# role Mixy

Collection of distinct objects with Real weights

```
role Mixy does Baggy { }
```

A role for collections of weighted values. See Mix and MixHash. `Mixy`

objects differ from Baggy objects in that the weights of `Mixy`

are Reals rather than Ints.

# Methods

## method total

```
method total(--> Real)
```

Returns the sum of all the weights

```
mix('a', 'b', 'c', 'a', 'a', 'd').total == 6; # True
{a => 5.6, b => 2.4}.Mix.total == 8; # True
```

## method roll

```
method roll($count = 1)
```

Similar to a Bag.roll, but with `Real`

weights rather than integral ones.

# See Also

# Type graph

# Routines supplied by role Baggy

Mixy does role Baggy, which provides the following methods:

## (Baggy) method grab

Defined as:

```
multi method grab(Baggy:D:) returns Any
multi method grab(Baggy:D: $count) returns Array:D
```

Like pick, a `grab`

returns a random selection of elements, weighted by the values corresponding to each key. Unlike `pick`

, it works only on mutable structures, e.g. BagHash. Use of `grab`

on an immutable structure results in an `X::Immutable`

exception. If `*`

is passed as `$count`

, or `$count`

is greater than or equal to the total of the invocant, then `total`

elements from the invocant are returned in a random sequence.

Grabbing decrements the grabbed key's weight by one (deleting the key when it reaches 0). By definition, the `total`

of the invocant also decreases by one, so the probabilities stay consistent through subsequent `grab`

operations.

```
my $cars = ('Ford' => 2, 'Rover' => 3).BagHash;
say $cars.grab; # Ford
say $cars.grab(2); # [Rover Rover]
say $cars.grab(*); # [Rover Ford]
my $breakfast = ('eggs' => 2, 'bacon' => 3).Bag;
say $breakfast.grab;
CATCH { default { put .^name, ': ', .Str } };
# OUTPUT: «X::Immutable: Cannot call 'grab' on an immutable 'Bag'»
```

## (Baggy) method grabpairs

Defined as:

```
multi method grabpairs(Baggy:D:) returns Any
multi method grabpairs(Baggy:D: $count) returns List:D
```

Returns a `Pair`

or a `List`

of `Pair`

s depending on the version of the method being invoked. Each `Pair`

returned has an element of the invocant as its key and the elements weight as its value. Unlike pickpairs, it works only on mutable structures, e.g. BagHash. Use of `grabpairs`

on 'an immutable structure results in an `X::Immutable`

exception. If `*`

is passed as `$count`

, or `$count`

is greater than or equal to the number of elements of the invocant, then all element/weight `Pair`

s from the invocant are returned in a random sequence.

What makes `grabpairs`

different from pickpairs is that the 'grabbed' elements are in fact removed from the invocant.

```
my $breakfast = (eggs => 2, bacon => 3).BagHash;
say $breakfast.grabpairs; # bacon => 3
say $breakfast; # BagHash.new(eggs(2))
say $breakfast.grabpairs(1); # [eggs => 2]
say $breakfast.grabpairs(*); # []
my $diet = ('eggs' => 2, 'bacon' => 3).Bag;
say $diet.grabpairs;
CATCH { default { put .^name, ': ', .Str } };
# OUTPUT: «X::Immutable: Cannot call 'grabpairs' on an immutable 'Bag'»
```

## (Baggy) method pick

Defined as:

```
multi method pick(Baggy:D:) returns Any
multi method pick(Baggy:D: $count) returns Seq:D
```

Like an ordinary list pick, but returns keys of the invocant weighted by their values, as if the keys were replicated the number of times indicated by the corresponding value and then list pick used. The underlying metaphor for picking is that you're pulling colored marbles out a bag. (For "picking with replacement" see roll instead). If `*`

is passed as `$count`

, or `$count`

is greater than or equal to the total of the invocant, then `total`

elements from the invocant are returned in a random sequence.

Note that each `pick`

invocation maintains its own private state and has no effect on subsequent `pick`

invocations.

```
my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.pick; # eggs
say $breakfast.pick(2); # (eggs bacon)
say $breakfast.total; # 4
say $breakfast.pick(*); # (bacon bacon bacon eggs)
```

## (Baggy) method pickpairs

Defined as:

```
multi method pickpairs(Baggy:D:) returns Pair:D
multi method pickpairs(Baggy:D: $count) returns List:D
```

Returns a `Pair`

or a `List`

of `Pair`

s depending on the version of the method being invoked. Each `Pair`

returned has an element of the invocant as its key and the elements weight as its value. The elements are 'picked' without replacement. If `*`

is passed as `$count`

, or `$count`

is greater than or equal to the number of elements of the invocant, then all element/weight `Pair`

s from the invocant are returned in a random sequence.

