## MATLAB

### Setup

Once you have downloaded POGS, open MATLAB and type

1 | >> cd <pogs>/src/interface_matlab |

in the MATLAB console. The string

1 | ```
<pogs>
``` |

```
```

must be replaced with the directory to which POGS was downloaded. To compile wrapper type
1 | >> pogs_setup |

Alternatively typing

1 | >> pogs_setup gpu |

will compile the GPU version.

### MATLAB-specific usage

The MATLAB interface is a single MEX-function, with signature

1 | [x, y, l, optval] = pogs(A, f, g, params) |

Inputs:

is the data matrix of dimension \(m n\).1

`A`

and1

`f`

are structs with fields1

`g`

,1

`h`

,1

`a`

,1

`b`

,1

`c`

and1

`d`

, each of which must either be a vector of dimension \( m \) (resp. \( n \)) or a scalar. If a scalar is specified, then it is assumed that the scalar should be repeated \( m \) (resp. \( n \)) times. Multiple problems can be solved with the same matrix \( A \), if1

`e`

and1

`f`

are specified as struct arrays.1

`g`

Optional Inputs:

is a struct with fields1

`params`

,1

`rel_tol`

,1

`abs_tol`

,1

`rho`

,1

`max_iter`

and1

`quiet`

.1

`adaptive_rho`

Outputs:

and1

`x`

are the solution vectors \(x^\star_\text{pogs}\) resp. \(y^\star_\text{pogs}\), and have dimension \( m \) resp. \( n \).1

`y`

is the dual variable \(\lambda^\star_\text{pogs}\) corresponding to the constraint \(Ax = y\) and has dimension \( m \).1

`l`

is the value of the objective \(p^\star_\text{pogs}\) at the solution (\(p^\star_\text{pogs} = f(y^\star_\text{pogs}) + g(x^\star_\text{pogs})\)).1

`optval`

For more information type

1 | >> help pogs |

### \(h\)-Functions

The values

1 | ```
f.h
``` |

```
```

and 1

```
g.h
```

can be specified using one of 16 functions. These are
1 2 | kAbs, kExp, kHuber, kIdentity, kIndBox01, kIndEq0, kIndGe0, kIndLe0, kLogistic, kMaxNeg0, kMaxPos0, kNegEntr, kNegLog, kRecipr, kSquare, kZero |

For example to specify that \(g_j(x_j) = |x_j|\) for \(j = 1\ldots 4\) and \(g_5(x_5) = I(x_5 = 0)\), use the syntax

1 | >> g.h = [kAbs(4); kIndEq0]; |

See Functions for a more detailed explanation of the functions and their usage.

### Example Usage

See the examples listed on the left-hand side under Examples.