Help on module particula.util.radius_cutoff in particula.util:
NAME
particula.util.radius_cutoff - determing the radius cutoff for particle distribution
FUNCTIONS
cut_rad(cutoff=array(0.9999), gsigma=array(1.25), mode=<Quantity(1e-07, 'meter')>, force_radius_start=None, force_radius_end=None, **kwargs)
This routine determins the radius cutoff for the particle distribution
Inputs:
cutoff (float) coverage cutoff (default: .9999)
gsigma (float) geometric standard deviation (default: 1.25)
mode (float) mean radius of the particles (default: 1e-7)
Returns:
(starting radius, ending radius) float tuple
DATA
lognorm = <scipy.stats._continuous_distns.lognorm_gen object>
A lognormal continuous random variable.
As an instance of the `rv_continuous` class, `lognorm` object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.
Methods
-------
rvs(s, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, s, loc=0, scale=1)
Probability density function.
logpdf(x, s, loc=0, scale=1)
Log of the probability density function.
cdf(x, s, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, s, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, s, loc=0, scale=1)
Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, s, loc=0, scale=1)
Log of the survival function.
ppf(q, s, loc=0, scale=1)
Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, s, loc=0, scale=1)
Inverse survival function (inverse of ``sf``).
moment(order, s, loc=0, scale=1)
Non-central moment of the specified order.
stats(s, loc=0, scale=1, moments='mv')
Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(s, loc=0, scale=1)
(Differential) entropy of the RV.
fit(data)
Parameter estimates for generic data.
See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
keyword arguments.
expect(func, args=(s,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
Expected value of a function (of one argument) with respect to the distribution.
median(s, loc=0, scale=1)
Median of the distribution.
mean(s, loc=0, scale=1)
Mean of the distribution.
var(s, loc=0, scale=1)
Variance of the distribution.
std(s, loc=0, scale=1)
Standard deviation of the distribution.
interval(confidence, s, loc=0, scale=1)
Confidence interval with equal areas around the median.
Notes
-----
The probability density function for `lognorm` is:
.. math::
f(x, s) = \frac{1}{s x \sqrt{2\pi}}
\exp\left(-\frac{\log^2(x)}{2s^2}\right)
for :math:`x > 0`, :math:`s > 0`.
`lognorm` takes ``s`` as a shape parameter for :math:`s`.
The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``lognorm.pdf(x, s, loc, scale)`` is identically
equivalent to ``lognorm.pdf(y, s) / scale`` with
``y = (x - loc) / scale``. Note that shifting the location of a distribution
does not make it a "noncentral" distribution; noncentral generalizations of
some distributions are available in separate classes.
Suppose a normally distributed random variable ``X`` has mean ``mu`` and
standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
distributed with ``s = sigma`` and ``scale = exp(mu)``.
Examples
--------
>>> import numpy as np
>>> from scipy.stats import lognorm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> s = 0.954
>>> mean, var, skew, kurt = lognorm.stats(s, moments='mvsk')
Display the probability density function (``pdf``):
>>> x = np.linspace(lognorm.ppf(0.01, s),
... lognorm.ppf(0.99, s), 100)
>>> ax.plot(x, lognorm.pdf(x, s),
... 'r-', lw=5, alpha=0.6, label='lognorm 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 = lognorm(s)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of ``cdf`` and ``ppf``:
>>> vals = lognorm.ppf([0.001, 0.5, 0.999], s)
>>> np.allclose([0.001, 0.5, 0.999], lognorm.cdf(vals, s))
True
Generate random numbers:
>>> r = lognorm.rvs(s, size=1000)
And compare the histogram:
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
The logarithm of a log-normally distributed random variable is
normally distributed:
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy import stats
>>> fig, ax = plt.subplots(1, 1)
>>> mu, sigma = 2, 0.5
>>> X = stats.norm(loc=mu, scale=sigma)
>>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
>>> x = np.linspace(*X.interval(0.999))
>>> y = Y.rvs(size=10000)
>>> ax.plot(x, X.pdf(x), label='X (pdf)')
>>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
>>> ax.legend()
>>> plt.show()
u = <pint.registry.UnitRegistry object>
FILE
/opt/hostedtoolcache/Python/3.11.9/x64/lib/python3.11/site-packages/particula/util/radius_cutoff.py
