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

 [Matplotlib-users] Fwd: python version of nnls/fnnls From: Graeme O'Keefe - 2006-05-25 10:44:47 Attachments: Message as HTML ```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 (http://=20= newton.foodsci.kvl.dk/users/rasmus.html, code available at http://=20 http://www.ub.es/gesq/mcr/als/fnnls.m, and also available on Matlab 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 = Tdelay-=20 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 ```

 [Matplotlib-users] python version of nnls/fnnls From: Graeme O'Keefe - 2006-05-25 03:40:33 Attachments: Message as HTML ```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 (http://=20= newton.foodsci.kvl.dk/users/rasmus.html, code available at http://=20 http://www.ub.es/gesq/mcr/als/fnnls.m, and also available on Matlab 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 = Tdelay-=20 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 ```
 [Matplotlib-users] Fwd: python version of nnls/fnnls From: Graeme O'Keefe - 2006-05-25 10:44:47 Attachments: Message as HTML ```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 (http://=20= newton.foodsci.kvl.dk/users/rasmus.html, code available at http://=20 http://www.ub.es/gesq/mcr/als/fnnls.m, and also available on Matlab 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 = Tdelay-=20 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 ```
 Re: [Matplotlib-users] Fwd: python version of nnls/fnnls From: Alan G Isaac - 2006-05-25 15:18:27 ```On Thu, 25 May 2006, Graeme O'Keefe apparently wrote: > fnnls.py And it is ... where? Cheers, Alan Isaac ```
 Fwd: [Matplotlib-users] Fwd: python version of nnls/fnnls From: Graeme O'Keefe - 2006-05-25 15:39:59 Attachments: Message as HTML ```Seems the last email didn't deliver the attachement (even though I =20 received it back?) The attachment is here again but just in case, here's the code as =20 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@... # 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 > Date: 25 May 2006 8:46:07 PM > To: matplotlib user list > 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 > > ```