def test_mathtools_partition_integer_by_ratio_02():
r'''Partition integer n according to ratio.
'''
partition = mathtools.partition_integer_by_ratio(10, [1, 2])
assert partition == [3, 7]
partition = mathtools.partition_integer_by_ratio(10, [3, 1])
assert partition == [8, 2]
partition = mathtools.partition_integer_by_ratio(-10, [-3, 2])
assert partition == [6, -4]
def partition_sequence_by_ratio_of_lengths(sequence, lengths):
'''Partitions `sequence` by ratio of `lengths`.
::
>>> sequence = tuple(range(10))
::
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 2],
... )
[(0, 1, 2), (3, 4), (5, 6, 7, 8, 9)]
Uses rounding magic to avoid fractional part lengths.
Returns list of `sequence` objects.
'''
from abjad.tools import sequencetools
lengths = mathtools.partition_integer_by_ratio(len(sequence), lengths)
return sequencetools.partition_sequence_by_counts(
sequence,
lengths,
cyclic=False,
overhang=False,
)
def partition_sequence_by_ratio_of_lengths(sequence, lengths):
'''Partitions `sequence` by ratio of `lengths`.
::
>>> sequence = tuple(range(10))
::
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 2],
... )
[(0, 1, 2), (3, 4), (5, 6, 7, 8, 9)]
Uses rounding magic to avoid fractional part lengths.
Returns list of `sequence` objects.
'''
from abjad.tools import sequencetools
lengths = mathtools.partition_integer_by_ratio(len(sequence), lengths)
return sequencetools.partition_sequence_by_counts(
sequence,
lengths,
cyclic=False,
overhang=False,
)
def __call__(self, divisions=None):
r'''Calls rounded ratio division maker on `division`.
.. container:: example
**Example 1.** Calls maker on nonempty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> lists = maker([(7, 4), (6, 4)])
>>> for list_ in lists:
... list_
[Division(4, 4), Division(3, 4)]
[Division(3, 4), Division(3, 4)]
Returns list of division lists.
.. container:: example
**Example 2.** Calls maker on empty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> maker([])
[]
Returns empty list.
Returns possibly empty list of division lists.
'''
input_divisions = divisions or []
if not input_divisions:
return []
output_division_lists = []
ratios = self._get_ratios()
for i, input_division in enumerate(input_divisions):
input_division = durationtools.Division(input_division)
ratio = ratios[i]
numerators = mathtools.partition_integer_by_ratio(
input_division.numerator,
ratio,
)
output_division_list = [
durationtools.Division(
numerator,
input_division.denominator,
)
for numerator in numerators
]
output_division_lists.append(output_division_list)
return output_division_lists
def test_mathtools_partition_integer_by_ratio_01():
r'''Partition integer n according to ratio.
'''
t = mathtools.partition_integer_by_ratio(10, [1])
assert t == [10]
t = mathtools.partition_integer_by_ratio(10, [1, 1])
assert t == [5, 5]
t = mathtools.partition_integer_by_ratio(10, [1, -1, -1])
assert t == [3, -4, -3]
t = mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1])
assert t == [-3, -2, -3, -2]
t = mathtools.partition_integer_by_ratio(-10, [1, 1, 1, 1, 1])
assert t == [-2, -2, -2, -2, -2]
def __call__(self, divisions=None):
r'''Calls rounded ratio division maker on `division`.
.. container:: example
**Example 1.** Calls maker on nonempty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> lists = maker([(7, 4), (6, 4)])
>>> for list_ in lists:
... list_
[NonreducedFraction(4, 4), NonreducedFraction(3, 4)]
[NonreducedFraction(3, 4), NonreducedFraction(3, 4)]
Returns list of division lists.
.. container:: example
**Example 2.** Calls maker on empty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> maker([])
[]
Returns empty list.
Returns possibly empty list of division lists.
