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`data.sparse`

- Sparse data containers- Module:
**data.sparse** -
This module provides a

*sparse vector*and*sparse matrix*, a space efficient data container indexed by nonnegative integer(s), and a*sparse table*, a hash table using a sparse vector as a backing storage.

A sparse vector associates a nonnegative integer index
to a value. It has *vector* in its name since it is indexed
by an integer, but it isn’t like a flat array on contiguous memory;
it’s more like an associative array. (Internally, the current
implementation uses compact trie structure.)
It is guaranteed that you can store a value with index at least
up to `2^32-1`

; the actual maximum bits of indexes can
be queried by `sparse-vector-max-index-bits`

.
(We have a plan to remove the maximum bits limitation in future).

Unlike ordinary vectors, you don’t need to specify the size of a sparse vector when you create one. You can just set a value to any index in the supported range.

(define v (make-sparse-vector)) (sparse-vector-set! v 0 'a) (sparse-vector-ref v 0) ⇒ a (sparse-vector-set! v 100000000 'b) (sparse-vector-ref v 100000000) ⇒ b ;; set! also work (set! (sparse-vector-ref v 100) 'c) (sparse-vector-ref v 100) ⇒ c

If you try to access an element that hasn’t been set,
an error is signaled by default. You can set
a default value for each vector, or give a
fallback value to `sparse-vector-ref`

, to suppress the error.

```
(sparse-vector-ref v 1) ⇒ error
(sparse-vector-ref v 1 'noval) ⇒ noval
(let1 w (make-sparse-vector #f :default 'x)
(sparse-vector-ref w 1)) ⇒ x
```

A sparse matrix is like a sparse vector, except it can be indexed by a pair of integers.

A sparse table works just like a hash table, but it uses a sparse vector to store the values using hashed number of the keys.

The main reason of these sparse data containers are for memory efficiency. If you want to store values in a vector but knows you’ll use only some entries sparsely, obviously it is waste to allocate a large vector and to leave many entries unused. But it is worse than that; Gauche’s GC doesn’t like a large contiguous region of memory. Using lots of large vectors adds GC overhead quickly. It becomes especially visible when you store large number of entries (like >100,000) into hash tables, since Gauche’s builtin hash tables use a flat vector as a backing storage. You’ll see the heap size grows quickly and GC runs more frequently and longer. On the other hand, sparse table works pretty stable with large number of entries.

Sparse data containers does have overhead on access speed. They are a bit slower than the ordinary hash tables, and much slower than ordinary vectors. We should note, however, as the number of entries grow, access time on ordinary hash tables grows quicker than sparse tables and eventually two become comparable.

It depends on your application which you should use, and if you’re not sure, you need to benchmark. As a rule of thumb, if you use more than several hashtables each of which contains more than a few tens of thousands of entries, sparse tables may work better. If you see GC Warnings telling “repeated allocation of large blocks”, you should definitely consider sparse tables.

• Sparse vectors: | ||

• Sparse matrixes: | ||

• Sparse tables: |

Next: Sparse matrixes, Previous: Sparse data containers, Up: Sparse data containers [Contents][Index]

- Class:
**<sparse-vector-base>** -
{

`data.sparse`} An abstract base class of sparse vectors. Inherits`<dictionary>`

and`<collection>`

. Note that sparse vectors are*not*`<sequence>`

; even they can be indexable by integers, they don’t have means of*ordered*access.Sparse vector may be a general vector that can contain any Scheme objects (like

`<vector>`

), or a specialized vector that can contain only certain types of numbers (like`<s8vector>`

etc.).All of these sparse vectors can be accessed by the same API.

Sparse vectors also implements the Collection API (see Collection framework) and the Dictionary API (see Dictionary framework).

- Class:
**<sparse-vector>** - Class:
**<sparse-**`TAG`vector> -
{

`data.sparse`} The actual sparse vector classes. Inherits`<sparse-vector-base>`

. An instance of`<sparse-vector>`

can contain any Scheme objects.`TAG`either one of`s8`

,`u8`

,`s16`

,`u16`

,`s32`

,`u32`

,`s64`

,`u64`

,`f16`

,`f32`

, or`f64`

. The range of values an instance of those classes can hold is the same as the corresponding`<`

class in`TAG`vector>`gauche.uvector`

(see Uniform vectors). That is,`<sparse-u8vector>`

can have exact integer values between 0 and 255.

