Source code for openquake.hazardlib.gsim.bindi_2017

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2014-2022 GEM Foundation
#
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Affero General Public License for more details.
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# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <http://www.gnu.org/licenses/>.
"""
Module exports :class:`BindiEtAl2017Rjb`,
               :class:`BindiEtAl2017Rhypo`
"""
import numpy as np
from scipy.constants import g

from openquake.baselib.general import CallableDict
from openquake.hazardlib.gsim.base import GMPE, CoeffsTable
from openquake.hazardlib import const
from openquake.hazardlib.imt import PGA, SA

CONSTANTS = {"mref": 4.5, "mh": 6.5,  "rref": 1.0}


def _get_distance_scaling(dist_type, C, ctx, mag):
    """
    Implements the distance scaling function F(M, R) presented in equations
    2 and 3. In the case of Joyner-Boore distance then the fixed-depth
    term h is required
    """
    r_h = _get_rh(dist_type, C, ctx)
    return (C["c1"] + C["c2"] * (mag - CONSTANTS["mref"])) * np.log(
        r_h / CONSTANTS["rref"]) + C["c3"] * (r_h - CONSTANTS["rref"])


def _get_magnitude_scaling(C, mag):
    """
    Implements the magnitude scaling function F(M) presented in equation 4
    """
    d_m = CONSTANTS["mh"] - CONSTANTS["mref"]
    return np.where(mag < CONSTANTS["mh"],
                    C["e1"] + C["b1"] * (mag - CONSTANTS["mref"]) +
                    C["b2"] * (mag - CONSTANTS["mref"]) ** 2.,
                    C["e1"] + C["b3"] * (mag - CONSTANTS["mh"]) +
                    C["b1"] * d_m + C["b2"] * d_m ** 2.)


_get_rh = CallableDict()


@_get_rh.add("rjb")
def _get_rh_1(kind, C, ctx):
    """
    Returns the distance incorporating the fixed depth term, h
    """
    return np.sqrt(ctx.rjb ** 2. + C["h"] ** 2.)


@_get_rh.add("rhypo")
def _get_rh_2(kind, C, ctx):
    """
    In this case only the hypocentral distance is needed - return this
    directly
    """
    return ctx.rhypo


def _get_site_term(C, vs30):
    """
    Returns the linear site amplification term given in equation 5
    """
    return C["sA"] * np.log(vs30 / 800.0)


[docs]class BindiEtAl2017Rjb(GMPE): """ Implements the European GMPE of Bindi et al. (2017) for use in moderate-seismicity regions: D.Bindi, F. Cotton, S. R. Kotha, C. Bosse, D. Stromeyer and G. Gruenthal (2017) "Application-driven ground motion prediction equation for seismic hazard assessments in non-cratonic moderate-seismicity areas", J. Seismology, 21(5), 1201 - 1218 Two different GMPEs are supported here """ #: Supported tectonic region type is 'stable shallow crust' DEFINED_FOR_TECTONIC_REGION_TYPE = const.TRT.STABLE_CONTINENTAL #: GMPE is defined only for PGA and SA (PGV coefficients not made public) DEFINED_FOR_INTENSITY_MEASURE_TYPES = {PGA, SA} #: Supported intensity measure component is the geometric mean of two #: horizontal components DEFINED_FOR_INTENSITY_MEASURE_COMPONENT = const.IMC.AVERAGE_HORIZONTAL #: Supported standard deviation types are inter-event, intra-event #: and total DEFINED_FOR_STANDARD_DEVIATION_TYPES = { const.StdDev.TOTAL, const.StdDev.INTER_EVENT, const.StdDev.INTRA_EVENT} #: Required site parameter is only Vs30 REQUIRES_SITES_PARAMETERS = {'vs30'} #: Required rupture parameter is magnitude REQUIRES_RUPTURE_PARAMETERS = {'mag'} #: Required distance measure is Rjb REQUIRES_DISTANCES = {'rjb'} def __init__(self, adjustment_factor=1.0, **kwargs): super().