CoCoA:HowTo:Handle Matlab Matrices
Having a matrix in Matlab and load it into CoCoA4 is not a very easy thing to do. First, the representation is slightly different, second you have to adjust Matlab's IEEE notation of floats into a presentation CoCoA is able to read.
This howto explains, how this can be solved.
Exporting from Matlab to ANSI
The Code to create a almost CoCoa-like list of lists from a Matrix M in Matlab is the following:
S = '['; for i=1:1:Rows if i == 1 S = [S, '[']; else S = [S, ',[']; end; for j=1:1:(Columns-1) S = [ S, num2str(M(i,j)),',']; end; S = [ S, num2str(M(i,Columns)),']']; end; S = [S,']'];
code by dheldt 12:25, 8 Sep 2005 (CEST) (M is a Rows x Columns - matrix)
No we have something like:
M = [[1,0.333333333];[2,25, 0.000000000000004]]
S = [[1,0.33333],[2.25,4e-015]]
Importing from ANSI into CoCoA
We have to strip the exponential notation into a CoCoA readable format. My suggestion to achieve this, is using a list construction in CoCoa.
We can interpret the e in the exponential representation as an indeterminate in Q[e]. Then the leading term of a number is the mantisse in any way. If there is a second term, we know that this term represent the exponent, so P-LM(P) represents the exponent. If there is only one term P-LM(P) equals 0. So LC(P)*10^(LC(P-LM(P)) multiplies the mantisse (LC(P)) with 10^exponent.
In CoCoAL this looks like
Use Q[e]; S := ... -- put the String S here K := ; ForEach P In S Do L := NewList(0); ForEach N In P Do If Not(N=0) Then Append(L, LC(N)*10^(LC(N - LM(N))) ); Else Append(L, 0); EndIf; EndForEach; Append(K,L); EndForEach; -- outdated version: --K := [ -- [ LC(N)*10^(LC(N - LM(N)) ) -- | N In P ] -- | P In S]; -- this code does not work with 0 in S, because LM(0) is not defined!
And now we have a list of list K with valid numbers. For example
S := [[1,0.33333],[2.25,4e-015]];
K := [[1, 33333/100000], [9/4, 1/250000000000000];