def test_roots_6():
# Test 6.1
# No MS roots to compare to.
f = lambda x, y: (y - 2 * x) * (y + 0.5 * x)
g = lambda x, y: x * (x**2 + y**2 - 1)
yroots = solve([f, g], [-1, -1], [1, 1])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest6_1.csv',
delimiter=',')
pass_or_fail([f, g], yroots, chebfun_roots, 6.1)
# Test 6.2
# This one we find more than them, but it's the correct number of roots.
# No MS roots to compare to.
f = lambda x, y: (y - 2 * x) * (y + .5 * x)
g = lambda x, y: (x - .0001) * (x**2 + y**2 - 1)
yroots = solve([f, g], [-1, -1], [1, 1])
#chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest6_2.csv', delimiter=',')
actual_roots = np.array([[1 / 10000, -1 / 20000], [1 / 10000, 1 / 5000],
[-2 / np.sqrt(5), 1 / np.sqrt(5)],
[-1 / np.sqrt(5), -2 / np.sqrt(5)],
[1 / np.sqrt(5), 2 / np.sqrt(5)],
[2 / np.sqrt(5), -1 / np.sqrt(5)]])
pass_or_fail([f, g], yroots, actual_roots, 6.2)
# Test 6.3
f = lambda x, y: 25 * x * y - 12
g = lambda x, y: x**2 + y**2 - 1
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest6_3ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 6.3)
def test_roots_2_5():
import time
# Test 2.5
f = lambda x, y: 2 * y * np.cos(y**2) * np.cos(2 * x) - np.cos(y)
g = lambda x, y: 2 * np.sin(y**2) * np.sin(2 * x) - np.sin(x)
print(
"Because this was listed as \"slow\", we timed it. On the same machine, there was little difference."
)
start = time.time()
solve([f, g], [-4, -4], [4, 4])
end = time.time()
print("Time:", end - start, "s")
yroots = solve([f, g], [-4, -4], [4, 4], plot=False)
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_5ms.csv',
delimiter=',')
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest2_5.csv',
delimiter=',')
verbose_pass_or_fail([f, g],
yroots,
m_sq_roots,
2.5,
tol=2.220446049250313e-12,
cheb_roots=chebfun_roots)
def test_roots_3():
# Test 3.1
# No MS roots to compare to, so we compare to Chebfun's roots.
f = lambda x, y: ((x - .3)**2 + 2 * (y + 0.3)**2 - 1)
g = lambda x, y: ((x - .49)**2 + (y + .5)**2 - 1) * (
(x + 0.5)**2 + (y + 0.5)**2 - 1) * ((x - 1)**2 + (y - 0.5)**2 - 1)
yroots = solve([f, g], [-1, -1], [1, 1])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest3_1.csv',
delimiter=',')
pass_or_fail([f, g], yroots, chebfun_roots, 3.1)
# Test 3.2
# No MS roots to compare to, so we compare to Chebfun's roots.
f = lambda x, y: ((x - 0.1)**2 + 2 * (y - 0.1)**2 - 1) * (
(x + 0.3)**2 + 2 * (y - 0.2)**2 - 1) * (
(x - 0.3)**2 + 2 * (y + 0.15)**2 - 1) * ((x - 0.13)**2 + 2 *
(y + 0.15)**2 - 1)
g = lambda x, y: (2 * (x + 0.1)**2 + (y + 0.1)**2 - 1) * (
2 * (x + 0.1)**2 +
(y - 0.1)**2 - 1) * (2 * (x - 0.3)**2 + (y - 0.15)**2 - 1) * (
(x - 0.21)**2 + 2 * (y - 0.15)**2 - 1)
yroots = solve([f, g], [-1, -1], [1, 1])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest3_2.csv',
delimiter=',')
pass_or_fail([f, g], yroots, chebfun_roots, 3.2)
def test_roots_2_4():
import time
# Test 2.4
f = lambda x, y: np.exp(x - 2 * x**2 - y**2) * np.sin(10 *
(x + y + x * y**2))
g = lambda x, y: np.exp(-x + 2 * y**2 + x * y**2) * np.sin(10 * (
x - y - 2 * x * y**2))
print(
"Because this was listed as \"slow\", we timed it. On the same machine, there was little difference."
