# lmitool

Graphical tool for solving linear matrix inequations.

### Syntax

lmitool(filename) txt=lmitool(probname,varlist,datalist)

### Arguments

- filename
a string referring to a

`.sci`

function- probname
a string containing the name of the problem

- varlist
a string containing the names of the unknown matrices (separated by commas if there are more than one)

- datalist
a string containing the names of data matrices (separated by commas if there are more than one)

- txt
a string providing information on what the user should do next

### Description

`lmitool(filename)`

is used to redefine interactively a LMI problem,
`filename`

must have been initially generated by `lmitool`

.
In the non interactive mode, `txt=lmitool(probname,varlist,datalist)`

generates a file in the current directory. The name of this file
is obtained by adding `.sci`

to the end of `probname`

.
This file is the skeleton of a solver function and the corresponding
evaluation function needed by `lmisolver`

.

### Examples

// Find diagonal matrix X (i.e. X = diag(diag(X), p=1) such that //A1'*X+X*A1+Q1 < 0, A2'*X+X*A2+Q2 < 0 (q=2) and trace(X) is maximized // Constants rand("seed", 0); n = 2; A1 = rand(n, n); A2 = rand(n, n); Xs = diag(1:n); Q1 = -(A1'*Xs+Xs*A1+0.1*eye()); Q2 = -(A2'*Xs+Xs*A2+0.2*eye()); lmitool("prob", "X", "A1, A2"); // Create prob.sci deletefile "prob.sci"; copyfile("SCI/modules/optimization/demos/prob_bak.sci", "prob.sci"); // Replace prob.sci by prob_bak.sci exec("prob.sci", -1); X = prob(A1, A2) // Run optimization, X = [1.0635042 0; 0 2.0784841] [Y, Z, c] = prob_eval(X); // Check evaluation function value at the point found // Y = 0 // Z = list([0.0731600 0.7080179; 0.7080179 0.7186999], [0.1154910 0.5345239; 0.5345239 1.4843684]) // c = -1.0635042 deletefile "prob.sci"; // Delete created file

### See also

- lmisolver — Solve linear matrix inequations.

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