'''
input_divisions = divisions or []
if not input_divisions:
return []
output_division_lists = []
ratios = self._get_ratios()
for i, input_division in enumerate(input_divisions):
input_division = mathtools.NonreducedFraction(input_division)
ratio = ratios[i]
numerators = mathtools.partition_integer_by_ratio(
input_division.numerator,
ratio,
)
output_division_list = [
mathtools.NonreducedFraction(
numerator,
input_division.denominator,
)
for numerator in numerators
]
output_division_lists.append(output_division_list)
return output_division_lists
def partition_sequence_by_ratio_of_lengths(sequence, ratio):
'''Partitions `sequence` by `ratio` of lengths.
.. container:: example
**Example 1.** Partitions sequence by ``1:1:1`` ratio:
::
>>> sequence = list(range(10))
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 1],
... )
[[0, 1, 2], [3, 4, 5, 6], [7, 8, 9]]
Returns list of lists.
.. container:: example
**Example 2.** Partitions sequence by ``1:1:2`` ratio:
::
>>> sequence = tuple(range(10))
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 2],
... )
[(0, 1, 2), (3, 4), (5, 6, 7, 8, 9)]
Returns list of tuples.
Uses the rounding magic implemented in
``mathtools.partition_integer_by_ratio()`` to avoid fractional part
lengths.
Returns list of `sequence` objects.
'''
from abjad.tools import sequencetools
if sequence is None:
callback = sequencetools.PartitionByRatioOfLengthsCallback(
ratio=ratio,
)
return callback
ratio = mathtools.Ratio(ratio)
counts = mathtools.partition_integer_by_ratio(len(sequence), ratio)
return sequencetools.partition_sequence_by_counts(
sequence,
counts,
cyclic=False,
overhang=Exact,
)
def partition_sequence_by_ratio_of_lengths(sequence, ratio):
'''Partitions `sequence` by `ratio` of lengths.
.. container:: example
**Example 1.** Partitions sequence by ``1:1:1`` ratio:
::
>>> sequence = list(range(10))
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 1],
... )
[[0, 1, 2], [3, 4, 5, 6], [7, 8, 9]]
Returns list of lists.
.. container:: example
**Example 2.** Partitions sequence by ``1:1:2`` ratio:
::
>>> sequence = tuple(range(10))
>>> sequencetools.partition_sequence_by_ratio_of_lengths(
... sequence,
... [1, 1, 2],
... )
[(0, 1, 2), (3, 4), (5, 6, 7, 8, 9)]
Returns list of tuples.
Uses the rounding magic implemented in
``mathtools.partition_integer_by_ratio()`` to avoid fractional part
lengths.
Returns list of `sequence` objects.
'''
from abjad.tools import sequencetools
if sequence is None:
callback = sequencetools.PartitionByRatioOfLengthsCallback(
ratio=ratio, )
return callback
ratio = mathtools.Ratio(ratio)
counts = mathtools.partition_integer_by_ratio(len(sequence), ratio)
return sequencetools.partition_sequence_by_counts(
sequence,
counts,
cyclic=False,
overhang=Exact,
)
def __call__(self, expr, rotation=None):
r'''Calls ratio selector callback on `expr`.
Returns tuple of selections.
'''
assert isinstance(expr, tuple), repr(expr)
assert len(expr) == 1, repr(expr)
assert isinstance(expr[0], selectiontools.Selection), repr(expr)
selection = expr[0]
counts = mathtools.partition_integer_by_ratio(
len(selection),
self.ratio,
)
selections = sequencetools.partition_sequence_by_counts(
selection,
counts=counts,
)
return tuple(selections)
def __call__(self, expr, rotation=None):
r'''Calls ratio selector callback on `expr`.
Returns tuple of selections.
'''
assert isinstance(expr, tuple), repr(expr)
assert len(expr) == 1, repr(expr)
assert isinstance(expr[0], selectiontools.Selection), repr(expr)
selection = expr[0]
counts = mathtools.partition_integer_by_ratio(
len(selection),
self.ratio,
)
selections = sequencetools.partition_sequence_by_counts(
selection,
counts=counts,
)
return tuple(selections)
def drift(m, grid, n, mask):
'''Creates subdivision grid under m;
divides m leaves into n sections;
subdivides sections in mask.