- Function:
**make-sparse-vector***:optional type :key default* {

`data.sparse`} Creates an empty sparse vector. The`type`argument can be`#f`

(default), one of subclasses of`<sparse-vector-base>`

, or a symbol of either one of`s8`

,`u8`

,`s16`

,`u16`

,`s32`

,`u32`

,`s64`

,`u64`

,`f16`

,`f32`

, or`f64`

.If

`type`is omitted or`#f`

, a`<sparse-vector>`

is created. If it is a class, an instance of the class is created (It is an error to pass a class that is not a subclass of`<sparse-vector-base>`

.) If it is a symbol, an instance of corresponding`<sparse-`

is created.`TAG`vector>You can specify the default value of the vector by

`default`keyword argument. If given, the vector behaves as if it is filled with the default value (but the vector iterator only picks the values explicitly set).Note that you have to give the optional argument as well to specify the keyword argument.

(define v (make-sparse-vector 'u8 :default 128)) (sparse-vector-ref v 0) ⇒ 128

- Function:
**sparse-vector-max-index-bits** {

`data.sparse`} Returns maximum number of bits of allowed integer. If this returns 32, the index up to`(expt 2 32)`

is supported. It is guaranteed that this is at least 32.

In the following entries, the argument `sv` denotes
an instance of sparse vector; an error is signaled if other
object is passed.

- Function:
**sparse-vector-copy***sv* {

`data.sparse`} Returns a copy of a sparse vector`sv`.

- Function:
**sparse-vector-ref***sv k :optional fallback* {

`data.sparse`} Returns`k`-th element of a sparse vector`sv`, where`k`must an exact integer.If the sparse vector doesn’t have a value for

`k`, it behaves as follows:- If
`fallback`is given, it is returned. - Otherwise, if the vector has the default value, it is returned.
- Otherwise, an error is signaled.

- If

- Function:
**sparse-vector-set!***sv k value* {

`data.sparse`} Sets`value`for`k`-th element of a sparse vector`sv`.`K`must be a nonnegative exact integer, and below the maximum allowed index.If

`sv`is a numeric sparse vector,`value`must also be within the allowed range, or an error is signaled.

- Function:
**sparse-vector-num-entries***sv* {

`data.sparse`} Returns the number of entries in`sv`.

- Function:
**sparse-vector-exists?***sv k* {

`data.sparse`} Returns`#t`

if`sv`has an entry for index`k`,`#f`

otherwise.

- Function:
**sparse-vector-delete!***sv k* {

`data.sparse`} Deletes the`k`-th entry of`sv`. If`sv`had the entry , returns`#t`

. If`sv`didn’t have the entry, returns`#f`

.

- Function:
**sparse-vector-clear!***sv* {

`data.sparse`} Empties a sparse vector.

- Function:
**sparse-vector-inc!***sv k delta :optional (fallback 0)* {

`data.sparse`} This is a shortcut of the following. It is especially efficient for numeric sparse vectors.(sparse-vector-set! sv k (+ (sparse-vector-ref sv k fallback) delta))

If the result of addition exceeds the allowed value range of

`sv`, an error is signaled. In future we’ll allow an option to clamp the result value within the range.

- Function:
**sparse-vector-update!***sv k proc :optional fallback* - Function:
**sparse-vector-push!***sv k val* - Function:
**sparse-vector-pop!***sv k :optional fallback* {

`data.sparse`} Convenience routines to fetch-and-update an entry of a sparse vector. Works just like`hash-table-update!`

,`hash-table-push!`

and`hash-table-pop!`

; (see Hashtables).

The following procedures traverses a sparse vector. Note that elements are not visited in the order of index; it’s just like hash table traversers.

At this moment, if you want to walk a sparse vector with
increasing/decreasing index order, you have to get a list
of keys by `sparse-vector-keys`

, sort it, then use
it to retrieve values.
We may add an option in future to `make-sparse-vector`

so that
those walk operation will be more convenient.

- Function:
**sparse-vector-fold***sv proc seed* {

`data.sparse`} For each entry in`sv`, calls`proc`as`(proc`

, where`k_n``v_n``seed_n`)`k_n`is an index and`v_n`is a value for it, and`seed_n`is the returned value of the previous call to`proc`if`n``>=`

1, and`seed`if`n`= 0. Returns the value of the last call of`proc`.

- Function:
**sparse-vector-for-each***sv proc* - Function:
**sparse-vector-map***sv proc* {

`data.sparse`} Calls`proc`

with index and value, e.g.`(proc k value)`

, for each element of`sv`.The results of

`proc`are discarded by`sparse-vector-for-each`

, and gathered to a list and returned by`sparse-vector-map`

.

