Alex ....
Thanks for posting your generalized numarray eigenvalue solution ....
It's been almost 30 years since I've looked at any characteristic equation, eigenvalue, eignevector type of processing and at this point I don't recall many of the particulars ....
Not being sure about the nature of the monic( p ) function, I implemented it as an element-wise division of each of the coefficients ....
Is this anywhere near the correct interpretation for monic( p ) ?
Using the version below, Python complained about the line ....
. M[ -1 , : ] = -p[ : -1 ]
So, in view of you comments about slicing in you follow-up, I tried without the slicing on the right ....
. . M[ -1 , : ] = -p[ -1 ]
The following code will run and produce results, but I'm wondering if I've totally screwed it up since the results I obtain are different from those obtained from the specific 5th order Numeric solution previously posted here ....
. from numarray import * . . import numarray.linear_algebra as LA . . def monic( this_list ) : . . m = [ ] . . last_item = this_list[ -1 ] . . for this_item in this_list : . . m.append( this_item / last_item ) . . return m . . . def roots( p ) : . . p = monic( p ) . . n = len( p ) # degree of polynomial . . z = zeros( ( n , n ) ) . . M = asarray( z , typecode = 'f8' ) # typecode = c16, complex . . M[ : -1 , 1 : ] = identity( n - 1 ) . . M[ -1 , : ] = -p[ -1 ] # removed : slicing on the right . . return LA.eigenvalues( M ) . . . coeff = [ 1. , 3. , 5. , 7. , 9. ] . . print ' Coefficients ..' . print . print ' %s' % coeff . print . print ' Eigen Values .. ' . print . . eigen_values = roots( coeff ) . . for this_value in eigen_values : . . print ' %s' % this_value .
Any clues would be greatly appreciated ....
-- Stanley C. Kitching Human Being Phoenix, Arizona -- http://mail.python.org/mailman/listinfo/python-list
