Affine Atoms¶

All of the atoms listed here are affine in their arguments.

AddExpression
MulExpression
DivExpression
Bmat
conv
cumsum
diag
diff
hstack
index
kron
matmul
multiply
promote
reshape
sum
trace
transpose
NegExpression
upper_tri
vec
vstack

AddExpression ¶

class cvxpy.atoms.affine.add_expr.AddExpression(arg_groups)[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom

The sum of any number of expressions.

MulExpression ¶

class cvxpy.atoms.affine.binary_operators.MulExpression(lh_exp, rh_exp)[source]¶

Bases: cvxpy.atoms.affine.binary_operators.BinaryOperator

Matrix multiplication.

The semantics of multiplication are exactly as those of NumPy’s matmul function, except here multiplication by a scalar is permitted. MulExpression objects can be created by using the ‘*’ operator of the Expression class.

Parameters

lh_exp (Expression) – The left-hand side of the multiplication.
rh_exp (Expression) – The right-hand side of the multiplication.

DivExpression ¶

class cvxpy.atoms.affine.binary_operators.DivExpression(lh_expr, rh_expr)[source]¶

Bases: cvxpy.atoms.affine.binary_operators.BinaryOperator

Division by scalar.

Can be created by using the / operator of expression.

Bmat ¶

cvxpy.atoms.affine.bmat.bmat(block_lists)[source]¶

Constructs a block matrix.

Takes a list of lists. Each internal list is stacked horizontally. The internal lists are stacked vertically.

Parameters: block_lists (list of lists) – The blocks of the block matrix.
Returns: The CVXPY expression representing the block matrix.
Return type: CVXPY expression

conv ¶

class cvxpy.atoms.affine.conv.conv(lh_expr, rh_expr)[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom

1D discrete convolution of two vectors.

The discrete convolution \(c\) of vectors \(a\) and \(b\) of lengths \(n\) and \(m\), respectively, is a length-\((n+m-1)\) vector where

\[c_k = \sum_{i+j=k} a_ib_j, \quad k=0, \ldots, n+m-2.\]

Parameters

lh_expr (Constant) – A constant 1D vector or a 2D column vector.
rh_expr (Expression) – A 1D vector or a 2D column vector.

cumsum ¶

class cvxpy.atoms.affine.cumsum.cumsum(expr: cvxpy.expressions.expression.Expression, axis: int = 0)[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom, cvxpy.atoms.axis_atom.AxisAtom

Cumulative sum.

expr¶

The expression being summed.

Type: CVXPY expression

axis¶

The axis to sum across if 2D.

Type: int

diag ¶

cvxpy.atoms.affine.diag.diag(expr) → Union[cvxpy.atoms.affine.diag.diag_mat, cvxpy.atoms.affine.diag.diag_vec][source]¶

Extracts the diagonal from a matrix or makes a vector a diagonal matrix.

Parameters: expr (Expression or numeric constant) – A vector or square matrix.
Returns: An Expression representing the diagonal vector/matrix.
Return type: Expression

diff ¶

cvxpy.atoms.affine.diff.diff(x, k: int = 1, axis: int = 0)[source]¶

Vector of kth order differences.

Takes in a vector of length n and returns a vector of length n-k of the kth order differences.

diff(x) returns the vector of differences between adjacent elements in the vector, that is

[x[2] - x[1], x[3] - x[2], …]

diff(x, 2) is the second-order differences vector, equivalently diff(diff(x))

diff(x, 0) returns the vector x unchanged

hstack ¶

cvxpy.atoms.affine.hstack.hstack(arg_list) → cvxpy.atoms.affine.hstack.Hstack[source]¶

Horizontal concatenation of an arbitrary number of Expressions.

Parameters: arg_list (list of Expression) – The Expressions to concatenate.

index ¶

class cvxpy.atoms.affine.index.index(expr, key, orig_key=None)[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom

Indexing/slicing into an Expression.

CVXPY supports NumPy-like indexing semantics via the Expression class’ overloading of the [] operator. This is a low-level class constructed by that operator, and it should not be instantiated directly.

Parameters

expr (Expression) – The expression indexed/sliced into.
key – The index/slicing key (i.e. expr[key[0],key[1]]).

kron ¶

class cvxpy.atoms.affine.kron.kron(lh_expr, rh_expr)[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom

Kronecker product.

matmul ¶

cvxpy.atoms.affine.binary_operators.matmul(lh_exp, rh_exp) → cvxpy.atoms.affine.binary_operators.MulExpression [source]¶: Matrix multiplication.

multiply ¶

class cvxpy.atoms.affine.binary_operators.multiply(lh_expr, rh_expr)[source]¶

Bases: cvxpy.atoms.affine.binary_operators.MulExpression

Multiplies two expressions elementwise.

promote ¶

cvxpy.atoms.affine.promote.promote(expr: cvxpy.expressions.expression.Expression, shape: Tuple[int, …])[source]¶

Promote a scalar expression to a vector/matrix.

Parameters

expr (Expression) – The expression to promote.
shape (tuple) – The shape to promote to.

Raises

ValueError – If expr is not a scalar.

reshape ¶

class cvxpy.atoms.affine.reshape.reshape(expr, shape: Tuple[int, int], order: str = 'F')[source]¶

Bases: cvxpy.atoms.affine.affine_atom.AffAtom

Reshapes the expression.

Vectorizes the expression then unvectorizes it into the new shape. The entries are reshaped and stored in column-major order, also known as Fortran order.

Parameters