Skip to main content

numerics - Any way of solving this system of nonlinear equations with non integer powers?


I have a system of four nonlinear equations. Some of the exponents are fractions. I was wondering if this is what is causing NSolve to run for hours without giving any results.


I first create a list of parameters that I eventually want to play around with to see how results change. This parameter list is "dat". I then specify the equations as follows:


dat = {alpha -> 1/3, beta -> 1/3, sigma -> 1/3, gam -> 0.5, 
  psy -> 0.5, delta -> 0.5, vu -> 0.5, a -> 1, A -> 1/3, B -> 1/3, 

  C -> 1/3, Ls -> 10, T -> 10, mc -> 1.5}

{p2 - w^psy pw^gam ((psy/gam)^gam + (gam/psy)^psy) == 0, 
  Ls - (beta/w)^(alpha + sigma) (pw/(alpha (1 + a C r T)))^
      alpha (r/sigma)^sigma (w Ls delta + r T A) - (pw psy/w gam)^
      gam ((w Ls vu + r T B)/p2) == 0, 
  T - (sigma/r)^(alpha + beta) (w/beta)^
      beta (pw/(alpha (1 + a C r T)))^alpha (w Ls delta + r T A) == 0, 
  pw - (((((1 + a C r T) alpha)/pw)^(beta + sigma) (w/beta)^
           beta (r/sigma)^

           sigma (w Ls delta + r T A) +  ((w gam)/(psy pw))^
           psy ((w Ls vu + r T B)/p2)) mc (1 + 
         a C r T))/((((1 + a C r T) alpha)/pw)^(beta + sigma) (w/
           beta)^beta (r/sigma)^
         sigma (w Ls delta + r T A)  + ((w gam)/(psy pw))^
         psy ((w Ls vu + r T B)/p2) (1 + a C r T)) == 0} /. dat

And then proceed with NSolve:


NSolve[%, {w, r, p2, pw}, Reals]


But Nothing happens. I tried using Rationalize but it does not seem to help. I am new to Mathematica so I hope that I am doing something wrong and that I missed something and can solve the system. Any suggestions?


Finally, how can I loop and redo this calculation with different parameters in the "dat" list?




Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

How to remap graph properties?

Graph objects support both custom properties, which do not have special meanings, and standard properties, which may be used by some functions. When importing from formats such as GraphML, we usually get a result with custom properties. What is the simplest way to remap one property to another, e.g. to remap a custom property to a standard one so it can be used with various functions? Example: Let's get Zachary's karate club network with edge weights and vertex names from here: http://nexus.igraph.org/api/dataset_info?id=1&format=html g = Import[ "http://nexus.igraph.org/api/dataset?id=1&format=GraphML", {"ZIP", "karate.GraphML"}] I can remap "name" to VertexLabels and "weights" to EdgeWeight like this: sp[prop_][g_] := SetProperty[g, prop] g2 = g // sp[EdgeWeight -> (PropertyValue[{g, #}, "weight"] & /@ EdgeList[g])] // sp[VertexLabels -> (# -> PropertyValue[{g, #}, "name"]...
Post a Comment
Read more