Class
NumCosmoMathStatsDist1d
Description [src]
abstract class NumCosmoMath.StatsDist1d : GObject.Object
{
/* No available fields */
}Base class for one-dimensional probability distributions on $[x_i, x_f]$.
A subclass provides the density $p(x)$, which need not be normalized, and $-2\ln p(x)$.
With NcmStatsDist1d:compute-cdf, ncm_stats_dist1d_prepare() integrates the cumulative
distribution as an ODE to NcmStatsDist1d:reltol, in at least 1000 steps, and in units of
$p(x_\mathrm{mode})\,(x_f - x_i)$, so its accuracy depends neither on the scale of $p$ nor
on that of $x$. The inverse is a Steffen spline through the same knots with $x$ and the
probability swapped; it is monotone and stays in $[x_i, x_f]$. Setting $x_i = x_f$ gives a point mass at
$x_i$. The mode search uses an internal minimizer, so one object must not be used from
several threads at once.
Instance methods
ncm_stats_dist1d_eval_inv_pdf
Evaluates the inverse of the cumulative distribution, the $x$ with
$\int_{x_i}^x p(x^\prime)\,\mathrm{d}x^\prime = u$. Returns $x_i$ for $u \leq 0$ and $x_f$ for
$u \geq 1$. Requires NcmStatsDist1d:compute-cdf.
ncm_stats_dist1d_eval_inv_pdf_tail
Evaluates the $x$ with $\int_x^{x_f} p(x^\prime)\,\mathrm{d}x^\prime = v$, that is
ncm_stats_dist1d_eval_inv_pdf() at $1 - v$, so v below $\epsilon$ is not resolved.
Returns $x_f$ for $v \leq 0$ and $x_i$ for $v \geq 1$. Requires NcmStatsDist1d:compute-cdf.
ncm_stats_dist1d_eval_m2lnp
Evaluates $-2\ln p(x)$ of the density as given by the subclass, without the normalization, see ncm_stats_dist1d_eval_norma().
ncm_stats_dist1d_eval_mode
Locates the maximum of the density: the minimum of $-2\ln p$ on 1000 equally spaced
points, refined by Brent’s method between the two neighbouring grid points to a relative
tolerance $\sqrt{\mathrm{reltol}}$ and an absolute tolerance, the larger of
NcmStatsDist1d:abstol and $\sqrt{\mathrm{reltol}}$ times the grid spacing. The
absolute tolerance is what stops the refinement of a mode at zero.
When the two best grid points tie, Brent’s method refines between them. The grid point is
returned when it is $x_i$ or $x_f$, or when a neighbour has zero density.
Warns if the refinement stops before its tolerance, or leaves its bracket unchanged for
ten iterations.
ncm_stats_dist1d_eval_norma
Gets the integral of the subclass density over $[x_i, x_f]$, computed by
ncm_stats_dist1d_prepare(); 1 without NcmStatsDist1d:compute-cdf.
ncm_stats_dist1d_eval_p
Evaluates the density at x divided by the normalization. Without
NcmStatsDist1d:compute-cdf the normalization is 1 and the density is not normalized.
ncm_stats_dist1d_eval_pdf
Evaluates the cumulative distribution $\int_{x_i}^x p(x^\prime)\,\mathrm{d}x^\prime$.
Requires NcmStatsDist1d:compute-cdf; x is not checked.
ncm_stats_dist1d_gen
Draws a value from the distribution by inverting the cumulative distribution at a
uniform deviate. Requires NcmStatsDist1d:compute-cdf.
ncm_stats_dist1d_get_current_h
Gets the kernel bandwidth of a kernel density estimate. Aborts for a subclass that does not implement it.
ncm_stats_dist1d_prepare
Calls the subclass prepare and then, when $x_i \neq x_f$ and NcmStatsDist1d:compute-cdf is
TRUE, locates the mode, integrates the cumulative distribution and the normalization, and
builds the inverse. Must be called after changing $x_i$, $x_f$ or the density. Aborts if
$x_f < x_i$ or if the density at the mode is not positive and finite.
ncm_stats_dist1d_set_compute_cdf
Sets NcmStatsDist1d:compute-cdf. Without it ncm_stats_dist1d_prepare() computes neither
the normalization nor the cumulative distribution and its inverse.
Signals
Signals inherited from GObject (1)
GObject::notify
The notify signal is emitted on an object when one of its properties has its value set through g_object_set_property(), g_object_set(), et al.
Class structure
struct NumCosmoMathStatsDist1dClass {
gdouble (* p) (
NcmStatsDist1d* sd1,
gdouble x
);
gdouble (* m2lnp) (
NcmStatsDist1d* sd1,
gdouble x
);
void (* prepare) (
NcmStatsDist1d* sd1
);
gdouble (* get_current_h) (
NcmStatsDist1d* sd1
);
}No description available.
Class members
p: gdouble (* p) ( NcmStatsDist1d* sd1, gdouble x )No description available.
m2lnp: gdouble (* m2lnp) ( NcmStatsDist1d* sd1, gdouble x )No description available.
prepare: void (* prepare) ( NcmStatsDist1d* sd1 )No description available.
get_current_h: gdouble (* get_current_h) ( NcmStatsDist1d* sd1 )No description available.
Virtual methods
NumCosmoMath.StatsDist1dClass.get_current_h
Gets the kernel bandwidth of a kernel density estimate. Aborts for a subclass that does not implement it.
NumCosmoMath.StatsDist1dClass.prepare
Calls the subclass prepare and then, when $x_i \neq x_f$ and NcmStatsDist1d:compute-cdf is
TRUE, locates the mode, integrates the cumulative distribution and the normalization, and
builds the inverse. Must be called after changing $x_i$, $x_f$ or the density. Aborts if
$x_f < x_i$ or if the density at the mode is not positive and finite.