"""
Copyright 2013 Steven Diamond
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
from typing import List, Tuple
import numpy as np
from scipy.sparse import csc_matrix
import cvxpy.lin_ops.lin_op as lo
import cvxpy.lin_ops.lin_utils as lu
from cvxpy.atoms.affine.affine_atom import AffAtom
from cvxpy.atoms.affine.reshape import reshape
from cvxpy.atoms.affine.vec import vec
from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions.expression import Expression
[docs]class upper_tri(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])
"""
def __init__(self, expr) -> None:
super(upper_tri, self).__init__(expr)
@AffAtom.numpy_numeric
def numeric(self, values):
"""Vectorize the upper triagonal entries.
"""
value = np.zeros(self.shape[0])
count = 0
for i in range(values[0].shape[0]):
for j in range(values[0].shape[1]):
if i < j:
value[count] = values[0][i, j]
count += 1
return value
def validate_arguments(self) -> None:
"""Checks that the argument is a square matrix.
"""
if not self.args[0].ndim == 2 or self.args[0].shape[0] != self.args[0].shape[1]:
raise ValueError(
"Argument to upper_tri must be a square matrix."
)
def shape_from_args(self) -> Tuple[int, int]:
"""A vector.
"""
rows, cols = self.args[0].shape
return (rows*(cols-1)//2, 1)
def is_atom_log_log_convex(self) -> bool:
"""Is the atom log-log convex?
"""
return True
def is_atom_log_log_concave(self) -> bool:
"""Is the atom log-log concave?
"""
return True
def graph_implementation(
self, arg_objs, shape: Tuple[int, ...], data=None
) -> Tuple[lo.LinOp, List[Constraint]]:
"""Vectorized strictly upper triagonal entries.
Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
return (lu.upper_tri(arg_objs[0]), [])
[docs]def vec_to_upper_tri(expr, strict: bool = False):
"""Reshapes a vector into an upper triangular matrix in
row-major order. The strict argument specifies whether an upper or a strict upper triangular
matrix should be returned.
Inverts cp.upper_tri.
"""
expr = Expression.cast_to_const(expr)
if not expr.is_vector():
raise ValueError("The input must be a vector.")
if expr.ndim != 1:
expr = vec(expr)
ell = expr.shape[0]
if strict:
# n * (n-1)/2 == ell
n = ((8 * ell + 1) ** 0.5 + 1) // 2
else:
# n * (n+1)/2 == ell
n = ((8 * ell + 1) ** 0.5 - 1) // 2
n = int(n)
if not (n * (n + 1) // 2 == ell or n * (n - 1) // 2 == ell):
raise ValueError("The size of the vector must be a triangular number.")
# form a matrix P, of shape (n**2, ell).
# the i-th block of n rows of P gives the entries of the i-th row
# of the upper-triangular matrix associated with expr.
# compute expr2 = P @ expr
# compute expr3 = reshape(expr2, shape=(n, n)).T
# expr3 is the matrix formed by reading length-n blocks of expr2,
# and letting each block form a row of expr3.
k = 1 if strict else 0
row_idx, col_idx = np.triu_indices(n, k=k)
P_rows = n*row_idx + col_idx
P_cols = np.arange(ell)
P_vals = np.ones(P_cols.size)
P = csc_matrix((P_vals, (P_rows, P_cols)), shape=(n**2, ell))
expr2 = P @ expr
expr3 = reshape(expr2, (n, n)).T
return expr3