)
start = time.time()
solve([f, g], [-1, -1], [1, 1])
end = time.time()
print("Time:", end - start, "s")
yroots = solve([f, g], [-1, -1], [1, 1], plot=False)
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_4ms.csv',
delimiter=',')
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest2_4.csv',
delimiter=',')
verbose_pass_or_fail([f, g],
yroots,
m_sq_roots,
2.4,
cheb_roots=chebfun_roots)
def test_roots_1():
# Test 1.1
f = lambda x, y: 144 * (x**4 + y**4) - 225 * (x**2 + y**2
) + 350 * x**2 * y**2 + 81
g = lambda x, y: y - x**6
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest1_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 1.1)
# Test 1.2
f = lambda x, y: (y**2 - x**3) * ((y - 0.7)**2 - (x - 0.3)**3) * (
(y + 0.2)**2 - (x + 0.8)**3) * ((y + 0.2)**2 - (x - 0.8)**3)
g = lambda x, y: ((y + .4)**3 - (x - .4)**2) * (
(y + .3)**3 - (x - .3)**2) * ((y - .5)**3 - (x + .6)**2) * (
(y + 0.3)**3 - (2 * x - 0.8)**3)
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('chebfun_test_output/cftest1_2.csv', delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 1.2)
# Test 1.3
f = lambda x, y: y**2 - x**3
g = lambda x, y: (y + .1)**3 - (x - .1)**2
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest1_3ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 1.3)
# Test 1.4
f = lambda x, y: x - y + .5
g = lambda x, y: x + y
yroots = solve([f, g], [-1, -1], [1, 1])
# Single root has to be in matrix form because yroots
# returns the roots in matrix form.
a_roots = np.array([[-.25, .25]])
pass_or_fail([f, g], yroots, a_roots, 1.4)
# Test 1.5
f = lambda x, y: y + x / 2 + 1 / 10
g = lambda x, y: y - 2.1 * x + 2
yroots = solve([f, g], [-1, -1], [1, 1])
# Single root has to be in matrix form because yroots
# returns the roots in matrix form.
a_roots = np.array([[0.730769230769231, -0.465384615384615]])
pass_or_fail([f, g], yroots, a_roots, 1.5)
def test_roots_2():
# Test 2.1
f = lambda x, y: np.cos(10 * x * y)
g = lambda x, y: x + y**2
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 2.1)
# Test 2.2
f = lambda x, y: x
g = lambda x, y: (x - .9999)**2 + y**2 - 1
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_2ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 2.2)
# Test 2.3
f = lambda x, y: np.sin(4 * (x + y / 10 + np.pi / 10))
g = lambda x, y: np.cos(2 * (x - 2 * y + np.pi / 7))
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_3ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 2.3)
# Test 2.4
f = lambda x, y: np.exp(x - 2 * x**2 - y**2) * np.sin(10 *
(x + y + x * y**2))
g = lambda x, y: np.exp(-x + 2 * y**2 + x * y**2) * np.sin(10 * (
x - y - 2 * x * y**2))
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_4ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 2.4)
