Skip to main content

evaluation - General::ivar is not a valid variable when plotting - what actually causes this and how to avoid it?


I was just evaluating a couple of expressions and started to get errors like this:


General::ivar: -1.49994 is not a valid variable. >>
General::ivar: -1.43871 is not a valid variable. >>
General::ivar: -1.37749 is not a valid variable. >>
General::stop: Further output of General::ivar will be 
               suppressed during this calculation. >>

I'm doing nothing complicated - currently, I simply did this:


f[x_]:=x^2 + 2x + 1

Plot[f[x], {x, -4, 4}]
Solve[f[x] == 4]
g[x_]:=D[f[x], x]
Plot[g[x], {x, -2, 2}]
// ^ errors caused by this

Actually, this isn't the exact quadratic I am investigating, but it is a quadratic and I expected this to work. I googled, as you'd expect, and found this Stack Overflow question which suggested:


Plot[Evaluate[g[x]], {x, -2, 2}]

As a workaround.



It works - my question is, why doesn't that set of instructions generate that error (I can see it is something to do with replacing, but why is one plot different from the other?) and how can I avoid it? Is there something I should specifically have done in forming g?



Answer



The problem lies in g[x_] := D[f[x], x]; remember that what SetDelayed (that is, :=) does is to replace stuff on the right corresponding to patterns on the left before evaluating. Thus, when one does something like g[2] (and something like this happens within Plot[]), you are in fact evaluating D[f[2], 2], and since one cannot differentiate with respect to a constant ;), you get the General::ivar error message.


If you use Set instead (that is, g[x_] = D[f[x], x]), f[x] is differentiated first before the result of D[] is assigned to g[x_]. Since what's on the right of g[x_] is now an actual function, Plot[] no longer has a reason to complain.


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