[Scipy-tickets] [SciPy] #1454: patch to allow optimize of nonsquare or degenerate systems

SciPy Trac scipy-tickets@scipy....
Sun Jun 5 04:58:59 CDT 2011


#1454: patch to allow optimize of nonsquare or degenerate systems
----------------------------+-----------------------------------------------
 Reporter:  dstahlke        |       Owner:  somebody   
     Type:  enhancement     |      Status:  needs_work 
 Priority:  normal          |   Milestone:  Unscheduled
Component:  scipy.optimize  |     Version:  devel      
 Keywords:                  |  
----------------------------+-----------------------------------------------
Changes (by pv):

  * status:  needs_review => needs_work


Comment:

 The requirement "# conditions = # equations" applies only to the large-
 scale nonlinear equation solvers, not to the optimization routines. You
 probably want to use the least-squares solver (`scipy.optimize.leastsq`),
 if it works for your problem size, rather than the nonlinear equation
 solvers.

 Currently, there are no large-scale least-squares solvers in scipy.
 Implementations (based on literature) would be very welcome.

 Changing the inversion of the Jacobian to a least-squares solution is
 indeed one way to move from nonlinear equations to nonlinear least-square.
 However, doing it with `pinv` does not make so much sense to me, since if
 it works, the problem is small enough for the dense
 `scipy.optimize.leastsq` solver to work with. Also, I'm not sure if the
 convergence and step size criteria in the inexact Newton need to be
 adjusted from nonlin-LSQ.

 So I don't believe this patch should go in, as it is now.

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1454#comment:2>
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