"""
A collection of classes for mapping indices to variable names and vice versa.
"""
from openmdao.utils.array_utils import shape_to_len
# default size of array for which we use a FlatRangeMapper instead of a RangeTree
MAX_FLAT_RANGE_SIZE = 10000
[docs]class RangeMapper(object):
"""
A mapper of indices to variable names and vice versa.
Parameters
----------
sizes : iterable of (key, size) tuples
Iterable of (key, size) tuples. key must be hashable.
Attributes
----------
size : int
Total size of all of the sizes combined.
_key2range : dict
Dictionary mapping key to an index range.
"""
[docs] def __init__(self, sizes):
"""
Initialize a RangeMapper.
"""
self._key2range = {}
start = 0
for key, size in sizes:
self._key2range[key] = (start, start + size)
start += size
self.size = start
[docs] @staticmethod
def create(sizes, max_flat_range_size=MAX_FLAT_RANGE_SIZE):
"""
Return a mapper that maps indices to variable names and relative indices.
Parameters
----------
sizes : iterable of (key, size)
Iterable of (key, size) tuples.
max_flat_range_size : int
If the total array size is less than this, a FlatRangeMapper will be returned instead
of a RangeTree.
Returns
-------
FlatRangeMapper or RangeTree
A mapper that maps indices to variable key and relative indices.
"""
size = sum(size for _, size in sizes)
return FlatRangeMapper(sizes) if size <= max_flat_range_size else RangeTree(sizes)
[docs] def key2range(self, key):
"""
Get the range corresponding to the given key.
Parameters
----------
key : object (must be hashable)
Data corresponding to an index range.
Returns
-------
tuple of (int, int)
The range of indices corresponding to the given key.
"""
return self._key2range[key]
[docs] def key2size(self, key):
"""
Get the size corresponding to the given key.
Parameters
----------
key : object (must be hashable)
Key corresponding to an index range.
Returns
-------
int
The size corresponding to the given key.
"""
start, stop = self._key2range[key]
return stop - start
[docs] def __getitem__(self, idx):
"""
Find the key corresponding to the given index.
Parameters
----------
idx : int
The index into the full array.
"""
raise NotImplementedError("__getitem__ method must be implemented by subclass.")
[docs] def __iter__(self):
"""
Iterate over (key, start, stop) tuples.
Yields
------
(obj, int, int)
(key, start index, stop index), where key is a hashable object.
"""
raise NotImplementedError("__getitem__ method must be implemented by subclass.")
[docs] def inds2keys(self, inds):
"""
Find the set of keys corresponding to the given indices.
Parameters
----------
inds : iter of int
The array indices.
Returns
-------
set of object
The set of keys corresponding to the given indices.
"""
return {self[idx] for idx in inds}
[docs] def between_iter(self, start_key, stop_key):
"""
Iterate over (key, start, stop) tuples between the given start and stop keys.
Parameters
----------
start_key : object
Key corresponding to an index range.
stop_key : object
Key corresponding to an index range.
Yields
------
(obj, int, int)
(key, relative start index, relative stop index), where key is a hashable object.
"""
started = False
for key, (start, stop) in self._key2range.items():
if key == start_key:
yield (key, 0, stop - start)
if start_key == stop_key:
break
started = True
elif started:
if key == stop_key:
yield (key, 0, stop - start)
break
else:
yield (key, 0, stop - start)
[docs] def overlap_iter(self, key, other):
"""
Find the set of keys that overlap between this mapper and another.
Parameters
----------
key : object
Key corresponding to an index range.
other : RangeMapper
Another mapper.
Yields
------
(obj, int, int, obj, int, int)
(key, start, stop, otherkey, otherstart, otherstop).
"""
start, stop = self._key2range[key]
start_key, start_rel = other.index2key_rel(start)
if start_key is None:
return
stop_key, stop_rel = other.index2key_rel(stop - 1)
overlaps = [list(tup) for tup in other.between_iter(start_key, stop_key)]
overlaps[0][1] = start_rel
overlaps[-1][2] = stop_rel + 1
start = stop = 0
for k, kstart, kstop in overlaps:
stop += kstop - kstart
yield (key, start, stop, k, kstart, kstop)
start = stop
[docs] def dump(self):
"""
Dump the contents of the mapper to stdout.
"""
for key, (start, stop) in self._key2range.items():
print(f'{key}: {start} - {stop}')
[docs]class RangeTreeNode(RangeMapper):
"""
A node in a binary search tree of sizes, mapping key to an index range.
Parameters
----------
key : object
Data corresponding to an index range.
start : int
Starting index of the variable.
stop : int
Ending index of the variable.
Attributes
----------
key : object
Data corresponding to an index range.
start : int
Starting index of the variable.
stop : int
Ending index of the variable.
left : RangeTreeNode or None
Left child node.
right : RangeTreeNode or None
Right child node.
