plot.py 58.2 KB
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import math
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import re
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import random
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import logging
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import os
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import os.path as op
import numpy as num
from scipy import signal
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from pyrocko import beachball, guts, trace, util, gf
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from pyrocko import hudson
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from grond import core
from matplotlib import pyplot as plt
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from matplotlib import cm, patches, gridspec
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from pyrocko.cake_plot import colors, \
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    str_to_mpl_color as scolor, light

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from pyrocko.plot import mpl_init, mpl_papersize, mpl_margins

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logger = logging.getLogger('grond.plot')

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km = 1000.


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def amp_spec_max(spec_trs, key):
    amaxs = {}
    for spec_tr in spec_trs:
        amax = num.max(num.abs(spec_tr.ydata))
        k = key(spec_tr)
        if k not in amaxs:
            amaxs[k] = amax
        else:
            amaxs[k] = max(amaxs[k], amax)

    return amaxs


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def ordersort(x):
    isort = num.argsort(x)
    iorder = num.empty(isort.size)
    iorder[isort] = num.arange(isort.size)
    return iorder


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def nextpow2(i):
    return 2**int(math.ceil(math.log(i)/math.log(2.)))


def fixlim(lo, hi):
    if lo == hi:
        return lo - 1.0, hi + 1.0
    else:
        return lo, hi


def str_dist(dist):
    if dist < 10.0:
        return '%g m' % dist
    elif 10. <= dist < 1.*km:
        return '%.0f m' % dist
    elif 1.*km <= dist < 10.*km:
        return '%.1f km' % (dist / km)
    else:
        return '%.0f km' % (dist / km)


def str_duration(t):
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    s = ''
    if t < 0.:
        s = '-'
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    t = abs(t)
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    if t < 10.0:
        return s + '%.2g s' % t
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    elif 10.0 <= t < 3600.:
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        return s + util.time_to_str(t, format='%M:%S min')
    elif 3600. <= t < 24*3600.:
        return s + util.time_to_str(t, format='%H:%M h')
    else:
        return s + '%.1f d' % (t / (24.*3600.))
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def scale_axes(ax, scale):
    from matplotlib.ticker import ScalarFormatter

    class FormatScaled(ScalarFormatter):
        @staticmethod
        def __call__(value, pos):
            return u'%d' % (value * scale)

    ax.get_xaxis().set_major_formatter(FormatScaled())
    ax.get_yaxis().set_major_formatter(FormatScaled())


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def eigh_sorted(mat):
    evals, evecs = num.linalg.eigh(mat)
    iorder = num.argsort(evals)
    return evals[iorder], evecs[:, iorder]


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def make_norm_trace(a, b, exponent):
    tmin = max(a.tmin, b.tmin)
    tmax = min(a.tmax, b.tmax)
    c = a.chop(tmin, tmax, inplace=False)
    bc = b.chop(tmin, tmax, inplace=False)
    c.set_ydata(num.abs(c.get_ydata() - bc.get_ydata())**exponent)
    return c


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class GrondModel(object):
    def __init__(self, **kwargs):
        self.listeners = []
        self.set_problem(None)

    def add_listener(self, listener):
        self.listeners.append(listener)

    def set_problem(self, problem):

        self.problem = problem
        if problem:
            nparameters = problem.nparameters
            ntargets = problem.ntargets
        else:
            nparameters = 0
            ntargets = 0

        nmodels = 0
        nmodels_capacity = 1024

        self._xs_buffer = num.zeros(
            (nmodels_capacity, nparameters), dtype=num.float)
        self._misfits_buffer = num.zeros(
            (nmodels_capacity, ntargets, 2), dtype=num.float)

        self.xs = self._xs_buffer[:nmodels, :]
        self.misfits = self._misfits_buffer[:nmodels, :, :]

        self.data_changed()

    @property
    def nmodels(self):
        return self.xs.shape[0]

