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extraction Scilab Group Scilab Function extraction
NAME
extraction - matrix and list entry extraction
CALLING SEQUENCE
x(i,j)
x(i)
[...]=l(i)
[...]=l(k1)...(kn)(i) or [...]=l(list(k1,...,kn,i))
l(k1)...(kn)(i,j) or l(list(k1,...,kn,list(i,j))
PARAMETERS
x : matrix of any possible types
l : list variable
i,j : indices
k1,...kn : indices
DESCRIPTION
MATRIX CASE
i and j, can be:
- real scalars or vectors or matrices with positive elements.
* r=x(i,j) designs the matrix r such as
r(l,k)=x(int(i(l)),int(j(k))) for l from 1 to size(i,'*') and
k from 1 to size(j,'*'). i (j) Maximum value must be less or
equal to size(x,1) (size(x,2)).
* r=x(i) with x a 1x1 matrix designs the matrix r such as
r(l,k)=x(int(i(l)),int(i(k))) for l from 1 to size(i,1) and k
from 1 to size(i,2). Note that in this case index i is valid
only if all its entries are equal to one.
* r=x(i) with x a row vector designs the row vector r such as
r(l)=x(int(i(l))) for l from 1 to size(i,'*') i Maximum
value must be less or equal to size(x,'*').
* r=x(i) with x a matrix with one or more columns designs the
column vector r such as r(l) (l from 1 to size(i,'*')) designs
the int(i(l)) entry of the column vector formed by the
concatenation of the x's columns. i Maximum value must be
less or equal to size(x,'*').
- the : symbol which stands for "all elements".
* r=x(i,:) designs the matrix r such as r(l,k)=x(int(i(l)),k))
for l from 1 to size(i,'*') and k from 1 to size(x,2)
* r=x(:,j) designs the matrix r such as r(l,k)=x(l,int(j(k)))
for l from 1 to size(r,1) and k from 1 to size(j,'*').
* r=x(:) designs the column vector r formed by the column
concatenations of x columns. It is equivalent to
matrix(x,size(x,'*'),1).
- vector of boolean. If an index (i or j )is a vector of booleans
it is interpreted as find(i) or respectively find(j)
- a polynomial. If an index (i or j )is a vector of polynomials
or implicit polynomial vector it is interpreted as horner(i,m) or
respectively horner(j,n) where m and n are associated x
dimensions. Even if this feature works for all polynomials, it
is recommended to use polynomials in $ for readability.
LIST OR TLIST CASE
If they are present the ki give the path to a sub-list entry of l data
structure. They allow a recursive extraction without intermediate
copies. The [...]=l(k1)...(kn)(i) and [...]=l(list(k1,...,kn,i))
instructions are interpreted as: lk1 = l(k1) .. = .. lkn
= lkn-1(kn) [...] = lkn(i) And the l(k1)...(kn)(i,j) and
l(list(k1,...,kn,list(i,j)) instructions are interpreted as: lk1
= l(k1) .. = .. lkn = lkn-1(kn) lkn(i,j) i and
j, can be: When path points on more than one list component the
instruction must have as many left hand side arguments as selected
components. But if the extraction syntax is used within a function
input calling sequence each returned list component is added to the
function calling sequence.
Note that, l(list() is the same as l.
- real scalar or vector or matrix with positive elements.
[r1,...rn]=l(i) extracts the i(k) elements from the list l and
store them in rk variable for k from 1 to size(i,'*')
- the : symbol which stands for "all elements".
- a vector of booleans. If i is a vector of booleans it is
interpreted as find(i).
- a polynomial. If i is a vector of polynomials or implicit
polynomial vector it is interpreted as horner(i,m) where
m=size(l). Even if this feature works for all polynomials, it is
recommended to use polynomials in $ for readability.
k1,..kn may be :
- real positive scalar.
- a polynomial,interpreted as horner(ki,m) where m is the
corresponding sub-list size.
REMARKS
- a character string associated with a sub-list entry name.
For soft coded matrix types such as rational functions and state space
linear systems, x(i) syntax may not be used for vector element extraction
due to confusion with list element extraction. x(1,j) or x(i,1) syntax
must be used.
EXAMPLE
// MATRIX CASE
a=[1 2 3;4 5 6]
a(1,2)
a([1 1],2)
a(:,1)
a(:,3:-1:1)
a(1)
a(6)
a(:)
a([%t %f %f %t])
a([%t %f],[2 3])
a(1:2,$-1)
a($:-1:1,2)
a($)
//
x='test'
x([1 1;1 1;1 1])
//
b=[1/%s,(%s+1)/(%s-1)]
b(1,1)
b(1,$)
b(2) // the numerator
// LIST OR TLIST CASE
l=list(1,'qwerw',%s)
l(1)
[a,b]=l([3 2])
l($)
x=tlist(l(2:3)) //form a tlist with the last 2 components of l
//
dts=list(1,tlist(['x';'a';'b'],10,[2 3]));
dts(2)('a')
dts(2)('b')(1,2)
[a,b]=dts(2)(['a','b'])
SEE ALSO
find, horner, parents
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