---------------------------------------------------------
lines 6-89 of file: python/dismod_at/average_integrand.py
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{xrst_begin average_integrand}
{xrst_spell
  tol
}

Compute The Average Integrand
#############################

Syntax
******
{xrst_literal
   # BEGIN_AVERAGE_INTEGRAND
   # END_AVERAGE_INTEGRAND
}
{xrst_literal
   # BEGIN_RETURN
   # END_RETURN
}

Purpose
*******
The :ref:`predict_command-name` is a much faster way to calculate these values.
This routine is easier to use and provides independent testing of the
dismod_at integrators.

rate_fun
********
This is a dictionary and it's possible keys are the
:ref:`rate names<rate_table@rate_name>` .
If a *key* is a key in the dictionary,

   *value* = *rate_fun* [ *key* ]( *age* , *time* )

returns a float equal to the value of the specified rate
at the specified age and time (where *age* and *time* are floats).
Note that *age* will always be zero when evaluating

   *value* = *rate_fun* [ ``'pini'`` ]( *age* , *time* )

If a rate name is not in the *rate_fun*, the corresponding rate is zero.

integrand_name
**************
This string is one of the
:ref:`integrand names<integrand_table@integrand_name>` .

grid
****
This argument defines the grid for trapezoidal integration.
(The dismod_at integrands are often non-smooth and so a low order integration
method is called for.)
The *grid* is a dictionary with the following keys:

age
===
*grid* [ ``'age'`` ] is a list of floats containing the grid points
for the average w.r.t. age.
These points are monotone increasing, the first (last) point is the
lower (upper) age limit for the average

time
====
*grid* [ ``'time'`` ] is a list of floats containing the grid points
for the average w.r.t. time.
These points are monotone increasing, the first (last) point is the
lower (upper) time limit for the average

abs_tol
*******
This float is an absolute error bound, that the integrator will achieve.

avg
***
The return value *avg* is the corresponding
:ref:`average integrand<avg_integrand@Average Integrand, A_i>` .
{xrst_toc_hidden
   example/user/average_integrand.py
}

Example
*******
The file :ref:`user_average_integrand.py-name` contains an example and test of this routine.

{xrst_end average_integrand}