    @property
    def nmodels_capacity(self):
        return self._xs_buffer.shape[0]

    def append(self, xs, misfits):
        assert xs.shape[0] == misfits.shape[0]

        nmodels_add = xs.shape[0]

        nmodels = self.nmodels
        nmodels_new = nmodels + nmodels_add
        nmodels_capacity_new = max(1024, nextpow2(nmodels_new))

        nmodels_capacity = self.nmodels_capacity
        if nmodels_capacity_new > nmodels_capacity:
            xs_buffer = num.zeros(
                (nmodels_capacity_new, self.problem.nparameters),
                dtype=num.float)

            misfits_buffer = num.zeros(
                (nmodels_capacity_new, self.problem.ntargets, 2),
                dtype=num.float)

            xs_buffer[:nmodels, :] = self._xs_buffer[:nmodels]
            misfits_buffer[:nmodels, :] = self._misfits_buffer[:nmodels]
            self._xs_buffer = xs_buffer
            self._misfits_buffer = misfits_buffer

        self._xs_buffer[nmodels:nmodels+nmodels_add, :] = xs
        self._misfits_buffer[nmodels:nmodels+nmodels_add, :, :] = misfits

        nmodels = nmodels_new

        self.xs = self._xs_buffer[:nmodels, :]
        self.misfits = self._misfits_buffer[:nmodels, :, :]

        self.data_changed()

    def data_changed(self):
        for listener in self.listeners:
            listener()


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def draw_sequence_figures(model, plt, misfit_cutoff=None, sort_by='misfit'):
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    problem = model.problem

    imodels = num.arange(model.nmodels)
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    bounds = problem.get_parameter_bounds() + problem.get_dependant_bounds()
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    xref = problem.get_xref()
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    xs = model.xs

    npar = problem.nparameters
    ndep = problem.ndependants

    gms = problem.global_misfits(model.misfits)
    gms_softclip = num.where(gms > 1.0, 0.2 * num.log10(gms) + 1.0, gms)

    isort = num.argsort(gms)[::-1]

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    if sort_by == 'iteration':
        imodels = imodels[isort]
    elif sort_by == 'misfit':
        imodels = num.arange(imodels.size)
    else:
        assert False

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    gms = gms[isort]
    gms_softclip = gms_softclip[isort]
    xs = xs[isort, :]

    iorder = num.empty_like(isort)
    iorder = num.arange(iorder.size)

    if misfit_cutoff is None:
        ibest = num.ones(gms.size, dtype=num.bool)
    else:
        ibest = gms < misfit_cutoff

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    def config_axes(axes, nfx, nfy, impl, iplot, nplots):
        if (impl - 1) % nfx != nfx - 1:
            axes.get_yaxis().tick_left()

        if (impl - 1) >= (nfx * (nfy-1)) or iplot >= nplots - nfx:
            axes.set_xlabel('Iteration')
            if not (impl - 1) / nfx == 0:
                axes.get_xaxis().tick_bottom()
        elif (impl - 1) / nfx == 0:
            axes.get_xaxis().tick_top()
            axes.set_xticklabels([])
        else:
            axes.get_xaxis().set_visible(False)

    fontsize = 10.0

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    nfx = 2
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    nfy = 3
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    # nfz = (npar + ndep + 1 - 1) / (nfx*nfy) + 1
    cmap = cm.YlOrRd
    cmap = cm.jet
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    msize = 1.5
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    axes = None
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    figs = []
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    fig = None
    alpha = 0.5
    for ipar in xrange(npar):
        impl = ipar % (nfx*nfy) + 1

        if impl == 1:
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            fig = plt.figure(figsize=mpl_papersize('a5', 'landscape'))
            labelpos = mpl_margins(fig, nw=nfx, nh=nfy, w=7., h=5., wspace=7.,
                                   hspace=2., units=fontsize)
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            figs.append(fig)
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        par = problem.parameters[ipar]

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        axes = fig.add_subplot(nfy, nfx, impl)
        labelpos(axes, 2.5, 2.0)

