The TABLE Input function

FlexPDE supports a tabular data import function:

name = TABLE ( 'filename' )        

This statement imports a data table from the named file and associates the data with the defined name.

Normally, the statement appears in a parameter definition (in the DEFINITIONS section or as a regional parameter definition in a REGION clause), and the table data are associated with the given name.

TABLE can also be used in arithmetic expressions, in which case the data are unique to that specific evaluation.        

TABLE data are interpolated with linear, bilinear or trilinear interpolation on the specified data grid.

FlexPDE can accept (import) and generate (export) non-analytic data through external one, two, or three dimensional table files.  This feature is useful for modeling systems where experimental data is available and for interfacing with other software programs.

Table import files are ASCII text files, and can be generated with any ASCII text editor, by user programs designed to generate tables, or by FlexPDE itself, using the EXPORT plot modifier or the TABLE output statement (see MONITORS and PLOTS).

Modifying Table Coordinates

In the normal case, the name(s) of the table coordinate(s) are given in the table file itself.  However, an alternative form of the TABLE input function can be used to rename the coordinates:

name = TABLE ( 'filename', coord1 [,coord2...] )        

In this case, the coordinates named in the file will be over-ridden by the stated coordinate names.  These names must have been defined before their use in the TABLE statement.

When the parameter name is used in subsequent computations, the current values of the table coordinates will be used to interpolate the value.  For instance, if the table coordinates are the spatial coordinates X and Y, then during computations or plotting, the named parameter will take on a spatial distribution corresponding to the table data spread over the problem domain.

See the TABLEDEF statement for an alternative form of table input.

See the SPLINETABLE statement for an alternative form of table interpolation.

Examples:

Samples | Misc | Table.pde

Smoothing Table Data

In one- and two-dimensional TABLEs and SPLINETABLEs, the data may optionally be smoothed before interpolation.  This process is invoked by a smoothing control before the TABLE operator:

name = SMOOTH(wavelength) TABLE ( 'filename', coord1 [,coord2...] )        

wavelength is the size limit for retained frequency components in the data (smearing distance).

Blocking Table Data

In one-dimensional TABLEs, the data may optionally be converted to histogram interpretation.  This process is invoked by a blocking control before the TABLE operator:

name = BLOCK TABLE ( 'filename', coord1 [,coord2...] )        

Each entry in the table is assumed to define a constant value that persists from its definition point until the definition point of the next entry in the table.

Because discontinuous data can cause convergence failure in the solution process, BLOCKed tables are implemented by inserting a transition ramp at each table point.  The transition width is one tenth of the smaller of the intervals adjoining the table point.