- Function:
**sparse-vector-keys***sv* - Function:
**sparse-vector-values***sv* {

`data.sparse`} Returns a list of all keys and all values in`sv`, respectively.

Next: Sparse tables, Previous: Sparse vectors, Up: Sparse data containers [Contents][Index]

A sparse matrix is like a sparse vector, except it can be indexed by two nonnegative integers.

Note: This implementation of sparse matrixes aims at a reasonable space efficiency for sparse matrixes without knowing its structure beforehand (imagine, for example, a 2D map with some scattered landmarks). If what you want is a sparse matrix implementation for efficient numeric calculations, with certain particular structures, probably the access speed of this module isn’t suitable.

Currently, each index can have half of bits of
`sparse-vector-max-index-bits`

. We’ll remove
this limitation in future.

- Class:
**<sparse-matrix-base>** -
{

`data.sparse`} An abstract base class of sparse matrixes. Inherits`<collection>`

.Like sparse vectors, a sparse matrix can be of type that can store any Scheme objects, or that can store only certain types of numbers.

All of these sparse matrix subtypes can be accessed by the same API.

- Class:
**<sparse-matrix>** - Class:
**<sparse-**`TAG`matrix> -
{

`data.sparse`} The actual sparce matrix classes. Inherits`<sparse-matrix-base>`

. An instance of`<sparse-matrix>`

can contain any Scheme objects.`TAG`either one of`s8`

,`u8`

,`s16`

,`u16`

,`s32`

,`u32`

,`s64`

,`u64`

,`f16`

,`f32`

, or`f64`

. The range of values an instance of those classes can hold is the same as the corresponding`<`

class in`TAG`vector>`gauche.uvector`

(see Uniform vectors). That is,`<sparse-u8matrix>`

can have exact integer values between 0 and 255.

- Function:
**make-sparse-matrix***:optional type :key default* {

`data.sparse`} Creates an empty sparse matrix. The`type`argument can be`#f`

(default), one of subclasses of`<sparse-matrix-base>`

, or a symbol of either one of`s8`

,`u8`

,`s16`

,`u16`

,`s32`

,`u32`

,`s64`

,`u64`

,`f16`

,`f32`

, or`f64`

.If

`type`is omitted or`#f`

, a`<sparse-matrix>`

is created. If it is a class, an instance of the class is created (It is an error to pass a class that is not a subclass of`<sparse-matrix-base>`

.) If it is a symbol, an instance of corresponding`<sparse-`

is created.`TAG`matrix>You can specify the default value of the matrix by

`default`keyword argument. If given, the vector behaves as if it is filled with the default value (but the matrix iterator only picks the values explicitly set).Note that you have to give the optional argument as well to specify the keyword argument.

- Function:
**sparse-matrix-num-entries***mat* {

`data.sparse`} Returns the number of entries explicitly set in a sparse matrix`mat`.

- Function:
**sparse-matrix-ref***mat x y :optional fallback* {

`data.sparse`} Returns an element indexed by (`x`,`y`) in a sparse matrix`mat`. If the indexed element isn’t set,`fallback`is returned if provided; otherwise, if the matrix has the default value, it is returned; otherwise, an error is raised.

- Function:
**sparse-matrix-set!***mat x y value* {

`data.sparse`} Set`value`to the sparse matrix`mat`at the location (`x`,`y`).

- Function:
**sparse-matrix-exists?***mat x y* {

`data.sparse`} Returns`#t`

iff the sparse matrix`mat`has a value at (`x`,`y`).

- Function:
**sparse-matrix-clear!***mat* {

`data.sparse`} Empties the sparse matrix`mat`.

- Function:
**sparse-matrix-delete!***mat x y* {

`data.sparse`} Remove the value at (`x`,`y`) from the sparse matrix`mat`.

- Function:
**sparse-matrix-copy***mat* {

`data.sparse`} Returns a fresh copy of`mat`.

- Function:
**sparse-matrix-update!***mat x y proc :optional fallback* {

`data.sparse`} Call`proc`with the value at (`x`,`y`) of the sparse matrix, and sets the result of`proc`as the new value of the location.The optional

`fallback`argument works just like`sparse-matrix-ref`

; if provided, it is passed to`proc`in case the matrix doesn’t have a value at (`x`,`y`). If`fallback`isn’t provided and the matrix doesn’t have a value at the location, the default value of the matrix is used if it has one. Otherwise, an error is signalled.

