How to get multiple interpolated Y values from many X’s

Have you ever wanted to bunch up all Y values corresponding to multiple X values from multiple datasets (plots) at one time using interpolation (or extrapolation) technique like in the following sample graph? One way to achieve such task is to apply the “Vertical Cursor” gadget multiple times as discussed in the forum post, http://www.originlab.com/forum/topic.asp?TOPIC_ID=20330 .

Although this is a handy interactive tool, if you have many specific X values to interpolate, you can try the following methods of interpolation applied on the worksheet data.

CASE-1: Using the “Interpolate/Extrapolate” menu

This method is only applicable when your desired X positions are equally spaced in a range. You can run this from “Analysis> Mathematics> Interpolate/Extrapolate” menu, then you enter the X Minimum and Maximum, as well as the Number of Points (after turning OFF the Auto check boxes). For example, you can enter: X Minimum=0, X Maximum=10, and Number of Points=11 , to produce Y values at 0, 1, 2, … , 10.

CASE-2: Using the “Interpolate/Extrapolate Y from X” menu

This method is useful when the number of source datasets are not many, but they may exist in various workbooks or worksheets. As a preparation of the procedure, first make a worksheet which has a column containing your desired X values to interpolate. For example, in the screenshot below, a new sheet “Results” is created, and you enter the X values to interpolate into the first column, A(X). (You only need this X column at this moment, so you may delete the empty B(Y).)

Now you can run the interpolation by “Analysis> Mathematics> Interpolate/Extrapolate Y from X” menu for each of your source Y dataset. You can specify the column for “X Values to Interpolate”. Note that the column part of the “Result of interpolation” has been set to “New;” in the specific worksheet ([Book1]Results in this sample) so that every time you run this menu command, the interpolated result is automatically added as a new column in the Results worksheet. Also, the recalculation mode is set to Auto so that it recalculates automatically when the X values to interpolate in Results worksheet are updated.  Repeat this step for all Y datasets.

CASE-3: Using a Script

If you have lots of source Y datasets to be interpolated, the method in CASE-2 takes tedious steps to interpolate all Y datasets. But, if your source datasets are arranged in a single worksheet with a regular pattern of designations like XYY…Y or XYXY…XY, you can accomplish all tasks in a single step with a help of simple script. For example, the following sample worksheet contains ten(10) Y datasets, and the X values to interpolate are stored in the first column in the second sheet(=Sheet2):

Try to run the following simple script (using “interp1” x-function).:

range rix=2!col(1); //X column to interpolate
range riy=2!col(2); //as we only need X column in this sheet
if(riy.getSize()==0) delete riy;  //if the 2nd column is empty, delete it.
page.active=1; //Sheet# of data sheet
doc -e DY {
  cn=colnum(%C); //next Y dataset
  interp1 -r 1 ix:=rix iy:=1!$(cn) ox:=2!<new> method:=0;
}

You get the whole result in a single run!