Internal error on eigenvalues of zero matrices.

[dantswain]

I noticed some errors on computing the eigenvalues of zero matrices (matrices consisting of all zeros).

Test definitions:

IN> numeric.eig([0]) 
OUT> {lambda: {x: [0], y: [0]},
      E: {x: [1], y: [0]}}
IN> numeric.eig([[0, 0], [0, 0]]) 
OUT> {lambda: {x: [0, 0], y: [0, 0]}, 
      E: {x: [[1, 0], [0, 1]],
          y: [[0, 0], [0, 0]] }}
IN> numeric.eig([[0, 0, 0], [0, 0, 0], [0, 0, 0]]) 
OUT> {lambda: {x: [0, 0, 0], y: [0, 0, 0]}, 
      E: {x: [[1, 0, 0], [0, 1, 0], [0, 0, 1]],
          y: [[0, 0, 0], [0, 0, 0], [0, 0, 0]] }}

Results:

132 FAIL numeric.eig([0])==>Error:numeric:toUpperHessenberg()onlyworksonsquarematrices!=={lambda:{x:[0],y:[0]},E:{x:[1],y:[0]}}
133 FAIL numeric.eig([[0,0],[0,0]])==>{lambda:{x:[0,0],y:},E:{x:[[1,1],[0,0]],y:}}!=={lambda:{x:[0,0],y:[0,0]},E:{x:[[1,0],[0,1]],y:[[0,0],[0,0]]}}
134 FAIL numeric.eig([[0,0,0],[0,0,0],[0,0,0]])==>Error:eig:internalerror!=={lambda:{x:[0,0,0],y:[0,0,0]},E:{x:[[1,0,0],[0,1,0],[0,0,1]],y:[[0,0,0],[0,0,0],[0,0,0]]}}

The size 1 case is degenerate, but should still work. The size 2 case correctly identifies the eigenvalues as zero (multiplicity 2) but doesn't choose eigenvalues to span the space. The size 3 case fails on an error in the house function. All cases could probably be handled by checking if the matrix is a zero matrix and then just returning zeros as the eigenvalues and the identity matrix as the eigenvector generator.

[sloisel]

There's a bug with matrices with repeated eigenvalues. I haven't had the
time to fix it.

On Tue, Nov 19, 2013 at 2:57 AM, Dan [email protected] wrote:

I noticed some errors on computing the eigenvalues of zero matrices
(matrices consisting of all zeros).

Test definitions:

IN> numeric.eig([0])
OUT> {lambda: {x: [0], y: [0]},
E: {x: [1], y: [0]}}
IN> numeric.eig([[0, 0], [0, 0]])
OUT> {lambda: {x: [0, 0], y: [0, 0]},
E: {x: [[1, 0], [0, 1]],
y: [[0, 0], [0, 0]] }}
IN> numeric.eig([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
OUT> {lambda: {x: [0, 0, 0], y: [0, 0, 0]},
E: {x: [[1, 0, 0], [0, 1, 0], [0, 0, 1]],
y: [[0, 0, 0], [0, 0, 0], [0, 0, 0]] }}

Results:

132 FAIL numeric.eig([0])==>Error:numeric:toUpperHessenberg()onlyworksonsquarematrices!=={lambda:{x:[0],y:[0]},E:{x:[1],y:[0]}}
133 FAIL numeric.eig([[0,0],[0,0]])==>{lambda:{x:[0,0],y:},E:{x:[[1,1],[0,0]],y:}}!=={lambda:{x:[0,0],y:[0,0]},E:{x:[[1,0],[0,1]],y:[[0,0],[0,0]]}}
134 FAIL numeric.eig([[0,0,0],[0,0,0],[0,0,0]])==>Error:eig:internalerror!=={lambda:{x:[0,0,0],y:[0,0,0]},E:{x:[[1,0,0],[0,1,0],[0,0,1]],y:[[0,0,0],[0,0,0],[0,0,0]]}}

The size 1 case is degenerate, but should still work. The size 2 case
correctly identifies the eigenvalues as zero (multiplicity 2) but doesn't
choose eigenvalues to span the space. The size 3 case fails on an error in
the house function. All cases could probably be handled by checking if
the matrix is a zero matrix and then just returning zeros as the
eigenvalues and the identity matrix as the eigenvector generator.

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Sébastien Loisel
Department of Mathematics
Heriot-Watt University
Riccarton EH14 4AS
United Kingdom
web: http://www.ma.hw.ac.uk/~loisel/
email: S.Loisel at hw.ac.uk
phone: +44 131 451 3234
fax: +44 131 451 3249