`interp(V;N;X;Y;E)`

Returns a particular interpolation of a given value based on a discrete set of data points, and if specified, extrapolates out-of-range values.

Syntax

interp(V;N;X;Y;E)

Input

Argument	Type	Description
`V`	integer or decimal	`V` is a column containing the values you wish to interpolate. A column name
`N`	integer	Determines the type of interpolation to perform `N` must be one of the following: `0` - zero-order "interpolation" (i.e., simple lookup) `1` - linear interpolation `2` - quadratic splines `3` - cubic splines
`X`	integer or decimal	`X` is any type of value or a list of numbers in a set you wish to interpolate. `X` may not contain repeated values. `X` may be omitted, in which case it is assumed to be 1,2,3,...,`Z`, where `Z` is the length of `Y`. A space- or comma-separated list of scalar values
`Y`	integer or decimal	`Y` is a list of numbers in a set you wish to interpolate. A space- or comma-separated list of scalar values
`E`	integer	A value of `1` or `0` that determines whether or not to extrapolate out-of-range values If `E`=`1`, out-of-range values will be extrapolated. If `E`=`0`, extrapolation is not done (i.e., result is N/A where `V` is outside of the range of `X`). Note: Extrapolation of higher-order splines is not typically meaningful.

Note: X and Y must be space- or comma-separated lists of equal length.

Return Value

Returns a decimal number corresponding to the interpolation of V using the method specified by N and the values specified by X and Y.

If E=1, out-of-range values will be extrapolated. If E is 0 and V is less than the lowest value in X or greater than the highest value in X, the result is N/A.

If V is N/A, the result is N/A.

Example

Let's use the <table> op to create a temporary table to help illustrate the use of interp(V;N;X;Y;E):

<table title="interp Example" cols="values" types="f">
2.5;
6;
8;
-2.5;
-100;
</table>

We'll use the values column from this table for our V parameter.

For X, we'll use the following list of values: 0,1,2,3,4,5,6 (note that this can be a space- or comma-separated list).

For Y, we'll use the following list of values: 0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794 (note that this can be a space- or comma-separated list).

The following Macro Language code shows how to use interp(V;N;X;Y;E) to interpolate the values in V based on the values in X and Y. We specify the type of interpolation using the N parameter and whether or not to extrapolate out-of-range values using the E parameter:

<willbe name="simple" value="interp(values;0;0 1 2 3 4 5 6;0 0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794;0)"/>
<willbe name="simple_ex" value="interp(values;0;0 1 2 3 4 5 6;0 0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.2794;1)"/>
<willbe name="linear" value="interp(values;1;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;0)"/>
<willbe name="linear_ex" value="interp(values;1;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;1)"/>
<willbe name="quadratic" value="interp(values;2;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;0)"/>
<willbe name="quadratic_ex" value="interp(values;2;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;1)"/>
<willbe name="cubic" value="interp(values;3;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;0)"/>
<willbe name="cubic_ex" value="interp(values;3;0,1,2,3,4,5,6;0,0.8415,0.9093,0.1411,-0.7568,-0.9589,-0.2794;1)"/>

This will give us the following results:

For those rows in the values column that are in the range of X (i.e., 2.5 and 6), the interpolated results are returned and are the same regardless of whether extrapolation has been specified or not.

For those values outside the range of X, the result is N/A in the simple, linear, quadratic, and cubic columns, since the E parameter is 0 for those columns. For the simple_ex, linear_ex, quadratic_ex, and cubic_ex columns, extrapolation is done since the E parameter is 1.