## 6.3.3 Sorting lists

Methods are provided for sorting data in lists. The simplest of these is the `sort()` method, which sorts the members into order of ascending value.1 The `reverse()` method can be used to invert the order of the list afterwards if descending order is wanted.

`pyxplot> a = [8,4,7,3,6,2]`
`pyxplot> print a.sort()`
`[2, 3, 4, 6, 7, 8]`
`pyxplot> print a.reverse()`
`[8, 7, 6, 4, 3, 2]`

### Custom sorting

Often, however, a custom ordering is wanted. The `sortOn(f)` method takes a function of two arguments as its input. The function `f(a,b)` should return if `a` is to be placed before `b` in the sorted list, if `a` is to be placed after `b` in the sorted list, and zero if the two elements have equal ranking.

The `cmp(a,b)` function is often useful in making comparison functions for use with the `sortOn(f)` method: it returns either , or depending on Pyxplot’s default way of comparing two objects. In the example below, we pass it the magnitude of `a` and `b` to sort a list in order of magnitude.

`pyxplot> absCmp(a,b) = cmp(abs(a),abs(b))`
`pyxplot> a = range(-8,8)`
`pyxplot> print a`
`vector(-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7)`
`pyxplot> a = a.list()`
`pyxplot> print a.sortOn(absCmp)`
`[0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5, -6, 6, -7, 7, -8]`
`pyxplot> print a.sort()`
`[-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7]`

In this example, the `range(start,end,step)` function is used to generate a raster of values between and . It outputs a vector, which is converted into a list using the vector’s `list()` method. More information about vectors is in Section 6.5.

The subroutine command, which is often used to implement more complicated sorting functions, will be covered in Section 7.8. For example, the function used above could have been written:

    subroutine absCmp(a,b)
     {
      return cmp(abs(a),abs(b))
     }

### Sorting lists of lists

The `sortOnElement(n)` method can be used to sort a list of lists on the th sub-element of each sublist.

`pyxplot> b = []`
`pyxplot> b.append([1797,1828,"Schubert"])`
`[[1797, 1828, "Schubert"]]`
`pyxplot> b.append([1770,1827,"Beethoven"])`
`[[1797, 1828, "Schubert"], [1770, 1827, "Beethoven"]]`
`pyxplot> b.append([1756,1791,"Mozart"])`
`[[1797, 1828, "Schubert"], [1770, 1827, "Beethoven"], [1756, 1791, "Mozart"]]`
`pyxplot> print b.sortOnElement(0)` # Order of birth
`[[1756, 1791, "Mozart"], [1770, 1827, "Beethoven"], [1797, 1828, "Schubert"]]`
`pyxplot> print b.sortOnElement(1)` # Order of death
`[[1756, 1791, "Mozart"], [1770, 1827, "Beethoven"], [1797, 1828, "Schubert"]]`
`pyxplot> print b.sortOnElement(2)` # Alphabetical order
`[[1770, 1827, "Beethoven"], [1756, 1791, "Mozart"], [1797, 1828, "Schubert"]]`

Footnotes

1. Non-numeric items are assigned arbitrary but consistent values for the purposes of sorting. Booleans are always lower-valued than numbers, but numbers are lower-valued than lists. Longer lists are always higher valued than shorter lists; larger dictionaries are always higher-valued than smaller dictionaries.