def anglevalue(phi,theta):
x = np.cos(phi)*np.sin(theta)
y = np.sin(phi)*np.sin(theta)
z = np.cos(theta)
xangle = np.arccos(x)
rv = cosine()
return rv.pdf(xangle*2 - np.pi)
def test_cosine(self):
from scipy.stats import cosine
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = cosine.stats(moments='mvsk')
x = np.linspace(cosine.ppf(0.01), cosine.ppf(0.99), 100)
ax.plot(x, cosine.pdf(x), 'r-', lw=5, alpha=0.6, label='cosine pdf')
rv = cosine()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
vals = cosine.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], cosine.cdf(vals))
r = cosine.rvs(size=1000)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
self.assertEqual(str(ax), "AxesSubplot(0.125,0.11;0.775x0.77)")
ax.xaxis.set_major_formatter(plt.NullFormatter())
# trick to show multiple legends
leg1 = ax.legend([l1], [l1.get_label()], loc=1)
leg2 = ax.legend([l2, l3], (l2.get_label(), l3.get_label()), loc=2)
ax.add_artist(leg1)
ax.set_title('Skew $\Sigma$ and Kurtosis $K$')
# next show distributions with different kurtosis
ax = fig.add_subplot(212)
x = np.linspace(-5, 5, 1000)
l1, = ax.plot(x, stats.laplace(0, 1).pdf(x), '--k',
label=r'${\rm Laplace,}\ K=+3$')
l2, = ax.plot(x, stats.norm(0, 1).pdf(x), '-k',
label=r'${\rm Gaussian,}\ K=0$')
l3, = ax.plot(x, stats.cosine(0, 1).pdf(x), '-.k',
label=r'${\rm Cosine,}\ K=-0.59$')
l4, = ax.plot(x, stats.uniform(-2, 4).pdf(x), ':k',
label=r'${\rm Uniform,}\ K=-1.2$')
ax.set_xlim(-5, 5)
ax.set_ylim(0, 0.55)
ax.set_xlabel('$x$')
ax.set_ylabel('$p(x)$')
# trick to show multiple legends
leg1 = ax.legend((l1, l2), (l1.get_label(), l2.get_label()), loc=2)
leg2 = ax.legend((l3, l4), (l3.get_label(), l4.get_label()), loc=1)
ax.add_artist(leg1)
plt.show()
ax.set_xlim(-5, 5)
ax.set_ylim(0, 0.7001)
ax.set_ylabel("$p(x)$", fontsize=16)
ax.xaxis.set_major_formatter(plt.NullFormatter())
# trick to show multiple legends
leg1 = ax.legend([l1], [l1.get_label()], loc=1)
leg2 = ax.legend([l2, l3], (l2.get_label(), l3.get_label()), loc=2)
ax.add_artist(leg1)
ax.set_title("Skew $\Sigma$ and Kurtosis $K$")
# next show distributions with different kurtosis
ax = fig.add_subplot(212)
x = np.linspace(-5, 5, 1000)
l1, = ax.plot(x, stats.laplace(0, 1).pdf(x), "--k", label=r"${\rm Laplace,}\ K=+3$")
l2, = ax.plot(x, stats.norm(0, 1).pdf(x), "-k", label=r"${\rm Gaussian,}\ K=0$")
l3, = ax.plot(x, stats.cosine(0, 1).pdf(x), "-.k", label=r"${\rm Cosine,}\ K=-0.59$")
l4, = ax.plot(x, stats.uniform(-2, 4).pdf(x), ":k", label=r"${\rm Uniform,}\ K=-1.2$")
ax.set_xlim(-5, 5)
ax.set_ylim(0, 0.6001)
ax.set_xlabel("$x$", fontsize=16)
ax.set_ylabel("$p(x)$", fontsize=16)
# trick to show multiple legends
leg1 = ax.legend((l1, l2), (l1.get_label(), l2.get_label()), loc=2)
leg2 = ax.legend((l3, l4), (l3.get_label(), l4.get_label()), loc=1)
ax.add_artist(leg1)
plt.show()
try:
latrange = datarange.ParseArg(resargs['latrange'])
longrange = datarange.ParseArg(resargs['longrange'])
if latrange.lower < -90.0 or latrange.upper > 90.0:
raise datarange.DataRangeError("Invalid latitude range")
if longrange.lower < 0.0 or longrange.upper > 360.0:
raise datarange.DataRangeError("Invalid longitude range")
except datarange.DataRangeError as e:
print "Error in lat/long range", e.args[0]
sys.exit(13)
longs = nr.uniform(longrange.lower, longrange.upper, size=number)
sizes = np.sqrt(nr.uniform(mindeg**2, maxdeg**2, size=number))
if resargs['cosdist']:
cosrv = cosine(scale = 90.0 / np.pi)
while 1:
lats = cosrv.rvs(size = number * 4)
lats = lats[(lats >= latrange.lower) & (lats <= latrange.upper)]
if len(lats) >= number:
break
lats = lats[0:number]
else:
lats = nr.uniform(latrange.lower, latrange.upper, size=number)
prop = np.zeros_like(longs) + 1.99
gsize = np.zeros_like(longs) + 10.0
repos = longs.argsort()
longs = longs[repos]
lats = lats[repos]
mean, var, skew, kurt = cosine.stats(moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(cosine.ppf(0.01),
cosine.ppf(0.99), 100)
ax.plot(x, cosine.pdf(x),
'r-', lw=5, alpha=0.6, label='cosine pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = cosine()
