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Describe how entries of matrix variable * X* relate
to decision variables

decinfo(lmisys) decX = decinfo(lmisys,X)

```
The function decinfo
expresses the entries of a matrix variable
```

* X* in
terms of the decision variables

`lmisys`

.
Each entry of If `X`

is the identifier of * X* supplied
by

`lmivar`

, the commanddecX = decinfo(lmisys,X)

returns an integer matrix `decX`

of the same
dimensions as * X* whose (

0 if

(*X*) is a hard zero*i, j*if*n*(*X*) =*i, j*(the*x*_{n}-th decision variable)*n*–

if*n*(*X*) = –*i, j**x*_{n}

`decX`

clarifies the structure
of * X* as well as its entry-wise dependence on

`lmivar`

).`decinfo`

can also be used
in interactive mode by invoking it with a single argument. It then
prompts the user for a matrix variable and displays in return the
decision variable content of this variable.

Consider an LMI with two matrix variables * X* and

=*X**x I*_{3}withscalar*x*rectangular of size 2-by-1*Y*

If these variables are defined by

setlmis([]) X = lmivar(1,[3 0]) Y = lmivar(2,[2 1]) : : lmis = getlmis

the decision variables in * X* and

dX = decinfo(lmis,X) dX = 1 0 0 0 1 0 0 0 1 dY = decinfo(lmis,Y) dY = 2 3

This indicates a total of three decision variables *x*_{1}, *x*_{2}, *x*_{3} that
are related to the entries of * X* and

$$X=\left(\begin{array}{ccc}{x}_{1}& 0& 0\\ 0& {x}_{1}& 0\\ 0& 0& {x}_{1}\end{array}\right),Y=\left(\begin{array}{c}{x}_{2}\\ x3\end{array}\right)$$

Note that the number of decision variables corresponds to the
number of free entries in * X* and

Suppose that the matrix variable * X* is symmetric
block diagonal with one 2-by-2 full block and one 2-by-2 scalar block,
and is declared by

setlmis([]) X = lmivar(1,[2 1;2 0]) : lmis = getlmis

The decision variable distribution in * X* can
be visualized interactively as follows:

decinfo(lmis) There are 4 decision variables labeled x1 to x4 in this problem. Matrix variable Xk of interest (enter k between 1 and 1, or 0 to quit): ?> 1 The decision variables involved in X1 are among {-x1,...,x4}. Their entry-wise distribution in X1 is as follows (0,j>0,-j<0 stand for 0,xj,-xj, respectively): X1 : 1 2 0 0 2 3 0 0 0 0 4 0 0 0 0 4 ********* Matrix variable Xk of interest (enter k between 1 and 1, or 0 to quit): ?> 0

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