Fwd: [Matplotlib-users] Fwd: python version of nnls/fnnls

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plain text:

#!/usr/bin/env python

#
# ported fnnls.m to fnnls.py
#
# gjok - 20050816
#

import sys, math
import numpy, numpy.linalg.linalg as la

def any(X)     : return len(numpy.nonzero(X)) !=3D 0
def find(X)    : return numpy.nonzero(X)
def norm(X, d) : return max(numpy.sum(abs(X)))

#
# x, w =3D fnnls(XtX, Xty, tol)
#
def fnnls(XtX, Xty, tol =3D 0) :
#FNNLS	Non-negative least-squares.
#
# 	Adapted from NNLS of Mathworks, Inc.
#          [x,w] =3D nnls(X, y)
#
#	x, w =3D fnnls(XtX,Xty) returns the vector X that solves x =3D =
pinv(XtX)=20
*Xty
#	in a least squares sense, subject to x >=3D 0.
#	Differently stated it solves the problem min ||y - Xx|| if
#	XtX =3D X'*X and Xty =3D X'*y.
#
#	A default tolerance of TOL =3D MAX(SIZE(XtX)) * NORM(XtX,1) * =
EPS
#	is used for deciding when elements of x are less than zero.
#	This can be overridden with x =3D fnnls(XtX,Xty,TOL).
#
#	[x,w] =3D fnnls(XtX,Xty) also returns dual vector w where
#	w(i) < 0 where x(i) =3D 0 and w(i) =3D 0 where x(i) > 0.
#
#	See also NNLS and FNNLSb

#	L. Shure 5-8-87
#	Revised, 12-15-88,8-31-89 LS.
#	(Partly) Copyright (c) 1984-94 by The MathWorks, Inc.

#	Modified by R. Bro 5-7-96 according to
#       Bro R., de Jong S., Journal of Chemometrics, 1997, 11, 393-401
# 	Corresponds to the FNNLSa algorithm in the paper
#=09
#	Rasmus bro
#	Chemometrics Group, Food Technology
#	Dept. Dairy and Food Science
#	Royal Vet. & Agricultural
#	DK-1958 Frederiksberg C
#	Denmark
#	rb...@kv...
#	http://newton.foodsci.kvl.dk/users/rasmus.html
#  Reference:
#  Lawson and Hanson, "Solving Least Squares Problems", Prentice-=20
Hall, 1974.
#

# initialize variables
     m =3D XtX.shape[0]
     n =3D XtX.shape[1]

     if tol =3D=3D 0 :
         eps =3D 2.2204e-16
         tol =3D 10 * eps * norm(XtX,1)*max(m, n);
     #end

     P =3D numpy.zeros(n, numpy.Int16)
     P[:] =3D -1
     Z =3D numpy.arange(0,n)

     z =3D numpy.zeros(m, numpy.Float)
     x =3D numpy.array(P)
     ZZ =3D numpy.array(Z)

     w =3D Xty - numpy.dot(XtX, x)

   # set up iteration criterion
     iter =3D 0
     itmax =3D 30 * n

   # outer loop to put variables into set to hold positive coefficients
     while any(Z) and any(w[ZZ] > tol) :
         wt =3D w[ZZ].max()
         t =3D find(w[ZZ] =3D=3D wt)
         t =3D t[-1:][0]
         t =3D ZZ[t]
         P[t] =3D t
         Z[t] =3D -1
         PP =3D find(P !=3D -1)

         ZZ =3D find(Z !=3D -1)
         if len(PP) =3D=3D 1 :
             XtyPP =3D Xty[PP]
             XtXPP =3D XtX[PP, PP]
             z[PP] =3D XtyPP / XtXPP
         else :
             XtyPP =3D numpy.array(Xty[PP])
             XtXPP =3D numpy.array(XtX[PP, numpy.array(PP)[:, =20
numpy.NewAxis]])
             z[PP] =3D numpy.dot(XtyPP, la.generalized_inverse(XtXPP))
         #end
         z[ZZ] =3D 0

# inner loop to remove elements from the positive set which no longer =20=

belong
         while any(z[PP] <=3D tol) and (iter < itmax) :
             iter +=3D 1
             iztol =3D find(z <=3D tol)
             ip =3D find(P[iztol] !=3D -1)
             QQ =3D iztol[ip]

             if len(QQ) =3D=3D 1 : alpha =3D x[QQ] / (x[QQ] - z[QQ])
             else :
                 x_xz =3D x[QQ] / (x[QQ] - z[QQ])
                 alpha =3D x_xz.min()
             #end

             x +=3D alpha * (z - x)
             iabs =3D find(abs(x) < tol)
             ip =3D find(P[iabs] !=3D -1)
             ij =3D iabs[ip]