Note that each `pickpairs`

invocation maintains its own private state and has no effect on subsequent `pickpairs`

invocations.

```
my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.pickpairs; # eggs => 1
say $breakfast.pickpairs(1); # (bacon => 3)
say $breakfast.pickpairs(*); # (eggs => 1 bacon => 3)
```

## (Baggy) method roll

Defined as:

```
multi method roll(Baggy:D:) returns Any:D
multi method roll(Baggy:D: $count) returns Seq:D
```

Like an ordinary list roll, but returns keys of the invocant weighted by their values, as if the keys were replicated the number of times indicated by the corresponding value and then list roll used. The underlying metaphor for rolling is that you're throwing `$count`

dice that are independent of each other, which (in bag terms) is equivalent to picking a colored marble out your bag and then putting it back, and doing this `$count`

times. In dice terms, the number of marbles corresponds to the number of sides, and the number of marbles of the same color corresponds to the number of sides with the same color. (For "picking without replacement" see pick instead).

If `*`

is passed to `$count`

, returns a lazy, infinite sequence of randomly chosen elements from the invocant.

```
my $breakfast = bag <eggs bacon bacon bacon>;
say $breakfast.roll; # bacon
say $breakfast.roll(3); # (bacon eggs bacon)
my $random_dishes := $breakfast.roll(*);
say $random_dishes[^5]; # (bacon eggs bacon bacon bacon)
```

## (Baggy) method pairs

Defined as:

```
method pairs(Baggy:D:) returns Seq:D
```

Returns all elements and their respective weights as a Seq of `Pair`

s where the key is the element itself and the value is the weight of that element.

```
my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.pairs;
say $seq.sort; # (bacon => 2 eggs => 1)
```

## (Baggy) method antipairs

Defined as:

```
method antipairs(Baggy:D:) returns Seq:D
```

Returns all elements and their respective weights as a Seq of Pairs, where the element itself is the value and the weight of that element is the key, i.e. the opposite of method pairs.

```
my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.antipairs;
say $seq.sort; # (1 => eggs 2 => bacon)
```

## (Baggy) method invert

Defined as:

```
method invert(Baggy:D:) returns Seq:D
```

Returns all elements and their respective weights as a Seq of Pairs, where the element itself is the value and the weight of that element is the key, i.e. the opposite of method pairs. Except for some esoteric cases `invert`

on a Baggy type returns the same result as antipairs.

```
my $breakfast = bag <bacon eggs bacon>;
my $seq = $breakfast.invert;
say $seq.sort; # (1 => eggs 2 => bacon)
```

## (Baggy) method classify-list

Defined as:

```
multi method classify-list(&test, *@list) returns Baggy:D
```

Transforms a list of values into a classification of those values according to `&test`

and stores the results in the invocant which is then returned. Each key represents the classification for one or more of the incoming list values, and the corresponding value contains the number of list values classified by `&test`

into the category of the associated key.

As an example, suppose that we have a list of `Int`

s which we would like to classify into two categories, namely even and odd numbers. Here's one way to solve this problem:

```
my $b = BagHash.new();
dd $b.classify-list( { $_ %% 2 ?? 'even' !! 'odd' }, (1, 7, 6, 3, 2) );
# returns: ("even"=>2,"odd"=>3).BagHash
```

The printed result shows us that of the numbers in the list two were classified as even and three as odd. Note that the result doesn't show us **which** numbers were classified as being even or odd. If that's what you want, use the classify routine in List instead.

## (Baggy) method categorize-list

Defined as:

```
multi method categorize-list(&test:(Any --> Bool), *@list) returns Baggy:D
```

Transforms a list of values into categorizations of those values according to `&test`

and stores the results in the invocant which is then returned. Each key represents one possible categorization for one or more of the incoming list values, and the corresponding value contains the number of list values categorized by `&test`

into the category of the associated key.

The signature for `&test`

contains one parameter of type `Any`

which simply means that `&test`

must be able to handle arguments of the same type as those in `*@list`

.

As an example, suppose that we have a list of `Int`

s each of which is either even or odd and, at the same time, prime or non-prime. We want to get hold of an aggregated result which shows us how many numbers were even, odd, prime and non-prime.

```
my $b = BagHash.new();
dd $b.categorize-list( { $_ %% 2 ?? 'even' !! 'odd',
$_.is-prime ?? 'prime' !! 'not prime'
}, (1, 7, 6, 3, 2) );
# returns: ("non-prime"=>2,"even"=>2,"prime"=>3,"odd"=>3).BagHash
```

The result shows us that of the numbers in the list two were categorized as even and three as odd. In addition the result also shows that three of the numbers were also categorized as prime and two as non-prime. Note that the result doesn't show us **which** numbers were categorized as being even, odd, prime or non-prime. If that is what you want, use the categorize routine in List instead.

It should also be noted that, unlike classify-list, which assumes that the return value of `&test`

is a single value, `categorize-list`

always assumes that the return value of `&test`

is a list of categories that are appropriate to the current value.

