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# mat2dec

Extract vector of decision variables from matrix variable values

## Syntax

```decvec = mat2dec(lmisys,X1,X2,X3,...)
```

## Description

Given an LMI system lmisys with matrix variables X1, . . ., XK and given values X1,...,Xk of X1, . . ., XK, mat2dec returns the corresponding value decvec of the vector of decision variables. Recall that the decision variables are the independent entries of the matrices X1, . . ., XK and constitute the free scalar variables in the LMI problem.

This function is useful, for example, to initialize the LMI solvers mincx or gevp. Given an initial guess for X1, . . ., XK, mat2dec forms the corresponding vector of decision variables xinit.

An error occurs if the dimensions and structure of X1,...,Xk are inconsistent with the description of X1, . . ., XK in lmisys.

## Examples

Consider an LMI system with two matrix variables X and Y such that

• X is a symmetric block diagonal with one 2-by-2 full block and one 2-by-2 scalar block.

• Y is a 2-by-3 rectangular matrix.

Particular instances of X and Y are

and the corresponding vector of decision variables is given by

```decv = mat2dec(lmisys,X0,Y0)

decv'

ans =
1     3     -1     5     1     2     3     4     5     6
```

Note that decv is of length 10 since Y has 6 free entries while X has 4 independent entries due to its structure. Use decinfo to obtain more information about the decision variable distribution in X and Y.