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Cmr three_sum and cographicnode (sagemath#10)
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Co-authored-by: J S <javier@javiers-mbp.mynetworksettings.com>
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@jsantillan3 @mkoeppe
2 people authored and mkoeppe committed Jun 2, 2024
1 parent 5dbc114 commit a14bd46
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174 changes: 171 additions & 3 deletions src/sage/matrix/matrix_cmr_sparse.pyx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -438,8 +438,132 @@ cdef class Matrix_cmr_chr_sparse(Matrix_cmr_sparse):
sum.set_immutable()
return sum

def three_sum(self, other, *args):
raise NotImplementedError
def three_sum(first_mat, second_mat, first_col_index1, first_col_index2, second_col_index1, second_col_index2):
r"""
Return the 3-sum matrix constructed from the given matrices ``first_mat`` and ``second_mat``, with 'first_col_index1'
and 'first_col_index2' being the indices of the column vectors of the matrix, which are identical except for one row
having a 0 in one column and the other a non-zero entry in that row. The method assumes the nonzero entry is one. The same assumptions
are made for 'second_mat' and its input index variables.
EXAMPLES::
sage: from sage.matrix.matrix_cmr_sparse import Matrix_cmr_chr_sparse
sage: M1 = Matrix_cmr_chr_sparse(MatrixSpace(ZZ, 5, 5, sparse=True),
....: [[1, 0, -1, 0, 1], [1, 1, 0, -1, 1], [0, 0, 1, 1, 1],
....: [1, 1, -1, 0, 0], [-1, -1, 0, 0,1]]); M1
[ 1 0 -1 0 1]
[ 1 1 0 -1 1]
[ 0 0 1 1 1]
[ 1 1 -1 0 0]
[-1 -1 0 0 1]
sage: M2 = Matrix_cmr_chr_sparse(MatrixSpace(ZZ, 5, 5, sparse=True),
....: [[1, 1, 1, 1, 1], [1, 1, 1, 0, 0], [1, 0, 1, 1, 0],
....: [0, 0, 0, 1, 1], [1, 1, 0, 0, 1]]); M2
[1 1 1 1 1]
[1 1 1 0 0]
[1 0 1 1 0]
[0 0 0 1 1]
[1 1 0 0 1]
sage: M3 = Matrix_cmr_chr_sparse.three_sum(M1, M2, 0, 1, 0, 1); M3
[ 0 -1 1 1 1 0]
[ 1 1 1 0 0 0]
[-1 0 0 1 1 0]
[ 0 0 1 -1 -1 0]
[-1 0 1 1 1 1]
[-1 0 1 1 0 0]
[-1 0 1 0 1 1]
[ 1 0 -1 0 0 1]
"""
fc = len(first_mat.columns())
sc = len(second_mat.columns())
fr = len(first_mat.rows())
sr = len(second_mat.rows())
if any([fc < 3, sc < 3, fr < 2, sr < 2]):
raise ValueError('Some matrix is not large enough to perform a 3-sum')
if any([first_col_index1 >= fc, first_col_index2 >= fc, second_col_index1 >= sc, second_col_index2 >= sc]):
raise ValueError('Some column indicated exceeds its matrix size')
first_col1 = first_mat.columns()[first_col_index1]
first_col2 = first_mat.columns()[first_col_index2]
second_col1 = second_mat.columns()[second_col_index1]
second_col2 = second_mat.columns()[second_col_index2]
fir_nrows = range(fr)
sec_nrows = range(sr)
valid1 = False
valid2 = False
for i in fir_nrows:
if (first_col1[i] == 1 and first_col2[i] == 0) or (first_col1[i] == 0 and first_col2[i] == 1):
subcol1 = tuple(first_col1[k] for k in fir_nrows if k != i)
subcol2 = tuple(first_col2[k] for k in fir_nrows if k != i)
if subcol1 == subcol2:
valid1 = True
first_row_index = i
break
for i in sec_nrows:
if (second_col1[i] == 1 and second_col2[i] == 0) or (second_col1[i] == 0 and second_col2[i] == 1):
subcol1 = tuple(second_col1[k] for k in sec_nrows if k != i)
subcol2 = tuple(second_col2[k] for k in sec_nrows if k != i)
if subcol1 == subcol2:
valid2 = True
second_row_index = i
break
if not (valid1 and valid2):
raise ValueError('indicated columns of Matrices are not of appropriate form for 3-sum')
first_subcol = first_mat.delete_rows([first_row_index]).columns()[first_col_index1]
second_subcol = first_mat.delete_rows([second_row_index]).columns()[second_col_index1]
first_submat = first_mat.delete_columns([first_col_index1, first_col_index2])
second_submat = second_mat.delete_columns([second_col_index1, second_col_index2])
first_row = first_submat.rows()[first_row_index]
second_row = second_submat.rows()[second_row_index]
first_submat = first_submat.delete_rows([first_row_index])
second_submat = second_submat.delete_rows([second_row_index])
first_subrows = first_submat.rows()
second_subrows = second_submat.rows()
upper_right_rows = first_subcol.tensor_product(second_row).rows()
lower_left_rows = second_subcol.tensor_product(first_row).rows()
n1 = len(first_submat.rows())
n2 = len(second_submat.rows())
row_list = []
for i in range(n1):
r = list(first_subrows[i])
u = list(upper_right_rows[i])
r.extend(u)
row_list.append(r)
for i in range(n2):
r = list(lower_left_rows[i])
u = list(second_subrows[i])
r.extend(u)
row_list.append(r)
return Matrix_cmr_chr_sparse._from_data(row_list, immutable = False)

