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
`+`	addition
`+=`	inplace addition
`-`	substraction
`*`	multiplication
`^`	Hadamard (elementwise) product
`@`	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 $\preceq$ , or set membership $\in$
`>>`	Löwner ordering $\succeq$ , or set membership $\ni$

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) $L_p-$ 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 $L_p$ - ball of radius `r`
`simplex(a)`	a standard simplex $\{x\geq 0: \Vert x \Vert_1 \leq a \}$
`truncated_simplex(a)`	a set of the form $\{ 0\leq x\leq 1: \Vert x \Vert_1 \leq a\}$ , or $\{x: \Vert x \Vert_\infty \leq 1; \Vert x \Vert_1 \leq a\}$

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

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