View source for Functions Min and Max

[[Category:Array-reducing functions]]
[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
[[Category:Math Functions]]

==Min(X, ''I''), Max(X, ''I'') ==
Return the smallest ('''Min''') or largest ('''Max''') value in array «X» over index «I». You can use them to find the smallest or largest value over an explicit list of values enclosed in square brackets, in which case you omit the index:
:<code>Max([a, b, c])</code>

This form evaluates <code>a, b</code>, and <code>c</code>, and finds the largest value among them.  For example:
:<code>Max([Sin(30), Tan(30), Cos(30)]) &rarr; 0.8660254</code>

Although index «I» is optional, we strongly recommend you include it even if «X» currently only has one index. You might expand the model so that «X» gets another index, <code>J</code>. Then '''Min'''(X) would be ambiguous. Analytica couldn't tell whether you meant '''Min'''(X, I) or '''Min'''(X, J), and might not interpret it the way you want. 

If «X» contains text values, it returns the first ('''Min''') or last ('''Max''') value in alphabetic order. If «X» contains mixed text and numbers, it treats text before or "smaller than" numbers. Thus,
:<code>Min(['A', 'B', 2]) &rarr; 'A'</code>
:<code>Max(['A', 'B', 2]) &rarr;  2</code>

It orders text as case sensitive unless you specify otherwise with the optional «CaseInsensitive» parameter (see below).

== Optional parameters ==
=== Multiple indexes ===
:<code>Min(X, I, J, K, ...)</code>
:<code>Min(X, I, J, K, ...)</code>

You can specify more than one index, e.g., <code>Max(X, I, J)</code> is equivalent to <code>Max(Max(X, I), J)</code>. This finds the maximum or minimum over all the specified indexes of «X».

=== IgnoreNonNumbers and IgnoreNAN===
These optional Boolean parameters require a named-parameter syntax. If «IgnoreNonNumbers» is set to true (<code>1</code>), it ignores non-numeric values.  If «IgnoreNAN» is set to <code>True (1)</code>, it ignores [[NaN]] values. It always ignores [[Null]] no matter what the parameter values.

:<code>Variable A :=</code>
:{| class="wikitable"
! colspan="7" | I &#9654;
|-
! 1 || 2 || 3 || 4 || 5 || 6 || 7
|-
| 56 || "a" || 4 || "1" || 3 || «null» || 45
|}

:<code>Min(A, I, IgnoreNonNumbers: True) &rarr; 3</code>
:<code>Max(A, I, IgnoreNonNumbers: True) &rarr; 56</code>

A [[NaN]] value occurs when an arithmetic operation is indeterminate, such as the result of a divide by zero.  These are would-be numeric values, but just indeterminate, so the result of a '''Min''' or '''Max''' on [[NaN]] is also [[NaN]].  These normally propagate so that you don't get misleading results downstream, but if you also want to ignore [[NaN]] values, then include «IgnoreNaN» set to true.

(''New to [[Analytica 5.3]]'') Date-time numbers are considered numeric, so these aren't ignored when only ignoreNonNumbers is set to true. To also ignore date-time numbers, set «ignoreDates» to true, e.g.,
:<code>Min(A, I, ignoreNonNumbers:True, ignoreDates:true )</code>

=== CaseInsensitive ===
Comparison of text values by '''Min''' and '''Max''' is done in a case-sensitive fashion by default.  You can specify the optional «caseInsensitive» parameter as true to do the comparison in a case-insensitive manner, e.g.:

:<code>Min(['DeBois', 'Debbie', 'Debutante']) &rarr; 'DeBois'</code>
:<code>Min(['DeBois', 'Debbie', 'Debutante'], CaseInsensitive: True) &rarr; 'Debbie'</code>

== CondMin(X, cond, ''I''), CondMax(X, cond, ''I'') ==
[[Syntax]]
:'''CondMin'''(X: Array[I]; cond: Boolean[I];  I: Index)
:'''CondMax'''(X: Array[I]; cond: Boolean[I];  I: Index)

Conditional '''Min''' and '''Max'''.  These return the smallest ('''CondMin''') or largest ('''CondMax''') values along a given index, but only along a subset of values as indicated by the parameter «cond».

When no cell satisfies «cond», the result of '''CondMax''' is -[[INF]], and the result of '''CondMin''' is [[INF]].

Starting with Analytica 4.4, '''CondMax''' and '''CondMin''' support the named parameter syntax and allow multiple indexes to be listed.  The optional flag parameter «CaseInsensitive» can be set to <code>True</code> (default is <code>False</code>).

== See Also==
* [[ArgMin and  ArgMax]]
* [[Ana:Fn:ArgMin_and_ArgMax| ArgMin]]
* [[Ana:Fn:ArgMin_and_ArgMax| ArgMax]]
* [[Array-reducing functions]]