def delete_rows(self, indices):
rows = self.rows()
row_list = []
n = len(rows)
for i in indices:
if i >= n:
raise ValueError('Found index greater than matrix size')
rows.pop(i)
for r in rows:
x = []
for i in range(len(r)):
x.append(r[i])
row_list.append(x)
return Matrix_cmr_chr_sparse._from_data(row_list, immutable = False)

def delete_columns(self, indices):
rows = self.rows()
n = len(rows)
row_list = []
for i in indices:
if i >= n:
raise ValueError('Found index greater than matrix size')
for r in rows:
x = []
for k in range(len(r)):
if not (k in indices):
x.append(r[k])
row_list.append(x)
return Matrix_cmr_chr_sparse._from_data(row_list, immutable = False)

def is_unimodular(self):
r"""
Expand Down Expand Up @@ -718,7 +842,51 @@ cdef class Matrix_cmr_chr_sparse(Matrix_cmr_sparse):
return False, NotImplemented # submatrix TBD

def is_cographic(self, *, time_limit=60.0, certificate=False):
raise NotImplementedError
r"""
EXAMPLES::
sage: from sage.matrix.matrix_cmr_sparse import Matrix_cmr_chr_sparse
sage: M = Matrix_cmr_chr_sparse(MatrixSpace(ZZ, 4, 9, sparse=True), [[1, 0, 0, 0, 1, -1, 1, 0, 0],
....: [0, 1, 0, 0, 0, 1, -1, 1, 0], [0, 0, 1, 0, 0, 0, 1, -1, 1],
....: [0, 0, 0, 1, 1, 0, 0, 1, -1]]); M
[ 1 0 0 0 1 -1 1 0 0]
[ 0 1 0 0 0 1 -1 1 0]
[ 0 0 1 0 0 0 1 -1 1]
[ 0 0 0 1 1 0 0 1 -1]
sage: M.is_cographic()
True
"""
cdef bool result
cdef CMR_GRAPH *graph = NULL
cdef CMR_GRAPH_EDGE* forest_edges = NULL
cdef CMR_GRAPH_EDGE* coforest_edges = NULL
cdef CMR_SUBMAT* submatrix = NULL
cdef CMR_GRAPHIC_STATISTICS stats

sig_on()
try:
if certificate:
CMR_CALL(CMRtestCographicMatrix(cmr, self._mat, &result, &graph, &forest_edges,
&coforest_edges, &submatrix, &stats, time_limit))
else:
CMR_CALL(CMRtestCographicMatrix(cmr, self._mat, &result, NULL, NULL,
NULL, NULL, &stats, time_limit))
finally:
sig_off()

if not certificate:
return <bint> result

if <bint> result:
sage_graph = _sage_graph(graph)
sage_forest_edges = tuple(_sage_edge(graph, forest_edges[row])
for row in range(self.nrows()))
sage_coforest_edges = tuple(_sage_edge(graph, coforest_edges[column])
for column in range(self.ncols()))
return True, (sage_graph, sage_forest_edges, sage_coforest_edges)

return False, NotImplemented # submatrix TBD


def is_network_matrix(self, *, time_limit=60.0, certificate=False):
r"""
Expand Down
41 changes: 35 additions & 6 deletions src/sage/matrix/seymour_decomposition.pyx
View file
Original file line number Diff line number Diff line change
Expand Up @@ -305,9 +305,33 @@ cdef class OneSumNode(SumNode):


cdef class TwoSumNode(SumNode):

pass
r"""
EXAMPLES::
sage: from sage.matrix.matrix_cmr_sparse import Matrix_cmr_chr_sparse
M = Matrix_cmr_chr_sparse(MatrixSpace(ZZ, 5, 5, sparse=True),
....: [[1, 1, 1, 1, 1], [1, 1, 1, 0, 0], [1, 0, 1, 1, 0]
....: ,[1, 0, 0, 1, 1], [1, 1, 0, 0, 1]]); M2
[1 1 1 1 1]
[1 1 1 0 0]
[1 0 1 1 0]
[1 0 0 1 1]
[1 1 0 0 1]
sage: M3 = Matrix_cmr_chr_sparse.two_sum(M2, M2, 0, 1); M3
[1 1 1 1|1 1 1 0 0]
[1 1 0 0|1 1 1 0 0]
[0 1 1 0|1 1 1 0 0]
[0 0 1 1|1 1 1 0 0]
[1 0 0 1|1 1 1 0 0]
[-------+---------]
[0 0 0 0|1 1 1 1 1]
[0 0 0 0|1 0 1 1 0]
[0 0 0 0|1 0 0 1 1]
[0 0 0 0|1 1 0 0 1]
sage: result, certificate = M3.is_totally_unimodular(certificate=True); certificate
TwoSumNode (9×9) with 2 children
"""
pass

cdef class ThreeSumNode(SumNode):

Expand Down Expand Up @@ -375,13 +399,18 @@ cdef class GraphicNode(BaseGraphicNode):


cdef class CographicNode(BaseGraphicNode):

pass
@cached_method
def graph(self):
r"""
Actually the cograph of matrix, in the case where it is not graphic.
"""
return _sage_graph(CMRdecCograph(self._dec))


cdef class PlanarNode(BaseGraphicNode):

pass
@cached_method
def cograph(self):
return _sage_graph(CMRdecCograph(self._dec))


cdef class SeriesParallelReductionNode(DecompositionNode):
Expand Down

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