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4492: block matrix constructor, reviewer edits
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@rbeezer
rbeezer committed Jan 13, 2011
1 parent 656f2e7 commit 1a09d97
Showing 1 changed file with 79 additions and 32 deletions.
111 changes: 79 additions & 32 deletions src/sage/matrix/constructor.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1438,7 +1438,7 @@ def ones_matrix(ring, nrows=None, ncols=None, sparse=False):
return matrix_space.MatrixSpace(ring, nrows, ncols, sparse).matrix([one]*nents)

def _determine_block_matrix_grid(sub_matrices):
"""
r"""
For internal use. This tries to determine the dimensions
of rows/columns when assembling the matrices in sub_matrices in a
rectangular grid. It returns a pair of lists containing
Expand Down Expand Up @@ -1499,17 +1499,17 @@ def _determine_block_matrix_grid(sub_matrices):
changing = True
col_widths[j] = sub_width
elif col_widths[j] != sub_width:
raise ValueError, "Incompatible submatrix widths"
raise ValueError("incompatible submatrix widths")
if sub_height is not None:
if row_heights[i] is None:
changing = True
row_heights[i] = sub_height
elif row_heights[i] != sub_height:
raise ValueError, "Incompatible submatrix heights"
raise ValueError("ncompatible submatrix heights")

if None in row_heights or None in col_widths:
if None in row_heights or None in col_widths:
raise ValueError, "Insufficient information to determine dimensions."
raise ValueError("insufficient information to determine dimensions.")

return (row_heights, col_widths)

Expand Down Expand Up @@ -1562,7 +1562,7 @@ def _determine_block_matrix_rows(sub_matrices):
if height is None:
height = M.nrows()
elif height != M.nrows():
raise ValueError, "Incompatible submatrix heights"
raise ValueError("incompatible submatrix heights")
elif not M:
found_zeroes = True
if len(R) == 0:
Expand All @@ -1581,15 +1581,15 @@ def _determine_block_matrix_rows(sub_matrices):
if total_width is None:
total_width = width
elif total_width != width:
raise ValueError, "Incompatible submatrix widths"
raise ValueError("incompatible submatrix widths")
row_heights[i] = height
else:
# We don't set height here even if we know it,
# to signal this row hasn't been fit yet.
unknowns = True

if total_width is None:
raise ValueError, "Insufficient information to determine submatrix widths"
raise ValueError("insufficient information to determine submatrix widths")

if unknowns:
# Do a second pass and see if the remaining rows can be
Expand Down Expand Up @@ -1628,29 +1628,29 @@ def _determine_block_matrix_rows(sub_matrices):
if height is not None:
remaining_width -= scalars * height
if remaining_width < 0:
raise ValueError, "Incompatible submatrix widths"
raise ValueError("incompatible submatrix widths")
if remaining_width > 0 and zero_state == 3:
raise ValueError, "Insufficient information to determine submatrix widths"
raise ValueError("insufficient information to determine submatrix widths")
if remaining_width > 0 and zero_state == 0:
raise ValueError, "Incompatible submatrix widths"
raise ValueError("ncompatible submatrix widths")
# otherwise, things fit
row_heights[i] = height
zero_widths[i] = remaining_width
elif zero_state != 0:
# if we don't know the height, and there are zeroes,
# we can't determine the height
raise ValueError, "Insufficient information to determine submatrix heights"
raise ValueError("insufficient information to determine submatrix heights")
elif total_width % len(R) != 0:
raise ValueError, "Incompatible submatrix widths"
raise ValueError("incompatible submatrix widths")
else:
height = int(total_width / len(R))
row_heights[i] = height

# If we got this far, then everything fits
return (row_heights, zero_widths, total_width)

def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivide=True):
"""
def block_matrix(*args, **kwds):
r"""
Returns a larger matrix made by concatenating submatrices
(rows first, then columns). For example, the matrix
Expand All @@ -1661,7 +1661,9 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
is made up of submatrices A, B, C, and D.
INPUT: The block_matrix command takes a list of submatrices to add
INPUT:
The block_matrix command takes a list of submatrices to add
as blocks, optionally preceded by a ring and the number of block rows
and block columns, and returns a matrix.
Expand Down Expand Up @@ -1729,8 +1731,6 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
[ 3 9| -3 -9|-5/12 3/8| 300 900]
[ 6 10| -6 -10| 1/4 -1/8| 600 1000]
::
sage: block_matrix([A, -A, ~A, 100*A], nrows=1)
[ 3 9| -3 -9|-5/12 3/8| 300 900]
[ 6 10| -6 -10| 1/4 -1/8| 600 1000]
Expand All @@ -1744,6 +1744,7 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
[-----------+-----------]
[ 0 0|x - 1 0]
[ 0 0| 0 x - 1]
sage: block_matrix(2, 2, [1/2, A, 0, x-1]).parent()
Full MatrixSpace of 4 by 4 dense matrices over Univariate Polynomial Ring in x over Rational Field
Expand Down Expand Up @@ -1775,6 +1776,51 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
sage: block_matrix([ [ A ], [ A ] ], sparse=False).parent()
Full MatrixSpace of 4 by 2 dense matrices over Integer Ring
Consecutive zero submatrices are consolidated. ::
sage: B = matrix(2, range(4))
sage: C = matrix(2, 8, range(16))
sage: block_matrix(2, [[B,0,0,B],[C]], subdivide=False)
[ 0 1 0 0 0 0 0 1]
[ 2 3 0 0 0 0 2 3]
[ 0 1 2 3 4 5 6 7]
[ 8 9 10 11 12 13 14 15]
Ambiguity is not tolerated. ::
sage: B = matrix(2, range(4))
sage: C = matrix(2, 8, range(16))
sage: block_matrix(2, [[B,0,B,0],[C]], subdivide=False)
Traceback (most recent call last):
...
ValueError: insufficient information to determine submatrix widths
Historically, giving only a flat list of submatrices, whose number
was a perfect square, would create a new matrix by laying out the submatrices
in a square grid. This behavior is now deprecated. ::
sage: A = matrix(2, 3, range(6))
sage: B = matrix(3, 3, range(9))
sage: block_matrix([A, A, B, B])
doctest:...: DeprecationWarning: invocation of block_matrix with just a list whose length is a perfect square is deprecated. See the documentation for details.
[0 1 2|0 1 2]
[3 4 5|3 4 5]
[-----+-----]
[0 1 2|0 1 2]
[3 4 5|3 4 5]
[6 7 8|6 7 8]
Historically, a flat list of matrices whose number is not a perfect square,
with no specification of the number of rows or columns, would raise an error.
This behavior continues, but could be removed when the deprecation above is
completed. ::
sage: A = matrix(2, 3, range(6))
sage: B = matrix(3, 3, range(9))
sage: block_matrix([A, A, A, B, B, B])
Traceback (most recent call last):
...
ValueError: must specify nrows or ncols for non-square block matrix.
"""
args = list(args)
sparse = kwds.get('sparse',None)
Expand All @@ -1788,7 +1834,7 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
if len(args) >= 1 and rings.is_Ring(args[0]):
# A ring is specified
if kwds.get('ring', args[0]) != args[0]:
raise ValueError, "Specified rings are not the same"
raise ValueError("base ring specified twice and they are different")
ring = args[0]
args.pop(0)
else:
Expand All @@ -1799,7 +1845,7 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
nrows = int(args[0])
args.pop(0)
if kwds.get('nrows', nrows) != nrows:
raise ValueError, "Number of rows specified in two places and they are not the same"
raise ValueError("number of rows specified twice and they are different")
except TypeError:
nrows = kwds.get('nrows', None)
else:
Expand All @@ -1811,7 +1857,7 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
ncols = int(args[0])
args.pop(0)
if kwds.get('ncols', ncols) != ncols:
raise ValueError, "Number of columns specified in two places and they are not the same"
raise ValueError("number of columns specified twice and they are different")
except TypeError:
ncols = kwds.get('ncols', None)
else:
Expand All @@ -1826,23 +1872,23 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
args = [[]]
if len(args) > 1:
print args
raise TypeError, "Invalid block_matrix invocation"
raise TypeError("invalid block_matrix invocation")

sub_matrices = args[0]

if is_Matrix(sub_matrices):
# a single matrix (check nrows/ncols/ring)
if (nrows is not None and nrows != 1) or \
(ncols is not None and ncols != 1):
raise ValueError, "Invalid nrows/ncols passed to block_matrix"
raise ValueError("invalid nrows/ncols passed to block_matrix")
if ring is not None:
M = M.change_ring(ring)
if sparse is not None and M.is_sparse() != sparse:
M = M.sparse_matrix() if sparse else M.dense_matrix()
return M

if not isinstance(sub_matrices, (list, tuple)):
raise TypeError, "Invalid block_matrix invocation"
raise TypeError("invalid block_matrix invocation")

subdivide = kwds.get('subdivide', True)

Expand All @@ -1853,18 +1899,18 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
if len(sub_matrices) == 0:
if (nrows is not None and nrows != 0) or \
(ncols is not None and ncols != 0):
raise ValueError, "Invalid nrows/ncols passed to block_matrix"
raise ValueError("invalid nrows/ncols passed to block_matrix")
elif isinstance(sub_matrices[0], (list, tuple)):
# A list of lists: verify all elements are lists, and if
# ncols is set, the lengths match.
if nrows is not None and len(sub_matrices) != nrows:
raise ValueError, "Invalid nrows passed to block_matrix"
raise ValueError("invalid nrows passed to block_matrix")
first_len = len(sub_matrices[0])
if ncols is not None and first_len != ncols:
raise ValueError, "Invalid ncols passed to block_matrix"
raise ValueError("invalid ncols passed to block_matrix")
same_length = all(isinstance(v, (list, tuple)) and len(v) == first_len for v in sub_matrices)
if subdivide and not same_length:
raise ValueError, "List of rows is not valid (rows are wrong types or lengths)"
raise ValueError("list of rows is not valid (rows are wrong types or lengths)")
try_grid = same_length
else:
# A flat list
Expand All @@ -1874,16 +1920,17 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
if ncols is None:
if n.is_square():
import warnings
warnings.warn("This invocation of block_matrix is deprecated. See its documentation for details.", DeprecationWarning, stacklevel=2)
warnings.warn("invocation of block_matrix with just a list whose length is a perfect square is deprecated. See the documentation for details.", DeprecationWarning, stacklevel=2)
nrows = ncols = n.sqrt()
else:
raise ValueError, "Must specify nrows or ncols for non-square block matrix."
# this form (ie just a flat list) could be allowed once deprecated invocation (above) goes away
raise ValueError("must specify nrows or ncols for non-square block matrix.")
else:
nrows = int(n/ncols)
elif ncols is None:
ncols = int(n/nrows)
if nrows * ncols != n:
raise ValueError, "Given number of rows (%s), columns (%s) incompatible with number of submatrices (%s)" % (nrows, ncols, n)
raise ValueError("given number of rows (%s), columns (%s) incompatible with number of submatrices (%s)" % (nrows, ncols, n))
# Now create a list of lists from this
sub_matrices = [ sub_matrices[i*ncols : (i+1)*ncols] for i in range(nrows) ]

Expand Down Expand Up @@ -1916,7 +1963,7 @@ def block_matrix(*args, **kwds): #sub_matrices, nrows=None, ncols=None, subdivid
(row_heights, col_widths) = _determine_block_matrix_grid(sub_matrices)
except ValueError as e:
if subdivide:
raise ValueError, e
raise ValueError(e)


if col_widths is None:
Expand Down Expand Up @@ -1979,7 +2026,7 @@ def block_diagonal_matrix(*sub_matrices, **kwds):
Create a block matrix whose diagonal block entries are given by
sub_matrices, with zero elsewhere.
See also ``block_matrix``.
See also :meth:`block_matrix`.
EXAMPLES::
Expand Down

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