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        axes.set_ylabel(par.get_label())
        axes.get_yaxis().set_major_locator(plt.MaxNLocator(4))
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        config_axes(axes, nfx, nfy, impl, ipar, npar+ndep+1)
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        axes.set_ylim(*fixlim(*par.scaled(bounds[ipar])))
        axes.set_xlim(0, model.nmodels)

        axes.scatter(
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            imodels[ibest], par.scaled(xs[ibest, ipar]), s=msize,
            c=iorder[ibest], edgecolors='none', cmap=cmap, alpha=alpha)

        axes.axhline(par.scaled(xref[ipar]), color='black', alpha=0.3)
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    for idep in xrange(ndep):
        # ifz, ify, ifx = num.unravel_index(ipar, (nfz, nfy, nfx))
        impl = (npar+idep) % (nfx*nfy) + 1

        if impl == 1:
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            fig = plt.figure(figsize=mpl_papersize('a5', 'landscape'))
            labelpos = mpl_margins(fig, nw=nfx, nh=nfy, w=7., h=5., wspace=7.,
                                   hspace=2., units=fontsize)
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            figs.append(fig)
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        par = problem.dependants[idep]

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        axes = fig.add_subplot(nfy, nfx, impl)
        labelpos(axes, 2.5, 2.0)

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        axes.set_ylabel(par.get_label())
        axes.get_yaxis().set_major_locator(plt.MaxNLocator(4))
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        config_axes(axes, nfx, nfy, impl, npar+idep, npar+ndep+1)

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        axes.set_ylim(*fixlim(*par.scaled(bounds[npar+idep])))
        axes.set_xlim(0, model.nmodels)

        ys = problem.make_dependant(xs[ibest, :], par.name)
        axes.scatter(
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            imodels[ibest], par.scaled(ys), s=msize, c=iorder[ibest],
            edgecolors='none', cmap=cmap, alpha=alpha)

        y = problem.make_dependant(xref, par.name)
        axes.axhline(par.scaled(y), color='black', alpha=0.3)
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    impl = (npar+ndep) % (nfx*nfy) + 1
    if impl == 1:
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        fig = plt.figure(figsize=mpl_papersize('a5', 'landscape'))
        labelpos = mpl_margins(fig, nw=nfx, nh=nfy, w=7., h=5., wspace=7.,
                               hspace=2., units=fontsize)
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        figs.append(fig)
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    axes = fig.add_subplot(nfy, nfx, impl)
    labelpos(axes, 2.5, 2.0)

    config_axes(axes, nfx, nfy, impl, npar+ndep, npar+ndep+1)
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    axes.set_ylim(0., 1.5)
    axes.set_yticks([0., 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4])
    axes.set_yticklabels(['0.0', '0.2', '0.4', '0.6', '0.8', '1', '10', '100'])

    axes.scatter(
        imodels[ibest], gms_softclip[ibest], c=iorder[ibest],
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        s=msize, edgecolors='none', cmap=cmap, alpha=alpha)

    axes.axhspan(1.0, 1.5, color=(0.8, 0.8, 0.8), alpha=0.2)
    axes.axhline(1.0, color=(0.5, 0.5, 0.5), zorder=2)
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    axes.set_xlim(0, model.nmodels)
    axes.set_xlabel('Iteration')

    axes.set_ylabel('Misfit')

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    return figs
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def draw_jointpar_figures(
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        model, plt, misfit_cutoff=None, ibootstrap=None, color=None,
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        exclude=None, include=None, draw_ellipses=False):
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    color = 'misfit'
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    # exclude = ['duration']
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    # include = ['magnitude', 'rel_moment_iso', 'rel_moment_clvd', 'depth']
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    neach = 6
    figsize = (8, 8)
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    # cmap = cm.YlOrRd
    # cmap = cm.jet
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    cmap = cm.coolwarm
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    msize = 1.5
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    problem = model.problem
    if not problem:
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        return []
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    xs = model.xs

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    bounds = problem.get_parameter_bounds() + problem.get_dependant_bounds()
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    for ipar in xrange(problem.ncombined):
        par = problem.combined[ipar]
        lo, hi = bounds[ipar]
        if lo == hi:
            if exclude is None:
                exclude = []

            exclude.append(par.name)
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    xref = problem.get_xref()
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    if ibootstrap is not None:
        gms = problem.bootstrap_misfits(model.misfits, ibootstrap)
    else:
        gms = problem.global_misfits(model.misfits)

    isort = num.argsort(gms)[::-1]

    gms = gms[isort]
    xs = xs[isort, :]

