Experimental (Semi-) Variogram

calculate the isotropic and anisotropic experimental (semi-) variogram

Description

variogram calculates the isotropic and anisotropic experimental variogram in various dimensions.

Syntax:
    d = variogram(x,y)
    d = variogram(x,y,'pn','pv',...)

The function uses parseargs (objectId=10670) by Malcolm wood as subfunction.

Currently, the function calculates all variogram values at one step. While this is fast for small data sets (n<2000), it may fail on large data sets owing to memory constraints. So far, I do not have a good workaround. If you face memory issues, I'd suggest to sample your data using e.g. randperm.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
parseargs: Simplifies input processing for functions with multiple options
This submission has inspired the following:
variogramfit, Ordinary Kriging

• MATLAB release: MATLAB 7.8 (R2009a)

[Shazux Gharasoo]

very nice program indeed. I had a question by the way. how the distance is calculated? direct distance or along X and Y streets?

[Wolfgang Schwanghart]

Hi Shazux,

the distance measure used here is the euclidean distance. I guess that is what you mean by direct distance, do you?

Best regards,
Wolfgang

[Shazux Gharasoo]

that was what I meant, thank you :)
one more question, how to pass the data that has been plot? i mean here:
plot(out.distance,out.val,marker)
I need to do some curve fitting on those values...

[Shazux Gharasoo]

sorry, I found out that these values are saved already in variable 'd' as a structure. thanks though

[Anthony Kendall]

Thanks a lot for this function, it works very well (though as you mentioned it is a bit of a memory hog, I had to subsample my data but the variogram was robust).

[Patrick A.]

Like Variogramfit, it is for me an invaluable contribution. Very nice code, very nice comments, well I've learned a lot with these two pieces of code, Thanks a lot !

[oskenund]

 

[Kibre. T.]

Very good. Does this code accept the other parameters such as nugget effect and sill?

[Wolfgang Schwanghart]

@Kibre. T.

Nugget effect and sill are required when you fit a variogram model to the experimental variogram and, hence, they are not accepted as parameters here. However, you may want to try variogramfit, which enables to set initial values for a nugget model and sill.

[Marian Axente]

Is there anything else we can use instead of IPDM since there is no such function on Matlab FEX

[Wolfgang Schwanghart]

@ Marian and others

I am sorry that IPDM is currently not available on the FEX. You can send me a mail via the contact formular with your email and I'll send you the function then. I'll be working on a workaround next week.

Thanks for your interest,
Wolfgang

[Amy]

 

[jorge parra]

Wolfgang,

Very good function; is possible calculate variograms at different angles, for example vertical and horizontal variograms? If you can do this how do you specify the angles and how do you plot them,
Thank you
Jorge

[Wolfgang Schwanghart]

Hi Jorge. I have just uploaded a new version with a bug removed. Please take this one as soon as it is available (probably by 25 Nov 2011). Then, in order to obtain variograms for different directions, just calculate the anisotropic variogram. E.g. for obtaining variograms in 0 and 90° direction, you can do following:

d = variogram([x y],z,...
'nrbins',50,'anisotropy',true,...
'thetastep',30);

plot(d.distance,...
d.val(:,find(d.theta==0 | d.theta==pi/2)));

You may choose tighter angular bins. In this case it will be 0+-15 and 90+-15.

HTH, Wolfgang

[jorge parra]

Thank you Wolfgang ,
I got both plots OK(for theta = 0 and theta = 90 degrees). Now I am trying to apply your program to a real data set but I am having some problems. The data set consist of 200 x 50 points (impedances) contained in a 2D rectangular cross section. The coordinates x and y and the impedance are arranged in three vectors, each of them of dimension 200x 50 = 10000. The function in the script file is given by:
d = variogram([x y], impedance, 'nrbins',50,'anisotropy',true, 'thetastep',30);
The error message: “ Anisotropy is only supported for 2D",

What am I doing wrong?
Jorge

[Wolfgang Schwanghart]

Hi Jorge,

are those data gridded? If yes, you should call the function like this:

d = variogram([x(:) y(:)], impedance(:), 'nrbins',50,'anisotropy',true,'thetastep',30);

Best regards,
Wolfgang

[Adam]