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### Highlights from Experimental (Semi-) Variogram

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# Experimental (Semi-) Variogram

19 Jun 2008 (Updated )

calculate the isotropic and anisotropic experimental (semi-) variogram

File Information
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. For large datasets you may thus want to use the 'subsample' option.

Acknowledgements

This file inspired Variogramfit and Ordinary Kriging.

MATLAB release MATLAB 7.8 (R2009a)
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Comments and Ratings (47)
04 Mar 2014

Fantastic code - just what I needed. However, I am trying to modify it a bit for cross-variogram. Can I do it this way: save the
lam = (y(iid(:,1))-y(iid(:,2)));
for two separate variable (say A and B) Combine=bsxfun(@times, lamA,lamB);
Combine_cross = accumarray([ixedge ixtheta],Combine,...
[21 7],fvar,nan);
Combine_cross(:,end)=Combine_cross(:,1);

Is this approach correct?
Thanks

25 Jan 2014

Hi Wolfgang!

Thank you for this, it is a very good one!

Could you please explain me, where is your algorithm calculate the separation (or lag) vector(h). Theoretically, if I am calculating a variogram, I use this formula:

gamma^2(h)=(1/2N(h))*sum(f(u+h)-f(u))^2

Did you used the same? If yes, how do you calculated h? (in which row?)

Thank you!

Zoltán

06 Dec 2013

@JG: Yes, [x y] can also be a nx1 vector with n number of points in time. Use datenum to calculate a numeric vector from your dates. Variogram doesn't do the conversion for you.

06 Dec 2013

Thanks Wolfgang. Also, can this be used for temporal separation too? i.e., can [x y] be time?

25 Nov 2013

@JG: This syntax is correct. Take care, however, if latitude and longitude refer to geographic coordinates... The function doesn't calculate distances on a sphere.

25 Nov 2013

Thanks for this!
I just want to make sure I'm using it correctly;

If I have latitude and longitude coordinates ([x y]), and my data (z),

I use: variogram([x y],z)

24 Sep 2013

@Edgar.

Hi Edgar, yes, this seems to be an error in the function. Thanks for reporting it! I hardly needed those plot options so I probably forgot to care for them when adding anisotropy. Regarding your earlier question, I suppose that this should be ok.

I'll see if I can make a update in the next couple of days. Unfortunately, my time to support these functions at the moment is quite scarce...

24 Sep 2013

Hi Wolfang,
When types "cloud1" and "cloud2" are used in combination with anisotropy, the function does not return an array (a column for each theta tested). I'm guessing this is an error in the function?

Best,
Edgar

10 Sep 2013

Hi Wolfang,

I'm working with meteorological data, I can see a mountain range drives the spatial variation of the meteorological fields. The mountain range has an orientation (larger axis) at 110° (calculated clockwise from top, i.e. positive latitud axis). The corresponding semi-variogram from your script would be the one at 20°? Thanks for your help. Really nice algorithm, congrats!

12 Aug 2013

Hi Wolfgang,
Yes, that's a decision that concerns me these days, because either I use one variogram per time sample or as i have a lot of timesamples, I can do a training phase for kriging and I get a variogram characteristic from the system, which I will use in the test phase. I am currently working on my own 3d kriging and i wanted to compare results.
Thank you very much!

09 Aug 2013

Hi Ricardo, I am afraid my kriging won't work in three dimensions. However, it shouldn't be a very big deal do modify the function to do so. However, I am skeptical how you want to handle time and space dimensions in calculating one variogram.

09 Aug 2013

Hi again,
I just realize the NaN make sense in my data.
But still i have some questions.
Once I already know that variogram can work with 3d input, I tryed the kriging script but it seems like the input is 2dimensional, is there a way to use 3D data on the kriging script?
I am working with temperature samples along a period of time, and i wonder if i can in the variogram function give as values the entire time samples matrix, instead only one time sample only.
I hope i am being clear enough.
Thank you so much

09 Aug 2013
09 Aug 2013

Thank you so much Wolfgang!
I tried and at the beginning i had an error but i changed what @Shen said
d = sqrt(sum((X(i,:)-X(j,:)).^2,2));
and it worked, but the d.val has a lot of NaN, is that OK? because I have very bad fits on the variogramfit script.
Thanks again

25 Jul 2013

@Riccardo: variogram supports higher dimensional data. In your case, just call the function like
variogram([x(:) y(:) z(:)], values, ...)

