Difference between revisions of "ArgMin and ArgMax"

Latest revision as of 23:14, 27 August 2019

Release:	4.6 • 5.0 • 5.1 • 5.2 • 5.3 • 5.4 • 6.0 • 6.1 • 6.2 • 6.3 • 6.4 • 6.5

ArgMax(r, i, position, first), ArgMin(r, i, position, first)

ArgMax(r, i) returns the value of index «i» for which array «r» contains the largest numerical value (or if «r» contains text, the last in alphabetic order.) More specifically, it returns a value, ix where r[i = ix] = Max(r, i). If there are ties, i.e. «r» has two or more values that are equal largest, it returns the value of «i» nearest the end. Similarly, ArgMin(r, i) returns the value of «i» for which «r» is smallest (or if «r» contains text, the first alphabetically.)

Optional flags:

position: (default:false) When true, it returns the index position -- 1 when the max or min appears in the first element.
first: (default:false) If True, it returns first position (rather than the default last when there are ties.

Use with multiple indexes

ArgMax(r, i) and ArgMin(r, i) expect «r» to be an array with index i, and return a result not indexed by i. If array «r» has any indexes in addition to «i», the result will retain those other indexes. For example, if «r» is indexed by «i» and j, it will return the value of «i» for which «r» is largest (or smallest) for each value of j.

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 and ArgMin return a value of the index. If you specify optional parameter «position» as True, they return the position instead of the value of the index containing the maximum (minimum). For example:

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

This helps avoid ambiguity when the index contains duplicate values.

History

The «first» attrribute was introduced in Analytica 5.2.

@@ Line 1: / Line 1: @@
 [[Category:Array-reducing functions]]
 [[Category:Doc Status C]] <!-- For Lumina use, do not change -->
+{{ReleaseBar}}
-= Functions ArgMax(x, i) and ArgMin(x, i)=
+== ArgMax(r, i'', position{{Release|5.2||, first}}''), ArgMin(r, i'', position{{Release|5.2||, first}}'')==
-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''.
+<code>'''ArgMax'''(r, i)</code> returns the value of index «i» for which array «r» contains the largest numerical value (or if  «r» contains text, the last in alphabetic order.) More specifically, it returns a value, ''ix'' where <code>r[i = ix] = Max(r, i)</code>. If there are ties, i.e. «r» has two or more values that are equal largest, it returns the value of «i» nearest the end.  Similarly, <code>'''ArgMin'''(r, i)</code> returns the value of «i» for which «r» is smallest (or if  «r» contains text, the first alphabetically.)
-ArgMin is new to Analytica 4.0.
+Optional flags:
+* '''''position''''': (default:false) When true, it returns the index position -- 1 when the max or min appears in the first element.{{Release|5.2||
+* '''''first''''': (default:false) If True, it returns  first position (rather than the default last when there are ties.}}
-== Declaration ==
+== Use with multiple indexes ==
- ArgMin( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )
+<code>'''ArgMax'''(r, i)</code> and <code>'''ArgMin'''(r, i)</code> expect «r» to be an array with index <code>i</code>, and return a result not indexed by <code>i</code>.  If array «r» has any indexes in addition to «i», the result will retain those other indexes.  For example, if «r» is indexed by «i» and ''j'', it will return the value of «i» for which «r» is largest (or smallest) for each value of ''j''.
-  ArgMax( R : vector[I] ; I : ... optional IndexType ; position : optional boolean )
-== When x has multiple indexes ==
+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.
+:<code>ArgMax(X, I: Mpg, Car_type)</code>
-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.
+It will then return an array dimensioned by a local index <code>.Dim</code> and any indexes of <code>X</code> that you did not list as parameters. Index <code>.Dim</code> will contain the names of the indexes given as parameters, <code>Mpg</code> and <code>Car_type</code>, in this case. The result will contain the values of Index <code>Mpg</code> and <code>Car_type</code> for which <code>X</code> is maximum (or minimum).
-== Searching over Multiple Indexes ==
+== Positional usage ==
-(new to 4.0)
+By default, '''ArgMax''' and '''ArgMin''' return a value of the index.  If you specify optional parameter «position» as <code>True</code>, they return the ''position'' instead of the ''value'' of the index containing the maximum (minimum).  For example:
+:<code>ArgMax(R: Profit, I: UnitPrice, Position: true)</code>
-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 ==
+== History ==
+The «first» attrribute was introduced in [[Analytica 5.2]].
-* [[Min]] and [[Max]]
+== See Also ==
-* [[CondMin]] and [[CondMax]]
+* [[Min]]
-* [[SubIndex]] and [[PositionInIndex]]
+* [[Max]]
+* [[CondMin]]
+* [[CondMax]]
+* [[SubIndex]]
+* [[PositionInIndex]]
+* [[Array-reducing functions]]