# Searching, sorting and selection


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``` python
import rustymath as rm
```

## Ordering

`rm.search` provides stable `sort`, `argsort` and `lexsort`,
`searchsorted`, integer `bincount`, class `counts` and `group_indices`.
These functions are also available directly on `rm`. Sorts work along
the last axis unless you give `axis`. Ordering and insertion searches
compare exactly and equate signed zeros. NaNs come last in ascending
order and first with `sort(..., descending=True)`.

``` python
scores = rm.array([8., 2, 5, 1, 9, 3])
rm.sort(scores), rm.argsort(scores)
```

    (Array([1.0, 2.0, 3.0, 5.0, 8.0, 9.0], dtype=float64),
     Array([3, 1, 5, 2, 0, 4], dtype=int64))

## Partial selection

`partition(x, k)` puts the item of rank `k` in its sorted position
without sorting either side. `argpartition` gives the positions instead
of the values. A negative rank counts from the end. Median and quantiles
use selection rather than fully sorting the array; `percentile` takes
probabilities in percent. Quantiles interpolate linearly between
neighbouring ranks:

``` python
rm.partition(scores, 2), rm.median(scores), rm.quantile(scores, [0.25, 0.5, 0.75])
```

    (Array([1.0, 2.0, 3.0, 5.0, 8.0, 9.0], dtype=float64),
     4.0,
     Array([2.25, 4.0, 7.25], dtype=float64))

## Matching and classification

`unique`, `index` and `isin` compare floats with a relative tolerance,
controlled by `ct` (default `rm.CT`). They match Booleans and integers
exactly. `unique` keeps values in order of first occurrence, with each
one’s first position, each item’s class number and each class’s size.
`index(x, y)` gives where in `x` each item of `y` first matches, or the
size of `x` where nothing does:

``` python
rm.unique([0.3, 1.0, 0.1 + 0.2]), rm.index([0.3, 1.0], 0.1 + 0.2)
```

    (Unique(values=Array([0.3, 1.0], dtype=float64), firsts=Array([0, 1], dtype=int64), numbers=Array([0, 1, 0], dtype=int64), counts=Array([2, 1], dtype=int64)),
     0)

Set operations use the same tolerant matching as `isin` and retain
first-occurrence order, rather than sorting their results. Their inputs
are flattened; `ct=0` selects exact matching.

``` python
rm.union1d([3, 1, 3, 2], [2, 4]), rm.intersect1d([3, 1, 3, 2], [2, 4]), rm.setdiff1d([3, 1, 3, 2], [2, 4])
```

    (Array([3, 1, 2, 4], dtype=int64),
     Array([2], dtype=int64),
     Array([3, 1], dtype=int64))