gsort

sorting by quick sort agorithm

Calling Sequence

[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 similarily 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 similarily 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 algorithme preserve the relative order of records with equal values.

When v is complex, the elements are sorted by magnitude, i.e., abs( v) . Only ‘g’ as second argument is managed with complex.

With complex numbers, gsort can be overloaded

see 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 ‘i’ or at the end with ‘d’ 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). .. _overloading: overloading.html .. _find: find.html