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.TH extraction 1 "September 1996" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
extraction - matrix and list entry extraction
.SH CALLING SEQUENCE
.nf
x(i,j)
x(i)
[...]=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))
.fi
.SH PARAMETERS
.TP 15
x
: matrix of any possible types
.TP 15
l
: list variable
.TP 15
i,j
: indices
.TP
k1,...kn
: indices
.SH DESCRIPTION
.TP 5
MATRIX CASE
\fVi\fR and \fVj\fR, can be:
.RS
.TP 3
-
real scalars or vectors or matrices with positive elements.
.RS
.TP 3
*
\fVr=x(i,j)\fR designs the matrix \fVr\fR such as
\fVr(l,k)=x(int(i(l)),int(j(k)))\fR for \fVl\fR from 1 to \fVsize(i,'*')\fR and
\fVk\fR from 1 to \fVsize(j,'*')\fR.
\fVi\fR (\fVj\fR) Maximum value must be
less or equal to \fVsize(x,1)\fR (\fVsize(x,2)\fR).
.TP 3
*
\fVr=x(i)\fR with \fVx\fR a 1x1 matrix designs the matrix \fVr\fR such as
\fVr(l,k)=x(int(i(l)),int(i(k)))\fR for \fVl\fR from 1 to \fVsize(i,1)\fR and
\fVk\fR from 1 to \fVsize(i,2)\fR.
Note that in this case index
\fVi\fR is valid only if all its entries are equal to one.
.TP 3
*
\fVr=x(i)\fR with \fVx\fR a row vector designs the row vector
\fVr\fR such as \fVr(l)=x(int(i(l)))\fR for \fVl\fR from 1 to
\fVsize(i,'*')\fR
\fVi\fR Maximum value must be
less or equal to \fVsize(x,'*')\fR.
.TP 3
*
\fVr=x(i)\fR with \fVx\fR a matrix with one or more columns designs
the column vector \fVr\fR such as \fVr(l)\fR (\fVl\fR from 1 to
\fVsize(i,'*')\fR) designs the \fVint(i(l))\fR entry of the column
vector formed by the concatenation of the \fVx\fR's columns.
\fVi\fR Maximum value must be
less or equal to \fVsize(x,'*')\fR.
.RE
.TP
-
the \fV : \fR symbol which stands for "all elements".
.RS
.TP 3
*
\fVr=x(i,:)\fR designs the matrix \fVr\fR such as
\fVr(l,k)=x(int(i(l)),k))\fR for \fVl\fR from 1 to \fVsize(i,'*')\fR and
\fVk\fR from 1 to \fVsize(x,2)\fR
.TP
*
\fVr=x(:,j)\fR designs the matrix \fVr\fR such as
\fVr(l,k)=x(l,int(j(k)))\fR for \fVl\fR from 1 to \fVsize(r,1)\fR and
\fVk\fR from 1 to \fVsize(j,'*')\fR.
.TP
*
\fVr=x(:)\fR designs the column vector \fVr\fR formed by the
column concatenations of\fV x\fR columns. It is equivalent to
\fVmatrix(x,size(x,'*'),1)\fR.
.RE
.TP
-
vector of boolean. If an index (\fVi\fR or \fVj\fR )is a vector of
booleans it is interpreted as \fVfind(i)\fR or respectively \fVfind(j)\fR
.TP
-
a polynomial. If an index (\fVi\fR or \fVj\fR )is a vector of
polynomials or implicit polynomial vector it is interpreted as
\fVhorner(i,m)\fR or respectively \fVhorner(j,n)\fR where \fVm\fR
and \fVn\fR are associated \fVx\fR dimensions.
Even if this feature works for all polynomials, it is recommended to
use polynomials in \fV$\fR for readability.
.RE
.TP
LIST OR TLIST CASE
If they are present the \fVki\fR give the path to a sub-list entry of
\fVl\fR data structure. They allow a recursive extraction without
intermediate copies.
The \fV[...]=l(k1)...(kn)(i)\fR and \fV[...]=l(list(k1,...,kn,i))\fR instructions are interpreted as:
\fVlk1 = l(k1)\fR
\fV .. = .. \fR
\fVlkn = lkn-1(kn)\fR
\fV[...] = lkn(i)\fR
And the \fVl(k1)...(kn)(i,j)\fR and \fVl(list(k1,...,kn,list(i,j))\fR
instructions are interpreted as:
\fVlk1 = l(k1)\fR
\fV .. = .. \fR
\fVlkn = lkn-1(kn)\fR
\fV lkn(i,j)\fR
\fVi\fR and \fVj\fR, can be:
When path points on more than one list component the instruction must
have as many left hand side arguments as selected components. But if the
extraction syntax is used within a function input calling sequence
each returned list component is added to the function calling sequence.
.RS
.TP 3
-
real scalar or vector or matrix with positive elements.
\fV[r1,...rn]=l(i)\fR extracts the \fVi(k)\fR elements from the list
l and store them in \fVrk\fR variable for \fVk\fR from 1 to
\fVsize(i,'*')\fR
.TP
-
the \fV : \fR symbol which stands for "all elements".
.TP
-
a vector of booleans. If \fVi\fR is a vector of
booleans it is interpreted as \fVfind(i)\fR.
.TP
-
a polynomial. If \fVi\fR is a vector of
polynomials or implicit polynomial vector it is interpreted as
\fVhorner(i,m)\fR where \fVm=size(l)\fR.
Even if this feature works for all polynomials, it is recommended to
use polynomials in \fV$\fR for readability.
.RE
.TP
\fVk1,..kn\fR may be :
.RS
.TP 3
-
real positive scalar.
.TP
-
a polynomial,interpreted as
\fVhorner(ki,m)\fR where \fVm\fR is the corresponding sub-list size.
.TP
- a character string associated with a sub-list entry name.
.RE
.SH REMARKS
For soft coded matrix types such as rational functions and state space
linear systems, \fVx(i)\fR syntax may not be used for vector element
extraction due to confusion with list element extraction. \fVx(1,j)\fR
or \fVx(i,1)\fR syntax must be used.
.SH EXAMPLE
.nf
// 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'])
.fi
.SH SEE ALSO
find, horner, parents
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