insertion partial variable assignation or modification
assignation partial variable assignation

## Syntax

    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

## Arguments

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

  If `x` is a matrix the indices `i` and `j`, may be:

  Real scalars or vectors or matrices

    In this case the values given as indices should be positive and only their integer part are taken into account.

    - 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, array `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 an `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 an `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 dimension `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

    The `:` symbol 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` dimensions. `size(x,'*')` must be equal to `size(a,'*')`.

  Vectors of boolean

    If an index (`i` or `j`) is a vector of booleans it is interpreted as `find(i)` or respectively `find(j)`.

  Polynomials

    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 insertion 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 (only its integer part is taken into account). `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()` deletes the `i`th 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 corresponding 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 must 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.

## Examples

    // 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($)=123
    a(1,%pi)=1 //equivalent to a(1,3)=1
    //
    x='test'
    x([4 5])=['4','5']
    //
    b=[1/%s,(%s+1)/(%s-1)]
    b(1,1)=0
    b(1,$)=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(%pi)=1 //equivalent to l(3)=1
    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
- parentheses
- extraction