For example:
drift(m, [[0, 1, 2, 3], [0, 1], [0, 2, 3, 3]], 9, (1, 2, 6))
Divide the entire rhythmic voice m into 9 sections;
then procede to subdivide only sections 1, 2 & 6 of those 9 sections;
leave sections 3, 4, 5, 7, 8, 9 unsubidivide;
when dividing elements in sections 1, 2 & 6,
interpret the 0, 1, 2, 3 in mask in the following way:
0 -- do not subdivide;
1 -- create eighth notes;
2 -- create sixteenth notes;
3 -- create thirty-second notes.
'''
grid = baca.tools.helianthate(grid, 1, 1)
grid = sequencetools.repeat_to_length(grid, len(m.leaves))
#sections = baca.tools.ratio(len(m.instances('Leaf')), [1] * n)
num_leaves = len(instances(m, '_Leaf'))
sections = mathtools.partition_integer_by_ratio(num_leaves, [1] * n)
pairs = sequencetools.list_pairwise_cumulative_sums_zero(sections)
sections = [range(*pair) for pair in pairs]
sections = reduce(operator.add, [sections[section - 1] for section in mask])
# 'sections' at this point is a flat zero-indexed list of elements in m
# to subdivide; for example [0, 1, 2, 3, 4, 35, 36, 37, 38, 39, 118, ...]
positions = [pair[-1] if pair[0] in sections else 0
for pair in enumerate(grid)]
# 'positions' is a look-up table implemented as a flat list;
# element 0 in 'positions' specifies how many times to subidivide 0 in m;
# element 1 in 'positions' specifies how many times to subidivide 1 in m;
# etc, ...
sekka.etc.transforms.subdivide(m, positions)
#baca.tools.abjad_subdivide(m, positions)
def make_territoires_parts():
ratio = [1] * 9
lengths = mathtools.partition_integer_by_ratio(164, ratio)
parts = sequencetools.partition_by_lengths(fully_labelled_cells, lengths)
parts = sequencetools.rotate(parts, -3)
territoires_parts = parts[:2] + parts[3:8]
originals = range(1, 9 + 1)
## territoires part numbers are [(4, 5), 6, (7, 8, 9, 1, 2), 3]
territoires_part_numbers = [4, 5, 7, 8, 9, 1, 2]
original_territoires_part_numbers = zip(originals, territoires_part_numbers)
parts = sequencetools.rotate(parts, -3)
manifolds_parts = parts[:4] + parts[5:]
## manifolds part numbers are [(7, 8, 9, 1), 2, (3, 4, 5, 6)]
manifolds_part_numbers = [7, 8, 9, 1, 3, 4, 5, 6]
original_manifolds_part_numbers = zip(originals, manifolds_part_numbers)
return territoires_parts, original_territoires_part_numbers, \
manifolds_parts, original_manifolds_part_numbers
def partition_sequence_by_ratio_of_weights(sequence, weights):
'''Partitions `sequence` by ratio of `weights`.
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [1, 1, 1])
[[1, 1, 1], [1, 1, 1, 1], [1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [1, 1, 1, 1])
[[1, 1, 1], [1, 1], [1, 1, 1], [1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [2, 2, 3])
[[1, 1, 1], [1, 1, 1], [1, 1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [3, 2, 2])
[[1, 1, 1, 1], [1, 1, 1], [1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1])
[[1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 2, 2]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1])
[[1, 1, 1, 1, 1, 1], [2, 2, 2], [2, 2, 2]]
Weights of parts of returned list equal `weights_ratio` proportions
with some rounding magic.
Returns list of lists.
'''
from abjad.tools import sequencetools
list_weight = mathtools.weight(sequence)
weights_parts = mathtools.partition_integer_by_ratio(list_weight, weights)
cumulative_weights = mathtools.cumulative_sums(weights_parts, start=None)
result = []
sublist = []
result.append(sublist)
current_cumulative_weight = cumulative_weights.pop(0)
for n in sequence:
if not isinstance(n, (int, long, float, fractions.Fraction)):
message = 'must be number: {!r}.'
message = message.format(n)
raise TypeError(message)
sublist.append(n)
while current_cumulative_weight <= \
mathtools.weight(sequencetools.flatten_sequence(result)):
try:
current_cumulative_weight = cumulative_weights.pop(0)
sublist = []
result.append(sublist)
except IndexError:
break
return result
def __call__(self, divisions=None):
r'''Calls rounded ratio division maker on `divisions`.
