Function

NumCosmoMathIntegralFixedcalibrate

Declaration [src] 

NcmIntegralFixed*
ncm_integral_fixed_calibrate (
  gint* F,
  gint* G,
  gdouble xl,
  gdouble xu,
  gdouble reltol,
  gdouble exact_F_integ,
  gulong max_total_nodes,
  guint* n_nodes_out,
  guint* rule_n_out
)

Description [src]

Searches the $(n_\mathrm{nodes}, \mathrm{rule}_n)$ configuration space for the fixed Gauss-Legendre rule of minimal total node count whose estimate of $\int F(x) G(x) \mathrm{d}x$ over [xl, xu] matches a high-resolution reference (n_nodes = 1000, rule_n = 7) to within reltol. The selected configuration must additionally reproduce $\int F \mathrm{d}x$ (via

ncm_integral_fixed_nodes_eval) to within reltol — this catches an F feature

narrower than the reference panel width, where the $F\,G$ test alone could false-pass because both reference and trial straddle it. The guard baseline is exact_F_integ when finite, otherwise the reference’s own $\int F$.

For each candidate rule_n the threshold $n_\mathrm{nodes}$ is bracketed by geometric growth and then pinned exactly by bisection (assuming convergence is monotone in $n_\mathrm{nodes}$), so the returned configuration is the true minimal-total rule rather than a geometric overshoot.

If no configuration within max_total_nodes meets the tolerance, the configuration with the smallest $F\,G$ error seen is used and a warning is emitted.

This function is not directly available to language bindings.

Parameters

F

Type: gint*

A pointer to a gsl_function, the integration weight (baked into the nodes).

The data is owned by the caller of the function.
G

Type: gint*

A pointer to a gsl_function, the slowly-varying factor probed at the nodes.

The data is owned by the caller of the function.
xl

Type: gdouble

The interval lower limit.

xu

Type: gdouble

The interval upper limit.

reltol

Type: gdouble

Target relative tolerance.

exact_F_integ

Type: gdouble

The exact value of $\int F \mathrm{d}x$ over [xl, xu] for the missed-mass guard, or GSL_NAN to fall back to the reference’s own $\int F \mathrm{d}x$.

max_total_nodes

Type: gulong

Ceiling on the total node count $(n_\mathrm{nodes}-1)\,r$.

n_nodes_out

Type: guint*

Receives the selected number of nodes.

The argument will be set by the function.
rule_n_out

Type: guint*

Receives the selected Gauss-Legendre rule order.

The argument will be set by the function.

Return value

Type: NcmIntegralFixed

A newly allocated NcmIntegralFixed at the selected configuration, with F already baked into its nodes (see

ncm_integral_fixed_calc_nodes).

The caller of the function takes ownership of the data, and is responsible for freeing it.