The second stage of a table lookup operation involves generating outputs that correspond to the supplied inputs. If the inputs match the values of indices specified in breakpoint data sets, the block outputs the corresponding values. However, if the inputs fail to match index values in the breakpoint data sets, Simulink^{®} estimates the output. In the block parameter dialog box, you can specify how to compute the output in this situation. The available lookup methods are described in the following sections.
When an input falls between breakpoint values, the block interpolates the output value using neighboring breakpoints. Most lookup table blocks have the following interpolation methods available:
Flat
— Disables
interpolation and uses the rounding operation titled Use
Input Below
. For more information, see Rounding Methods.
Nearest
— Disables
interpolation and returns the table value corresponding to the breakpoint
closest to the input. If the input is equidistant from two adjacent
breakpoints, the breakpoint with the higher index is chosen.
Linear
— Fits a
line between the adjacent breakpoints, and returns the point on that
line corresponding to the input.
Cubic spline
— Fits
a cubic spline to the adjacent breakpoints, and returns the point
on that spline corresponding to the input.
Note:
The Lookup Table Dynamic block does not let you
select an interpolation method. The 
Each interpolation method includes a tradeoff between computation time and the smoothness of the result. Although rounding is quickest, it is the least smooth. Linear interpolation is slower than rounding but generates smoother results, except at breakpoints where the slope changes. Cubic spline interpolation is the slowest method but produces the smoothest results.
When an input falls outside the range of a breakpoint data set, the block extrapolates the output value from a pair of values at the end of the breakpoint data set. Most lookup table blocks have the following extrapolation methods available:
Clip
— Disables
extrapolation and returns the table data corresponding to the end
of the breakpoint data set range. This does not provide protection
against outofrange values.
Linear
— If the
interpolation method is Linear
, this extrapolation
method fits a line between the first or last pair of breakpoints,
depending on whether the input is less than the first or greater than
the last breakpoint. If the interpolation method is Cubic
spline
, this extrapolation method fits a linear surface
using the slope of the interpolant at the first or last break point,
depending on whether the input is less than the first or greater than
the last breakpoint. The extrapolation method returns the point on
the generated linear surface corresponding to the input.
Cubic spline
— Fits
a cubic spline to the first or last pair of breakpoints, depending
if the input is less than the first or greater than the last breakpoint,
respectively. This method returns the point on that spline corresponding
to the input.
Note:
The Lookup Table Dynamic block does not let you
select an extrapolation method. The 
In addition to these methods, some lookup table blocks, such as the nD Lookup Table block, allow you to select an action to perform when encountering situations that require extrapolation. For instance, you can specify that Simulink generate either a warning or an error when the lookup table inputs are outside the ranges of the breakpoint data sets. To specify such an action, select it from the Diagnostic for outofrange input list on the block parameter dialog box.
If an input falls between breakpoint values or outside the range of a breakpoint data set and you do not specify interpolation or extrapolation, the block rounds the value to an adjacent breakpoint and returns the corresponding output value. For example, the Lookup Table Dynamic block lets you select one of the following rounding methods:
Use Input Nearest
—
Returns the output value corresponding to the nearest input value.
Use Input Below
—
Returns the output value corresponding to the breakpoint value that
is immediately less than the input value. If no breakpoint value exists
below the input value, it returns the breakpoint value nearest the
input value.
Use Input Above
—
Returns the output value corresponding to the breakpoint value that
is immediately greater than the input value. If no breakpoint value
exists above the input value, it returns the breakpoint value nearest
the input value.
In the following model,
the Lookup Table Dynamic block
accepts a vector of breakpoint data given by [5:5]
and
a vector of table data given by sinh([5:5])
.
The Lookup Table Dynamic block outputs the following values when using the specified lookup methods and inputs.
Lookup Method  Input  Output  Comment 



 N/A 

 N/A  


 N/A 

 The block uses the value for  


 The block uses the value for 

 The block uses the value for  


 The block uses the value for 

 The block uses the value for  


 The block uses the value for 