eigenvectors in maxima
- Subject: eigenvectors in maxima
- From: jason-sage at creativetrax.com
- Date: Thu, 28 May 2009 03:09:19 -0500
Robert Dodier wrote:
> Jason, I looked at the eigenvector code and it appears Maxima
> is just smashing all the vectors together, but it is easy to
> distinguish them. I've attached a patch so that eigenvectors
> returns [vals, vecs] where vals is a list of values and their
> multiplicities (just as it was before) and vecs is a list of lists
> of vectors (before it was just a list of vectors).
>
> Here is a sample session with the examples you gave.
> Sorry, it's probably a little messy. Comments, anyone?
>
This seems great, as far as I'm concerned. Thanks!
Jason
> (%i1) M1 : matrix ([0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 2]);
> [ 0 1 0 0 ]
> [ ]
> [ 0 0 0 0 ]
> (%o1) [ ]
> [ 0 0 2 0 ]
> [ ]
> [ 0 0 0 2 ]
> (%i2) [vals, vecs] : eigenvectors (M1);
> (%o2) [[[0, 2], [2, 2]], [[[1, 0, 0, 0]],
> [[0, 0, 1, 0], [0, 0, 0, 1]]]]
> (%i3) for i thru length (vals) do disp (val[i] = vals[i][1], mult[i] =
> vals[i][2], vec[i] = vecs[i]);
> val = 0
> 1
>
> mult = 2
> 1
>
> vec = [[1, 0, 0, 0]]
> 1
>
> val = 2
> 2
>
> mult = 2
> 2
>
> vec = [[0, 0, 1, 0], [0, 0, 0, 1]]
> 2
>
> (%o3) done
> (%i4) M2 : matrix ([0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 1], [0, 0, 0, 2]);
> [ 0 0 0 0 ]
> [ ]
> [ 0 0 0 0 ]
> (%o4) [ ]
> [ 0 0 2 1 ]
> [ ]
> [ 0 0 0 2 ]
> (%i5) [vals, vecs] : eigenvectors (M2);
> (%o5) [[[0, 2], [2, 2]], [[[1, 0, 0, 0], [0, 1, 0, 0]],
> [[0, 0, 1, 0]]]]
> (%i6) for i thru length (vals) do disp (val[i] = vals[i][1], mult[i] =
> vals[i][2], vec[i] = vecs[i]);
> val = 0
> 1
>
> mult = 2
> 1
>
> vec = [[1, 0, 0, 0], [0, 1, 0, 0]]
> 1
>
> val = 2
> 2
>
> mult = 2
> 2
> (%i1) M1 : matrix ([0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 2]);
> [ 0 1 0 0 ]
> [ ]
> [ 0 0 0 0 ]
> (%o1) [ ]
> [ 0 0 2 0 ]
> [ ]
> [ 0 0 0 2 ]
> (%i2) [vals, vecs] : eigenvectors (M1);
> (%o2) [[[0, 2], [2, 2]], [[[1, 0, 0, 0]],
> [[0, 0, 1, 0], [0, 0, 0, 1]]]]
> (%i3) for i thru length (vals) do disp (val[i] = vals[i][1], mult[i] =
> vals[i][2], vec[i] = vecs[i]);
> val = 0
> 1
>
> mult = 2
> 1
>
> vec = [[1, 0, 0, 0]]
> 1
>
> val = 2
> 2
>
> mult = 2
> 2
>
> vec = [[0, 0, 1, 0], [0, 0, 0, 1]]
> 2
>
> (%o3) done
> (%i4) M2 : matrix ([0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 1], [0, 0, 0, 2]);
> [ 0 0 0 0 ]
> [ ]
> [ 0 0 0 0 ]
> (%o4) [ ]
> [ 0 0 2 1 ]
> [ ]
> [ 0 0 0 2 ]
> (%i5) [vals, vecs] : eigenvectors (M2);
> (%o5) [[[0, 2], [2, 2]], [[[1, 0, 0, 0], [0, 1, 0, 0]],
> [[0, 0, 1, 0]]]]
> (%i6) for i thru length (vals) do disp (val[i] = vals[i][1], mult[i] =
> vals[i][2], vec[i] = vecs[i]);
> val = 0
> 1
>
> mult = 2
> 1
>
> vec = [[1, 0, 0, 0], [0, 1, 0, 0]]
> 1
>
> val = 2
> 2
>
> mult = 2
> 2
>
> vec = [[0, 0, 1, 0]]
> 2
>
> (%o6) done
>
> vec = [[0, 0, 1, 0]]
> 2
>
> (%o6) done
>
>
> FWIW
>
> Robert Dodier
>
> PS.
> --- share/matrix/eigen.mac 22 Nov 2007 17:11:14 -0000 1.4
> +++ share/matrix/eigen.mac 28 May 2009 04:09:26 -0000
> @@ -114,7 +114,7 @@
> unknowns:endcons(concat(notknwn,index1),unknowns),
> vectr:columnvector(unknowns),matrx:mat.vectr,
> nondiagonalizable:false,
> - listall:[eigvals],realonly:false,algebraic:true,
> + eigvecs:[],realonly:false,algebraic:true,
> for index1 thru count do
> (count:mi(count-part(multiplicities,index1)+1),
> mmatrx:matrx-part(eigvals,1,index1)*vectr,
> @@ -132,8 +132,8 @@
> (print(" "),print("algsys failure: the eigenvector(s) for the",
> index1,"th eigenvalue will be missing.")),
> if hermitianmatrix and %rnum>1 then unit:gramschmidt(unit),
> - listall:append(listall,unit)),
> - return(listall)))$
> + eigvecs:append(eigvecs,[unit])),
> + return([eigvals, eigvecs])))$
>
>
> /* the first arg is of the form [r1,r2,r3].
>
>