__init__(adjustment_factor=adjustment_factor, **kwargs) self.adjustment_factor = np.log(float(adjustment_factor))
[docs] def compute(self, ctx: np.recarray, imts, mean, sig, tau, phi): """ See :meth:`superclass method <.base.GroundShakingIntensityModel.compute>` for spec of input and result values. """ [dist_type] = self.REQUIRES_DISTANCES for m, imt in enumerate(imts): C = self.COEFFS[imt] mean[m] = (_get_magnitude_scaling(C, ctx.mag) + _get_distance_scaling(dist_type, C, ctx, ctx.mag) + _get_site_term(C, ctx.vs30)) # Mean is returned in terms of m/s^2. Need to convert to g mean[m] -= np.log(g) mean[m] += self.adjustment_factor tau[m] = C["tau"] phi[m] = C["phi"] sig[m] = np.sqrt(C['tau'] ** 2 + C['phi'] ** 2)
# Joyner-Boore COEFFS = CoeffsTable(sa_damping=5, table="""\ imt e1 b1 b2 b3 c1 c2 c3 h sA tau phi pga 0.635138 1.241105 -0.131810 -0.321920 -0.930850 0.143762 -0.010880 3.875582 -0.609150 0.495337 0.631336 0.0100 0.635138 1.241105 -0.131810 -0.321920 -0.930850 0.143762 -0.010880 3.875582 -0.609150 0.495337 0.631336 0.0200 0.705531 1.228780 -0.129160 -0.329230 -0.944120 0.145787 -0.010880 3.923887 -0.592970 0.502517 0.634714 0.0220 0.744105 1.219753 -0.127760 -0.332690 -0.949970 0.146859 -0.010880 3.948754 -0.583730 0.506053 0.636035 0.0250 0.835561 1.189969 -0.123500 -0.347660 -0.964520 0.150588 -0.010880 3.971356 -0.563480 0.514039 0.641710 0.0290 0.960622 1.149713 -0.120600 -0.364760 -0.981940 0.156387 -0.010980 3.932630 -0.533170 0.527573 0.649664 0.0300 0.982542 1.143429 -0.120050 -0.366740 -0.983330 0.157078 -0.011030 3.935425 -0.524880 0.530023 0.651497 0.0320 1.025696 1.136575 -0.117720 -0.379820 -0.985510 0.157380 -0.011130 4.000214 -0.510270 0.534272 0.654810 0.0350 1.098116 1.115775 -0.113590 -0.397190 -0.989340 0.159337 -0.011330 4.036096 -0.489150 0.541214 0.659647 0.0360 1.123583 1.105354 -0.111820 -0.402550 -0.990680 0.160659 -0.011410 4.016974 -0.480910 0.544125 0.661352 0.0400 1.206806 1.080443 -0.107980 -0.413370 -0.992560 0.163348 -0.011700 4.014361 -0.452990 0.556069 0.664047 0.0420 1.237455 1.078369 -0.108240 -0.415230 -0.990520 0.163407 -0.011860 4.054173 -0.445700 0.561054 0.666271 0.0440 1.251844 1.076735 -0.110540 -0.410250 -0.982740 0.163753 -0.012070 4.026577 -0.437860 0.567211 0.668650 0.0450 1.251626 1.075113 -0.111940 -0.404130 -0.976750 0.163945 -0.012200 3.970955 -0.434460 0.571350 0.670589 0.0460 1.256382 1.074434 -0.113630 -0.399360 -0.972150 0.164094 -0.012310 3.921404 -0.431610 0.575592 0.672206 0.0480 1.273180 1.070584 -0.115800 -0.404410 -0.965450 0.164738 -0.012500 3.830608 -0.425450 0.582299 0.675478 0.0500 1.268964 1.072599 -0.117110 -0.411960 -0.955390 0.164215 -0.012670 3.760774 -0.423150 0.584897 0.678273 0.0550 1.294806 