Build a hashable structural key for an Expression subtree. Variables/Parameters key by their ``.id`` (same source leaf -> same key). Constant

Use the Gershgorin Circle Theorem https://en.wikipedia.org/wiki/Gershgorin_circle_theorem As a sufficient condition for A being PSD

* Returns the matrix stored in the data field of LIN as a sparse eigen matrix * If COLUMN is true, the matrix is reshaped into a column vector which

Returns a sparse matrix that spaces out an expression. Parameters ---------- shape : tuple (rows in matrix, colum

Returns the gradient of the objective with respect to x.

Whether the problem will have constraints after canonicalization.

Check if constant has batch dimensions with product > 1. A batch-varying constant has different values for each batch element, requiring

Check that the variable is DPP in the given context.

Test if num is a positive integer power of 2. .. note:: Fails if num is a np.integer type like np.int32, np.int64, etc. This see

Check a *sufficient condition* that the expression is PSD, by checking if both arguments are PSD or both are NSD.

\returns an expression of the matrix Q as products of sparse Householder reflectors. * The common usage of this function is to apply it to a dense

\returns an expression of the matrix U, * The only operation available with this expression is the triangular solve * \code * y = b;

Returns the largest entry in x.

Evaluate objective. Returns obj_value float.

\returns the outer-stride of the underlying dense matrix * \sa DenseCoeffsBase::outerStride() */

Add linear operators. Parameters ---------- operators : list A list of linear operators. Returns ------- LinOp

* Return the array of supernode-to-column mapping */

Convert everything but None to an int.

\returns an expression of P H P^-1 where H is the matrix represented by \c *this */

Updates the problem state given the solver results. Updates problem.status, problem.value and value of primal and dual variables.

Given (A, b) in view, select the rows corresponding to the elements above the diagonal in the original expression. Note: The

Gives the (sub/super)gradient of the atom w.r.t. each argument. Matrix expressions are vectorized, so the gradient is a matrix. Args

Does the variable have lower bounds?

Does the variable have upper bounds?

Evaluates lazy constraints.

Reshape expression to scalar form (1,) for SOC constructor.

\brief Adjoint (conjugate transpose) of the Householder sequence. */

Broadcast the binary operator.

Check if this solver can handle a problem with the given structure. Parameters ---------- problem_form : ProblemForm

* Empty the pointer list */

\sa MatrixBase::coeff() * \warning the coordinates must fit into the referenced triangular part */

Adds the tensor a to b if they are both not none. If a (b) is not None but b (a) is None, returns a (b). Returns None if both

Returns the constraint values.

\returns the size of the main diagonal, which is min(rows(),cols()). * \sa rows(), cols(), SizeAtCompileTime. */

Convert from stacked sparse matrix.

This function checks if the problem has expressions of dimension greater than 2 or if it lacks C++ support, then raises a warning if the defa

Example problem that can be used within additional tests.

\returns a const pointer to the array of the number of non zeros of the inner vectors. * This function is aimed at interoperability with other l

Returns the solution to the original problem given the inverse_data.

Is the atom smooth?

Is the Leaf complex valued?

Is the expression concave?

Is the expression convex?

Is the expression log-log concave?

Is the expression log-log concave?

Is the expression log-log constant, ie, elementwise positive?

Is the expression log-log convex?

Is the expression log-log convex?

Check a *sufficient condition* that the expression is NSD, by checking if one argument is PSD and the other is NSD.

Is the expression positive?

Return a lower bound on the number of cones needed to represent the tuple. Based on two simple lower bounds. Examples -------- >

Extract the reduced representation of a leaf's value. Args: variable: The leaf whose attributes determine the reduction. value: I