matrix and list entry extraction
x(i) x(i,j) x(i,j,k,..) [...]=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))
matrix of any possible types
list variable
indices
indices
i
, j
,
k
,.. can be:
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,'*')
.
:
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)
.
If an index (i
or
j
) is a vector of booleans it is
interpreted as find(i)
or respectively
find(j)
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.
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
.
[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,'*')
:
which stands for "all elements".
If i
is a vector of booleans it is
interpreted as find(i)
.
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.
interpreted as horner(ki,m)
where
m
is the corresponding sub-list
size.
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.
// 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']) | ![]() | ![]() |