Difference between revisions of "ArgMin and ArgMax"

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[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
 
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= Functions ArgMin and ArgMax =
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= Functions ArgMax(x, i) and ArgMin(x, i)=
  
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ArgMax(x, i) returns the value of index i for which array x is largest. More specifically, it returns a value, ix, of i, such that x[i =ix] = Max(x, i). Similarly, ArgMin(x, i) returns the value of i for which x is ''smallest''. If there are ties (e.g., x has two identical values that are largest, it returns the one nearer the end of i.
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ArgMax(x, i) returns the value of index i corresponding to the largest value from array x, which must be indexed by i. More specifically, it returns a value, ix where x[i =ix] = Max(x, i). If there are ties, i.e. x has two or more values that are equal largest, it returns the value nearest the end of i.  Similarly, ArgMin(x, i) returns the value of i for which x is ''smallest''.  
  
 
ArgMin is new to Analytica 4.0.   
 
ArgMin is new to Analytica 4.0.   
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  ArgMax( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )
 
  ArgMax( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )
  
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== Single Index Usage ==
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== When x has multiple indexes ==
  
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When ArgMin or ArgMax is used with a single index, as in the following usage
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If array x has an index or indexes in addition to i, Argmax(x, i) or Argmin(x, i) return an array indexed by those other indexes, but not by i.  For example, if x is indexed by i and j, it will return the value of i for which x is largest (or smallest) for each value of j.
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ArgMax( R:Car_prices, I:Car_type )
 
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the value in index I is returned containing the extrema.
 
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If array x has indexes in addition to i, Argmax(x, i) or Argmin(x, i) will return an array indexed by those indexes (not including i).  For example, if x is indexed by i and j, it will return the value of i for which x is largest (or smallest) for each value of j.
 
  
 
== Searching over Multiple Indexes ==
 
== Searching over Multiple Indexes ==
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If you want to find the smallest or largest value of x over more than one index, you can list all those indexes: e.g.
 
If you want to find the smallest or largest value of x over more than one index, you can list all those indexes: e.g.
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  ArgMax(X, I: Mpg,Car_type )
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  ArgMax(X, I: Mpg, Car_type)
  
 
It will then return an array dimensioned by a local index .Dim and any indexes of X that you did not list as parameters. Index .Dim will contain the names of the indexes given as parameters, Mpg and Car_type, in this case. The result will contain the values of Index Mpg and Car_type for which X is maximum (or minimum).
 
It will then return an array dimensioned by a local index .Dim and any indexes of X that you did not list as parameters. Index .Dim will contain the names of the indexes given as parameters, Mpg and Car_type, in this case. The result will contain the values of Index Mpg and Car_type for which X is maximum (or minimum).
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By default, ArgMax (ArgMin) returns a value of the index.  If you specify optional parameter position as true, they return the position of the value in the index for which x is maximum (minumum) -- a number.  For example:
 
By default, ArgMax (ArgMin) returns a value of the index.  If you specify optional parameter position as true, they return the position of the value in the index for which x is maximum (minumum) -- a number.  For example:
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   ArgMax( R : Profit, I : UnitPrice, position : true )
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   ArgMax(R: Profit, I: UnitPrice, Position: true)
 
This helps avoid ambiguity when the index contains duplicate values.
 
This helps avoid ambiguity when the index contains duplicate values.
  

Revision as of 17:42, 5 June 2007


Functions ArgMax(x, i) and ArgMin(x, i)

ArgMax(x, i) returns the value of index i corresponding to the largest value from array x, which must be indexed by i. More specifically, it returns a value, ix where x[i =ix] = Max(x, i). If there are ties, i.e. x has two or more values that are equal largest, it returns the value nearest the end of i. Similarly, ArgMin(x, i) returns the value of i for which x is smallest.

ArgMin is new to Analytica 4.0.

Declaration

ArgMin( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )
ArgMax( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )

When x has multiple indexes

If array x has an index or indexes in addition to i, Argmax(x, i) or Argmin(x, i) return an array indexed by those other indexes, but not by i. For example, if x is indexed by i and j, it will return the value of i for which x is largest (or smallest) for each value of j.

Searching over Multiple Indexes

(new to 4.0)

If you want to find the smallest or largest value of x over more than one index, you can list all those indexes: e.g. 

ArgMax(X, I: Mpg, Car_type)

It will then return an array dimensioned by a local index .Dim and any indexes of X that you did not list as parameters. Index .Dim will contain the names of the indexes given as parameters, Mpg and Car_type, in this case. The result will contain the values of Index Mpg and Car_type for which X is maximum (or minimum).

Positional Usage

By default, ArgMax (ArgMin) returns a value of the index. If you specify optional parameter position as true, they return the position of the value in the index for which x is maximum (minumum) -- a number. For example: 

 ArgMax(R: Profit, I: UnitPrice, Position: true)

This helps avoid ambiguity when the index contains duplicate values.

Related Functions

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