def eye(row):
"""
Return a identical matrix.
"""
R = set(row)
if len(R) < 1:
return None
func = {(r, c): 1 for (r, c) in gutil.cartesianProduct(R, R) if r is c}
return matrix((R, R), func)
def addColumn(self, c, vec):
"""
Parameter 'c' is the label element to add vector as column vector.
"""
(R, C) = self.domain
if R == vec.domain and c in C:
D = gutil.cartesianProduct(R, set(c))
for d, entry in zip(D, vec.entries()):
self.func[d] = entry
def entries(self, d, mode='row'):
"""
Return entries of row vector or column set sorted by laxicogrhapical.
Parameter 'd' is element of row or column set.
mode : str{'row', 'col'} optional
'row'
The output is a row vector.
'col'
The output is a column vector.
"""
(row, col) = self.domain
if mode is 'row' and d in row:
domain = gutil.cartesianProduct(set(d), sorted(col))
elif mode is 'col' and d in col:
domain = gutil.cartesianProduct(set(d), sorted(row))
else:
return None
return [self.getItem(d) for d in domain]
def listlist2matrix(R, C, listlist):
"""
Return a matrix that entries are elements of listlist.
Parameter 'R' is label of row and 'P' is label of column.
"""
entries = [entry for row in listlist for entry in row]
D = gutil.cartesianProduct(R, C)
func = {(r, c): entry for (r, c), entry in zip(D, entries)}
return matrix((set(R), set(C)), func)
# row field. Column field is a domain of this function and
# row field is a codomain.
import gula.vec as gvec
import gula.mat as gmat
import gula.util as gutil
"""
R is row label of matrix.
C is column label of matrix.
"""
R = {'a', 'b'}
C = {'#', '@', '?'}
A = gmat.matrix((R, C),
{d: i + 1
for i, d in enumerate(gutil.cartesianProduct(R, C))})
print('Matrix A=')
print(A)
x = gvec.vector(C, {c: 1 for c in C})
print('Vector x=')
print(x)
"""
Set(Label) C is a domain of function.
Set R is a co-domain of function.
So, RxC matrix is model of (C->R) function.
"""
print('Dot product, A*x=b')
print('Vector b=')
print(gutil.dot(A, x))
def setItem(self, key, val):
(row, col) = self.domain
if key not in gutil.cartesianProduct(row, col):
return None
self.func[key] = val