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lines 5-69 of file: xrst/table/age_avg_table.xrst
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{xrst_begin age_avg_table}

The Age Average Table
#####################

Age Average Grid
****************
We use
:ref:`age_table@age@age_min` ,
:ref:`age_table@age@age_max` ,
to denote the minimum and maximum ages in the age table.
We use :ref:`option_table@Age Average Grid@ode_step_size`
to denote its value in the option table.
Let *N*  >= 1 be the minimum integer such that

    *s* = ( *age_max* ``-`` *age_min* ) / *N* <= *ode_step_size*

Define the set of age points
:math:`a_i = i * s` for :math:`i = 0, \ldots , N`, and define the set

.. math::

    S = \{ a_0, a_1 , \ldots , a_N \}

Note that :math:`a_0` is *age_min*
and :math:`a_N` is *age_max* .
The age average grid is the union of the set :math:`S`
and the set of age points in
:ref:`option_table@Age Average Grid@age_avg_split` .
This grid is used both for
:ref:`approximating averages<numeric_average-name>`
and for approximation the solution of the dismod_at
:ref:`avg_integrand@Ordinary Differential Equation` .
If :ref:`option_table@Age Average Grid@age_avg_split` is the empty set,
the age average grid is the set :math:`S`.

Creation
********
This table changes each time the
:ref:`option_table@Age Average Grid@ode_step_size` or the
:ref:`option_table@Age Average Grid@age_avg_split` changes.
These value can change without having to re-execute the
:ref:`init_command-name` .
For this reason, this table is re-written for each command
with the exception of the following:
:ref:`set<set_command-name>` ,
:ref:`db2csv<db2csv_command-name>` ,
:ref:`csv2db<csv2db_command-name>` ,
and
:ref:`modify<modify_command-name>` .

age_avg_id
**********
This column has type ``integer`` and is the primary key for
the this table.
Its initial value is zero, and it increments by one for each row.

age
***
This column has type ``real`` and is a monotone
increasing values in the age average grid.
The values are unique; i.e.,
none of the values are repeated.

{xrst_end age_avg_table}