topic Re: Bilinear interpolation in SAS in SAS Programming

Bilinear interpolation in SAS

NickVe — Tue, 31 Mar 2020 05:20:17 GMT

Is it possible to do bilinear interpolation in SAS?

For interpolation in one dimension I found that this can be easily done using the "proc expand" or a "proc transreg" (link: https://support.sas.com/kb/24/560.html).

However, for the case where I have 2 "input variables (x,y)" and one "output variable (z)" I have not found a good procedure.

Are there any good procedures to do bilinear interpolation in SAS?

Additional clarification on what I mean with "bilinear interpolation"

With bilinear I am aiming to the meaning that it has on WikiPedia (https://en.wikipedia.org/wiki/Bilinear_interpolation). This means that I have a list of (x,y,z) values, and that I am looking for some function that can fill in the missing z-values if I provide the missing z-values if I provide a list of (x,y) values within the range of the original provided values.

Interpolation methods that would be a great fit for my purpose:

bilinear interpolation: https://en.wikipedia.org/wiki/Bilinear_interpolation
bicubic interpolation: https://en.wikipedia.org/wiki/Bicubic_interpolation
nearest-neighbours interpolation: https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation

Although the latter one I personally do not prefer, it could also provide a solution to my problem.

Examples from other programming languages

Examples of the function I am looking for can also be found in other programming languages. All the examples accept a list of (X, Y, Z) values, together with a list of (X0, Y0) values for which the (Z) values are then determined so these can be added to a table.

MATLAB example (interp2): https://nl.mathworks.com/help/matlab/ref/interp2.html
Python example (interp2d): https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.interpolate.interp2d.html
R example (interp2): https://www.rdocumentation.org/packages/pracma/versions/1.9.9/topics/interp2
C++ example (libInterpolate): https://github.com/CD3/libInterpolate

Re: Bilinear interpolation in SAS

Reeza — Mon, 30 Mar 2020 16:19:01 GMT

Is a regression model an option?

PROC GLM?

Or RSREG?

Re: Bilinear interpolation in SAS

PGStats — Mon, 30 Mar 2020 19:31:21 GMT

If you have licence for SAS/GRAPH, look at the G3GRID procedure. It does linear, spline and smooth interpolations over a grid.

Re: Bilinear interpolation in SAS

PaigeMiller — Mon, 30 Mar 2020 19:45:52 GMT

I guess this all depends on the meaning of "bilinear", which wasn't specified in the original question, but my guessing is that splines are not "bilinear". Linear regression with 2 Xs (and only the linear terms) is what I think "bilinear" means.

Re: Bilinear interpolation in SAS

NickVe — Tue, 31 Mar 2020 05:01:28 GMT

Hi PaigeMiller,

Thank you for the advice, I will adjust my question to avoid all unclarities.

Re: Bilinear interpolation in SAS

NickVe — Tue, 31 Mar 2020 05:02:15 GMT

Just to clarify on what I mean with bilinear.

With bilinear I am aiming to the meaning that it has on WikiPedia (https://en.wikipedia.org/wiki/Bilinear_interpolation). This means that I have a list of (x,y,z) values, and that I am looking for some function that can fill in the missing z-values if I provide the missing z-values if I provide a list of (x,y) values within the range of the original provided values.

Re: Bilinear interpolation in SAS

NickVe — Tue, 31 Mar 2020 05:09:09 GMT

Hi Reeza,

Thank you for the suggestion! My personal drawback on this, is that I have a list of numbers (x, y, z) which we know to be exact. The goal is to estimate the z value for a new point (x,y). The function should pass trough the original numbers (x, y, z), as they are exact, and interpolate these number linearly (or in a smoothed way).

Re: Bilinear interpolation in SAS

NickVe — Tue, 31 Mar 2020 05:12:04 GMT

Hi PGStats,

I indeed saw the G3GRID procedure in my search, and this is in our licence.

However after reading the documentation I only found examples to make graphs. My goal is to add the z-value to a table of (x,y) values. Where the z-value is determined by an interpolation of a given (x, y, z) table. I am not sure if the G3GRID procedure can do this?

Re: Bilinear interpolation in SAS

PaigeMiller — Tue, 31 Mar 2020 10:34:16 GMT

PROC GLM will do this. It also allows for the prediction/interpolation of values of z for different values of (x,y) that were not used to build the model.

Re: Bilinear interpolation in SAS

Ksharp — Tue, 31 Mar 2020 11:11:09 GMT

It seems like imputing MISSING value.

Did you check PROC MI ?

Calling @Rick_SAS

Re: Bilinear interpolation in SAS

Rick_SAS — Tue, 31 Mar 2020 11:34:14 GMT

IMHO, you should fit a parametric model (PROC RSREG) or a nonparametric model (PROC LOESS) to the data. If these are spatial data, then there are specialized routines (such as PROC KRIGE) that you can use to model the response.

Re: Bilinear interpolation in SAS

PaigeMiller — Tue, 31 Mar 2020 11:53:43 GMT

I don't get the suggestion of LOESS or RSREG, the question specifically asks for linear interpolation.

Re: Bilinear interpolation in SAS

Rick_SAS — Tue, 31 Mar 2020 12:56:34 GMT

Yes, I am suggesting these as alternatives to the OP's request for linear interpolation. Also, my suggestions are smoothers; they do not necessarily pass through the data points.

The LOESS method has a SCORE statement that you can use to score new data:

data Grid;
call streaminit(12345);
do x = 0 to 10 by 2;
   do y = 0 to 10 by 2;
      z = abs(x-5) + abs(y-5) + round(rand("Normal"), 0.1);
      output;
   end;
end;
run;

data New;
do x = 1 to 9 by 2;
   do y = 1 to 9 by 2;
      output;
   end;
end;

proc loess data=Grid plots(only)=contourfit;
   model z = x y / degree=1;
   score data=New / print;
   ods exclude ScoreResults;
   ods output ScoreResults = ScoreOut;
run;

proc print data=ScoreOut(obs=10);
run;

Re: Bilinear interpolation in SAS

PGStats — Tue, 31 Mar 2020 16:56:29 GMT

To quote the documentation for proc G3GRID:

The G3GRID procedure does not produce graphics output. PROC G3GRID produces an output data set that you can use as the input data set for PROC G3D or PROC GCONTOUR.

Re: Bilinear interpolation in SAS

Rick_SAS — Tue, 31 Mar 2020 17:16:26 GMT

I just re-read the OP's comment that says

"I indeed saw the G3GRID procedure in my search, and this is in our license."

The first time I read it, I mistakenly thought the OP said that G3GRID wasn't licensed. If you have PROC G3GRID, it provides linear interpolation.

Re: Bilinear interpolation in SAS

NickVe — Tue, 14 Apr 2020 14:48:09 GMT

Dear all,

Thank you for the many responses. My hope was that there would be an easy method that constructed an interpolation(x, y) function (as is the case in the examples in Python, R, MATLAB and C++ shown in the original question). If I read the different responses correctly, this is not possible at all, am I correct with this?

The popular G3GRID method that is suggested does not seem to meet my criteria. The reason is that I have irregularly spaced datapoints that I wish to determine. This appears to be impossible using this method.

The MI method seems promising at first sight. However I only see examples where the imputation is done by either the "mean value" or by a "regression result". The documentation of this method does not discuss "interpolation".

My current "quick and dirty" workaround is by using the "proc discrim" procedure, to essentially do 1-nearest neighbour interpolation. This gives me the value of the nearest point as the "interpolation". This is a workable solution at the moment for me, although it is far from ideal.

As a recap: I have a series of regularly spaced (x0, y0, z0) values. I also have a (very large) series of irregularly spaced (x, y) values for which I want to determine the corresponding z values.

Re: Bilinear interpolation in SAS

PaigeMiller — Tue, 14 Apr 2020 14:58:51 GMT

@NickVe wrote:

Dear all,

Thank you for the many responses. My hope was that there would be an easy method that constructed an interpolation(x, y) function (as is the case in the examples in Python, R, MATLAB and C++ shown in the original question). If I read the different responses correctly, this is not possible at all, am I correct with this?

PROC GLM does this. Which was mentioned earlier in this thread.

Re: Bilinear interpolation in SAS

Rick_SAS — Tue, 14 Apr 2020 15:08:07 GMT

> If I read the different responses correctly, this is not possible at all, am I correct with this?

I would not say that is a correct statement. It is possible by using programming statements. The difficulty seems to be that the built-in SAS procedures that we have suggested have been rejected by you for various reasons. If I remember correctly, you do not want a global (or even local) statistical fit but want a bilinear fit based on values at the corner of the cell (in a regular grid) in which each point lives.

I've written about how to use 2-D binning to find the cell that each point belongs to. If you are a programmer, such a routine can be programmed in the SAS/IML language by using the definition of bilinear interpolation.

Re: Bilinear interpolation in SAS

NickVe — Wed, 15 Apr 2020 06:56:03 GMT

If I read the documentation correctly, "proc GLM" only provides a "linear fit", not an "interpolation" as is asked in the original question. Please correct me if I misread this.

Re: Bilinear interpolation in SAS

NickVe — Wed, 15 Apr 2020 07:23:30 GMT

This 2D binning article looks indeed promosing workaround to generate a regular grid from my irregularly spaced data. This could then be combined with the G3GRID method proposed above. Note however that this is still a workaround and technically not a solution to my problem.

The reason for rejecting the previous methods are that they do not answer the question:

"proc GLM" provides a "fit", not an "interpolation" as requested
"RSREG" provides a "fit", not an "interpolation" as requested
G3GRID only works for "regular grids", not irregularily shaped data as requested
"PROC MI" seems only to do missing imputation, not "interpolation"
"PROC LOESS" provides a "fit", not an "interpolation" as requested
"PROC KRIGE" performs krigging, with is again a "fit", not an "interpolation" as requested

The closest solution to my problem I have found seems to be the "proc discrim" method, which I use to make a 1NN interpolation. The advantage is that this meets the criteria of my question:

I can provide a "train" dataset of (X0, Y0, Z0) values
I can easily provide new values (X, Y) and obtain the corresponding (Z) values
This works for data that is not on a rectangular grid

For me personally this is the most viable solution at the moment. Unfortunately this only fits the nearest point, and does not perform linear interpolation.

I understand that I could write my own program in SAS to solve this issue, however that was not the question. I wanted to avoid "re-inventing the wheel" by working with the optimized SAS procedures as much as possible. My belief was that these "interpolation functionalities" would also be available in SAS since they are available in for example MATLAB, R, Python and C++ (see examples).