def test_integdom_matrix_determinants(self):
"""
>>> integdom_matrix_determinants()
Matrix determinant test passed.
"""
error = False
a = symbol('a')
# Feel like you have CPU time to burn?
# Raise the value of the upper bounds here...
for size in range(3, 22):
A = matrix( size, size)
# Populate one element in each row
for r in range( size-1):
A[r, randrange(0,size)] = dense_univariate_poly(a, 5)
# Set the last row to a linear combination of two others to
# guarantee that the determinant should be zero
for c in range(size):
A[size-1, c] = A[0,c] - A[size-2,c]
if A.determinant() != 0:
error = True
print "Determinant of", size, "x", size, "matrix", A
print "was not found to vanish!"
self.assertEqual(error,0)
def check_matrix_solve(m, n, p, degree):
"""
>>> # solve some numeric linear systems
>>> result = 0
>>> for n in range(1, 14):
... result += check_matrix_solve(n, n, 1, 0)
...
>>> if result:
... print "Numeric system checks failed."
... else:
... print "Numeric system checks passed."
...
Numeric system checks passed.
>>> # solve some underdetermined numeric systems
>>> result = 0
>>> for n in range(1, 14):
... result += check_matrix_solve(n+1, n, 1, 0)
...
>>> if result:
... print "Underdetermined system checks failed."
... else:
... print "Underdetermined system checks passed."
...
Underdetermined system checks passed.
>>> result = 0
>>> # solve some overdetermined numeric systems
>>> for n in range(1, 14):
... result += check_matrix_solve(n, n+1, 1, 0)
...
>>> if result:
... print "Overdetermined system checks failed."
... else:
... print "Overdetermined system checks passed."
...
Overdetermined system checks passed.
>>> # solve some multiple numeric systems
>>> result = 0
>>> for n in range(1, 14):
... result += check_matrix_solve(n, n, n/3+1, 0)
...
>>> if result:
... print "Multiple numeric systems checks failed."
... else:
... print "Multiple numeric systems checks passed."
...
Multiple numeric systems checks passed.
>>> # solve some symbolic linear systems
>>> result = 0
>>> for n in range(1, 8):
... result += check_matrix_solve(n, n, 1, 2)
...
>>> if result:
... print "Symbolic linear systems checks failed."
... else:
... print "Symbolic linear systems checks passed."
...
Symbolic linear systems checks passed.
"""
a = symbol('a')
A = matrix(m, n)
B = matrix(m, p)
for ro in range( min(m, n)):
for co in range(n):
A[ro,co] = dense_univariate_poly(a, degree)
for co in range(p):
B[ro,co] = dense_univariate_poly(a, degree)
for ro in range(n, m):
for co in range(n):
A[ro, co] = A[ro-1,co]
for co in range(p):
B[ro,co] = B[ro-1,co]
# Create a vector of n*p symbols all named "xrc" where r and c are ints
X = matrix(n,p)
for i in range(n):
for j in range(p):
X[i,j] = symbol("x" + str(i) + str(j))
soln = matrix(n, p)
# Solve the system A*X == B
sol = A.solve(X, B)
# Check the result with the original matrix
error = False
for ro in range(m):
for pco in range(p):
e = numeric(0)
for co in range(n):
e += A[ro,co]*sol[co,pco]
if (e-B[ro,pco]).normal() != 0:
error = True
if error:
print "Our solve method claims that A*X == B with matricies:"
print "A ==", A
print "X ==", X
print "B ==", B
print "X (the solution) == ", sol
return error