             Z[ij] =3D numpy.array(ij)
             P[ij] =3D -1
             PP =3D find(P !=3D -1)
             ZZ =3D find(Z !=3D -1)

             if len(PP) =3D=3D 1 :
                 XtyPP =3D Xty[PP]
                 XtXPP =3D XtX[PP, PP]
                 z[PP] =3D XtyPP / XtXPP
             else :
                 XtyPP =3D numpy.array(Xty[PP])
                 XtXPP =3D numpy.array(XtX[PP, numpy.array(PP)[:, =20
numpy.NewAxis]])
                 z[PP] =3D numpy.dot(XtyPP, =
la.generalized_inverse(XtXPP))
             #endif
             z[ZZ] =3D 0
         #end while
         x =3D numpy.array(z)
         w =3D Xty - numpy.dot(XtX, x)
     #end while

     return x, w

#end def

if __name__ =3D=3D '__main__' :
#
# test [x, w] =3D fnnls(Xt.X, Xt.y, tol)
# to solve min ||y - X.x|| s.t. x >=3D 0
#
# matlab:lsqnonneg
#   X =3D [1, 10, 4, 10; 4, 5, 1, 12; 5, 1, 9, 20];
#   y =3D [4; 7; 4]
#   x =3D lsqnonneg(X, y) =3D> x =3D [0.9312; 0.3683; 0; 0];
#

     X =3D numpy.array([[1, 10, 4, 10], [4, 5, 1, 12], [5, 1, 9, 20]], =20=

numpy.Float)
     y =3D numpy.array([4, 7, 4], numpy.Float)

     if False :
         X =3D numpy.array([[1, 10, 4, 10],
                          [4, 5, 1, 12],
                          [5, 1, 9, 20],
                          [4, 3, 2, 1]], numpy.Float)
         y =3D numpy.array([4, 7, 4, 1], numpy.Float)
     #end

     if False :
         X =3D numpy.zeros((20, 20), numpy.Float)
         for n in range(20) : X[n,:] =3D numpy.arange(0.0, 400.0, step =20=

=3D 20)
         y =3D numpy.arange(0.0, 20.0)
     #end
     Xt =3D numpy.transpose(numpy.array(X))
     x, w =3D fnnls(numpy.dot(Xt, X), numpy.dot(Xt, y))

     print 'X =3D ', X
     print 'y =3D ', y
     print 'x =3D ', x
#end if __name__ =3D=3D '__main__'

Begin forwarded message:

> From: Graeme O'Keefe <gj...@ne...>
> Date: 25 May 2006 8:46:07 PM
> To: matplotlib user list <mat...@li...>
> Subject: [Matplotlib-users] Fwd: python version of nnls/fnnls
>
>
> Dear matplotlibers,
>
> I seem to use Non Negative Least Squares every couple of months and =20=

> the most recent problem I solved reminded me that I meant to post =20
> this last November.
>
> fnnls.py is a port of fnnls.m which was written by Rasmus Bro =20
> (http://newton.foodsci.kvl.dk/users/rasmus.html, code available at =20
> http://www.ub.es/gesq/mcr/als/fnnls.m, and also available on Matlab =20=

> Central).
>
> I've retained Rasmus' comments and translated the matlab to python/=20
> numpy.
>
=EF=BF=BC
>
> I've used this to linearise problems such as:
> 	fitting Neutron TOF data with a E0 energy spectrum of gaussians =20=

> (with energy-resolutions a function of TOF =3D> E): exp(-((E - E0) / =20=

> deltaE)^2)
> 	fitting Cerebral Blood Flow data with a k-spectrum set of =20
> exponentials: exp(-kt)
> 	fitting BGO detector pulses (to detect/correct pile-up) with =20
> Tdelay-spectrum of exponentials: exp(-(t - Tdelay) / tau)
>
> Hope others find it as useful as I have.
>
> regards,
>
>
> Graeme
>
>
>
> Graeme O'Keefe, PhD, MACPSEM
> Principal Medical Physicist
> Centre for PET
> Austin Hospital
> Tel: (613)-9496-5767
> Fax: (613) 9458-5023
>
>