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# gsort

sorting by quick sort algorithm

### Syntax

[B [,k]]=gsort(A) [B [,k]]=gsort(A,option) [B [,k]]=gsort(A,option,direction)

### Arguments

- A
a real,an integer or a character string vector/matrix or a sparse vector.

- option
a character string. It gives the type of sort to perform:

'r' : each column of

`A`

is sorted'c': each row of

`A`

is sorted'g': all elements of

`A`

are sorted. It is the default value.'lr': lexicographic sort of the rows of

`A`

'lc': lexicographic sort of the columns of

`A`

- direction
a character string. It gives the ordering direction:

`'i'`

stand for increasing and`'d'`

for decreasing order (default).- B
an array with same type and dimensions as

`A`

.- k
a real array with integer values and same dimensions as

`A`

. Contains the origin indices.

### Description

`gsort`

implements a "quick sort" algorithm for
various data types.

`B=gsort(A,'g')`

,`B=gsort(A,'g','d')`

and`B=gsort(A)`

sort the elements of the array`A`

, seen as`A(:)`

in a decreasing order.`B=gsort(A,'g','i')`

sort the elements of the array`A`

in the increasing order.`B=gsort(A,'lr')`

sorts the rows of`A`

in lexical decreasing order.`B`

is obtained by a permutation of the rows of matrix`A`

in such a way that the rows of`B`

verify`B(i,:)>=B(j,:)`

if`i<j`

.`B=gsort(A,'lr','i')`

works similarly for increasing lexical order.`B=gsort(A,'lc')`

sorts the columns of`A`

in lexical decreasing order.`B`

is obtained by a permutation of the columns of matrix`A`

in such a way that the columns of`B`

verify`B(:,i)>=B(:,j)`

if`i<j`

.`B=gsort(A,'lc','i')`

works similarly for increasing lexical order.

If required the second return argument `k`

contains
the indices of the sorted values in `A`

. If
`[B,k]=gsort(A,'g')`

one has `B==A(k)`

.
**The algorithm preserve the relative order of
records with equal values.**

When `v`

is complex, the elements are sorted by
magnitude, i.e., abs(`v`

) .

With complex numbers, `gsort`

can be overloaded

Create macro: SCI/modules/elementary_functions/macros/%_gsort.sci

Overloading for not managed type (others than a real, an integer or a character string vector/matrix or a sparse vector.) is allowed.

if `v`

have `%nan`

or
`%inf`

as elements. gsort places these at the beginning
with `'d'`

or at the end with `'i'`

argument.

### Examples

alr=[1,2,2; 1,2,1; 1,1,2; 1,1,1]; [alr1,k]=gsort(alr,'lr','i') [alr1,k]=gsort(alr,'lc','i') v=int32(alr) gsort(v) gsort(v,'lr','i') gsort(v,'lc','i') v=['Scilab' '2.6' 'Scilab' '2.7' 'xcos' '2.7' 'Scilab' '3.1' 'xcos' '3.1' 'xcos' '4.0' 'Scilab' '4.0'] gsort(v,'lr','i') gsort(v,'lc','i')

### See also

- find — find indices of boolean vector or matrix true elements

- overloading — display, functions and operators overloading capabilities

### Bibliography

Quick sort algorithm from Bentley & McIlroy's "Engineering a Sort Function". Software---Practice and Experience, 23(11):1249-1265

### History

Version | Description |

5.4.0 | This function allows overloading for unmanaged type (others than a real, an integer or a character string vector/matrix or a sparse vector). |

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