Re: Help needed: defining a function of a vector variable

*To*: mathgroup at smc.vnet.net*Subject*: [mg18072] Re: [mg18016] Help needed: defining a function of a vector variable*From*: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>*Date*: Tue, 15 Jun 1999 01:43:31 -0400*Delivery-date*: Tue Jun 15 05:15:11 1999*Sender*: owner-wri-mathgroup at wolfram.com

If I understad correctly what you would liketo happen then your last idea works fine except that you must use := and not = in your definition. More explicitely, define the function functionarray by In[1]:= functionarray[d_,n_] := Array[d,n] Now, define a value for d (define it to be a function): In[2]:= d[x_]:=x^2 This creates a vector values function: In[3]:= functionarray[d,3] Out[3]= {1, 4, 9} You can also assign values to individual components: In[4]:= d[2]=5;functionarray[d,3] Out[4]= {1, 5, 9} -- Andrzej Kozlowski Toyama International University JAPAN http://sigma.tuins.ac.jp http://eri2.tuins.ac.jp ---------- >From: iaz at cs.umd.edu (Ilya Zavorine) To: mathgroup at smc.vnet.net >To: mathgroup at smc.vnet.net >Subject: [mg18072] [mg18016] Help needed: defining a function of a vector variable >Date: Sun, Jun 13, 1999, 4:52 AM > > Suppose I have an object (e.g. a matrix) which I want to consider as a function > of several variables. For instance, suppose the matrix is diagonal of size > N and the > variables are its diagonal elements. Logically I can also consider the same matrix > as a function of a single N-vector variable which would contain the > diagonal elements. > How should I define my matrix? Whatever the definition is, it has to satisfy 2 > requirements: > > (1) I need to be able to assign values both to specific variables and to the > whole vector. > > (2) The definition should be the same for any N, i.e. if I want to go from > N = 2 to N = 3 > or even to N = 10, I do not want to rewrite the whole thing from scratch. > > One way of defining a matrix would be something like this: > > M[d1_,d2_,d3_] = DiagonalMatrix[{d1,d2,d3}]; > > Clearly, this type of definition does not really satisfy either requirement > since it is > difficult to assign a value to the vector {d1,d2,d3} as a whole. Also, this > definition > has to be rewritten every time I change N. > > I've also tried doing something like this: > > Size = 3; > M[d_] = Array[d,Size]; > > This satisfies (2) but not (1). In fact Mathematica does not seem to relate > the variable d > in the left-hand side of the definition to the variable d inside Array. > > Is there a better way of doind this? > > Thanks for any help, > > Ilya