def test_funny_matrix_determinants(self):
"""
>>> funny_matrix_determinants()
'Funny' matrix determinant test passed.
"""
error = False
a = symbol('a')
b = symbol('b')
c = symbol('c')
for size in range(3, 8):
A = matrix(size, size)
for co in range(size-1):
# Populate one or two elements in each row
for ec in range(0, 2):
numer = sparse_tree(a, b, c, randrange(1, 4), True, True, False)
denom = numeric(0)
while denom == 0:
denom = sparse_tree(a, b, c, randrange(2), False, True, False)
A[randrange(size), co] = numer/denom
# Set the last column to a linear combination of two other columns to
# guarantee that the determinant is zero
for ro in range(size):
A[ro, size-1] = A[ro, 0] - A[ro,size-2]
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 test_rational_matrix_determinants(self):
"""
>>> rational_matrix_determinants()
Rational matrix determinants test passed.
"""
error = False
a = symbol('a')
b = symbol('b')
c = symbol('c')
for size in range( 3, 9):
A = matrix(size, size)
for r in range(size-1):
# Populate one or two elements in each row:
for ec in range(2):
numer = sparse_tree( a, b, c, randrange(1, 4),
False, False, False)
denom = numeric(0)
while denom == 0:
denom = sparse_tree( a, b, c, randrange(2),
False, False, False)
A[r, randrange(size)] = numer/denom
# set the last row to a linear combination of two other lines
# to guarantee that the determinant is zero:
for co in range(size):
A[size-1, co] = A[0,co] - A[size-2,co]
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 test_compare_matrix_determinants(self):
"""
>>> compare_matrix_determinants()
Matrix determinant comparison test passed.
"""
error = False
a = symbol('a')
for size in range(2, 8):
A = matrix(size, size)
for co in range(size):
for ro in range(size):
if randrange(size/2) == 0:
A[ro, co] = sparse_tree(a, a, a, randrange(3),
False, True, False)
det_gauss = A.determinant( determinant_algo.gauss)
det_laplace = A.determinant( determinant_algo.laplace)
det_divfree = A.determinant( determinant_algo.divfree)
det_bareiss = A.determinant( determinant_algo.bareiss)
if not (det_gauss - det_laplace).normal().is_zero() \
or not (det_bareiss - det_laplace).normal().is_zero() \
or not (det_divfree - det_laplace).normal().is_zero():
error = True
print "Determinant of", size, "x", size, "matrix", A
print "is inconsistent between different algorithms:"
print "Gauss elimination: ", det_gauss
print "Minor elimination: ", det_laplace
print "Division-free elim.: ", det_divfree
print "Fraction-free elim.: ", det_bareiss
self.assertEqual(error,0)
def test_symbolic_matrix_inverse(self):
"""
>>> symbolic_matrix_inverse()
Symbolic matrix inverse test passed.
"""
error = False
a = symbol('a')
b = symbol('b')
c = symbol('c')
for size in range(2, 6):
A = matrix(size, size)
while A.determinant() == 0:
for co in range(size):
for ro in range(size):
if randrange(size/2) == 0:
A[ro, co] = sparse_tree(a, b, c, randrange(2),
False, True, False)
B = A.inverse()
C = (A * B).evalm().normal()
ok = True
for ro in range(size):
for co in range(size):
elem = C[ro, co]
if ro == co and elem != 1:
print "non-unity", "(", ro, ",", co, ")", elem
ok = False
if ro != co and elem != 0:
print "nonzero", "(", ro, ",", co, ")", elem
ok = False
if not ok:
print "Inverse of ", size, "x", size, "matrix", A
print "errooneously returned:", B
print "Its determinant is: ", A.determinant()
error = True
self.assertEqual(error,0)