# Test 2.5
f = lambda x, y: 2 * y * np.cos(y**2) * np.cos(2 * x) - np.cos(y)
g = lambda x, y: 2 * np.sin(y**2) * np.sin(2 * x) - np.sin(x)
yroots = solve([f, g], [-4, -4], [4, 4])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest2_5ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 2.5, tol=2.220446049250313e-12)
def test_roots_4_2():
# Test 4.2
f = lambda x,y: ((90000*y**10 + (-1440000)*y**9 + (360000*x**4 + 720000*x**3 + 504400*x**2 + 144400*x + 9971200)*(y**8) +
((-4680000)*x**4 + (-9360000)*x**3 + (-6412800)*x**2 + (-1732800)*x + (-39554400))*(y**7) + (540000*x**8 +
2160000*x**7 + 3817600*x**6 + 3892800*x**5 + 27577600*x**4 + 51187200*x**3 + 34257600*x**2 + 8952800*x + 100084400)*(y**6) +
((-5400000)*x**8 + (-21600000)*x**7 + (-37598400)*x**6 + (-37195200)*x**5 + (-95198400)*x**4 +
(-153604800)*x**3 + (-100484000)*x**2 + (-26280800)*x + (-169378400))*(y**5) + (360000*x**12 + 2160000*x**11 +
6266400*x**10 + 11532000*x**9 + 34831200*x**8 + 93892800*x**7 + 148644800*x**6 + 141984000*x**5 + 206976800*x**4 +
275671200*x**3 + 176534800*x**2 + 48374000*x + 194042000)*(y**4) + ((-2520000)*x**12 + (-15120000)*x**11 + (-42998400)*x**10 +
(-76392000)*x**9 + (-128887200)*x**8 + (-223516800)*x**7 + (-300675200)*x**6 + (-274243200)*x**5 + (-284547200)*x**4 +
(-303168000)*x**3 + (-190283200)*x**2 + (-57471200)*x + (-147677600))*(y**3) + (90000*x**16 + 720000*x**15 + 3097600*x**14 +
9083200*x**13 + 23934400*x**12 + 58284800*x**11 + 117148800*x**10 + 182149600*x**9 + 241101600*x**8 + 295968000*x**7 +
320782400*x**6 + 276224000*x**5 + 236601600*x**4 + 200510400*x**3 + 123359200*x**2 + 43175600*x + 70248800)*(y**2) +
((-360000)*x**16 + (-2880000)*x**15 + (-11812800)*x**14 + (-32289600)*x**13 + (-66043200)*x**12 + (-107534400)*x**11 +
(-148807200)*x**10 + (-184672800)*x**9 + (-205771200)*x**8 + (-196425600)*x**7 + (-166587200)*x**6 + (-135043200)*x**5 +
(-107568800)*x**4 + (-73394400)*x**3 + (-44061600)*x**2 + (-18772000)*x + (-17896000))*y + (144400*x**18 + 1299600*x**17 +
5269600*x**16 + 12699200*x**15 + 21632000*x**14 + 32289600*x**13 + 48149600*x**12 + 63997600*x**11 + 67834400*x**10 +
61884000*x**9 + 55708800*x**8 + 45478400*x**7 + 32775200*x**6 + 26766400*x**5 + 21309200*x**4 + 11185200*x**3 + 6242400*x**2 +
3465600*x + 1708800)))
g = lambda x,y: 1e-4*(y**7 + (-3)*y**6 + (2*x**2 + (-1)*x + 2)*y**5 + (x**3 + (-6)*x**2 + x + 2)*y**4 + (x**4 + (-2)*x**3 + 2*x**2 +
x + (-3))*y**3 + (2*x**5 + (-3)*x**4 + x**3 + 10*x**2 + (-1)*x + 1)*y**2 + ((-1)*x**5 + 3*x**4 + 4*x**3 + (-12)*x**2)*y +
(x**7 + (-3)*x**5 + (-1)*x**4 + (-4)*x**3 + 4*x**2))
start = time()
yroots = solve([f,g],[-1, -1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_4.2.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_4.2.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 4.2, cheb_roots=chebfun_roots)