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    if misfit_cutoff is not None:
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        ibest = gms < misfit_cutoff
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        gms = gms[ibest]
        xs = xs[ibest]

    nmodels = xs.shape[0]

    if color == 'dist':
        mx = num.mean(xs, axis=0)
        cov = num.cov(xs.T)
        mdists = core.mahalanobis_distance(xs, mx, cov)
        color = ordersort(mdists)

    elif color == 'misfit':
        iorder = num.arange(nmodels)
        color = iorder

    elif color in problem.parameter_names:
        ind = problem.name_to_index(color)
        color = ordersort(problem.extract(xs, ind))
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    smap = {}
    iselected = 0
    for ipar in xrange(problem.ncombined):
        par = problem.combined[ipar]
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        if exclude and par.name in exclude or \
                include and par.name not in include:
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            continue
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        smap[iselected] = ipar
        iselected += 1

    nselected = iselected
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    if nselected < 2:
        logger.warn('cannot draw joinpar figures with less than two '
                    'parameters selected')
        return []
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    nfig = (nselected-2) / neach + 1
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    figs = []
    for ifig in xrange(nfig):
        figs_row = []
        for jfig in xrange(nfig):
            if ifig >= jfig:
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                figs_row.append(plt.figure(figsize=figsize))
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            else:
                figs_row.append(None)

        figs.append(figs_row)

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    for iselected in xrange(nselected):
        ipar = smap[iselected]
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        ypar = problem.combined[ipar]
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        for jselected in xrange(iselected):
            jpar = smap[jselected]
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            xpar = problem.combined[jpar]

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            ixg = (iselected - 1)
            iyg = jselected
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            ix = ixg % neach
            iy = iyg % neach

            ifig = ixg/neach
            jfig = iyg/neach

            aind = (neach, neach, (ix * neach) + iy + 1)

            fig = figs[ifig][jfig]

            axes = fig.add_subplot(*aind)

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            axes.axvline(0., color=scolor('aluminium3'), lw=0.5)
            axes.axhline(0., color=scolor('aluminium3'), lw=0.5)
            for spine in axes.spines.values():
                spine.set_edgecolor(scolor('aluminium5'))
                spine.set_linewidth(0.5)

            xmin, xmax = fixlim(*xpar.scaled(bounds[jpar]))
            ymin, ymax = fixlim(*ypar.scaled(bounds[ipar]))

            if ix == 0 or jselected + 1 == iselected:
                for (xpos, xoff, x) in [(0.0, 10., xmin), (1.0, -10., xmax)]:
                    axes.annotate(
                        '%.2g%s' % (x, xpar.get_unit_suffix()),
                        xy=(xpos, 1.05),
                        xycoords='axes fraction',
                        xytext=(xoff, 5.),
                        textcoords='offset points',
                        verticalalignment='bottom',
                        horizontalalignment='left',
                        rotation=45.)

            if iy == neach - 1 or jselected + 1 == iselected:
                for (ypos, yoff, y) in [(0., 10., ymin), (1.0, -10., ymax)]:
                    axes.annotate(
                        '%.2g%s' % (y, ypar.get_unit_suffix()),
                        xy=(1.0, ypos),
                        xycoords='axes fraction',
                        xytext=(5., yoff),
                        textcoords='offset points',
                        verticalalignment='bottom',
                        horizontalalignment='left',
                        rotation=45.)

            axes.set_xlim(xmin, xmax)
            axes.set_ylim(ymin, ymax)
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            axes.get_xaxis().set_ticks([])
            axes.get_yaxis().set_ticks([])

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            if iselected == nselected - 1 or ix == neach - 1:
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                axes.annotate(
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                    xpar.get_label(with_unit=False),
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                    xy=(0.5, -0.05),
                    xycoords='axes fraction',
                    verticalalignment='top',
                    horizontalalignment='right',
                    rotation=45.)