"""
__slots__ = ['key', 'start', 'stop', 'left', 'right']
[docs] def __init__(self, key, start, stop):
"""
Initialize a RangeTreeNode.
"""
self.key = key
self.start = start
self.stop = stop
self.left = None
self.right = None
def __repr__(self):
"""
Return a string representation of the RangeTreeNode.
"""
return f"RangeTreeNode({self.key}, ({self.start}:{self.stop}))"
[docs]class RangeTree(RangeMapper):
"""
A binary search tree of sizes, mapping key to an index range.
Allows for fast lookup of the key corresponding to a given index. The sizes must be
contiguous, but they can be of different sizes.
Search complexity is O(log2 n). Uses less memory than FlatRangeMapper when total array size is
large.
Parameters
----------
sizes : list of (key, start, stop)
Ordered list of (key, start, stop) tuples, where start and stop define the range of
indices for the key. Ranges must be contiguous. key must be hashable.
Attributes
----------
root : RangeTreeNode
Root node of the binary search tree.
"""
[docs] def __init__(self, sizes):
"""
Initialize a RangeTree.
"""
super().__init__(sizes)
ranges = []
start = stop = 0
for key, size in sizes:
stop += size
ranges.append((key, start, stop))
start = stop
self.root = self.build(ranges)
[docs] def __getitem__(self, idx):
"""
Find the key corresponding to the given index.
Parameters
----------
idx : int
The index into the full array.
Returns
-------
object or None
The key corresponding to the given index, or None if not found.
int or None
The rank corresponding to the given index, or None if not found.
"""
node = self.root
while node is not None:
if idx < node.start:
node = node.left
elif idx >= node.stop:
node = node.right
else:
return node.key
[docs] def __iter__(self):
"""
Iterate over (key, start, stop) tuples.
Yields
------
(obj, int, int)
(key, start index, stop index), where key is a hashable object.
"""
node = self.root
stack = [[node, node.left, node.right]]
while stack:
sub = stack[-1]
node, left, right = sub
if left:
stack.append([left, left.left, left.right])
sub[1] = None # zero left
else:
if right:
stack.append([right, right.left, right.right])
sub[2] = None # zero right
else:
stack.pop()
yield (node.key, node.start, node.stop)
[docs] def index2key_rel(self, idx):
"""
Find the key and relative index corresponding to the matched range.
Parameters
----------
idx : int
The index into the full array.
Returns
-------
obj or None
The key corresponding to the matched range, or None if not found.
int or None
The relative index into the matched range, or None if not found.
"""
node = self.root
while node is not None:
if idx < node.start:
node = node.left
elif idx >= node.stop:
node = node.right
else:
return node.key, idx - node.start
return None, None
[docs] def build(self, ranges):
"""
Build a binary search tree to map indices to variable key.
Parameters
----------
ranges : list of (key, start, stop)
List of (key, start, stop) tuples, where start and stop
define the range of indices for the key. Ranges must be ordered and contiguous.
key must be hashable.
Returns
-------
RangeTreeNode
Root node of the binary search tree.
"""
mid = len(ranges) // 2
key, start, stop = ranges[mid]
node = RangeTreeNode(key, start, stop)
left_slices = ranges[:mid]
right_slices = ranges[mid + 1:]
if left_slices:
node.left = self.build(left_slices)
if right_slices:
node.right = self.build(right_slices)
return node
[docs]class FlatRangeMapper(RangeMapper):
"""
A flat list mapping indices to variable key and relative indices.
Parameters
----------
sizes : list of (key, size)
Ordered list of (key, size) tuples. key must be hashable.
Attributes
----------
ranges : list of (key, start, stop)
List of (key, start, stop) tuples, where start and stop define the range of
indices for that key. Ranges must be contiguous. key must be hashable.
"""
[docs] def __init__(self, sizes):
"""
Initialize a FlatRangeMapper.
"""
super().__init__(sizes)
self.ranges = [None] * self.size
start = stop = 0
for key, size in sizes:
stop += size
self.ranges[start:stop] = [(key, start, stop)] * size
start = stop
[docs] def __getitem__(self, idx):
"""
Find the key corresponding to the given index.
Parameters
----------
idx : int
The index into the full array.
Returns
-------
object or None
The key corresponding to the given index, or None if not found.
"""
try:
return self.ranges[idx][0]
except IndexError:
return None
[docs] def __iter__(self):
"""
Iterate over (key, start, stop) tuples.
Yields
------
(obj, int, int)
(key, start index, stop index), where key is a hashable object.
"""
for key, (start, stop) in self._key2range.items():
yield (key, start, stop)
[docs] def index2key_rel(self, idx):
"""
Find the key and relative index corresponding to the matched range.
Parameters
----------
idx : int
The index into the full array.
Returns
-------
object or None
The key corresponding to the matched range, or None if not found.
int or None
The relative index into the matched range, or None if not found.
"""
try:
key, start, _ = self.ranges[idx]
except IndexError:
return (None, None)
return (key, idx - start)