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = cosine.ppf([0.001, 0.5, 0.999])
np.allclose([0.001, 0.5, 0.999], cosine.cdf(vals))
# True
# Generate random numbers:
r = cosine.rvs(size=1000)
# And compare the histogram:
ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
ax.add_artist(leg1)
ax.set_title('Skew $\Sigma$ and Kurtosis $K$')
# next show distributions with different kurtosis
ax = fig.add_subplot(212)
x = np.linspace(-5, 5, 1000)
l1, = ax.plot(x,
stats.laplace(0, 1).pdf(x),
'--k',
label=r'${\rm Laplace,}\ K=+3$')
l2, = ax.plot(x,
stats.norm(0, 1).pdf(x),
'-k',
label=r'${\rm Gaussian,}\ K=0$')
l3, = ax.plot(x,
stats.cosine(0, 1).pdf(x),
'-.k',
label=r'${\rm Cosine,}\ K=-0.59$')
l4, = ax.plot(x,
stats.uniform(-2, 4).pdf(x),
':k',
label=r'${\rm Uniform,}\ K=-1.2$')
ax.set_xlim(-5, 5)
ax.set_ylim(0, 0.6001)
ax.set_xlabel('$x$', fontsize=16)
ax.set_ylabel('$p(x)$', fontsize=16)
# trick to show multiple legends
leg1 = ax.legend((l1, l2), (l1.get_label(), l2.get_label()), loc=2)
leg2 = ax.legend((l3, l4), (l3.get_label(), l4.get_label()), loc=1)
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
def __init__(self,
hours_total=24,
day_fraction=0.5,
channels=None,
**kwargs):
"""
Initialize an irradiance source in the model domain
Args:
hours_total (int, float, PhysicalField): Number of hours in a diel period
day_fraction (float): Fraction (between 0 and 1) of diel period which is illuminated
(default: 0.5)
channels: See :meth:`.create_channel`
**kwargs: passed to superclass
"""
self.logger = kwargs.get('logger') or logging.getLogger(__name__)
self.logger.debug('Init in {}'.format(self.__class__.__name__))
kwargs['logger'] = self.logger
super(Irradiance, self).__init__(**kwargs)
#: the channels in the irradiance entity
self.channels = {}
#: the number of hours in a diel period
self.hours_total = PhysicalField(hours_total, 'h')
if not (1 <= self.hours_total.value <= 48):
raise ValueError('Hours total {} should be between (1, 48)'.format(
self.hours_total))
# TODO: remove (1, 48) hour constraint on hours_total
day_fraction = float(day_fraction)
if not (0 < day_fraction < 1):
raise ValueError("Day fraction should be between 0 and 1")
#: fraction of diel period that is illuminated
self.day_fraction = day_fraction
#: numer of hours in the illuminated fraction
self.hours_day = day_fraction * self.hours_total
#: the time within the diel period which is the zenith of radiation
self.zenith_time = self.hours_day
#: the intensity level at the zenith time
self.zenith_level = 100.0
C = 1.0 / numerix.sqrt(2 * numerix.pi)
# to scale the cosine distribution from 0 to 1 (at zenith)
self._profile = cosine(loc=self.zenith_time,
scale=C**2 * self.hours_day)
# This profile with loc=zenith means that the day starts at "midnight" and zenith occurs
# in the center of the daylength
#: a :class:`Variable` for the momentary radiance level at the surface
self.surface_irrad = Variable(name='irrad_surface',
value=0.0,
unit=None)
if channels:
for chinfo in channels:
self.create_channel(**chinfo)
self.logger.debug('Created Irradiance: {}'.format(self))
ax.xaxis.set_major_formatter(plt.NullFormatter())
# trick to show multiple legends
leg1 = ax.legend([l1], [l1.get_label()], loc=1)
leg2 = ax.legend([l2, l3], (l2.get_label(), l3.get_label()), loc=2)
ax.add_artist(leg1)
ax.set_title('Skew $\Sigma$ and Kurtosis $K$')
# next show distributions with different kurtosis
ax = fig.add_subplot(212)
x = np.linspace(-5, 5, 1000)
l1, = ax.plot(x, stats.laplace(0, 1).pdf(x), '--k',
label=r'${\rm Laplace,}\ K=+3$')
l2, = ax.plot(x, stats.norm(0, 1).pdf(x), '-k',
label=r'${\rm Gaussian,}\ K=0$')
l3, = ax.plot(x, stats.cosine(0, 1).pdf(x), '-.k',
label=r'${\rm Cosine,}\ K=-0.59$')
l4, = ax.plot(x, stats.uniform(-2, 4).pdf(x), ':k',
label=r'${\rm Uniform,}\ K=-1.2$')
ax.set_xlim(-5, 5)
ax.set_ylim(0, 0.55)
ax.set_xlabel('$x$')
ax.set_ylabel('$p(x)$')
# trick to show multiple legends
leg1 = ax.legend((l1, l2), (l1.get_label(), l2.get_label()), loc=2)
leg2 = ax.legend((l3, l4), (l3.get_label(), l4.get_label()), loc=1)
ax.add_artist(leg1)
plt.show()
