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lines 5-112 of file: xrst/table/smooth_table.xrst
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{xrst_begin smooth_table}
{xrst_spell
  model model
}

The Smoothing Table
###################

Purpose
*******
Each row of the ``smooth`` table defines a statistical
prior for a function of age and time.
To be more specific, each row corresponds to
a set of model :ref:`model_variables-name` that,
using :ref:`bilinear-name` interpolation,
define a function of age and time.
For each variable in the set its statistical prior is defined by a row of the
:ref:`smooth_grid_table-name` which specifies an
age, time, value prior, age difference prior, and time difference prior.
(The difference priors represent the smoothing in a mathematical sense.)

Empty
*****
The smooth table must not be empty because there
could be no :ref:`model_variables-name` in this case.

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

smooth_name
***********
This column has type ``text`` and has a different value for every row;
i.e., the names are unique and can act as substitutes for the primary key.
The names are intended to be easier for a human to remember than the ids.

n_age
*****
This column has type ``integer`` and is the number of age values
in this smoothing grid. It must be greater than zero.

n_time
******
This column has type ``integer`` and is the number of _time values
in this smoothing grid. It must be greater than zero.

mulstd_value_prior_id
*********************
This column has type ``integer`` and its value is the
:ref:`prior_table@prior_id` for the variable that multiplies the
:ref:`smooth_grid_table@value_prior_id` standard deviations
for this
:ref:`smooth_grid_table@smooth_id` .

null
====
If this variable is not needed,
use the value ``null`` (which corresponds to a multiplier of one).

mulstd_dage_prior_id
********************
This column has type ``integer`` and its value is the
:ref:`prior_table@prior_id` for the variable that multiplies the
:ref:`smooth_grid_table@dage_prior_id` standard deviations
for this
:ref:`smooth_grid_table@smooth_id` .

null
====
If this variable is not needed,
use the value ``null`` (which corresponds to a multiplier of one).

mulstd_dtime_prior_id
*********************
This column has type ``integer`` and its value is the
:ref:`prior_table@prior_id` for the variable that multiplies the
:ref:`smooth_grid_table@dtime_prior_id` standard deviations
for this
:ref:`smooth_grid_table@smooth_id` .

null
====
If this variable is not needed,
use the value ``null`` (which corresponds to a multiplier of one).

Removing an Age or Time
***********************
It is possible to remove an age (time) from the
:ref:`smooth_grid_table@Rectangular Grid`
for a specific *smooth_id* .
This is done by decreasing *n_age* ( *n_time* ) by one
and setting :ref:`smooth_grid_table@smooth_id` to null
for the points in the smooth_grid_table that are being removed.

Example
=======
:ref:`user_change_grid.py-name`

{xrst_comment
    example/table/smooth_grid_table.py is included by smooth_grid_table.omh
%}
Example
*******
The file :ref:`smooth_grid_table.py-name`
contains an example ``smooth`` table.

{xrst_end smooth_table}