def initial_code():
p0 = Plane(normal_vector=Vector(['1', '1', '1']), constant_term='1')
p1 = Plane(normal_vector=Vector(['0', '1', '0']), constant_term='2')
p2 = Plane(normal_vector=Vector(['1', '1', '-1']), constant_term='3')
p3 = Plane(normal_vector=Vector(['1', '0', '-2']), constant_term='2')
s = LinearSystem([p0, p1, p2, p3])
print s.indices_of_first_nonzero_terms_in_each_row()
print '{},{},{},{}'.format(s[0], s[1], s[2], s[3])
print len(s)
print s
s[0] = p1
print s
print MyDecimal('1e-9').is_near_zero()
print MyDecimal('1e-11').is_near_zero()
def intersection_with(self, ell):
try:
A, B = self.normal_vector.coordinates
C, D = ell.normal_vector.coordinates
k1, k2 = self.constant_term, ell.constant_term
x_numerator = D*k1 - B*k2
y_numerator = -C*k1 + A*k2
one_over_denom = Decimal('1')/(A*D - B*C)
return Vector([x_numerator, y_numerator]).times_scalar(one_over_denom)
except ZeroDivisionError:
if self == ell:
return self
else:
return None
def intersections_quiz():
ell1 = Line(normal_vector=Vector(['4.046', '2.836']), constant_term='1.21')
ell2 = Line(normal_vector=Vector(['10.115', '7.09']), constant_term='3.025')
print 'intersection 1:', ell1.intersection_with(ell2)
ell3 = Line(normal_vector=Vector(['7.204', '3.182']), constant_term='8.68')
ell4 = Line(normal_vector=Vector(['8.172', '4.114']), constant_term='9.883')
print 'intersection 2:', ell3.intersection_with(ell4)
ell5 = Line(normal_vector=Vector(['1.182', '5.562']), constant_term='6.744')
ell6 = Line(normal_vector=Vector(['1.773', '8.343']), constant_term='9.525')
print 'intersection 3:', ell5.intersection_with(ell6)
def coding_row_operations_quiz():
p0 = Plane(normal_vector=Vector(['1', '1', '1']), constant_term='1')
p1 = Plane(normal_vector=Vector(['0', '1', '0']), constant_term='2')
p2 = Plane(normal_vector=Vector(['1', '1', '-1']), constant_term='3')
p3 = Plane(normal_vector=Vector(['1', '0', '-2']), constant_term='2')
s = LinearSystem([p0, p1, p2, p3])
s.swap_rows(0, 1)
s0p1 = s[0] == p1
s1p0 = s[1] == p0
s2p2 = s[2] == p2
s3p3 = s[3] == p3
if not (s[0] == p1 and s[1] == p0 and s[2] == p2 and s[3] == p3):
print 'test case 1 failed'
s.swap_rows(1, 3)
if not (s[0] == p1 and s[1] == p3 and s[2] == p2 and s[3] == p0):
print 'test case 2 failed'
s.swap_rows(3, 1)
if not (s[0] == p1 and s[1] == p0 and s[2] == p2 and s[3] == p3):
print 'test case 3 failed'
s.multiply_coefficient_and_row(1, 0)
if not (s[0] == p1 and s[1] == p0 and s[2] == p2 and s[3] == p3):
print 'test case 4 failed'
s.multiply_coefficient_and_row(-1, 2)
if not (s[0] == p1 and s[1] == p0
and s[2] == Plane(normal_vector=Vector(['-1', '-1', '1']),
constant_term='-3') and s[3] == p3):
print 'test case 5 failed'
s.multiply_coefficient_and_row(10, 1)
if not (s[0] == p1 and s[1] == Plane(
normal_vector=Vector(['10', '10', '10']), constant_term='10')
and s[2] == Plane(normal_vector=Vector(['-1', '-1', '1']),
constant_term='-3') and s[3] == p3):
print 'test case 6 failed'
s.add_multiple_times_row_to_row(0, 0, 1)
if not (s[0] == p1 and s[1] == Plane(
normal_vector=Vector(['10', '10', '10']), constant_term='10')
and s[2] == Plane(normal_vector=Vector(['-1', '-1', '1']),
constant_term='-3') and s[3] == p3):
print 'test case 7 failed'
s.add_multiple_times_row_to_row(1, 0, 1)
if not (s[0] == p1 and s[1] == Plane(
normal_vector=Vector(['10', '11', '10']), constant_term='12')
and s[2] == Plane(normal_vector=Vector(['-1', '-1', '1']),
constant_term='-3') and s[3] == p3):
print 'test case 8 failed'
s.add_multiple_times_row_to_row(-1, 1, 0)
if not (s[0] == Plane(normal_vector=Vector(['-10', '-10', '-10']),
constant_term='-10')
and s[1] == Plane(normal_vector=Vector(['10', '11', '10']),
constant_term='12')
and s[2] == Plane(normal_vector=Vector(['-1', '-1', '1']),
constant_term='-3') and s[3] == p3):
print 'test case 9 failed'