Re: Summation Problem w/ 5.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg44125] Re: Summation Problem w/ 5.0*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Thu, 23 Oct 2003 07:15:47 -0400 (EDT)*Organization*: The University of Western Australia*References*: <bllp1h$c11$1@smc.vnet.net> <bmoda0$hph$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <bmoda0$hph$1 at smc.vnet.net>, andrea.knorr at engr.uconn.edu (Andrea) wrote: > I've imported several .csv files, and grouped several elements into > the lists "virus", "infected", and "uninfected", which are blood > concentrations. "vtime", "ytime", and "xtime" are the corresponding > points in time for when the concentrations were measured. To run or even test minfcn, the form of this data is required. > Below is the relevant code, which is basically for nonlinear regression: > > titer[lambda_, beta_, d_, k_, a_, u_] := > > Module[{soln, x, y, v, valueslist, xeval, yeval, veval}, > > soln = NDSolve[{ > x'[t] == lambda - d x[t] - beta x[t] v[t], > y'[t] == beta x[t] v[t] - a y[t], > v'[t] == k y[t] - u v[t], > x[0] == 10^9, y[0] == 0, v[0] == 10^9}, > {x, y, v}, {t, 0, 2500}]; > > xtiter = Evaluate[x[xtime] /. soln]; > ytiter = Evaluate[y[ytime] /. soln]; > vtiter = Evaluate[v[vtime] /. soln]; > > values = Table[Flatten[{xtiter, ytiter, vtiter}, 1]]; > values > ]; This code (a form of Kermack-MacKendrick disease model?), can be improved as follows. First, I think that it is better to use DSolve up find the numerical solution (up to the maximum time required) as interpolating functions: titer[lambda_, beta_, d_, k_, a_, u_][{xtime_,ytime_,vtime_}] := Module[{x, y, v}, {x, y, v} /. First[NDSolve[{ x'[t] == lambda - d x[t] - beta x[t] v[t], y'[t] == beta x[t] v[t] - a y[t], v'[t] == k y[t] - u v[t], x[0] == 10^9, y[0] == 0, v[0] == 10^9}, {x, y, v}, {t, 0, Max[{xtime,ytime,vtime}]}]] ] (You probably should use scaling to reduce the size of the initial values, say from 10^9 to 1). In this way, a solution (note again that scaling would help), e.g., endtimes = {100,120,150}; nsol = titer[10^7, 5 10^-10, 0.1, 500, 0.5, 5][endtimes] can be plotted (here v is scaled by 10^(-2)), Plot[Evaluate[{1, 1, 10^(-2)} Through[nsol[t]]], {t, 0, Min[endtimes]}, PlotRange -> All, PlotStyle -> {Hue[0], Hue[1/3], Hue[1/2]}]; and then separately compute the endpoints calcs = Inner[Compose, nsol, endtimes, List] > minfcn[lambda_, beta_, d_, k_, a_, u_] := > > Module[{i, j}, > > diffsum = > Sum[10000*(uninfected[[i, 2]] - calcs[[1, i]])^2 + > 10000*(infected[[i, 2]] - calcs[[2, i]])^2, {i, > Length[uninfected]}] + > Sum[(virus[[j, 2]] - calcs[[3, j]])^2, {j, Length[virus]}]; > diffsum > ] > > minfcn[10^7, 5*10^-10, 0.1, 500, 0.5, 5] > > When I evaluate "minfcn" with the values listed above, which are > "correct" published values, that's where I get my problem. If I > change the minfcn problem so that the sum doesn't cover the full > length of each list, but rather only up to a particular element, I get > one number. Any summation past that point results in the problem I > have described below. I do not understand the problem you are encountering. Values for "virus", "infected", and "uninfected" might help ... Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul