Warning

This part of the documentation has not been touched for a while. It might be incomplete, reference deprecated functions or make a claim that does not apply to the latest version of PICOS any more. On the bright side, code listings are validated and still work. Watch your step!

# Cheat Sheet¶

## Manipulate expressions¶

Operator

Interpretation

+

+=

-

substraction

*

multiplication

^

@

Kronecker product

|

scalar product

/

division

**

exponentiation

abs()

Euclidean (or Frobenius) norm

[]

slicing

&

horizontal concatenation

//

vertical concatenation

.T

transposition

.H

Hermitian transposition

.Tx

partial transposition

.conj

complex conjugate

.real

real part

.imag

imaginary part

## Create constraints¶

Operator

Interpretation

< or <=

less or equal

> or >=

larger or equal

==

equal

<<

Löwner ordering , or set membership >>

Löwner ordering , or set membership ## Create affine expressions¶

function

short doc

sum

sums a list of affine expressions

diag

diagonal matrix defined by its diagonal

diag_vect

vector of diagonal elements of a matrix

new_param

constant affine expression

trace

trace of a square affine expression

partial_transpose

partial transposition

partial_trace

partial trace

## Create convex expressions¶

function

short doc

geomean

geometric mean

norm

(generalized) norm

tracepow

trace of a p-th matrix power

detrootn

n-th root of determinant

sum_k_largest

sum of k largest elements

sum_k_smallest

sum of k smallest elements

sum_k_largest_lambda

sum of k largest eigenvalues

sum_k_smallest_lambda

sum of k smallest eigenvalues

lambda_max

largest eigenvalue

lambda_min

smallest eigenvalue

## Create sets¶

function

short doc

ball(r,p)

a - ball of radius r

simplex(a)

a standard simplex truncated_simplex(a)

a set of the form , or ### Get information on a problem¶

function

short doc

get_variable(name)

gets the variable object name

get_valued_variable(name)

gets the value of the variable name

check_current_value_feasibility()

are the current variable value feasible?

obj_value()

objective for the current variable values

.type

returns problem’s type

### Miscellaneous¶

function

short doc

available_solvers()

lists installed solvers

import_cbf()

imports data from a .cbf file

write_to_file()

writes problem to a file