25 Jul 2013

Hello Wolfgang,
I am trying to apply Kriging to a 3d mesh but first of all i don't know if i can use your variogram from a 3d data, it seems that only accepts X ans Y, not Z coordinates. Is there any way to use it with 3d input?
Thank you very much
Ricardo

02 Jan 2013

Hi Shen,

you are right! Thanks for pointing out this bug. Seems I have not thoroughly checked the multidimensional support since I've never needed it. I'll correct for it as soon as possible.

Thanks again,
Wolfgang

02 Jan 2013

Hi Wolfgang,

I am not sure if the following had been spotted:

In Line 253, when calculating the distances for more than two dimensions, the code was
d = sqrt(sum((X(i,:)-X(j,:)).^2));

I think it should be
d = sqrt(sum((X(i,:)-X(j,:)).^2,2));
as we need the sums of the rows but not the columns. After this correction, everything works perfectly in calculating 3-dimensional variograms.

Many thanks for your function. It is absolutely fabulous!

Best regards,
Shen

27 Dec 2012

@vipul utsav: the nugget variance is the variogram value at zero lag distance. You can estimate it visually from the experimental variogram or (better) use variogramfit (http://www.mathworks.de/matlabcentral/fileexchange/25948) to estimate it from the data.

27 Dec 2012

nugget variance from variogram ,how it is possible?

13 Dec 2012

@dd: Right now, this is not possible, but with a minor modification of the function, it is not a problem. Just enter following line in the section where the output for the type 'cloud1' is calculated (Line 202)

S.ij = iid(:,[1 2]);

This gives you the indices for each point pair. You can now take these to calculate e.g. the correlation coefficient for a binned lag distance.

x = rand(1000,1)*4-2;
y = rand(1000,1)*4-2;
z = 3*sin(x*15)+ randn(size(x));
d = variogram([x y],z,'type','cloud1');

% should give you this
d =

distance: [382476x1 double]
val: [382476x1 double]
ij: [382476x2 double]

distbins = unique(d.distance);

% calculate the correlation coefficient
% for the second distance bin
I = d.distance == distbins(2);

corrcoef(z(d.ij(I,1)),z(d.ij(I,2)))

ans =

1.0000 -0.2306
-0.2306 1.0000

Hope it works out for you.

Cheers, W.

13 Dec 2012

@ Wolfgang:
I would need it mostly for didactic purpose: how gamma, corr. and covar. are evolving along with lag distance.
Another question: how can I produce a crossplot of a variable between two lag distances?
Many thanks

12 Dec 2012

@dd: the covariance (C(h)) as a function of lag distance h is directly related to the semi-variogram (gamma(h)) and can be calculated by

gamma(h) = C(0)-C(h)

You can take the sill variance as C(0) but this only works for bounded variograms.

Why do you need the correlation or covariance?

12 Dec 2012

Hi Wolfgang,
I was wondering if there would be a simple way to include correlation and covariance in the analysis?
Thanks

12 Dec 2012
16 Aug 2012

Great function...helped me do a quick analysis of spatial correlation. One enhancement would be to return a handle to the plotted data, so users could change the color, symbols, etc.

11 Jun 2012

Hi Wolfgang,
I keep on getting these error messages when running this code. There's however nothing special to my data:

'Error using set
Bad property value found.
Object Name : axes
Property Name : 'XLim'
Values must be increasing and non-NaN.

Error in axis>LocSetLimits (line 208)
set(ax,...

Error in axis (line 94)
LocSetLimits(ax(j),cur_arg);

Error in variogram (line 217)
axis([0 params.maxdist 0 max(S.val)*1.1]);'

Any suggestion?
Cheers

06 Mar 2012
06 Mar 2012
06 Mar 2012
18 Jan 2012
28 Nov 2011

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

28 Nov 2011

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

24 Nov 2011

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

24 Nov 2011

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

14 Oct 2011
15 Jul 2011

@ 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

12 Jul 2011

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

08 Jul 2011

@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.

06 Jul 2011

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

25 Apr 2011
29 Sep 2010

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 !

26 Feb 2010

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).

17 Aug 2009

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

17 Aug 2009

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...

02 Aug 2009

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

30 Jul 2009

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

09 Feb 2010

dependence on consolidator was removed,
anisotropic experimental variogram is now supported.

21 Jul 2011

Removed dependency from IPDM. Fortunately, it is even faster now on my machine. The relatively large memory overhead is still unresolved. Added subsampling option.

24 Nov 2011

removed a bug in calculating the number of angular bins for anisotropic variograms.

09 Jan 2013

Bug removed that occurred when calculating the distances for more than two dimensions.