1.072646 -0.116210 -0.412610 -0.941150 0.162012 -0.013000 3.652581 -0.425790 0.593588 0.681858 0.0600 1.274268 1.076568 -0.112050 -0.392960 -0.914590 0.159776 -0.013410 3.550820 -0.421100 0.598143 0.684462 0.0650 1.284592 1.080960 -0.109190 -0.373250 -0.899380 0.157293 -0.013670 3.491090 -0.415050 0.600609 0.686179 0.0670 1.270761 1.080915 -0.108790 -0.366810 -0.888570 0.156759 -0.013800 3.400139 -0.413930 0.601248 0.685822 0.0700 1.259126 1.089845 -0.108850 -0.346960 -0.874880 0.154148 -0.013970 3.355068 -0.413490 0.603364 0.684155 0.0750 1.215838 1.121748 -0.110610 -0.324150 -0.848450 0.147315 -0.014190 3.235534 -0.411620 0.602686 0.682186 0.0800 1.151986 1.159183 -0.110220 -0.308890 -0.822660 0.139166 -0.014300 3.178012 -0.414330 0.598061 0.679445 0.0850 1.078880 1.193976 -0.106640 -0.302760 -0.799970 0.131684 -0.014330 3.102177 -0.421470 0.593599 0.678927 0.0900 1.016519 1.227105 -0.104830 -0.283490 -0.782200 0.124327 -0.014290 3.023759 -0.440030 0.590472 0.677846 0.0950 0.973402 1.256189 -0.105520 -0.265790 -0.769890 0.118147 -0.014190 3.026574 -0.461320 0.582793 0.678857 0.1000 0.925401 1.287379 -0.111830 -0.231010 -0.757490 0.112731 -0.014100 2.985996 -0.486610 0.576948 0.679655 0.1100 0.875791 1.340574 -0.116550 -0.209500 -0.742660 0.103309 -0.013870 2.968454 -0.527410 0.558266 0.681101 0.1200 0.828032 1.383584 -0.119730 -0.132090 -0.732610 0.093477 -0.013580 3.122213 -0.561160 0.541827 0.683444 0.1300 0.766340 1.428531 -0.122180 -0.099120 -0.723060 0.084934 -0.013250 3.123764 -0.604790 0.522968 0.685163 0.1330 0.752926 1.440635 -0.123390 -0.090410 -0.722610 0.082770 -0.013130 3.162190 -0.617940 0.520507 0.685210 0.1400 0.737791 1.468425 -0.127720 -0.075320 -0.724260 0.077987 -0.012880 3.286426 -0.645450 0.512704 0.684238 0.1500 0.736715 1.504067 -0.130450 -0.040160 -0.733400 0.071440 -0.012490 3.554848 -0.683200 0.500299 0.686074 0.1600 0.749177 1.525331 -0.132690 -0.029340 -0.750100 0.069666 -0.012040 3.687601 -0.723930 0.488304 0.689339 0.1700 0.760213 1.540786 -0.138410 -0.015620 -0.766220 0.069663 -0.011610 3.781996 -0.760640 0.475100 0.688702 0.1800 0.739452 1.563804 -0.138710 -0.021800 -0.775680 0.068009 -0.011250 3.856147 -0.790880 0.462568 0.686140 0.1900 0.730298 1.570019 -0.144490 -0.004910 -0.787040 0.069004 -0.010850 3.868169 -0.815350 0.452189 0.680811 0.2000 0.699276 1.588260 -0.149360 0.020797 -0.791930 0.067300 -0.010520 3.870361 -0.834000 0.441413 0.676819 0.2200 0.659139 1.637386 -0.161840 0.057295 -0.809450 0.063984 -0.009850 4.011015 -0.865780 0.430961 0.665048 0.2400 0.585197 1.670581 -0.168330 0.047490 -0.816190 0.063724 -0.009460 4.030252 -0.907470 0.418078 0.657967 0.2500 0.544202 1.676278 -0.169680 0.066640 -0.819600 0.065290 -0.009280 3.969146 -0.930390 0.414367 0.656646 0.2600 0.518890 1.690318 -0.172100 0.079712 -0.827790 0.064973 -0.009020 4.004102 -0.950260 0.407553 0.654576 0.2800 0.468023 1.718140 -0.171930 0.096277 -0.843840 0.063219 -0.008490 4.088128 -0.970900 0.402642 0.655900 0.2900 0.449715 1.730149 -0.173960 0.103671 -0.852910 0.063330 -0.008210 4.161005 -0.978320 0.400506 0.654953 0.3000 0.438012 