See Also
The graphical builtins allow you to use the x,y pairs in a graphical variable in other variables, and for other forms of computation. The simplest LOOKUP allows a different x input into the graphical. The others provide different variations.
This section describes the following builtins:
The LOOKUP builtin evaluates the <graphical variable> at the given <expression> (versus using the equation stored in the graphical function itself). This function uses the interpolation model (Continuous, Extrapolated or Discrete) specified in the graphical.
The LOOKUPAREA builtin returns the area under the <graphical variable> for all X values between <fromx> and <tox>. For example, a graphical that is constant at 1 will have an area given by the <tox>-<fromx>. This is a convenient function for normalizing the output of graphical.
If <fromx> is omitted, the computation will be made from the beginning of the graphical. If both <fromx> and <tox> are omitted the computation will be made over the entire graphical. You can change the order of <fromx> and <tox) - so that LOOKUPAREA(var,3,5) is the same as LOOKUPAREA(var,5,3).
For continuous and stepwise graphicals LOOKUPAREA will ignore (effectively treat as 0) values below the minimum X value of the graphical or above the maximum X value.
For extrapolated graphicals the area is computed using the extrapolated value.
The LOOKUPINV builtin reverses the normal lookup logic returning the x value in the <graphical variable> that would generate the given <expression> as output. As long as the graphical is monotonic (the y value getting bigger for each successive x value, or the y value getting smaller for each successive x value) it will return a value. If the graphical is marked as Extrapolated it will use extrapolation to compute a value, otherwise it will return the first or last point when out of range.
If a graphical is not monotonic (including starting of stopping with a flat spot), the first x value to generate the y value will be returned. If there y value is out of range then NAN will be returned.
These LOOKUP builtins (along with LOOKUPAREA above), allow you to get information about the values in a graphical function. LOOKUPMIN and LOOKUPMAX find the minimum and maximum Y values in a graphical. LOOKUPMEAN is different in that it finds the mean X value treating the Y values as probabilities (to find the mean Y values use LOOKUPEA(var,x1,x2)/(x2-x1). All take the same arguments.
<graphical variable> is a variable that is a graphical. If the variable is not a graphical these builtins will all return NAN. If the graphical values are being controlled via import, a change from the Results Panela, or a Graphical Input Device on the interface the newly set graphical will be used. If it is being controlled at a constant value (for example via a slider), the original graphical will be used. If this argument is used by itself then the full range of the X axis will be used.
<tox> is the last value of X to consider. If there is no value for <fromx> the first X value in the graphical will be used.
<fromx> is the first value of X to consider.
Note The values of <tox> and <fromx> can be provided in either order. So that LOOKUPMAX(var,1,7) and LOOKUPMAX(var,7,1) return the same value.
LOOKUPMEAN is a specialized builtin that will normally be called with only a single argument. It treats the graphical values between <fromx> and <tox> as describing a probability density function (pdf) and computes what amounts to the expected value of X given that pdf. This can be very useful when working with LOOKUPRANDOM, and adjusting the delay time for a conveyor using a profile as described in Spreading Conveyor Inputs.
Most commonly, LOOKUPMEAN will be used on a distribution with the x axis ranging from 0 to 1. For example, to determine the appropriate transit time for a conveyor to achieve a desired average delay you would use:
delay_profile ((0,0),(0.5,1),(0.8,0.01),(0.1,0))
average_delay = 8
transit_time=INIT(average_delay/LOOKUPMEAN(delay_profile)
The conveyor would then use transit_time as the transit time, and the inflow would use delay_profile as the profile.
Note The above equations require that the graphical be defined on the range 0 to 1, otherwise the max value will be distorted and the mean transit time through the conveyor will not be average_delay. Alternatively, using INIT(average_delay/(LOOKUPMEAN(delay_profile)-x_min)/(x_max-x_min)) would work