            if iy == 0:
                axes.annotate(
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                    ypar.get_label(with_unit=False),
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                    xy=(-0.05, 0.5),
                    xycoords='axes fraction',
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                    verticalalignment='top',
                    horizontalalignment='right',
                    rotation=45.)
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            fx = problem.extract(xs, jpar)
            fy = problem.extract(xs, ipar)
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            axes.scatter(
                xpar.scaled(fx),
                ypar.scaled(fy),
                c=color,
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                s=msize, alpha=0.5, cmap=cmap, edgecolors='none')
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            if draw_ellipses:
                cov = num.cov((xpar.scaled(fx), ypar.scaled(fy)))
                evals, evecs = eigh_sorted(cov)
                evals = num.sqrt(evals)
                ell = patches.Ellipse(
                    xy=(num.mean(xpar.scaled(fx)), num.mean(ypar.scaled(fy))),
                    width=evals[0]*2,
                    height=evals[1]*2,
                    angle=num.rad2deg(num.arctan2(evecs[1][0], evecs[0][0])))

                ell.set_facecolor('none')
                axes.add_artist(ell)
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            fx = problem.extract(xref, jpar)
            fy = problem.extract(xref, ipar)
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            ref_color = scolor('aluminium6')
            ref_color_light = 'none'
            axes.plot(
                xpar.scaled(fx), ypar.scaled(fy), 's',
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                mew=1.5, ms=5, mfc=ref_color_light, mec=ref_color)
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    figs_flat = []
    for figs_row in figs:
        figs_flat.extend(fig for fig in figs_row if fig is not None)

    return figs_flat

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def draw_solution_figure(
        model, plt, misfit_cutoff=None, beachball_type='full'):

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    fontsize = 10.

    fig = plt.figure(figsize=(6, 2))
    axes = fig.add_subplot(1, 1, 1, aspect=1.0)
    fig.subplots_adjust(left=0., right=1., bottom=0., top=1.)
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    problem = model.problem
    if not problem:
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        logger.warn('problem not set')
        return []
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    xs = model.xs

    if xs.size == 0:
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        logger.warn('empty models vector')
        return []
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    gms = problem.global_misfits(model.misfits)
    isort = num.argsort(gms)
    iorder = num.empty_like(isort)
    iorder[isort] = num.arange(iorder.size)[::-1]

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    mean_source = core.get_mean_source(problem, model.xs)
    best_source = core.get_best_source(problem, model.xs, model.misfits)
    ref_source = problem.base_source

    for xpos, label in [
            (0., 'Full'),
            (2., 'Isotropic'),
            (4., 'Deviatoric'),
            (6., 'CLVD'),
            (8., 'DC')]:

        axes.annotate(
            label,
            xy=(1+xpos, 3),
            xycoords='data',
            xytext=(0., 0.),
            textcoords='offset points',
            ha='center',
            va='center',
            color='black',
            fontsize=fontsize)

    decos = []
    for source in [best_source, mean_source, ref_source]:
        mt = source.pyrocko_moment_tensor()
        deco = mt.standard_decomposition()
        decos.append(deco)

    moment_full_max = max(deco[-1][0] for deco in decos)

    for ypos, label, deco, color_t in [
            (2., 'Ensemble best', decos[0], scolor('aluminium5')),
            (1., 'Ensemble mean', decos[1], scolor('scarletred1')),
            (0., 'Reference', decos[2], scolor('aluminium3'))]:

        [(moment_iso, ratio_iso, m_iso),
         (moment_dc, ratio_dc, m_dc),
         (moment_clvd, ratio_clvd, m_clvd),
         (moment_devi, ratio_devi, m_devi),
         (moment_full, ratio_full, m_full)] = deco

        size0 = moment_full / moment_full_max

        axes.annotate(
            label,
            xy=(-2., ypos),
            xycoords='data',
            xytext=(0., 0.),
            textcoords='offset points',
            ha='left',
            va='center',
            color='black',
            fontsize=fontsize)

        for xpos, mt_part, ratio, ops in [
                (0., m_full, ratio_full, '-'),
                (2., m_iso, ratio_iso, '='),
                (4., m_devi, ratio_devi, '='),
                (6., m_clvd, ratio_clvd, '+'),
                (8., m_dc, ratio_dc, None)]:

