algorithm for non-dimensionalization

[gyromagnetic]

Hi,
I am trying to non-dimensionalize some data I have obtained. There are
no 'standard' dimensionless groups for my application, so I would like
to obtain the 'best' non-dimensional groups based on some statistical
measures of the resulting transformed data.

At this point, I am looking for a way to generate dimensionless
groupings from a set of base units. I would like to have a way to
output all dimensionless groups that comprise no more than some
specified number of fundamental (or base) units.

For instance, if I have data like the following:

dat1(length), dat2(time), dat3(length), dat4(length/time),
dat5(length^2)

and I want dimensionless groups with no more than four base units, I
would like a result like the following:

dat1/dat3, dat1/(dat2*dat4), dat5/(dat1*dat3), dat5/(dat2*dat4*dat1),
....

I plan to code this in Python, and would appreciate any thoughts you
might have about algorithms or approaches to carry out this task.

Thank you.

-g

[Paolino]

gy**********@gmail.com wrote:

Hi,
I am trying to non-dimensionalize some data I have obtained. There are
no 'standard' dimensionless groups for my application, so I would like
to obtain the 'best' non-dimensional groups based on some statistical
measures of the resulting transformed data.

At this point, I am looking for a way to generate dimensionless
groupings from a set of base units. I would like to have a way to
output all dimensionless groups that comprise no more than some
specified number of fundamental (or base) units.

For instance, if I have data like the following:

dat1(length), dat2(time), dat3(length), dat4(length/time),
dat5(length^2)

and I want dimensionless groups with no more than four base units, I
would like a result like the following:

dat1/dat3, dat1/(dat2*dat4), dat5/(dat1*dat3), dat5/(dat2*dat4*dat1),
...

I plan to code this in Python, and would appreciate any thoughts you
might have about algorithms or approaches to carry out this task.

Thank you.

-g

Thinking more,it's an eigenvector problem.

Where all dat* magnitudes are expressed as a vector of integers in the
dimensions space,and the result vector is all 0.

IE
E=[m][L^2][T^-2]
v=[L][T^-1]
f=[T^-1]
p=[m][L][T^-1]
.......
in the mass,lenght,time space are

[1,2,-2]
[0,1,-1]
[0,0,-1]
[1,1,-1]

say matrix D

then

D*[x1,x2,x3,x4]=[0,0,0] (looking for adimensionals)

So you are looking for an eigenvector formed by only integers.

Ciao Paolino



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