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insertion(1) Scilab Function insertion(1)
NAME
insertion - matrix and list insertion or modification
CALLING SEQUENCE
x(i,j)=a
x(i)=a
l(i)=a
l(k1)...(kn)(i)=a or l(list(k1,...,kn,i))=a
l(k1)...(kn)(i,j)=a or l(list(k1,...,kn,list(i,j))=a
PARAMETERS
x : matrix of any kind (constant, sparse, polynomial,...)
l : list
i,j : indices
k1,...kn : indices with integer value
a : new entry value
DESCRIPTION
MATRIX CASE
i and j, may be:
- real scalars or vectors or matrices with positive elements.
* if a is a matrix with dimensions (size(i,'*'),size(j,'*'))
x(i,j)=a returns a new x matrix such as
x(int(i(l)),int(j(k)))=a(l,k) for l from 1 to size(i,'*') and
k from 1 to size(j,'*'), other initial entries of x are
unchanged.
if a is a scalar x(i,j)=a returns a new x matrix such as
x(int(i(l)),int(j(k)))=a for l from 1 to size(i,'*') and k from 1
to size(j,'*'), other initial entries of x are unchanged.
If i or j maximum value exceed corresponding x matrix dimension x
is previously extended to the required dimensions with zeros
entries for standard matrices, 0 length character string for string
matrices and false values for boolean matrices.
* x(i,j)=[] kills rows specified by i if j matches all columns of
x or kills columns specified by j if i matches all rows of x. In
other cases x(i,j)=[] produce an error.
* x(i)=a with a a vector returns a new x matrix such as
x(int(i(l)))=a(l) for l from 1 to size(i,'*') , other initial
entries of x are unchanged.
x(i)=a with a a scalar returns a new x matrix such as
x(int(i(l)))=a for l from 1 to size(i,'*') , other initial entries
of x are unchanged.
If i maximum value exceed size(x,1), x is previously extended to
the required dimension with zeros entries for standard matrices, 0
length character string for string matrices and false values for
boolean matrices.
if x is a 1x1 matrix a may be a row (respectively a column)
vector with dimension size(i,'*'). Resulting x matrix is a
row (respectively a column) vector
if x is a row vector a must be a row vector with dimension
size(i,'*')
if x is a column vector a must be a column vector with dimen-
sion size(i,'*')
if x is a general matrix a must be a row or column vector with
dimension size(i,'*') and i maximum value cannot exceed
size(x,'*'),
* x(i)=[] kills entries specified by i.
- the : symbol which stands for "all elements".
* x(i,:)=a is interpreted as x(i,1:size(x,2))=a
* x(:,j)=a is interpreted as x(1:size(x,1),j)=a
* x(:)=a returns in x the a matrix reshaped according to x dimen-
sions. size(x,'*') must be equal to size(a,'*')
- 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 dimen-
sions.
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)=a and l(list(k1,...,kn,i)=a) instructions are
interpreted as:
lk1 = l(k1)
.. = ..
lkn = lkn-1(kn)
lkn(i) = a
lkn-1(kn) = lkn
.. = ..
l(k1) = lk1
And the l(k1)...(kn)(i,j)=a and l(list(k1,...,kn,list(i,j))=a
instructions are interpreted as:
lk1 = l(k1)
.. = ..
lkn = lkn-1(kn)
lkn(i,j) = a
lkn-1(kn) = lkn
.. = ..
l(k1) = lk1
i may be :
- a real non negative scalar.
l(0)=a adds an entry on the "left" of the list
l(i)=a sets the i entry of the list l to a. if i>size(l), l is
previously extended with zero length entries (undefined).
l(i)=null() suppress the ith list entry.
- a polynomial. If i is a polynomial 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 correspond-
ing sub-list size.
- a character string associated with a sub-list entry name.
REMARKS
For soft coded matrix types such as rational functions and state space
linear systems, x(i) syntax may not be used for vector entry insertion due
to confusion with list entry insertion. x(1,j) or x(i,1) syntax must be
used.
EXAMPLE
// MATRIX CASE
a=[1 2 3;4 5 6]
a(1,2)=10
a([1 1],2)=[-1;-2]
a(:,1)=[8;5]
a(1,3:-1:1)=[77 44 99]
a(1)=%s
a(6)=%s+1
a(:)=1:6
a([%t %f],1)=33
a(1:2,$-1)=[2;4]
a($:-1:1,1)=[8;7]
a($)=123
//
x='test'
x([4 5])=['4','5']
//
b=[1/%s,(%s+1)/(%s-1)]
b(1,1)=0
b(1,$)=b(1,$)+1
b(2)=[1 2] // the numerator
// LIST OR TLIST CASE
l=list(1,'qwerw',%s)
l(1)='Changed'
l(0)='Added'
l(6)=['one more';'added']
//
//
dts=list(1,tlist(['x';'a';'b'],10,[2 3]));
dts(2)('a')=33
dts(2)('b')(1,2)=-100
SEE ALSO
find, horner, parents, extraction
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