Affine Atoms¶
All of the atoms listed here are affine in their arguments.
AddExpression¶
MulExpression¶
- class cvxpy.atoms.affine.binary_operators.MulExpression(lh_exp, rh_exp)[source]¶
Bases:
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¶
bmat¶
- cvxpy.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
conj¶
conv¶
- class cvxpy.conv(lh_expr, rh_expr)[source]¶
Bases:
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.cumsum(expr: Expression, axis: int = 0)[source]¶
Bases:
AffAtom
,AxisAtom
Cumulative sum.
- expr¶
The expression being summed.
- Type:
CVXPY expression
- axis¶
The axis to sum across if 2D.
- Type:
int
diag¶
- cvxpy.diag(expr) Union[diag_mat, 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:
diff¶
- cvxpy.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¶
imag¶
index¶
- class cvxpy.atoms.affine.index.index(expr, key, orig_key=None)[source]¶
Bases:
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¶
matmul¶
- cvxpy.matmul(lh_exp, rh_exp) MulExpression [source]¶
Matrix multiplication.
multiply¶
- class cvxpy.multiply(lh_expr, rh_expr)[source]¶
Bases:
MulExpression
Multiplies two expressions elementwise.
partial_trace¶
- cvxpy.partial_trace(expr, dims: Tuple[int], axis: Optional[int] = 0)[source]¶
Assumes \(\texttt{expr} = X_1 \otimes \cdots \otimes X_n\) is a 2D Kronecker product composed of \(n = \texttt{len(dims)}\) implicit subsystems. Letting \(k = \texttt{axis}\), the returned expression represents the partial trace of \(\texttt{expr}\) along its \(k^{\text{th}}\) implicit subsystem:
\[\text{tr}(X_k) (X_1 \otimes \cdots \otimes X_{k-1} \otimes X_{k+1} \otimes \cdots \otimes X_n).\]- Parameters:
expr (
Expression
) – The 2D expression to take the partial trace of.dims (tuple of ints.) – A tuple of integers encoding the dimensions of each subsystem.
axis (int) – The index of the subsystem to be traced out from the tensor product that defines expr.
partial_transpose¶
- cvxpy.partial_transpose(expr, dims: Tuple[int], axis: Optional[int] = 0)[source]¶
Assumes \(\texttt{expr} = X_1 \otimes ... \otimes X_n\) is a 2D Kronecker product composed of \(n = \texttt{len(dims)}\) implicit subsystems. Letting \(k = \texttt{axis}\), the returned expression is a partial transpose of \(\texttt{expr}\), with the transpose applied to its \(k^{\text{th}}\) implicit subsystem:
\[X_1 \otimes ... \otimes X_k^T \otimes ... \otimes X_n.\]- Parameters:
expr (
Expression
) – The 2D expression to take the partial transpose of.dims (tuple of ints.) – A tuple of integers encoding the dimensions of each subsystem.
axis (int) – The index of the subsystem to be transposed from the tensor product that defines expr.
promote¶
- cvxpy.atoms.affine.promote.promote(expr: 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.
psd_wrap¶
real¶
reshape¶
- class cvxpy.reshape(expr, shape: Tuple[int, int], order: str = 'F')[source]¶
Bases:
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:
expr (Expression) – The expression to promote.
shape (tuple or int) – The shape to promote to.
order (F(ortran) or C) –
scalar_product¶
- class cvxpy.scalar_product(x, y)[source]¶
Bases:
Return the standard inner product (or “scalar product”) of (x,y).
- Parameters:
x (Expression, int, float, NumPy ndarray, or nested list thereof.) – The conjugate-linear argument to the inner product.
y (Expression, int, float, NumPy ndarray, or nested list thereof.) – The linear argument to the inner product.
- Returns:
expr – The standard inner product of (x,y), conjugate-linear in x. We always have
expr.shape == ()
.- Return type:
Notes
The arguments
x
andy
can be nested lists; these lists will be flattened independently of one another.For example, if
x = [[a],[b]]
andy = [c, d]
(witha,b,c,d
real scalars), then this function returns an Expression representinga * c + b * d
.
sum¶
- cvxpy.sum(expr, axis: Optional[int] = None, keepdims: bool = False) None [source]¶
Sum the entries of an expression.
- Parameters:
expr (Expression) – The expression to sum the entries of.
axis (int) – The axis along which to sum.
keepdims (bool) – Whether to drop dimensions after summing.
trace¶
- class cvxpy.trace(expr)[source]¶
Bases:
AffAtom
The sum of the diagonal entries of a matrix.
- Parameters:
expr (Expression) – The expression to sum the diagonal of.
transpose¶
NegExpression¶
upper_tri¶
- class cvxpy.upper_tri(expr)[source]¶
Bases:
AffAtom
The vectorized strictly upper-triagonal entries.
The vectorization is performed by concatenating (partial) rows. For example, if
A = np.array([[10, 11, 12, 13], [14, 15, 16, 17], [18, 19, 20, 21], [22, 23, 24, 25]])
then we have
upper_tri(A).value == np.array([11, 12, 13, 16, 17, 21])
vec¶
- cvxpy.vec(X)[source]¶
Flattens the matrix X into a vector in column-major order.
- Parameters:
X (Expression or numeric constant) – The matrix to flatten.
- Returns:
An Expression representing the flattened matrix.
- Return type: