# Difference between revisions of "Suffix"

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A '''suffix''' is a kind of [[subarray]] which is like a [[prefix]] except that values are taken from the end of the array rather than the beginning: a [[vector]] is a suffix of another vector if it is no longer than that vector, and shares all of its trailing [[element]]s. In [[leading axis theory]], an array may be considered a suffix of another array of the same [[rank]] if the same relation holds with [[major cell]]s in place of elements. The function [[Drop]] produces suffixes of its right argument when the left argument is non-negative. | A '''suffix''' is a kind of [[subarray]] which is like a [[prefix]] except that values are taken from the end of the array rather than the beginning: a [[vector]] is a suffix of another vector if it is no longer than that vector, and shares all of its trailing [[element]]s. In [[leading axis theory]], an array may be considered a suffix of another array of the same [[rank]] if the same relation holds with [[major cell]]s in place of elements. The function [[Drop]] produces suffixes of its right argument when the left argument is non-negative. | ||

− | In analogy to [[prefix]] testing, whether an array is a suffix may be tested using [[Take]] with a [[ | + | In analogy to [[prefix]] testing, whether an array is a suffix may be tested using [[Take]] with a [[negate]]d left argument and [[Match]]. The only difference is the negation. |

<source lang=apl> | <source lang=apl> | ||

isSuffix ← {((≢⍺)≤(≢⍵)) ∧ ⍺≡(-≢⍺)↑⍵} | isSuffix ← {((≢⍺)≤(≢⍵)) ∧ ⍺≡(-≢⍺)↑⍵} | ||

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[[Iverson notation]] included the notion of a suffix vector <math>\omega^j(n)</math> consisting of <math>n-j</math> zeros followed by <math>j</math> ones; such a vector could be used to produce a length-<math>j</math> suffix of a length-<math>n</math> vector using [[Compress]]. The earliest versions of [[APL\360]] adapted this notation by defining a suffix function <source lang=apl inline>n ⍵ j</source> before removing it in favor of [[Take]] with a negative left argument. | [[Iverson notation]] included the notion of a suffix vector <math>\omega^j(n)</math> consisting of <math>n-j</math> zeros followed by <math>j</math> ones; such a vector could be used to produce a length-<math>j</math> suffix of a length-<math>n</math> vector using [[Compress]]. The earliest versions of [[APL\360]] adapted this notation by defining a suffix function <source lang=apl inline>n ⍵ j</source> before removing it in favor of [[Take]] with a negative left argument. | ||

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+ | [[Category:Array relationships]] |

## Latest revision as of 14:10, 30 April 2020

A **suffix** is a kind of subarray which is like a prefix except that values are taken from the end of the array rather than the beginning: a vector is a suffix of another vector if it is no longer than that vector, and shares all of its trailing elements. In leading axis theory, an array may be considered a suffix of another array of the same rank if the same relation holds with major cells in place of elements. The function Drop produces suffixes of its right argument when the left argument is non-negative.

In analogy to prefix testing, whether an array is a suffix may be tested using Take with a negated left argument and Match. The only difference is the negation.

```
isSuffix ← {((≢⍺)≤(≢⍵)) ∧ ⍺≡(-≢⍺)↑⍵}
'fix' isSuffix 'suffix'
1
'suff' isSuffix 'suffix'
0
```

We can also use an `isPrefix`

function directly by reversing both its arguments. In the second definition below, this relation is written more succinctly in a tacit style using the Over operator.

```
isSuffix ← {(⊖⍺)isPrefix(⊖⍵)}
isSuffix ← isPrefix⍥⊖
```

In leading axis theory, the cell shape of each k-cell in an array is a suffix of that array's shape, while the frame is a prefix of the shape.

Iverson notation included the notion of a suffix vector consisting of zeros followed by ones; such a vector could be used to produce a length- suffix of a length- vector using Compress. The earliest versions of APL\360 adapted this notation by defining a suffix function `n ⍵ j`

before removing it in favor of Take with a negative left argument.