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 pointslope
— Fits a line between
the adjacent breakpoints, and returns the point on that line corresponding
to the input. This is the equation for linear pointslope, where
x is the input data, y is the
output table data
(x_{i},y_{i}
is the coordinate of the table data), and f is the
fraction. For more information on
x_{i},y_{i},
see About Lookup Table Blocks.
$$f=\frac{x{x}_{i}}{{x}_{i+1}{x}_{i}}$$
$$y={y}_{i}+f({y}_{i+1}{y}_{i})$$
Cubic spline
— Fits a cubic spline to
the adjacent breakpoints, and returns the point on that spline corresponding
to the input.
Linear Lagrange
— Fits a line between the
adjacent breakpoints using firstorder Lagrange interpolation, and returns
the point on that line corresponding to the input. This is the equation for
linear Lagrange, where x is the input data,
y is the output table data, and f
is the fraction. f is constrained to range from 0 to less
than 1 ([0,1)
). For more information on
x and y, see About Lookup Table Blocks.
$$f=\frac{x{x}_{i}}{{x}_{i+1}{x}_{i}}$$
$$y=(1f){y}_{i}+f{y}_{i+1}$$
If the extrapolation method is Linear
, the
extrapolation value is calculated based on the selected linear interpolation
method. For example, if the interpolation method is Linear Lagrange, the
extrapolation method inherits the Linear Lagrange equation to compute the
extrapolated value.
Akima spline
— Fits an Akima spline to
the adjacent breakpoints, and returns the point on that spline corresponding
to the input. The interpolation method works only with the
Akima spline
extrapolation method. The
modified Akima cubic Hermite interpolation method has these properties:
It produces fewer undulations than Cubic spline.
It is more efficient for realtime applications than Cubic spline.
Unlike Cubic spline, it does not produce overshoots.
Unlike Cubic spline, it supports nonscalar signals.
Note
The Lookup Table Dynamic block does not let you select an
interpolation method. The InterpolationExtrapolation
option in the Lookup Method field of the block parameter
dialog box performs linear interpolation.
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 smooth results. Akima spline 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
or
Akima spline
, this extrapolation method fits
a linear surface using the slope of the interpolation 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.
If the extrapolation method is Linear
, the
extrapolation value is calculated based on the selected linear interpolation
method. For example, if the interpolation method is Linear Lagrange, the
extrapolation method inherits the Linear Lagrange equation to compute the
extrapolated value.
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.
Akima spline
— Fits an Akima 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 InterpolationExtrapolation
option in the Lookup Method field of the block parameter
dialog box performs linear extrapolation.
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