1.742259 -0.179910 0.116360 -0.861500 0.063859 -0.008000 4.217235 -0.982850 0.398426 0.654131 0.3200 0.435852 1.767679 -0.189340 0.128703 -0.883920 0.064745 -0.007540 4.439888 -0.987550 0.393950 0.650810 0.3400 0.404536 1.797985 -0.195110 0.115054 -0.899800 0.064053 -0.007100 4.399340 -0.993250 0.384897 0.649751 0.3500 0.382972 1.810384 -0.197220 0.099968 -0.906200 0.064678 -0.006920 4.368682 -0.999760 0.384327 0.649189 0.3600 0.349214 1.821998 -0.198100 0.084615 -0.908870 0.065198 -0.006770 4.366836 -1.006870 0.385376 0.648155 0.3800 0.280029 1.840613 -0.202330 0.060432 -0.910860 0.067799 -0.006580 4.269163 -1.013800 0.384998 0.647082 0.4000 0.216017 1.862263 -0.206160 0.067862 -0.915170 0.068428 -0.006360 4.254286 -1.016590 0.383209 0.648535 0.4200 0.172509 1.879301 -0.212120 0.083118 -0.924180 0.070022 -0.006110 4.267693 -1.014390 0.380057 0.646898 0.4400 0.139057 1.894512 -0.220880 0.096344 -0.933450 0.072375 -0.005880 4.267138 -1.008760 0.378131 0.645543 0.4500 0.123479 1.903496 -0.223920 0.098657 -0.938110 0.072849 -0.005780 4.314011 -1.007770 0.377127 0.645109 0.4600 0.092663 1.914621 -0.226230 0.113557 -0.939190 0.072457 -0.005700 4.373658 -1.006970 0.374313 0.644466 0.4800 0.064142 1.925415 -0.231520 0.119283 -0.950590 0.074303 -0.005460 4.503590 -1.004980 0.376973 0.642511 0.5000 0.015134 1.933643 -0.229620 0.126283 -0.957250 0.074768 -0.005220 4.570597 -1.004220 0.378237 0.639470 0.5500 -0.107970 1.951700 -0.239610 0.164680 -0.971840 0.078830 -0.004640 4.510815 -1.006060 0.383912 0.635885 0.6000 -0.210030 1.967164 -0.235140 0.136069 -0.988640 0.082926 -0.004190 4.583048 -1.003190 0.397759 0.634794 0.6500 -0.318340 1.994321 -0.231640 0.106534 -0.998240 0.085986 -0.003910 4.624840 -0.997570 0.410119 0.631284 0.6670 -0.377670 1.999595 -0.227650 0.094506 -0.995190 0.087318 -0.003870 4.550387 -0.994190 0.415335 0.630272 0.7000 -0.461320 2.010666 -0.224060 0.086120 -0.997760 0.089917 -0.003720 4.398042 -0.984550 0.421072 0.626758 0.7500 -0.602990 2.023635 -0.222370 0.039362 -0.994020 0.095549 -0.003580 4.174297 -0.964820 0.430431 0.623797 0.8000 -0.737520 2.041943 -0.218890 0.054982 -0.990400 0.097224 -0.003500 4.062969 -0.942860 0.437310 0.622591 0.8500 -0.833250 2.058361 -0.213530 0.031862 -0.997750 0.099138 -0.003280 4.055099 -0.929260 0.442478 0.625612 0.9000 -0.913750 2.082115 -0.206790 -0.001830 -1.006360 0.098959 -0.003070 4.199566 -0.928390 0.455462 0.624580 0.9500 -1.027550 2.107107 -0.200650 -0.029910 -1.003330 0.097355 -0.002960 4.189130 -0.924830 0.471674 0.622931 1.0000 -1.116170 2.130210 -0.201780 -0.017300 -1.006680 0.096426 -0.002820 4.231572 -0.915310 0.479707 0.620973 1.1000 -1.281600 2.155173 -0.200600 -0.030950 -1.013040 0.100472 -0.002480 4.180282 -0.892360 0.490696 0.618982 1.2000 -1.541750 2.181763 -0.180260 -0.031330 -0.995630 0.098812 -0.002330 4.022894 -0.881650 0.502163 0.615611 1.3000 -1.695110 2.211878 -0.169820 -0.049360 -0.999650 0.098186 -0.002050 4.073868 -0.868980 0.520770 0.609101 1.4000 -1.843290 2.235781 -0.158540 -0.008240 -1.008190 0.095328 -0.001720 4.219321 -0.867660 0.529452 0.604887 1.5000 -1.901680 2.229950 -0.155900 0.012115 -1.032620 0.100703 -0.001370 4.401009 -0.852200 0.540605 0.604146 1.6000 -2.008610 2.256904 -0.159130 0.035439 -1.040790 0.100755 -0.001170 4.443051 -0.831210 0.544404 0.600164 1.7000 -2.131090 2.258859 -0.146030 0.043698 -1.043480 0.098506 -0.001000 4.642552 -0.809230 0.550368 0.599125 1.8000 -2.212390 2.282670 -0.148270 0.043236 -1.051520 0.098118 -0.000850 4.880542 -0.796600 0.556535 0.598574 1.9000 -2.293230 2.330732 -0.162870 0.083305 -1.059710 0.094681 -0.000660 5.151302 -0.795890 0.550160 0.597577 2.0000 -2.335640 2.339893 -0.153660 0.062914 -1.081170 0.095849 -0.000450 5.404803 -0.782790 0.548455 0.594664 2.2000 -2.583710 2.328118 -0.106080 0.085979 -1.070680 0.090160 -0.000490 5.458659 -0.769760 0.555283 0.596546 2.4000 -2.757660 2.366893 -0.099200 0.137943 -1.065930 0.082511 -0.000430 5.577205 -0.759120 0.555954 0.590970 2.5000 -2.911190 2.389345 -0.094020 0.174453 -1.039020 0.077098 -0.000670 5.662470 -0.738660 0.558695 0.589879 2.6000 -2.980700 2.436770 -0.110630 0.259638 -1.035520 0.070752 -0.000670 5.977967 -0.728720 0.558466 0.587132 2.8000 -2.985610 2.403452 -0.093490 0.313060 -1.067010 0.072788 -0.000570 6.541798 -0.685760 0.523922 0.589979 3.0000 -3.118900 2.396847 -0.081150 0.381270 -1.063110 0.070630 -0.000670 6.815989 -0.676270 0.524274 0.591716 3.2000 -3.296140 2.418203 -0.071370 0.439181 -1.046650 0.065154 -0.000810 7.011276 -0.663990 0.515799 0.592432 3.4000 -3.296240 2.441129 -0.094510 0.479797 -1.057270 0.067191 -0.000870 7.209539 -0.651160 0.522075 0.588690 3.5000 -3.327090 2.441528 -0.090670 0.504891 -1.062860 0.068069 -0.000870 7.507757 -0.643560 0.523420 0.584815 3.6000 -3.476920 2.457411 -0.074510 0.540008 -1.039050 0.062581 -0.001010 7.768941 -0.632120 0.534581 0.581911 3.8000 -3.568780 2.414174 -0.066080 0.556090 -1.035910 0.071428 -0.001140 7.884801 -0.631060 0.538444 0.573748 4.0000 -3.719730 2.410756 -0.062210 0.581531 -1.020870 0.075380 -0.001280 7.944414 -0.617710 0.530623 0.568737 """)
[docs]class BindiEtAl2017Rhypo(BindiEtAl2017Rjb): """ Version of the Bindi et al. (2017) GMPE using hypocentral distance. """ #: Required distance measure is Rhypo (eq. 1). REQUIRES_DISTANCES = set(('rhypo', )) # Hypocentral COEFFS = CoeffsTable(sa_damping=5, table="""\ imt e1 b1 b2 b3 c1 c2 c3 sA tau phi pga 1.494544 1.514441 -0.09357000 0.33240700 -1.15213 0.09175100 -0.00930000 -0.61492 0.50156400 0.63757400 0.0100 1.494544 1.514441 -0.09357000 0.33240700 -1.15213 0.09175100 -0.00930000 -0.61492 0.50156400 0.63757400 0.0200 1.570345 1.503896 -0.09074000 0.32841500 -1.16673 0.09346100 -0.00929000 -0.59877 0.50877700 0.64092400 0.0220 1.610601 1.494865 -0.08933000 0.32517400 -1.17294 0.09459200 -0.00929000 -0.58954 0.51221500 0.64221300 0.0250 1.715268 1.466781 -0.08502000 0.31234200 -1.19098 0.09800100 -0.00927000 -0.56930 0.52020600 0.64762700 0.0290 1.861380 1.428625 -0.08179000 0.29794300 -1.21392 0.10342500 -0.00933000 -0.53904 0.53402200 0.65550100 0.0300 1.886291 1.421821 -0.08125000 0.29616200 -1.21608 0.10426900 -0.00937000 -0.53074 0.53642400 0.65719700 0.0320 1.923407 1.413206 -0.07893000 0.28318900 -1.21652 0.10507100 -0.00949000 -0.51611 0.54071300 0.66029500 0.0350 1.998679 1.392584 -0.07470000 0.26943700 -1.22112 0.10705800 -0.00968000 -0.49500 0.54785700 0.66475400 0.0360 2.028152 1.381789 -0.07285000 0.26414200 -1.22348 0.10849800 -0.00975000 -0.48678 0.55085900 0.66638200 0.0400 2.109385 1.353035 -0.06875000 0.25141800 -1.22451 0.11223800 -0.01006000 -0.45885 0.56311600 0.66891400 0.0420 2.130849 1.348203 -0.06893000 0.24849100 -1.21988 0.11301400 -0.01024000 -0.45157 0.56809300 0.67111500 0.0440 2.139374 1.342776 -0.07114000 0.25033600 -1.21041 0.11427900 -0.01046000 -0.44371 0.57433300 0.67347500 0.0450 2.139921 1.339719 -0.07243000 0.25529700 -1.20457 0.11480000 -0.01059000 -0.44030 0.57857200 0.67536700 0.0460 2.145808 1.338217 -0.07400000 0.25986500 -1.20022 0.11514700 -0.01070000 -0.43746 0.58288600 0.67695800 0.0480 2.164007 1.332446 -0.07590000 0.25331300 -1.19373 0.11626200 -0.01088000 -0.43129 0.58957800 0.68023800 0.0500 2.158757 1.332431 -0.07709000 0.24452000 -1.18335 0.11620700 -0.01106000 -0.42897 0.59230900 0.68296200 0.0550 2.192883 1.332603 -0.07585000 0.25047800 -1.17146 0.11400500 -0.01137000 -0.43164 0.60146300 0.68639100 0.0600 2.164618 1.329451 -0.07168000 0.26589700 -1.14287 0.11339100 -0.01179000 -0.42686 0.60562500 0.68874400 0.0650 2.169851 1.332136 -0.06863000 0.28788100 -1.12631 0.11130800 -0.01205000 -0.42078 0.60763400 0.69027700 0.0670 2.159330 1.331516 -0.06817000 0.29447400 -1.11649 0.11084400 -0.01218000 -0.41964 0.60815200 0.68978000 0.0700 2.138568 1.336694 -0.06819000 0.31214000 -1.10021 0.10913800 -0.01237000 -0.41914 0.61004800 0.68803200 0.0750 2.088161 1.370326 -0.06962000 0.34301300 -1.07214 0.10181800 -0.01259000 -0.41729 0.60913500 0.68604000 0.0800 2.013020 1.409712 -0.06915000 0.36648400 -1.04365 0.09311800 -0.01272000 -0.42000 0.60454300 0.68316700 0.0850 1.926213 1.447195 -0.06540000 0.37911800 -1.01749 0.08490100 -0.01277000 -0.42717 0.59996000 0.68264100 0.0900 1.863184 1.490262 -0.06411000 0.41339200 -1.00019 0.07517100 -0.01271000 -0.44537 0.59525600 0.68178700 0.0950 1.816356 1.524769 -0.06400000 0.44298200 -0.98736 0.06745900 -0.01261000 -0.46721 0.58942800 0.68276300 0.1000 1.769731 1.561097 -0.07001000 0.48625300 -0.97568 0.06073600 -0.01250000 -0.49272 0.58237600 0.68358000 0.1100 1.713437 1.627587 -0.07485000 0.52838300 -0.95971 0.04800300 -0.01228000 -0.53342 0.56406700 0.68482000 0.1200 1.650659 1.679477 -0.07830000 0.62138000 -0.94611 0.03595100 -0.01200000 -0.56717 0.54751100 0.68670900 0.1300 1.587248 1.736100 -0.08075000 0.67076800 -0.93659 0.02452600 -0.01167000 -0.61086 0.52868700 0.68824800 0.1303 1.572885 1.750059 -0.08207000 0.68211600 -0.93605 0.02189100 -0.01155000 -0.62402 0.52600300 0.68838000 0.1400 1.552383 1.779373 -0.08622000 0.69997700 -0.93656 0.01664200 -0.01130000 -0.65256 0.51624500 0.68789600 0.1500 1.542832 1.822970 -0.08971000 0.74863400 -0.94369 0.00828200 -0.01093000 -0.68928 0.50509700 0.68942400 0.1600 1.560224 1.853572 -0.09209000 0.76894100 -0.96193 0.00426100 -0.01046000 -0.73004 0.49248800 0.69259000 0.1700 1.579203 1.874846 -0.09809000 