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            if ratio > 1e-4:
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                try:
                    beachball.plot_beachball_mpl(
                        mt_part, axes,
                        beachball_type='full',
                        position=(1.+xpos, ypos),
                        size=0.9*size0*math.sqrt(ratio),
                        size_units='data',
                        color_t=color_t,
                        linewidth=1.0)

                except beachball.BeachballError, e:
                    logger.warn(str(e))
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                    axes.annotate(
                        'ERROR',
                        xy=(1.+xpos, ypos),
                        ha='center',
                        va='center',
                        color='red',
                        fontsize=fontsize)

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            else:
                axes.annotate(
                    'N/A',
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                    xy=(1.+xpos, ypos),
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                    ha='center',
                    va='center',
                    color='black',
                    fontsize=fontsize)

            if ops is not None:
                axes.annotate(
                    ops,
                    xy=(2. + xpos, ypos),
                    ha='center',
                    va='center',
                    color='black',
                    fontsize=fontsize)
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    axes.axison = False
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    axes.set_xlim(-2.25, 9.75)
    axes.set_ylim(-0.5, 3.5)
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    return [fig]

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def draw_contributions_figure(model, plt):

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    fontsize = 10.

    fig = plt.figure(figsize=mpl_papersize('a5', 'landscape'))
    labelpos = mpl_margins(fig, nw=2, nh=2, w=7., h=5., wspace=2.,
                           hspace=5., units=fontsize)
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    problem = model.problem
    if not problem:
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        logger.warn('problem not set')
        return []
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    xs = model.xs

    if xs.size == 0:
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        logger.warn('empty models vector')
        return []
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    imodels = num.arange(model.nmodels)

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    gms = problem.global_misfits(model.misfits)**problem.norm_exponent
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    isort = num.argsort(gms)[::-1]

    gms = gms[isort]

    gms_softclip = num.where(gms > 1.0, 0.1 * num.log10(gms) + 1.0, gms)

    gcms = problem.global_contributions(model.misfits)
    gcms = gcms[isort, :]

    jsort = num.argsort(gcms[-1, :])[::-1]

    # ncols = 4
    # nrows = ((problem.ntargets + 1) - 1) / ncols + 1

    axes = fig.add_subplot(2, 2, 1)
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    labelpos(axes, 2.5, 2.0)

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    axes.set_ylabel('Relative contribution (smoothed)')
    axes.set_ylim(0.0, 1.0)

    axes2 = fig.add_subplot(2, 2, 3, sharex=axes)
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    labelpos(axes2, 2.5, 2.0)

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    axes2.set_xlabel('Tested model, sorted descending by global misfit value')

    axes2.set_ylabel('Square of misfit')

    axes2.set_ylim(0., 1.5)
    axes2.axhspan(1.0, 1.5, color=(0.8, 0.8, 0.8))
    axes2.set_yticks([0., 0.2, 0.4, 0.6, 0.8, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5])
    axes2.set_yticklabels(
        ['0.0', '0.2', '0.4', '0.6', '0.8', '1', '10', '100', '1000', '10000',
         '100000'])

    axes2.set_xlim(imodels[0], imodels[-1])

    rel_ms_sum = num.zeros(model.nmodels)
    rel_ms_smooth_sum = num.zeros(model.nmodels)
    ms_smooth_sum = num.zeros(model.nmodels)
    b = num.hanning(100)
    b /= num.sum(b)
    a = [1]
    ii = 0
    for itarget in jsort:
        target = problem.targets[itarget]
        ms = gcms[:, itarget]
        ms = num.where(num.isfinite(ms), ms, 0.0)
        if num.all(ms == 0.0):
            continue

        rel_ms = ms / gms

        rel_ms_smooth = signal.filtfilt(b, a, rel_ms)

        ms_smooth = rel_ms_smooth * gms_softclip

        rel_poly_y = num.concatenate(
            [rel_ms_smooth_sum[::-1], rel_ms_smooth_sum + rel_ms_smooth])
        poly_x = num.concatenate([imodels[::-1], imodels])

