Group Abstract

Message Boards

WOLFRAM COMMUNITY

8K Views

2 Replies

0 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Mathematics Mathematica Algebra

Syntax for Nested Functions

Nick Hare

Posted 11 years ago

I'm hoping this is a relatively simple question, but I'm quite new to Mathematica and am struggling with exactly how to express what I'd like it to do. The following isn't what I'm trying to do, but a very simplified example with the same fundamental issue. We want to calculate the total weight of a collection of balls 1, 2,...,N. There are only a certain number of types of ball, 1, 2,...T. Ball number x is of type balltype[x]. The weight of a ball of type x is weight[x]. So the weight of ball number x is expressed by weight[balltype[x]]. I want to define the function that is the total weight of all N balls, and it should be something like: totalweight[weight_, balltype_, N_] := Sum[weight[balltype[x]], {x, 1, N}] The problem is that I'm not now sure how then to ask for the derivative of totalweight with respect to the weight of a specific type of ball, say weight[1]. The answer should be something like Sum[Boole[balltype[x]=1],{x,1,N}] i.e. the total number of balls of type 1 that are in the collection, although there are may be many ways to express this. My question is: how can I express the function totalweight properly, and how (for example) would I ask for the derivative of totalweight wrt the weight of a particular ball type weight[x]? This seems like a simple sort of problem, but I can't seem to find anything addressing it, although that could be because I don't know the right terms to search for. Very many thanks in advance.

POSTED BY: Nick Hare

2 Replies

Sort By:

Nick Hare

Posted 11 years ago

POSTED BY: Nick Hare

Erik Mahieu

Posted 11 years ago

To understand your problem, I made small example and set up a function to find the total weight of all balls of a certain type: In[3]:= SeedRandom[1234](10 ball types with a different weight each \ between 10 and 50) ballWeightsByType = RandomReal[{10, 50}, 10] Out[4]= {45.0643, 30.8786, 13.4489, 25.1165, 10.4658, 47.0906, \ 31.7503, 29.1733, 19.814, 40.3958} In[5]:= (random collection of 50 balls identified by their ball type) In[6]:= ballsByType = RandomInteger[{1, 10}, 50] Out[6]= {3, 9, 9, 1, 5, 8, 4, 7, 6, 4, 8, 10, 1, 5, 5, 3, 3, 5, 8, 6, \ 9, 3, 3, 7, 8, 3, 6, 3, 1, 3, 8, 10, 6, 7, 8, 1, 10, 6, 8, 8, 8, 10, \ 8, 8, 6, 1, 6, 5, 4, 10} In[7]:= (get weight of balltype x) In[8]:= ballWeight[x_?IntegerQ] := First@Take[ballWeightsByType, {x}] In[9]:= ballWeight[7] Out[9]= 31.7503 In[10]:= (list of {type,weight} of all 50 balls sorted by type) In[11]:= lst = SortBy[{#, ballWeight[#]} & /@ ballsByType, First] Out[11]= {{1, 45.0643}, {1, 45.0643}, {1, 45.0643}, {1, 45.0643}, {1, 45.0643}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {4, 25.1165}, {4, 25.1165}, {4, 25.1165}, {5, 10.4658}, {5, 10.4658}, {5, 10.4658}, {5, 10.4658}, {5, 10.4658}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {7, 31.7503}, {7, 31.7503}, {7, 31.7503}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {9, 19.814}, {9, 19.814}, {9, 19.814}, {10, 40.3958}, {10, 40.3958}, {10, 40.3958}, {10, 40.3958}, {10, 40.3958}} In[12]:= (number of balls of type 7) In[13]:= Count[lst, {7, _}] Out[13]= 3 In[14]:= (weight of all balls of type 6) In[15]:= % ballWeight[7] Out[15]= 31.7503 Null In[16]:= weightTotalByType[type_?IntegerQ] := Count[lst, {type, _}]ballWeight[type] In[17]:= weightTotalByType[7] Out[17]= 95.2508 In[18]:= (list of {type,total weight of all balls of type} of all 50 \ balls sorted by type) In[19]:= {#, weightTotalByType[#]} & /@ Range[10] Out[19]= {{1, 225.322}, {2, 0.}, {3, 107.591}, {4, 75.3496}, {5, 52.3289}, {6, 329.635}, {7, 95.2508}, {8, 320.906}, {9, 59.4419}, {10, 201.979}} Attachments:*

To understand your problem, I made small example and set up a function to find the total weight of all balls of a certain type:

In[3]:= SeedRandom[1234](*10 ball types with a different weight each \
between 10 and 50*)
ballWeightsByType = RandomReal[{10, 50}, 10]

Out[4]= {45.0643, 30.8786, 13.4489, 25.1165, 10.4658, 47.0906, \
31.7503, 29.1733, 19.814, 40.3958}

In[5]:= (*random collection of 50 balls identified by their ball type*)

In[6]:= ballsByType = RandomInteger[{1, 10}, 50]

Out[6]= {3, 9, 9, 1, 5, 8, 4, 7, 6, 4, 8, 10, 1, 5, 5, 3, 3, 5, 8, 6, \
9, 3, 3, 7, 8, 3, 6, 3, 1, 3, 8, 10, 6, 7, 8, 1, 10, 6, 8, 8, 8, 10, \
8, 8, 6, 1, 6, 5, 4, 10}

In[7]:= (*get weight of balltype x*)

In[8]:= ballWeight[x_?IntegerQ] := First@Take[ballWeightsByType, {x}]

In[9]:= ballWeight[7]

Out[9]= 31.7503

In[10]:= (*list of {type,weight} of all 50 balls sorted by type*)

In[11]:= lst = SortBy[{#, ballWeight[#]} & /@ ballsByType, First]

Out[11]= {{1, 45.0643}, {1, 45.0643}, {1, 45.0643}, {1, 45.0643}, {1, 
  45.0643}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 
  13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 13.4489}, {3, 
  13.4489}, {4, 25.1165}, {4, 25.1165}, {4, 25.1165}, {5, 
  10.4658}, {5, 10.4658}, {5, 10.4658}, {5, 10.4658}, {5, 
  10.4658}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 
  47.0906}, {6, 47.0906}, {6, 47.0906}, {6, 47.0906}, {7, 
  31.7503}, {7, 31.7503}, {7, 31.7503}, {8, 29.1733}, {8, 
  29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 
  29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 29.1733}, {8, 
  29.1733}, {8, 29.1733}, {9, 19.814}, {9, 19.814}, {9, 19.814}, {10, 
  40.3958}, {10, 40.3958}, {10, 40.3958}, {10, 40.3958}, {10, 40.3958}}

In[12]:= (*number of balls of type 7*)

In[13]:= Count[lst, {7, _}]

Out[13]= 3

In[14]:= (*weight of all balls of type 6*)

In[15]:= % ballWeight[7]

Out[15]= 31.7503 Null

In[16]:= weightTotalByType[type_?IntegerQ] := 
 Count[lst, {type, _}]*ballWeight[type]

In[17]:= weightTotalByType[7]

Out[17]= 95.2508

In[18]:= (*list of {type,total weight of all balls of type} of all 50 \
balls sorted by type*)

In[19]:= {#, weightTotalByType[#]} & /@ Range[10]

Out[19]= {{1, 225.322}, {2, 0.}, {3, 107.591}, {4, 75.3496}, {5, 
  52.3289}, {6, 329.635}, {7, 95.2508}, {8, 320.906}, {9, 
  59.4419}, {10, 201.979}}

POSTED BY: Erik Mahieu

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback