8000 ENH: add block() function to create block arrays by sotte · Pull Request #5057 · numpy/numpy · GitHub
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ENH: add block() function to create block arrays #5057

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3d4c5d1
ENH: add block() function.
sotte Sep 7, 2014
9de9266
Move comment about matlab notation comment to Note section.
sotte Jan 21, 2016
a3765e7
rename tup_tup to arrays
sotte Jan 21, 2016
a529167
Simplify if
sotte Jan 21, 2016
a716e4d
Better examples in docstring
sotte Jan 21, 2016
3dcedce
*args version of block
sotte Feb 8, 2016
8b97ad9
Unittest for unneeded []
sotte Feb 10, 2016
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113 changes: 110 additions & 3 deletions numpy/core/shape_base.py
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Original file line number Diff line number Diff line change
@@ -1,10 +1,11 @@
from __future__ import division, absolute_import, print_function

__all__ = ['atleast_1d', 'atleast_2d', 'atleast_3d', 'vstack', 'hstack',
'stack']
__all__ = ['atleast_1d', 'atleast_2d', 'atleast_3d', 'block', 'hstack',
'stack', 'vstack']


from . import numeric as _nx
from .numeric import asanyarray, newaxis
from .numeric import array, asanyarray, newaxis

def atleast_1d(*arys):
"""
Expand Down Expand Up @@ -202,6 +203,7 @@ def vstack(tup):
dstack : Stack arrays in sequence depth wise (along third dimension).
concatenate : Join a sequence of arrays along an existing axis.
vsplit : Split array into a list of multiple sub-arrays vertically.
block : Create block arrays.

Notes
-----< 10000 /span>
Expand Down Expand Up @@ -253,6 +255,7 @@ def hstack(tup):
dstack : Stack arrays in sequence depth wise (along third axis).
concatenate : Join a sequence of arrays along an existing axis.
hsplit : Split array along second axis.
block : Create block arrays.

Notes
-----
Expand All @@ -279,6 +282,7 @@ def hstack(tup):
else:
return _nx.concatenate(arrs, 1)


def stack(arrays, axis=0):
"""
Join a sequence of arrays along a new axis.
Expand All @@ -305,6 +309,7 @@ def stack(arrays, axis=0):
--------
concatenate : Join a sequence of arrays along an existing axis.
split : Split array into a list of multiple sub-arrays of equal size.
block : Create block arrays.

Examples
--------
Expand Down Expand Up @@ -348,3 +353,105 @@ def stack(arrays, axis=0):
sl = (slice(None),) * axis + (_nx.newaxis,)
expanded_arrays = [arr[sl] for arr in arrays]
return _nx.concatenate(expanded_arrays, axis=axis)


def block(*arrays):
"""
Create a block array consisting of other arrays.

You can create a block array with the same notation you use for
`np.array`.

Parameters
----------
arrays : sequence of sequence of ndarrays
1-D arrays are treated as row vectors.

Returns
-------
stacked : ndarray
The 2-D array formed by stacking the given arrays.

See Also
--------
stack : Stack arrays in sequence along a new dimension.
hstack : Stack arrays in sequence horizontally (column wise).
vstack : Stack arrays in sequence vertically (row wise).
dstack : Stack arrays in sequence depth wise (along third dimension).
concatenate : Join a sequence of arrays together.
vsplit : Split array into a list of multiple sub-arrays vertically.

Notes
-----
``block`` is similar to Matlab's "square bracket stacking": ``[A A; B B]``

Examples
--------
Stacking in a row:
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A blank line is needed here, or it won't render correctly.

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All other function in shape_base.py are exactly like this. I'll build the docs and check..

< 10000 /p>

>>> A = np.array([[1, 2, 3]])
>>> B = np.array([[2, 3, 4]])
>>> block([A, B])
array([[1, 2, 3, 2, 3, 4]])

Stacking in a column:
>>> A = np.array([[1, 2, 3]])
>>> B = np.array([[2, 3, 4]])
>>> block(A, B)
array([[1, 2, 3],
[2, 3, 4]])

1-D vectors are treated as row arrays
>>> a = np.array([1, 1])
>>> b = np.array([2, 2])
>>> block([a, b])
array([[1, 1, 2, 2]])

>>> a = np.array([1, 1])
>>> b = np.array([2, 2])
>>> block(a, b)
array([[1, 1],
[2, 2]])

The tuple notation also works:
>>> A = np.ones((2, 2))
>>> B = 2 * A
>>> block((A, B))
array([[1, 1, 2, 2],
[1, 1, 2, 2]])

Block matrix with arbitrary shaped elements
>>> One = np.array([[1, 1, 1]])
>>> Two = np.array([[2, 2, 2]])
>>> Three = np.array([[3, 3, 3, 3, 3, 3]])
>>> four = np.array([4, 4, 4, 4, 4, 4])
>>> five = np.array([5])
>>> six = np.array([6, 6, 6, 6, 6])
>>> Zeros = np.zeros((2, 6), dtype=int)
>>> block([One, Two],
... Three,
... four,
... [five, six],
... Zeros)
array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 3, 3, 3],
[4, 4, 4, 4, 4, 4],
[5, 6, 6, 6, 6, 6],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0]])


"""
if len(arrays) < 1:
raise TypeError("need at least one array to create a block array")

result = []
for row in arrays:
if isinstance(row, (list, tuple)):
result.append(hstack(row))
else:
result.append(row)

if len(result) > 1:
return vstack(result)
else:
return atleast_2d(result[0])
132 changes: 128 additions & 4 deletions numpy/core/tests/test_shape_base.py
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Original file line number Diff line number Diff line change
@@ -1,11 +1,14 @@
from __future__ import division, absolute_import, print_function

import warnings
import numpy as np
from numpy.compat import long
from numpy.core import (array, arange, atleast_1d, atleast_2d, atleast_3d,
vstack, hstack, newaxis, concatenate, stack)
from numpy.testing import (TestCase, assert_, assert_raises, assert_array_equal,
assert_equal, run_module_suite, assert_raises_regex)
block, vstack, hstack, newaxis, concatenate, stack)
from numpy.testing import (TestCase, assert_, assert_raises,
assert_array_equal, assert_equal, run_module_suite,
assert_raises_regex, assert_almost_equal)

from numpy.compat import long

class TestAtleast1d(TestCase):
def test_0D_array(self):
Expand Down Expand Up @@ -315,5 +318,126 @@ def test_stack():
stack, [m, m])


class TestBlock(TestCase):
def test_block_simple_row_wise(self):
A = np.ones((2, 2))
B = 2 * A
desired = np.array([[1, 1, 2, 2],
[1, 1, 2, 2]])
result = block([A, B])
assert_almost_equal(desired, result)
# with tuples
result = block((A, B))
assert_almost_equal(desired, result)

def test_block_simple_column_wise(self):
A = np.ones((2, 2))
B = 2 * A
expected = np.array([[1, 1],
[1, 1],
[2, 2],
[2, 2]])
result = block(A, B)
assert_almost_equal(expected, result)

def test_block_needless_brackts(self):
A = np.ones((2, 2))
B = 2 * A
expected = np.array([[1, 1],
[1, 1],
[2, 2],
[2, 2]])
result = block([A], [B]) # here are the needless brackets
assert_almost_equal(expected, result)

def test_block_with_1d_arrays_row_wise(self):
# # # 1-D vectors are treated as row arrays
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
expected = np.array([[1, 2, 3, 2, 3, 4]])
result = block([a, b])
assert_almost_equal(expected, result)

def test_block_with_1d_arrays_multiple_rows(self):
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
expected = np.array([[1, 2, 3, 2, 3, 4],
[1, 2, 3, 2, 3, 4]])
result = block([a, b], [a, b])
assert_almost_equal(expected, result)

def test_block_with_1d_arrays_column_wise(self):
# # # 1-D vectors are treated as row arrays
a = np.array([1, 2, 3])
b = np.array([2, 3, 4])
expected = np.array([[1, 2, 3],
[2, 3, 4]])
result = block(a, b)
assert_almost_equal(expected, result)

def test_block_mixed_1d_and_2d(self):
A = np.ones((2, 2))
B = np.array([2, 2])
result = block(A, B)
expected = np.array([[1, 1],
[1, 1],
[2, 2]])
assert_almost_equal(expected, result)

def test_block_complex(self):
# # # a bit more complex
One = np.array([[1, 1, 1]])
Two = np.array([[2, 2, 2]])
Three = np.array([[3, 3, 3, 3, 3, 3]])
four = np.array([4, 4, 4, 4, 4, 4])
five = np.array([5])
six = np.array([6, 6, 6, 6, 6])
Zeros = np.zeros((2, 6))

result = block([One, Two],
Three,
four,
[five, six],
Zeros)
expected = np.array([[1, 1, 1, 2, 2, 2],
[3, 3, 3, 3, 3, 3],
[4, 4, 4, 4, 4, 4],
[5, 6, 6, 6, 6, 6],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0]])
assert_almost_equal(result, expected)

# additional [] around rows should not have any influence
result = block([One, Two],
Three,
[four],
[five, six],
Zeros)
assert_almost_equal(result, expected)

result = block([One, Two],
[Three],
[four],
[five, six],
Zeros)
assert_almost_equal(result, expected)

result = block([One, Two],
[Three],
[four],
[five, six],
[Zeros])
assert_almost_equal(result, expected)

def test_block_with_mismatched_shape(self):
a = np.array([0, 0])
b = np.eye(2)
assert_raises(ValueError, np.block, (a, b))
assert_raises(ValueError, np.block, (b, a))

def test_not_list_or_tuple_as_input(self):
assert_raises(TypeError, np.block)

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I'm missing a few tests for bad-weather behavior: empty arrays, and arrays with mismatched shapes.

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Good idea. I found a bug. I would have expected this to throw an exception.

     >>> a = np.array([0, 0])
    >>> b = np.eye(2)
    >>> np.block(((a, a), b))
    array([[0, 0. 0, 0],
           [1, 0, 0, 1]])

b is hstacked to [1, 0, 0, 1].


if __name__ == "__main__":
run_module_suite()
0