How to interpolate values of x-axis using y-axis values as reference?

I want to do interpolation. I am using the following code

                                   yreq = interp1(x,y,xreq)

This code gives me the value of the parameter on y-axis when i give it the value of x-axis. What i want is to find the value of the x-axis while giving it the value of y-axis. Can it work? I tried switching the x and y axes but it didn't work. Any help will be appreciated. Thanks

[Stephen23]

Are the data strictly monotonic?

[Daniyal Ali]

Yes

[dpb]

Show what "didn't work" consists of. If, as Stephen notes, the data are monotonic, there's no difference to interp1. Of course, you have to request a value within the range of y as the input as well as swap the two datasets.

Answer 1

[Star Strider]

If your y data are strictly monotonically increasing (as interp1 requires, since you are using it to interpolate your x data), one possibility to explain the reason ‘it didn’t work’ is that you are asking it to extrapolate.

Try this:

xreq = interp1(y,x,yreq,'linear','extrap')

[Daniyal Ali]

Thanks for your answer. Can you also tell me how to do it for the data which is not monotonically increasing? in case i have to do it for that kind of data.

[Star Strider]

My pleasure.

You cannot do it for data that is not monotonically increasing, because there is no way to determine the ‘correct’ value for an independent variable with more than one value of a dependent variable. This applies for duplicated values of the independent variable and also applies an independent variable that ‘doubles back’ on itself.

For neighbouring and duplicated values of the independent variable, the usual way to do this is to add very small (about 1E-8 times the value of the independent variable) increasing values to each of the neighbouring duplicated values so that they are then monotonically increasing. So for instance, this sequence:

M = [1  9
     2  8
     3 10
     3  9
     3 12
     4 15];

would become something like:

M = [1      9
     2      8
     3.001 10
     3.002  9
     3.003 12
     4     15];

but with smaller added values. That works with interp1.

For independent variable data that oscillate, you would have to develop your own interpolation method. You could perhaps do piece-wise interpolation with polyfit and polyval.

[Daniyal Ali]

Thanks a lot!

[Star Strider]

My pleasure!