Minimum
⌊

Minimum (⌊
), Min, or Lesser of is a dyadic scalar function which returns the smaller of its two arguments. The name "Minimum" is sometimes also used for the Minimum Reduce ⌊/
, which returns the smallest element of a vector (this usage is related to the minimum of a function). Minimum is paired with Maximum, which returns the greater argument rather than the smaller, and shares the glyph ⌊
with the Floor function. It is not subject to comparison tolerance, since the result will be exactly equal to one argument, and there is no reason to choose a larger argument even if the two arguments are tolerantly equal. As a Boolean function, Minimum is identical to And.
Examples
Minimum finds the smaller of two numbers:
2.4 ⌊ 1.9
1.9
Together with Maximum, it can clamp an array of numbers to a range (closed interval), here from 0 to 1:
0 ⌈ 1 ⌊ ¯0.2 ¯0.1 0.3 0.8 1 1.3
0 0 0.3 0.8 1 1
Because the complex numbers do not form an ordered field, attempting to take the minimum with a complex argument yields a DOMAIN ERROR.
3 ⌊ 3j1
DOMAIN ERROR
3⌊3J1
∧
Reduction
Minimum Reduce finds the smallest element in an entire vector:
⌊/ 4 3 2 3 1 5 7
1
To find the index of the minimum, Index Of can be used to search for it. A shorter, but usually slower, method is to take the First of the vector's Grade.
{⍵⍳⌊/⍵} 4 3 2 3 1 5 7
5
⊃⍋ 4 3 2 3 1 5 7
5
The two solutions may differ when comparison tolerance is not zero, because Index Of uses tolerant comparison but Grade does not. The first solution will return a smaller index if an element that is tolerantly but not exactly equal to the minimum is found at that index.
Reducing over an empty axis yields the largest representable number, as that is the identity element for Minimum. This value is usually ∞
(for dialects that support infinities) or 1.797693135E308
(with 64bit floats) or 1E6145
(with 128bit decimal floats).
External links
Documentation
APL builtins [edit]  

Primitive functions  
Scalar  
Monadic  Conjugate ∙ Negate ∙ Signum ∙ Not ∙ Roll ∙ Type  
Dyadic  Add ∙ Subtract ∙ Equal to (Xnor) ∙ Not Equal to (Xor) ∙ Minimum ∙ Maximum ∙ Comparison functions  
NonScalar  
Structural  Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Reverse ∙ Raze ∙ Mix ∙ Cut (K) ∙ Pair ∙ Replicate ∙ Partitioned Enclose  
Selection  Take ∙ Drop ∙ Unique ∙ Identity ∙ Select  
Selector  Index generator ∙ Interval Index ∙ Indices  
Computational  Match ∙ Not Match ∙ Nub Sieve ∙ Format ∙ Execute  
Primitive operators  Monadic  Each ∙ Replicate  
Dyadic  Reverse Compose  
Quad names  
Arrays  Index origin ∙ Migration level  
Functions  
Operators  
Other  Zilde ∙ High minus ∙ Function axis 