pencil.calc.accuracy
====================

.. py:module:: pencil.calc.accuracy


Functions
---------

.. autoapisummary::

   pencil.calc.accuracy.twonorm_accuracy
   pencil.calc.accuracy.order_accuracy
   pencil.calc.accuracy.twonorm_array
   pencil.calc.accuracy.twonorm
   pencil.calc.accuracy.maxerror
   pencil.calc.accuracy.twonorm_accuracy2D
   pencil.calc.accuracy.twonorm_accuracy1D


Module Contents
---------------

.. py:function:: twonorm_accuracy(simulations, field='ux', strip=0, var_file='ogvar.dat', direction='x', noerr=True, quiet=True)

   Assessment of accuracy of simulation:
   Computes the two-norm error of all available simulation, where the simulation
   with the maximum amount of grid points is used as the correct/reference solution.
   E.g., for runs with grid points assessment of accuracy of x-component of velocity
   along the y-direction, for runs with grid points nxgrid = n, 2n, 4n, 8n, compute

   || u_n - u_0 || = dy \sum\limits_{n=0}^n (sqrt(u_n(x_n)-u_0(x_8n)))

   for all runs (except for the 8n case, used as reference).

   Requires that the runs have matching grids, that is, grid refined by a factor of 2m,
   and grids adjusted so that the grid point overlap (needs ofset if periodic BC is used).

   call signature:
     twonorm_accuracy(simulations)

   Keyword arguments:

   *simulations*
     array of simulation names to be included in the computations

   *field*
     variable used in accuracy assessment

   *strip*:
     index for strip along coordinate

   *var_file*:
     name of varfile to read from each sim

   *direction*:
     compute two-norm along 'x' or 'y' direction

   *noerr*:
     set to false if you want to return an array of maximum error along strip, in
     addition to the two-norm

   Returns
     array of two-norms where the larges array is used as base


.. py:function:: order_accuracy(simulations=[], nstrips=0, twonorm_arr=[], field='ux', var_file='ogvar.dat', direction='x')

   Compute an estimate of the order of accuracy, using two-norms where
   the finest grid is used as reference solution u_0.
   Return array of orders of accuracy, where each order p is for computation along one strip.

   p = log(||u(\Delta x) - u_0|| / ||u(\Delta x/2) - u_0||)/log(2)

   Keyword arguments:

   *simulations*
     array of simulation names to be included in the computations

   *nstrips*
     number of strips to include in twonorm_array
     twonorm is computed along each strip, and the strips must coencide on the each
     grid used in such a grid refinement study

   *twonorm_arr*
     array of computed two-normes, if these are available
     if empty, routine will compute these

   *field*
     variable used in accuracy assessment

   *varfile*:
     name of varfile to read from each sim

   *direction*:
     compute two-norm along 'x' or 'y' direction


.. py:function:: twonorm_array(simulations, nstrips, field='ux', var_file='ogvar.dat', direction='x')

   Compute twonorm_accuracy along the selected direction, for a number of 'strips'.
   See twonorm_accuracy for details.

   call signature:
       twonorm_array(simulations,nstrips)

   Keyword arguments:

   *simulations*
     array of simulation names to be included in the computations

   *nstrips*
     number of strips to include in twonorm_array
     twonorm is computed along each strip, and the strips must coencide on the each
     grid used in such a grid refinement study

   *field*
     variable used in accuracy assessment

   *varfile*:
     name of varfile to read from each sim

   *direction*:
     compute two-norm along 'x' or 'y' direction


.. py:function:: twonorm(u1, u2, dx)

   Compute the two-norm error of two spatial vectors u1 and u2.
   The distance between grid points used in calculation is dx.


.. py:function:: maxerror(u1, u2)

   Find the larges error between values from u1 and u2 (for the
   same indices).


.. py:function:: twonorm_accuracy2D(simulations, field='ur', var_file='ogvar.dat', noerr=True, quiet=True)

   Assessment of accuracy of simulation:
   Computes the two-norm error of all available simulation, where the simulation
   with the maximum amount of grid points is used as the correct/reference solution.
   E.g., for runs with grid points assessment of accuracy of x-component of velocity
   along the y-direction, for runs with grid points nxgrid = n, 2n, 4n, 8n, compute

   || u_n - u_0 || = dy \sum\limits_{n=0}^n (sqrt(u_n(x_n)-u_0(x_8n)))

   for all runs (except for the 8n case, used as reference).

   Requires that the runs have matching grids, that is, grid refined by a factor of 2m,
   and grids adjusted so that the grid point overlap (needs ofset if periodic BC is used).

   call signature:
     twonorm_accuracy(simulations)

   Keyword arguments:

   *simulations*
     array of simulation names to be included in the computations

   *field*
     variable used in accuracy assessment

   *varfile*:
     name of varfile to read from each sim

   *noerr*:
     set to false if you want to return an array of maximum error along strip, in
     addition to the two-norm

   Returns
     array of two-norms where the larges array is used as base


.. py:function:: twonorm_accuracy1D(simulations, field='ur', strip=1, direction='r', varfile='ogvar.dat', noerr=True, quiet=True)

   Assessment of accuracy of simulation:
   Computes the two-norm error of all available simulation, where the simulation
   with the maximum amount of grid points is used as the correct/reference solution.
   E.g., for runs with grid points assessment of accuracy of x-component of velocity
   along the y-direction, for runs with grid points nxgrid = n, 2n, 4n, 8n, compute

   || u_n - u_0 || = dy \sum\limits_{n=0}^n (sqrt(u_n(x_n)-u_0(x_8n)))

   for all runs (except for the 8n case, used as reference).

   Requires that the runs have matching grids, that is, grid refined by a factor of 2m,
   and grids adjusted so that the grid point overlap (needs ofset if periodic BC is used).

   call signature:
     twonorm_accuracy(simulations)

   Keyword arguments:

   *simulations*
     array of simulation names to be included in the computations

   *field*
     variable used in accuracy assessment

   *varfile*:
     name of varfile to read from each sim

   *noerr*:
     set to false if you want to return an array of maximum error along strip, in
     addition to the two-norm

   Returns
     array of two-norms where the larges array is used as base