def test_roots_1_2():
# Test 1.2
f = lambda x,y: (y**2-x**3)*((y-0.7)**2-(x-0.3)**3)*((y+0.2)**2-(x+0.8)**3)*((y+0.2)**2-(x-0.8)**3)
g = lambda x,y: ((y+.4)**3-(x-.4)**2)*((y+.3)**3-(x-.3)**2)*((y-.5)**3-(x+.6)**2)*((y+0.3)**3-(2*x-0.8)**3)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
# Get Polished results (Newton polishing misses roots)
yroots2 = solve([f,g],[-1,-1],[1,1], abs_approx_tol=[1e-8, 1e-12], rel_approx_tol=[1e-15, 1e-18],\
max_cond_num=[1e5, 1e2], good_zeros_factor=[100,100], min_good_zeros_tol=[1e-5, 1e-5],\
check_eval_error=[True,True], check_eval_freq=[1,2], plot=False, target_tol=[1e-13, 1e-13])
actual_roots = np.load('Polished_results/polished_1.2.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_1.2.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, yroots2, 1.2, cheb_roots=chebfun_roots, tol=2.220446049250313e-10)
def test_roots_3_2():
# Test 3.2
f = lambda x,y: ((x-0.1)**2+2*(y-0.1)**2-1)*((x+0.3)**2+2*(y-0.2)**2-1)*((x-0.3)**2+2*(y+0.15)**2-1)*((x-0.13)**2+2*(y+0.15)**2-1)
g = lambda x,y: (2*(x+0.1)**2+(y+0.1)**2-1)*(2*(x+0.1)**2+(y-0.1)**2-1)*(2*(x-0.3)**2+(y-0.15)**2-1)*((x-0.21)**2+2*(y-0.15)**2-1)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_3.2.npy')
yroots2 = solve([f,g],[-1,-1],[1,1], abs_approx_tol=[1e-8, 1e-15], rel_approx_tol=[1e-12, 1e-29],\
max_cond_num=[1e5, 1e2], good_zeros_factor=[100,100], min_good_zeros_tol=[1e-5, 1e-5],\
check_eval_error=[True,True], check_eval_freq=[1,1], plot=False)
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_3.2.csv', delimiter=',')
actual_roots = chebfun_roots
return t, verbose_pass_or_fail([f,g], yroots, yroots2, 3.2, cheb_roots=chebfun_roots, tol=2.220446049250313e-11)
def test_roots_7():
# Test 7.1
f = lambda x, y: (x**2 + y**2 - 1) * (x - 1.1)
g = lambda x, y: (25 * x * y - 12) * (x - 1.1)
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest7_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 7.1)
# Test 7.2
f = lambda x, y: y**4 + (-1) * y**3 + (2 * x**2) * (y**2) + (3 * x**2
) * y + (x**4)
h = lambda x, y: y**10 - 2 * (x**8) * (y**2) + 4 * (x**4) * y - 2
g = lambda x, y: h(2 * x, 2 * (y + .5))
yroots = solve([f, g], [-1, -1], [1, 1])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest7_2.csv',
delimiter=',')
assert residuals_pass_or_fail([f], yroots) and residuals_pass_or_fail(
[g], yroots, tol=2.220446049250313e-10), "Test 7.2 failed."
# Test 7.3
c = 1.e-09
f = lambda x, y: np.cos(x * y / (c**2)) + np.sin(3 * x * y / (c**2))
g = lambda x, y: np.cos(y / c) - np.cos(2 * x * y / (c**2))
yroots = solve([f, g], [-1e-9, -1e-9], [1e-9, 1e-9])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest7_3.csv',
delimiter=',')
assert residuals_pass_or_fail([f, g], yroots,
tol=2.220446049250313e-9), "Test 7.3 fails."
