Skip to main content

factorization - Lists of coefficients of derivatives


I want to extract two separate lists of coefficients of derivatives. If I have, for example,


cl= A1*D[P[x, y], {x, 1}] + A2*D[P[x, y], {x, 2}] + 
    A3*D[Q[x, y], {y, 3}] + A4*D[Q[x, y], {y, 1}];


I want to extract the lists {A1, A2} and {A3, A4} but do not want to type all the derivative expressions into command CoefficientList. I want to extract these lists programmatically because of I have a very long list of derivatives in my actual problem, which I thought was too long to post here.


The following seems to work, but how can I do it without typing in the list of derivatives?


Coefficient[cl, {D[P[x, y], {x, 1}], D[P[x, y], {x, 2}]}]
Coefficient[cl, {D[Q[x, y], {y, 3}], D[Q[x, y], {y, 1}]}]

Longer example


 cl2=B1*Derivative[0, 1, 0][R][x, y, z] + 
 B2*Derivative[2, 0, 0][R][x, y, z] + 
 B4*Derivative[2, 1, 3][V][x, y, z] + 
 B3*Derivative[3, 2, 1][R][x, y, z] + B5*Derivative[4, 1, 5][V][x, y, z] + B0*V[x, y, z]  + B00*R[x, y, z];


I need list of coefficients and list of derivatives parallel to know for which derivative is appropriate coefficient. But if I have zero derivatives, they don't appear in the list?



Answer



Also borrowing from Daniel's comment, perhaps you would like:


cl = A1*D[P[x, y], {x, 1}] + A2*D[P[x, y], {x, 2}] + 
     A3*D[Q[x, y], {y, 3}] + A4*D[Q[x, y], {y, 1}];

Cases[cl, coef_ * Derivative[__][x_][__] :> {x, coef}, 1];

{#[[1, 1]], #[[All, 2]]} & /@ GatherBy[%, First]



{{Q, {A4, A3}}, {P, {A1, A2}}}

Or somewhat less transparently as a one-liner:


Reap[Cases[cl, coef_*Derivative[__][x_][__] :> Sow[coef, x], 1], _, List][[2]]


{{Q, {A4, A3}}, {P, {A1, A2}}}



Based on the comments below I believe you may use:


Reap[Cases[cl2, coef_ * d : Derivative[__][_][__] :> Sow[coef, d], 1], _, List][[2]]

Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

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

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

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