Lookup table

A lookup table is an array that can replace an expensive computation with a linear interpolation. A good way to understand the usage of this module is to run:

make
./usage_example

After which you can inspect the file usage_example.f90 to see how you can incorporate the module in your own programs.

Requirements

A modern Fortran compiler, such as gfortran 4.8 or newer.

Examples

• usage_example.f90 Shows several examples of how values can be looked up, a good starting point.
• test_lookup_table_performance.f90 Compares the performance of different types of lookups.
• test_lookup_table_index.f90 Tests whether the correct indices in the table are retrieved
• test_lookup_table_2d.f90 Simple example of a 2D lookup table
• test_find_index_performance.f90 Compares the performance of linear search, binary search and automatically switching between the two.

Creating a lookup table

Lookup tables are created with a call to the function LT_create:

lt = LT_create(x_min, x_max, n_rows, n_cols, xspacing)

Here n_rows controls how many x-values are stored. The x-spacing of the lookup table can be set to:

• LT_xspacing_linear (the default, in which the spacing is given by dx = (x_max - x_min) / (n_rows - 1))
• LT_xspacing_quadratic for quadratic spacing
• LT_xspacing_cubic for cubic spacing, which is a bit slower

The argument n_cols specifies how many different columns you want to store, but it also possible to add extra columns later with LT_add_col.

The columns of a table are set using LT_set_col:

call LT_set_col(lt, col_ix, x, y)

where x and y are vectors of the same length, with the only requirement that the x array is sorted from low to high. These y values will be linearly interpolated and stored in the table. Alternatively, it is possible to directly specify the y-values in a column:

call LT_set_col_data(lt, col_ix, y)

Getting values from a table

There are multiple ways to get values from a lookup table:

• You can directly look up a single column at some x-coordinate, using LT_get_col
• You can get all the columns at some x-coordinate, using LT_get_mcol
• You can also get a location in the table with a LT_loc_t object, and then do lookups using that object. This can be used to speed up multiple lookups of different columns

The type lt_loc_t is defined as:

type LT_loc_t
   integer  :: low_ix   !< The x-value lies between low_ix and low_ix+1
   real(dp) :: low_frac !< The distance from low_ix (up to low_ix+1), given
                        !< as a real number between 0 and 1.
end type LT_loc_t

Contributors

• Jannis Teunissen
• Margreet Nool (Documentation)