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        add_args = {}
        if ii < 20:
            add_args['label'] = '%s (%.2g)' % (
                target.string_id(), num.mean(rel_ms[-1]))

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        axes.fill(
            poly_x, rel_poly_y,
            alpha=0.5,
            color=colors[ii % len(colors)],
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            **add_args)
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        poly_y = num.concatenate(
            [ms_smooth_sum[::-1], ms_smooth_sum + ms_smooth])

        axes2.fill(poly_x, poly_y, alpha=0.5, color=colors[ii % len(colors)])

        rel_ms_sum += rel_ms

        # axes.plot(imodels, rel_ms_sum, color='black', alpha=0.1, zorder=-1)

        ms_smooth_sum += ms_smooth
        rel_ms_smooth_sum += rel_ms_smooth
        ii += 1

    axes.legend(
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        title='Contributions (top twenty)',
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        bbox_to_anchor=(1.05, 0.0, 1.0, 1.0),
        loc='upper left',
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        ncol=1, borderaxespad=0., prop={'size': 9})
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    axes2.plot(imodels, gms_softclip, color='black')
    axes2.axhline(1.0, color=(0.5, 0.5, 0.5))

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    return [fig]

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def draw_bootstrap_figure(model, plt):

    fig = plt.figure()

    problem = model.problem
    gms = problem.global_misfits(model.misfits)

    imodels = num.arange(model.nmodels)

    axes = fig.add_subplot(1, 1, 1)

    gms_softclip = num.where(gms > 1.0, 0.1 * num.log10(gms) + 1.0, gms)

    ibests = []
    for ibootstrap in xrange(problem.nbootstrap):
        bms = problem.bootstrap_misfits(model.misfits, ibootstrap)
        isort_bms = num.argsort(bms)[::-1]

        ibests.append(isort_bms[-1])

        bms_softclip = num.where(bms > 1.0, 0.1 * num.log10(bms) + 1.0, bms)
        axes.plot(imodels, bms_softclip[isort_bms], color='red', alpha=0.2)

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    isort = num.argsort(gms)[::-1]
    iorder = num.empty(isort.size)
    iorder[isort] = imodels

    axes.plot(iorder[ibests], gms_softclip[ibests], 'x', color='black')

    m = num.median(gms[ibests])
    s = num.std(gms[ibests])

    axes.axhline(m+s, color='black', alpha=0.5)
    axes.axhline(m, color='black')
    axes.axhline(m-s, color='black', alpha=0.5)

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    axes.plot(imodels, gms_softclip[isort], color='black')

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    axes.set_xlim(imodels[0], imodels[-1])
    axes.set_xlabel('Tested model, sorted descending by global misfit value')
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    return [fig]

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def gather(l, key, sort=None, filter=None):
    d = {}
    for x in l:
        if filter is not None and not filter(x):
            continue

        k = key(x)
        if k not in d:
            d[k] = []

        d[k].append(x)

    if sort is not None:
        for v in d.itervalues():
            v.sort(key=sort)

    return d


def plot_trace(axes, tr, **kwargs):
    return axes.plot(tr.get_xdata(), tr.get_ydata(), **kwargs)


def plot_taper(axes, t, taper, **kwargs):
    y = num.ones(t.size) * 0.9
    taper(y, t[0], t[1] - t[0])
    y2 = num.concatenate((y, -y[::-1]))
    t2 = num.concatenate((t, t[::-1]))
    axes.fill(t2, y2, **kwargs)


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def plot_dtrace(axes, tr, space, mi, ma, **kwargs):
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    t = tr.get_xdata()
    y = tr.get_ydata()
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    y2 = (num.concatenate((y, num.zeros(y.size))) - mi) / \
        (ma-mi) * space - (1.0 + space)
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    t2 = num.concatenate((t, t[::-1]))
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    axes.fill(
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        t2, y2,
        clip_on=False,
        **kwargs)

