack.idct(p_spec, type=3) return cos
[docs] def setSamplingMethod(self, method): """ Set the sampling method """ assert method in CovarianceConfig.sampling_method.choices self.config.sampling_method = method self._clear(config=True, spectrum=False) self.evChanged.notify() self._log.debug('Changed sampling method to %s' % method)
[docs] def setSpatialBins(self, nbins): """ Set number of spatial bins """ self.config.spatial_bins = nbins self._clear(config=True, spectrum=False) self.evChanged.notify() self._log.debug('Changed spatial distance bins to %s' % nbins)
[docs] def setSpatialPairs(self, npairs): """ Set number of random spatial pairs """ self.config.spatial_pairs = npairs self._clear(config=True, spectrum=False) self.evChanged.notify() self._log.debug('Changed random pairs to %s' % npairs)
def setModelFunction(self, model): assert model in CovarianceConfig.model_function.choices self.config.model_function = model self._clear(config=True, spectrum=True) self.evChanged.notify() self._log.debug('Changed model function to %s' % model) def getModelFunction(self): if self.config.model_function == 'exponential': return modelCovarianceExponential if self.config.model_function == 'exponential_cosine': return modelCovarianceExponentialCosine @property_cached def covariance_spectral(self): """ Covariance function estimated directly from the power spectrum of displacement noise patch using the cosine transform. :type: tuple, :class:`numpy.ndarray` (covariance, distance) """ power_spec, k, dk, _, _, _ = self.powerspecNoise1D() # power_spec -= self.variance d = num.arange(1, power_spec.size+1) * dk cov = self._powerCosineTransform(power_spec) return cov, d @property_cached def covariance_spatial(self): self._log.debug('Estimating covariance (spatial)...') nbins = self.config.spatial_bins npairs = self.config.spatial_pairs noise_data = self.noise_data.ravel() grdE = self.noise_data_gridE grdN = self.noise_data_gridN max_distance = min(abs(grdE.min() - grdE.max()), abs(grdN.min() - grdN.max())) dist_bins = num.linspace(0, max_distance, nbins + 1) grdE = grdE.ravel() grdN = grdN.ravel() # Select random coordinates rstate = num.random.RandomState(noise_data.size) rand_idx = rstate.randint(0, noise_data.size, (2, npairs)) idx0 = rand_idx[0, :] idx1 = rand_idx[1, :] distances = num.sqrt((grdN[idx0] - grdN[idx1])**2 + (grdE[idx0] - grdE[idx1])**2) cov_all = noise_data[idx0] * noise_data[idx1] vario_all = (noise_data[idx0] - noise_data[idx1])**2 bins = num.digitize(distances, dist_bins, right=True) bin_distances = dist_bins[1:] - dist_bins[1]/2 covariance = num.full_like(bin_distances, fill_value=num.nan) variance = num.full_like(bin_distances, fill_value=num.nan) for ib in range(nbins): selection = bins == ib if selection.sum() != 0: covariance[ib] = num.nanmean(cov_all[selection]) variance[ib] = num.nanmean(vario_all[selection])/2 self._structure_spatial = (variance[~num.isnan(variance)], bin_distances[~num.isnan(variance)]) covariance[0] = num.nan return (covariance[~num.isnan(covariance)], bin_distances[~num.isnan(covariance)])
[docs] def getCovariance(self): """ Calculate the covariance function :return: The covariance and distance :rtype: tuple """ if self.config.sampling_method == 'spatial': return self.covariance_spatial elif self.config.sampling_method == 'spectral': return self.covariance_spectral
@property def covariance_model(self, regime=0): """ Covariance model parameters for :func:`~kite.covariance.modelCovariance` retrieved from :attr:`~kite.Covariance.getCovarianceFunction`. .. note:: using this function implies several model fits: (1) fit of the spectrum and (2) the cosine transform. Not sure about the consequences, if this is useful and/or meaningful. :getter: Get the parameters. :type: tuple, ``a`` and ``b`` """ if self.config.model_coefficients is None: covariance, distance = self.getCovariance() model = self.getModelFunction() if self.config.model_function == 'exponential': coeff = (num.mean(covariance), num.mean(distance)) elif self.config.model_function == 'exponential_cosine': coeff = (num.mean(covariance), num.mean(distance), num.mean(distance)*-.1, .1) func = self.getModelFunction() # Testing penalty function def model(*args): distance, a, b, c, d = args res = func(*args) penalty = 0. if distance[-1]/b > (distance[-1]+c)/d: penalty = (b-d) * coeff[0] self._log.warning('Penalty %f' % penalty) return res + penalty # Overwrite with pure model function model = self.getModelFunction() # noqa try: coeff, _ = sp.optimize.curve_fit( model, distance, covariance, p0=coeff) except RuntimeError: self._log.warning('Could not fit the %s' ' covariance model' % self.config.model_function) finally: self.config.model_coefficients = tuple(map(float, coeff)) return self.config.model_coefficients @property def covariance_model_rms(self): """ :getter: RMS missfit between :class:`~kite.Covariance.covariance_model` and :class:`~kite.Covariance.getCovarianceFunction` :type: float """ cov, d = self.getCovariance() model = self.getModelFunction() cov_mod = model(d, *self.covariance_model) return num.sqrt(num.mean((cov - cov_mod)**2)) @property_cached def structure_spatial(self): self.covariance_spatial return self._structure_spatial @property_cached def structure_spectral(self): """ Structure function derived from ``noise_patch`` :type: tuple, :class:`numpy.ndarray` (structure_spectral, distance) Adapted from """ power_spec, k, dk, _, _, _ = self.powerspecNoise1D() d = num.arange(1, power_spec.size+1) * dk def structure_spectral(power_spec, d, k): struc_func = num.zeros_like(k) for i, d in enumerate(d): for ik, tk in enumerate(k): # struc_func[i] += (1. - num.cos(tk*d))*power_spec[ik] struc_func[i] += (1. - sp.special.j0(tk*d))*power_spec[ik] struc_func *= 2./1 return struc_func struc_func = structure_spectral(power_spec, d, k) return struc_func, d
[docs] def getStructure(self, method=None): """ Get the structure function :param method: Either `spatial` or `spectral`, if `None` the method is taken from config :type method: str (optional) :return: (variance, distance) :rtype: tuple """ if method is None: method = self.config.sampling_method if method == 'spatial': return self.structure_spatial elif method == 'spectral': return self.structure_spectral
@property def variance(self): """ Variance of data noise estimated from the high-frequency end of power spectrum. :setter: Set the variance manually :getter: Retrieve the variance :type: float """ return self.config.variance @variance.setter def variance(self, value): self.config.variance = float(value) # self._clear(config=False, spectrum=False, spatial=False) self.evChanged.notify() @variance.getter def variance(self): if self.config.variance is None and \ self.config.sampling_method == 'spatial': structure_spatial, dist = self.structure_spatial last_20p = -int(structure_spatial.size * .2) self.config.variance = float( num.mean(structure_spatial[(last_20p):])) elif (self.config.variance is None and self.config.sampling_method == 'spectral'): power_spec, k, dk, spectrum, _, _ = self.powerspecNoise1D() cov, _ = self.covariance_spectral ma = self.covariance_model[0] # print(cov[1]) ps = power_spec * spectrum.size # print(spectrum.size) # print(num.mean(ps[-int(ps.size/9.):-1])) var = num.median(ps[-int(ps.size/9.):]) + ma self.config.variance = float(var) return self.config.variance
[docs] def export_weight_matrix(self, filename): """ Export the full :attr:`~kite.Covariance.weight_matrix` to an ASCII file. The data can be loaded through :func:`numpy.loadtxt`. :param filename: path to export to :type filename: str """ self._log.debug('Exporting Covariance.weight_matrix to %s' % filename) header = 'Exported kite.Covariance.weight_matrix, '\ 'for more information visit\n'\ '\nThe matrix is symmetric and ordered by\n' header += ', '.join([ for l in self.quadtree.leaves]) num.savetxt(filename, self.weight_matrix, header=header)
@property_cached def plot(self): """ Simple overview plot to summarize the covariance estimations. """ from kite.plot2d import CovariancePlot return CovariancePlot(self) @property_cached def plot_syntheticNoise(self): """ Simple overview plot to summarize the covariance estimations. """ from kite.plot2d import SyntheticNoisePlot return SyntheticNoisePlot(self)