0.78589400 -0.98040 0.00282000 -0.01001000 -0.76676 0.47859900 0.69214900 0.1800 1.560126 1.900628 -0.09861000 0.78013100 -0.99052 0.00046300 -0.00964000 -0.79702 0.46530800 0.69022300 0.1900 1.561523 1.913600 -0.10464000 0.79985100 -1.00487 -0.00025000 -0.00923000 -0.82148 0.45437400 0.68465600 0.2000 1.534762 1.937215 -0.10968000 0.82878000 -1.01098 -0.00329000 -0.00888000 -0.84010 0.44301400 0.68059700 0.2200 1.486267 1.990180 -0.12257000 0.86321000 -1.02611 -0.00754000 -0.00824000 -0.87190 0.43256700 0.66935000 0.2400 1.407764 2.026004 -0.12928000 0.84990100 -1.03164 -0.00851000 -0.00786000 -0.91362 0.41991800 0.66273500 0.2500 1.375784 2.032175 -0.13109000 0.86268700 -1.03746 -0.00701000 -0.00766000 -0.93658 0.41548000 0.66200600 0.2600 1.352420 2.047970 -0.13334000 0.87710100 -1.04635 -0.00787000 -0.00740000 -0.95647 0.40921100 0.66013800 0.2800 1.310876 2.087583 -0.13339000 0.90472700 -1.06524 -0.01251000 -0.00685000 -0.97718 0.40352100 0.66127700 0.2900 1.288881 2.100521 -0.13569000 0.90948300 -1.07335 -0.01267000 -0.00658000 -0.98462 0.40096600 0.66060000 0.3000 1.275442 2.114611 -0.14176000 0.92162200 -1.08149 -0.01264000 -0.00637000 -0.98919 0.39883000 0.65986500 0.3200 1.255382 2.138187 -0.15163000 0.92530000 -1.09884 -0.01132000 -0.00595000 -0.99388 0.39422400 0.65689500 0.3400 1.234872 2.175803 -0.15724000 0.91628300 -1.11747 -0.01372000 -0.00551000 -0.99965 0.38489700 0.65633800 0.3500 1.214958 2.188117 -0.15939000 0.89716700 -1.12411 -0.01305000 -0.00532000 -1.00617 0.38438500 0.65620900 0.3600 1.178177 2.198759 -0.16041000 0.87692100 -1.12582 -0.01232000 -0.00519000 -1.01325 0.38563900 0.65527800 0.3800 1.117221 2.213072 -0.16498000 0.83988600 -1.12981 -0.00874000 -0.00498000 -1.02015 0.38538000 0.65455800 0.4000 1.053371 2.231908 -0.16904000 0.83842700 -1.13403 -0.00745000 -0.00477000 -1.02292 0.38398900 0.65644500 0.4200 1.014572 2.248211 -0.17528000 0.84750800 -1.14429 -0.00570000 -0.00452000 -1.02071 0.38116300 0.65503100 0.4400 0.988765 2.263190 -0.18432000 0.85492200 -1.15559 -0.00333000 -0.00427000 -1.01503 0.37938500 0.65371600 0.4500 0.971080 2.271611 -0.18755000 0.85507600 -1.15965 -0.00273000 -0.00418000 -1.01402 0.37821100 0.65322600 0.4600 0.934947 2.278561 -0.18987000 0.86410300 -1.15919 -0.00227000 -0.00411000 -1.01319 0.37542700 0.65263700 0.4800 0.890134 2.282694 -0.19561000 0.85586000 -1.16594 0.00115000 -0.00392000 -1.01115 0.37804600 0.65100100 0.5000 0.837695 2.288490 -0.19402000 0.85597200 -1.17172 0.00211100 -0.00369000 -1.01039 0.37890200 0.64813900 0.5500 0.730056 2.304199 -0.20478000 0.87788100 -1.19033 0.00661400 -0.00308000 -1.01218 0.38382600 0.64484800 0.6000 0.620431 2.321087 -0.20035000 0.84052000 -1.20522 0.01013500 -0.00265000 -1.00922 0.39717400 0.64339000 0.6500 0.515740 2.346797 -0.19738000 0.79998800 -1.21571 0.01357000 -0.00237000 -1.00356 0.40864100 0.63980100 0.6670 0.464230 2.351350 -0.19355000 0.78406800 -1.21478 0.01501100 -0.00231000 -1.00016 0.41360900 0.63869800 0.7000 0.400679 2.363368 -0.18899000 0.77142200 -1.22305 0.01705500 -0.00211000 -0.99075 0.41944700 0.63539300 0.7500 0.263690 2.363957 -0.18745000 0.69625900 -1.22008 0.02550900 -0.00197000 -0.97102 0.42917900 0.63348100 0.8000 0.129816 2.375162 -0.18395000 0.69659900 -1.21642 0.02879900 -0.00189000 -0.94913 0.43599900 0.63299400 0.8500 0.025422 2.392046 -0.17872000 0.66186200 -1.22113 0.03092100 -0.00170000 -0.93538 0.44140600 0.63645800 0.9000 -0.069930 2.411239 -0.17222000 0.62036500 -1.22569 0.03175500 -0.00153000 -0.93452 0.45399700 0.63563800 0.9500 -0.169440 2.440097 -0.16570000 0.59649300 -1.22731 0.02900700 -0.00136000 -0.93139 0.47009100 0.63398700 1.0000 -0.265860 2.458374 -0.16692000 0.60123700 -1.22842 0.02921500 -0.00125000 -0.92189 0.47768700 0.63264900 1.1000 -0.416510 2.470917 -0.16339000 0.55695800 -1.23923 0.03553300 -0.00087000 -0.89927 0.48787700 0.63147600 1.2000 -0.676110 2.489858 -0.14316000 0.54136400 -1.22206 0.03537000 -0.00072000 -0.88874 0.49853000 0.62884300 1.3000 -0.852810 2.521182 -0.13235000 0.51865900 -1.21955 0.03436000 -0.00051000 -0.87598 0.51607900 0.62246900 1.4000 -1.027320 2.541416 -0.11945000 0.55094900 -1.22072 0.03196700 -0.00025000 -0.87443 0.52496000 0.61893700 1.5000 -1.091190 2.533838 -0.11504000 0.56338100 -1.24382 0.03696100 0.00008140 -0.85909 0.53547200 0.61796200 1.6000 -1.203170 2.569142 -0.12202000 0.59349300 -1.25013 0.03601600 0.00027400 -0.83843 0.53827100 0.61437200 1.7000 -1.342010 2.567601 -0.10904000 0.59760200 -1.24860 0.03440000 0.00041600 -0.81596 0.54366400 0.61391700 1.8000 -1.464790 2.583144 -0.11012000 0.58584200 -1.24529 0.03546200 0.00047500 -0.80287 0.54944500 0.61386400 1.9000 -1.588030 2.626960 -0.12239000 0.62424800 -1.24246 0.03210200 0.00058900 -0.80291 0.54388400 0.61357700 2.0000 -1.665130 2.630186 -0.11339000 0.59597700 -1.25353 0.03463800 0.00068900 -0.78964 0.54160400 0.61145600 2.2000 -1.963860 2.603575 -0.06043000 0.61244200 -1.22940 0.03030700 0.00054700 -0.77741 0.54894500 0.61511200 2.4000 -2.200470 2.650725 -0.05391000 0.67350500 -1.20835 0.02147900 0.00048400 -0.76743 0.55054600 0.61181100 2.5000 -2.394560 2.662607 -0.05076000 0.69011300 -1.16970 0.01964100 0.00014000 -0.74665 0.55237900 0.61151800 2.6000 -2.518890 2.699475 -0.06517000 0.76896700 -1.15124 0.01503400 0.00001320 -0.73657 0.55053000 0.60974800 2.8000 -2.632480 2.659062 -0.04832000 0.80778700 -1.15291 0.01954700 -0.00013000 -0.69291 0.51851600 0.61430300 3.0000 -2.841610 2.639776 -0.03570000 0.85876400 -1.12781 0.02050000 -0.00043000 -0.68331 0.51793400 0.61678100 3.2000 -3.079350 2.656785 -0.02557000 0.91052300 -1.09559 0.01631800 -0.00069000 -0.66901 0.51229200 0.61741600 3.4000 -3.053530 2.708866 -0.05286000 0.94438500 -1.11408 0.01575500 -0.00066000 -0.65883 0.51883900 0.61307300 3.5000 -3.123440 2.700877 -0.04946000 0.96057000 -1.10921 0.01845800 -0.00074000 -0.65059 0.51995800 0.60896600 3.6000 -3.315890 2.703451 -0.03308000 0.98451700 -1.07375 0.01543600 -0.00097000 -0.63882 0.53285400 0.60589900 3.8000 -3.428990 2.646549 -0.02495000 0.97546100 -1.06479 0.02724100 -0.00115000 -0.63825 0.53727300 0.59715100 4.0000 -3.599560 2.629226 -0.02208000 0.97803700 -1.04398 0.03440400 -0.00134000 -0.62463 0.52996100 0.59149600 """)