## (Baggy) method keys

Defined as:

```
method keys(Baggy:D:) returns List:D
```

Returns a list of all keys in the `Baggy`

object without taking their individual weights into account as opposed to kxxv.

```
my $breakfast = bag <eggs spam spam spam>;
say $breakfast.keys.sort; # (eggs spam)
my $n = ("a" => 5, "b" => 2).BagHash;
say $n.keys.sort; # (a b)
```

## (Baggy) method values

Defined as:

```
method values(Baggy:D:) returns List:D
```

Returns a list of all values, i.e. weights, in the `Baggy`

object.

```
my $breakfast = bag <eggs spam spam spam>;
say $breakfast.values.sort; # (1 3)
my $n = ("a" => 5, "b" => 2, "a" => 1).BagHash;
say $n.values.sort; # (2 6)
```

## (Baggy) method kv

Defined as:

```
method kv(Baggy:D:) returns List:D
```

Returns a list of keys and values interleaved.

```
my $breakfast = bag <eggs spam spam spam>;
say $breakfast.kv; # (spam 3 eggs 1)
my $n = ("a" => 5, "b" => 2, "a" => 1).BagHash;
say $n.kv; # (a 6 b 2)
```

## (Baggy) method kxxv

Defined as:

```
method kxxv(Baggy:D:) returns List:D
```

Returns a list of the keys of the invocant, with each key multiplied by its weight. Note that `kxxv`

only works for `Baggy`

types which have integer weights, i.e. Bag and BagHash.

```
my $breakfast = bag <spam eggs spam spam bacon>;
say $breakfast.kxxv.sort; # (bacon eggs spam spam spam)
my $n = ("a" => 0, "b" => 1, "b" => 2).BagHash;
say $n.kxxv; # (b b b)
```

## (Baggy) method elems

Defined as:

```
method elems(Baggy:D:) returns Int:D
```

Returns the number of elements in the `Baggy`

object without taking the individual elements weight into account.

```
my $breakfast = bag <eggs spam spam spam>;
say $breakfast.elems; # 2
my $n = ("b" => 9.4, "b" => 2).MixHash;
say $n.elems; # 1
```

## (Baggy) method total

Defined as:

```
method total(Baggy:D:)
```

Returns the sum of weights for all elements in the `Baggy`

object.

```
my $breakfast = bag <eggs spam spam bacon>;
say $breakfast.total; # 4
my $n = ("a" => 5, "b" => 1, "b" => 2).BagHash;
say $n.total; # 8
```

## (Baggy) method default

Defined as:

```
method default(Baggy:D:) returns Int:D
```

Returns zero.

```
my $breakfast = bag <eggs bacon>;
say $breakfast.default; # 0
```

## (Baggy) method hash

Defined as:

```
method hash(Baggy:D:) returns Hash:D
```

Returns a Hash where the elements of the invocant are the keys and their respective weights the values;

```
my $breakfast = bag <eggs bacon bacon>;
my $h = $breakfast.hash;
say $h.WHAT; # (Hash)
say $h; # {bacon => 2, eggs => 1}
```

## (Baggy) method Bool

Defined as:

```
method Bool(Baggy:D:) returns Bool:D
```

Returns `True`

if the invocant contains at least one element.

```
my $breakfast = ('eggs' => 1).BagHash;
say $breakfast.Bool; # True (since we have one element)
$breakfast<eggs> = 0; # weight == 0 will lead to element removal
say $breakfast.Bool; # False
```

## (Baggy) method Set

Defined as:

```
method Set() returns Set:D
```

Returns a Set whose elements are the keys of the invocant.

```
my $breakfast = (eggs => 2, bacon => 3).BagHash;
say $breakfast.Set; # set(bacon, eggs)
```

## (Baggy) method SetHash

Defined as:

```
method SetHash() returns SetHash:D
```

Returns a SetHash whose elements are the keys of the invocant.

```
my $breakfast = (eggs => 2, bacon => 3).BagHash;
my $sh = $breakfast.SetHash;
say $sh.WHAT; # (SetHash)
say $sh.elems; # 2
```

## (Baggy) method ACCEPTS

Defined as:

```
method ACCEPTS($other) returns Bool:D
```

Used in smart-matching if the right-hand side is a `Baggy`

.

If the right hand side is the type object, i.e. `Baggy`

, the method returns `True`

if `$other`

does `Baggy`

otherwise `False`

is returned.

If the right hand side is a `Baggy`

object, `True`

is returned only if `$other`

has the same elements, with the same weights, as the invocant.

```
my $breakfast = bag <eggs bacon>;
say $breakfast ~~ Baggy; # True
say $breakfast.does(Baggy); # True
my $second-breakfast = (eggs => 1, bacon => 1).Mix;
say $breakfast ~~ $second-breakfast; # True
my $third-breakfast = (eggs => 1, bacon => 2).Bag;
say $second-breakfast ~~ $third-breakfast; # False
```