.. container:: example
**Example 1.** Calls maker on nonempty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> lists = maker([(7, 4), (6, 4)])
>>> for list_ in lists:
... list_
[Division((4, 4)), Division((3, 4))]
[Division((3, 4)), Division((3, 4))]
Returns list of division lists.
.. container:: example
**Example 2.** Calls maker on empty input:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
>>> maker([])
[]
Returns empty list.
.. container:: example
**Example 3.** Works with start offset:
::
>>> maker = makertools.SplitByRoundedRatiosDivisionCallback(
... ratios=[mathtools.Ratio([1, 1])],
... )
::
>>> divisions = [(7, 4), (6, 4)]
>>> divisions = [durationtools.Division(_) for _ in divisions]
>>> divisions[0]._start_offset = Offset(1, 4)
>>> divisions
[Division((7, 4), start_offset=Offset(1, 4)), Division((6, 4))]
::
>>> division_lists = maker(divisions)
>>> len(division_lists)
2
::
>>> for division in division_lists[0]:
... division
Division((4, 4), start_offset=Offset(1, 4))
Division((3, 4), start_offset=Offset(5, 4))
::
>>> for division in division_lists[1]:
... division
Division((3, 4), start_offset=Offset(2, 1))
Division((3, 4), start_offset=Offset(11, 4))
Returns possibly empty list of division lists.
'''
from experimental import makertools
divisions = divisions or []
if not divisions:
return []
divisions, start_offset = makertools.DivisionMaker._to_divisions(
divisions)
start_offset = divisions[0].start_offset
division_lists = []
ratios = self._get_ratios()
for i, division in enumerate(divisions):
ratio = ratios[i]
numerators = mathtools.partition_integer_by_ratio(
division.numerator,
ratio,
)
division_list = [
durationtools.Division((numerator, division.denominator))
for numerator in numerators
]
division_lists.append(division_list)
division_lists, start_offset = makertools.DivisionMaker._to_divisions(
division_lists,
start_offset=start_offset,
)
return division_lists
def partition_sequence_by_ratio_of_weights(sequence, weights):
'''Partitions `sequence` by ratio of `weights`.
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [1, 1, 1])
[[1, 1, 1], [1, 1, 1, 1], [1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [1, 1, 1, 1])
[[1, 1, 1], [1, 1], [1, 1, 1], [1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [2, 2, 3])
[[1, 1, 1], [1, 1, 1], [1, 1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1] * 10, [3, 2, 2])
[[1, 1, 1, 1], [1, 1, 1], [1, 1, 1]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1])
[[1, 1, 1, 1, 1, 1, 2, 2], [2, 2, 2, 2]]
::
>>> sequencetools.partition_sequence_by_ratio_of_weights(
... [1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2], [1, 1, 1])
[[1, 1, 1, 1, 1, 1], [2, 2, 2], [2, 2, 2]]
Weights of parts of returned list equal `weights_ratio` proportions
with some rounding magic.
Returns list of lists.
'''
from abjad.tools import sequencetools
if not isinstance(sequence, collections.Sequence):
message = 'must be sequence: {!r}.'
message = message.format(sequence)
raise Exception(message)
list_weight = mathtools.weight(sequence)
weights_parts = mathtools.partition_integer_by_ratio(list_weight, weights)
cumulative_weights = mathtools.cumulative_sums(weights_parts, start=None)
result = []
sublist = []
result.append(sublist)
current_cumulative_weight = cumulative_weights.pop(0)
for n in sequence:
if not isinstance(n, (int, float, fractions.Fraction)):
message = 'must be number: {!r}.'
message = message.format(n)
raise TypeError(message)
sublist.append(n)
while current_cumulative_weight <= \
mathtools.weight(sequencetools.flatten_sequence(result)):
try:
current_cumulative_weight = cumulative_weights.pop(0)
sublist = []
result.append(sublist)
except IndexError:
break
return result