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Re: correlation function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg128774] Re: correlation function
*From*: Dana DeLouis <dana01 at me.com>
*Date*: Sat, 24 Nov 2012 02:30:07 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
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> ListConvolve and ListCorrelate should give same results when given right parameters.
Hi. They are very similar, but they do work differently.
It would help if you gave a 'small' example of what you are really trying to do.
Some thoughts on why you are not getting results you expect could be:
-Your FourierParameter is not set correctly.
-You are cutting off your data too much with {1,1}
-You are rotating the second vector, when you don't mean to.
With you large data (ie 309 data points), I get the same results.
v = << Your Data as posted >>
v//Length
309
SetOptions[{Fourier,InverseFourier},FourierParameters->{1,-1}] ;
ListCorrelate[v,v,{1,1}];
InverseFourier[Fourier[Reverse[v]]*Fourier[v]]//Reverse;
%%==%
True
InverseFourier[Fourier[v]^2];
ListConvolve[v,v,{1,1}];
%%==%
True
With either way, the above are always equal. Again, it depends on what you are doing.
>> ListConvolve and ListCorrelate should give same results
They operate slightly differently.
Here, we don't rotate v2, by using 0, to make it easier to see.
v1=v2={a,b,c};
// Here, we keep v2 as is, and shift it right to left
ListCorrelate[v1,v2,{1,1},0]
{a^2+b^2+c^2,a b+b c,a c}
// Here, we reverse v2, but shift it left to right
ListConvolve[v1,v2,{1,1},0]
{a^2,2 a b,b^2+2 a c}
// So, they will always be slightly different. By reversing v2, it's the same as ListConvolve, except we are going left to right.
// This is just the opposite of right to left. Add 'Reverse to make this equal to ListConvolve.
ListConvolve[v1,v2//Reverse,{1,1},0]
{a c,a b+b c,a^2+b^2+c^2}
This is the same as ListCorrelate, only backwards.
As a fun side note, when I've done InverseFourier[Fourier[v]^2 ] in other languages, it was to square a very large number.
For example, to do slow school-method multiplication, one would not chop the data off with {1,1}, but use {1,-1}.
Here's an example of 123 * 123
n=123;
v=n//IntegerDigits
{1,2,3}
// Don't rotate (use 0), and have the last digit of v2 (ie 9), end when it gets to the last digit of v1 (use -1)
ListConvolve[v,v,{1,-1},0]
{1,4,10,12,9}
// This is the correct answer in Base 10. To adjust, for the 12, we keep the 2, and carry the 1. 10+1 == 1, carry the 1, etc.
// The function FromDigits with default base 10 does all this for us:
FromDigits[%]
15129
// Same Answer:
n*n
15129
Here's a technique to try to see what's going on. Experiment with ListCorrelate as well.
// Here is what you have
ListConvolve[{a,b,c},{d,e,f},{1,1}] //MatrixForm
// This is what you are really doing. You're rotating {d,e,f} around.
ListConvolve[{a,b,c},{d,e,f},{1,1},{d,e,f},Times,Plus] //MatrixForm
// Same, but not adding.
ListConvolve[{a,b,c},{d,e,f},{1,1},{d,e,f},Times,List] //MatrixForm
// Different Start / End
ListConvolve[{a,b,c},{d,e,f},{1,1},0,Times,List] //MatrixForm
ListConvolve[{a,b,c},{d,e,f},{1,-1},0,Times,List] //MatrixForm
Now that I've seen the above, I may have said things backwards with regards to v1,v2. However, the results are the same.
Good Luck.
= = = = = = = = = =
HTH :>)
Dana DeLouis
Mac & Mathematica 8
= = = = = = = = = =
On Friday, November 23, 2012 3:38:21 AM UTC-5, jure lapajne wrote:
> Professor (physicist) said this function is called correlation =
function. Than I talked to someone from mathematics department and he =
said it's some sort of discrete convolution, so it really depends on =
person, how he/she calls it. ListConvolve and ListCorrelate should give =
same results when given right parameters. I think there is something =
strange about my data (linked in previous post), because I also have =
some other data and when I use them I get correct (same) results. I =
tried all the code in above answers and with given data nothing works. I =
think I'll just use fourier transform method because it returns =
symmetric data (which is correct) in contrast to ListCorrelate and =
ListConvolve which return asymmetric data.
>
> Thank you all.
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