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 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 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.