fundamental principle of multiplication

i have 4 numbers as a row vector, p=[ 1 -1 j -j ];

Now, total number of different 4 digit numbers formed using elements of "p" is 4^4=256

Thus i need a 256*4 matrix.

How to create such a 256*4 matrix ?

[Image Analyst]

What is a 4 digit number? Can you give an example of the first 6 rows of what you want at the result?

[a]

@Image Analyst:

Here a 4 digit number is like,

1 1 1 1 ; 1 1 1 -1 ; 1 1 1 i ; 1 1 1 -i ; 1 1 -1 1; ... and so on(till 256 row vectors hence a 256x4 matrix).

first 6 rows of required data matrix are in text file attached.Please find the attached. (and the data need not be in that order).

But required matrix should be a "256x4 Complex double" having all rows unique.Any help ?

Answer 1

[Jos (10584)]

p = [ 1 -1 j -j ] ;
[a,b,c,d] = ndgrid(p) ;
M = [a(:) b(:) c(:) d(:)]

[a]

Thank you Jos (10584).

Answer 2

[Sean de Wolski]

[xx,yy,zz,qq] = ndgrid('1234');
V = [xx(:) yy(:) xx(:) qq(:)]

[a]

@Sean de Wolski: Thank You for your Answer.

But it is making "V" as a "256x4 char".

I want a "256x4 complex double".

I tried to use

>>str2num(V)

but it gives a "256x1 complex double" matrix.

[Cedric]

@Sean: I don't think that it works as expected..

 >> size(unique(V, 'rows'))
 ans =
    64     4

[a]

@cedric

yeah.

All rows are not unique.

In my case it should be all unique rows and matrix size should be 256x4 complex double.

Answer 3

[Cedric]

I guess that the following would work. I didn't think too much about it though and there must be a simpler or even trivial solution..

 >> ID = mod(floor((0:255).' * 2.^[0:-2:-6]), 4) + 1 ;
 >> p(ID)

Check

 >> size(unique(ID, 'rows'))
 ans =
   256     4

[a]

@cedric:

thank you for your answer but yeah you are right that there must be a simpler or even trivial solution.

[Cedric]

Just in case nobody proposes a better solution, the way this one works is comparable to the way you build tables of binary codes.. you build the first column as 01010101.., the second as 0011001100.., the third as 000011110000.., and so on. My solution does the same in base 4.