Affine Atoms¶
All of the atoms listed here are affine in their arguments.
MulExpression¶
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class
cvxpy.atoms.affine.binary_operators.MulExpression(lh_exp, rh_exp)[source]¶ Bases:
cvxpy.atoms.affine.binary_operators.BinaryOperatorMatrix 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.
Bmat¶
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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 (
listoflists) – The blocks of the block matrix.- Returns
The CVXPY expression representing the block matrix.
- Return type
CVXPY expression
conv¶
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class
cvxpy.atoms.affine.conv.conv(lh_expr, rh_expr)[source]¶ Bases:
cvxpy.atoms.affine.affine_atom.AffAtom1D 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.
diag¶
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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 (
Expressionornumeric constant) – A vector or square matrix.- Returns
An Expression representing the diagonal vector/matrix.
- Return type
diff¶
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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
index¶
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class
cvxpy.atoms.affine.index.index(expr, key, orig_key=None)[source]¶ Bases:
cvxpy.atoms.affine.affine_atom.AffAtomIndexing/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]]).
matmul¶
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cvxpy.atoms.affine.binary_operators.matmul(lh_exp, rh_exp) → cvxpy.atoms.affine.binary_operators.MulExpression[source]¶ Matrix multiplication.
multiply¶
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class
cvxpy.atoms.affine.binary_operators.multiply(lh_expr, rh_expr)[source]¶ Bases:
cvxpy.atoms.affine.binary_operators.MulExpressionMultiplies two expressions elementwise.
reshape¶
-
class
cvxpy.atoms.affine.reshape.reshape(expr, shape: Tuple[int, …], order: str = 'F')[source]¶ Bases:
cvxpy.atoms.affine.affine_atom.AffAtomReshapes 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 (
tupleorint) – The shape to promote to.order (
F(ortran)orC) –
upper_tri¶
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class
cvxpy.atoms.affine.upper_tri.upper_tri(expr)[source]¶ Bases:
cvxpy.atoms.affine.affine_atom.AffAtomThe 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]) ```