- Function:
**sparse-matrix-inc!***mat x y delta :optional fallback* {

`data.sparse`}(sparse-matrix-update! mat x y (cut + <> delta) fallback)

- Function:
**sparse-matrix-push!***mat x y val* {

`data.sparse`}(sparse-matrix-update! mat x y (cut cons val <>) '())

- Function:
**sparse-matrix-pop!***mat x y* {

`data.sparse`}(rlet1 r #f (sparse-matrix-update! mat x y (^p (set! r (car p)) (cdr p))))

- Function:
**sparse-matrix-fold***mat proc seed* {

`data.sparse`} Loop over values in the sparse matrix`mat`. The procedure`proc`is called with four arguments,`x`,`y`,`val`and`seed`, for each index (`x`,`y`) which has the value`val`. The initial value of`seed`is the one given to`sparse-matrix-fold`

, and the result of`proc`is passed as the next seed value. The last result of`proc`is returned from`sparse-matrix-fold`

.The procedure

`proc`is only called on the entries that’s actually has a value, and the order of which the procedure is called is undefined.

- Function:
**sparse-matrix-map***mat proc* {

`data.sparse`}(sparse-matrix-fold sv (^[x y v s] (cons (proc x y v) s)) '()))

- Function:
**sparse-matrix-for-each***mat proc* {

`data.sparse`}(sparse-matrix-fold sv (^[x y v _] (proc x y v)) #f))

- Function:
**sparse-matrix-keys***mat* {

`data.sparse`}(sparse-matrix-fold sv (^[x y _ s] (cons (list x y) s)) '())

- Function:
**sparse-matrix-values***mat* {

`data.sparse`}(sparse-matrix-fold sv (^[x y v s] (cons v s)) '())

Previous: Sparse matrixes, Up: Sparse data containers [Contents][Index]

- Class:
**<sparse-table>** -
{

`data.sparse`} A class for sparse table. Inherits`<dictionary>`

and`<collection>`

.Operationally sparse tables are the same as hash tables, but the former consumes less memory in trade of slight slower access. (Roughly x1.5 to x2 access time when the table is small. As the table gets larger the difference becomes smaller.)

- Function:
**make-sparse-table***comparator* {

`data.sparse`} Creates and returns an empty sparse table. The`comparator`argument specifies how to compare and hash keys; it must be either a comparator (see Basic comparators), or one of the symbols`eq?`

,`eqv?`

,`equal?`

and`string=?`

, like hash tables (see Hashtables). If it is a symbol,`eq-comparator`

,`eqv-comparator`

,`equal-comparator`

or`string-comparator`

are used, respectively.

- Function:
**sparse-table-comparator***st* {

`data.sparse`} Returns the comparator used in the sparse table`st`.

- Function:
**sparse-table-copy***st* {

`data.sparse`} Returns a copy of a sparse table`st`.

- Function:
**sparse-table-num-entries***st* {

`data.sparse`} Returns the number of entries in a sparse table`st`.

- Function:
**sparse-table-ref***st key :optional fallback* {

`data.sparse`} Retrieves a value associated to the`key`in`st`. If no entry with`key`exists,`fallback`is returned when it is provided, or an error is signaled otherwise.

- Function:
**sparse-table-set!***st key value* {

`data.sparse`} Sets`value`with`key`in`st`.

- Function:
**sparse-table-exists?***st key* {

`data.sparse`} Returns`#t`

if an entry with`key`exists in`st`,`#f`

otherwise.

- Function:
**sparse-table-delete!***st key* {

`data.sparse`} Deletes an entry with`key`in`st`if it exists. Returns`#t`

if an entry is actually deleted, or`#f`

if there hasn’t been an entry with`key`.

- Function:
**sparse-table-clear!***st* {

`data.sparse`} Empties`st`.

- Function:
**sparse-table-update!***st key proc :optional fallback* - Function:
**sparse-table-push!***st key val* - Function:
**sparse-table-pop!***st key :optional fallback* {

`data.sparse`}

- Function:
**sparse-table-fold***st proc seed* - Function:
**sparse-table-for-each***st proc* - Function:
**sparse-table-map***st proc* {

`data.sparse`}

- Function:
**sparse-table-keys***st* - Function:
**sparse-table-values***st* {

`data.sparse`}

Previous: Sparse matrixes, Up: Sparse data containers [Contents][Index]