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def plot_spectrum(
        axes, spec_syn, spec_obs, fmin, fmax, space, mi, ma,
        syn_color='red', obs_color='black',
        syn_lw=1.5, obs_lw=1.0, color_vline='gray', fontsize=9.):

    fpad = (fmax - fmin) / 6.

    for spec, color, lw in [
            (spec_syn, syn_color, syn_lw),
            (spec_obs, obs_color, obs_lw)]:

        f = spec.get_xdata()
        mask = num.logical_and(fmin - fpad <= f, f <= fmax + fpad)

        f = f[mask]
        y = num.abs(spec.get_ydata())[mask]

        y2 = (num.concatenate((y, num.zeros(y.size))) - mi) / \
            (ma-mi) * space - (1.0 + space)
        f2 = num.concatenate((f, f[::-1]))
        axes2 = axes.twiny()
        axes2.set_axis_off()

        axes2.set_xlim(fmin - fpad * 5, fmax + fpad * 5)

        axes2.plot(f2, y2, clip_on=False, color=color, lw=lw)
        axes2.fill(f2, y2, alpha=0.1, clip_on=False, color=color)

    axes2.plot([fmin, fmin], [-1.0 - space, -1.0], color=color_vline)
    axes2.plot([fmax, fmax], [-1.0 - space, -1.0], color=color_vline)

    for (text, fx, ha) in [
            ('%.3g Hz' % fmin, fmin, 'right'),
            ('%.3g Hz' % fmax, fmax, 'left')]:

        axes2.annotate(
            text,
            xy=(fx, -1.0),
            xycoords='data',
            xytext=(
                fontsize*0.4 * [-1, 1][ha == 'left'],
                -fontsize*0.2),
            textcoords='offset points',
            ha=ha,
            va='top',
            color=color_vline,
            fontsize=fontsize)

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def plot_dtrace_vline(axes, t, space, **kwargs):
    axes.plot([t, t], [-1.0 - space, -1.0], **kwargs)


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def draw_fits_figures_statics(ds, model, plt):
    from pyrocko.orthodrome import latlon_to_ne_numpy
    problem = model.problem

    for target in problem.targets:
        target.set_dataset(ds)

    gms = problem.global_misfits(model.misfits)
    isort = num.argsort(gms)
    gms = gms[isort]
    xs = model.xs[isort, :]
    xbest = xs[0, :]
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    source = problem.get_source(xbest)

    ms, ns, results = problem.evaluate(xbest, result_mode='full')

    figures = []

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    def decorateAxes(ax, title):
        ax.set_title(title)
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        ax.set_xlabel('[km]')
        scale_axes(ax, 1./km)
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        ax.set_aspect('equal')

    def drawRectangularOutline(ax):
        source.regularize()
        fn, fe = source.outline(cs='xy').T
        offset_n, offset_e = latlon_to_ne_numpy(
            sat_target.lats[0], sat_target.lons[0],
            source.lat, source.lon)
        fn += offset_n
        fe += offset_e
        ax.plot(offset_e, offset_n, marker='o')
        ax.plot(fe, fn, marker='o')
        # ax.fill(fe, fn, color=(0.5, 0.5, 0.5), alpha=0.5)
        # ax.plot(fe[:2], fn[:2], linewidth=2., color='black', alpha=0.5)

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    def mapDisplacementGrid(displacements, scene):
        qt = scene.quadtree
        array = num.empty_like(scene.displacement)
        array.fill(num.nan)
        for syn_v, l in zip(displacements, qt.leaves):
            array[l._slice_rows, l._slice_cols] = syn_v
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        array[scene.displacement_mask] = num.nan
        return array

    def drawTiles(ax, scene):
        rect = scene.quadtree.getMPLRectangles()
        for r in rect:
            r.set_edgecolor((.4, .4, .4))
            r.set_linewidth(.5)
            r.set_facecolor('none')
        map(ax.add_artist, rect)

        ax.scatter(scene.quadtree.leaf_coordinates[:, 0],