extraction

Matrix case

i, j, k,.. can be:

a real scalar or a vector or a matrix with positive elements.

• r=x(i,j) builds 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 builds 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 builds 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 builds the column vector r such as r(l) (l from 1 to size(i,'*')) contains 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,:) builds 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) builds 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(:) builds the column vector r formed by the column concatenations of x columns. It is equivalent to matrix(x,size(x,'*'),1).

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 dimensions. Even if this feature works for all polynomials, it is recommended to use polynomials in $ for readability.

For matrices with more than 2 dimensions (see:hypermatrices) the dimensionality is automatically reduced when right-most dimensions are equal to 1.

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 instructions

[...]=l(k1)...(kn)(i)

and

[...]=l(list(k1,...,kn,i))

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)

When path points to 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 as function parameters, each returned list component is added to the function parameters.

Note that l(list()) is the same as l.

i and j may be:

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 variables 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.

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 element extraction due to confusion with list element extraction. x(1,j) or x(i,1) syntax must be used.