# Test 7.4
f = lambda x, y: np.sin(3 * np.pi * x) * np.cos(x * y)
g = lambda x, y: np.sin(3 * np.pi * y) * np.cos(np.sin(x * y))
yroots = solve([f, g], [-1, -1], [1, 1])
chebfun_roots = np.loadtxt('tests/chebfun_test_output/cftest7_4.csv',
delimiter=',')
assert pass_or_fail([f, g],
yroots,
chebfun_roots,
7.4,
test_type='residual')
def test_roots_9():
# Test 9.1
f = lambda x, y: x**2 + y**2 - .9**2
g = lambda x, y: np.sin(x * y)
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest9_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 9.1)
# Test 9.2
f = lambda x, y: x**2 + y**2 - .49**2
g = lambda x, y: (x - .1) * (x * y - .2)
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest9_2ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 9.2)
def test_roots_8():
# Test 8.1
f = lambda x, y: np.sin(10 * x - y / 10)
g = lambda x, y: np.cos(3 * x * y)
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest8_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 8.1)
# Test 8.2
f = lambda x, y: np.sin(10 * x - y / 10) + y
g = lambda x, y: np.cos(10 * y - x / 10) - x
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest8_2ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 8.2)
def test_roots_5():
# Test 5.1
f = lambda x, y: 2 * x * y * np.cos(y**2) * np.cos(2 * x) - np.cos(x * y)
g = lambda x, y: 2 * np.sin(x * y**2) * np.sin(3 * x * y) - np.sin(x * y)
yroots = solve([f, g], [-2, -2], [2, 2])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest5_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 5.1)
def test_roots_1_4():
# Test 1.4
f = lambda x, y: x - y + .5
g = lambda x, y: x + y
yroots = solve([f, g], [-1, -1], [1, 1], plot=False)
# Single root has to be in matrix form because yroots
# returns the roots in matrix form.
a_roots = np.array([[-.25, .25]])
verbose_pass_or_fail([f, g], yroots, a_roots, test_num=1.4)
def test_roots_1_5():
# Test 1.5
f = lambda x, y: y + x / 2 + 1 / 10
g = lambda x, y: y - 2.1 * x + 2
yroots = solve([f, g], [-1, -1], [1, 1], plot=False)
# Single root has to be in matrix form because yroots
# returns the roots in matrix form.
a_roots = np.array([[0.730769230769231, -0.465384615384615]])
verbose_pass_or_fail([f, g], yroots, a_roots, 1.5)
def test_roots_7_4():
# Test 7.4
f = lambda x,y: np.sin(3*np.pi*x)*np.cos(x*y)
g = lambda x,y: np.sin(3*np.pi*y)*np.cos(np.sin(x*y))
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_7.4.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_7.4.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 7.4, cheb_roots=chebfun_roots)
def test_roots_7_1():
# Test 7.1
f = lambda x,y: (x**2+y**2-1)*(x-1.1)
g = lambda x,y: (25*x*y-12)*(x-1.1)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_7.1.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_7.1.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 7.1, cheb_roots=chebfun_roots)
def test_roots_6_3():
# Test 6.3
f = lambda x,y: 25*x*y - 12
g = lambda x,y: x**2+y**2-1
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_6.3.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_6.3.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 6.3, cheb_roots=chebfun_roots)
def test_roots_6_2():
# Test 6.2
f = lambda x,y: (y - 2*x)*(y+.5*x)
g = lambda x,y: (x-.0001)*(x**2+y**2-1)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.array([[1/10000,-1/20000],[1/10000, 1/5000],[-2/np.sqrt(5),1/np.sqrt(5)],[-1/np.sqrt(5),-2/np.sqrt(5)],[1/np.sqrt(5),2/np.sqrt(5)],[2/np.sqrt(5),-1/np.sqrt(5)]])
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_6.2.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 6.2, cheb_roots=chebfun_roots, tol=2.220446049250313e-11)
def test_roots_5():
# Test 5.1
f = lambda x,y: 2*x*y*np.cos(y**2)*np.cos(2*x)-np.cos(x*y)
g = lambda x,y: 2*np.sin(x*y**2)*np.sin(3*x*y)-np.sin(x*y)
start = time()
yroots = solve([f,g],[-2,-2],[2,2], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_5.1.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_5.1.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 5.1, cheb_roots=chebfun_roots)
def test_roots_4():
# Test 4.1
# This system hs 4 true roots, but ms fails (finds 5).
f = lambda x, y: np.sin(3 * (x + y))
g = lambda x, y: np.sin(3 * (x - y))
yroots = solve([f, g], [-1, -1], [1, 1])
m_sq_roots = np.loadtxt('tests/chebfun_test_output/cftest4_1ms.csv',
delimiter=',')
pass_or_fail([f, g], yroots, m_sq_roots, 4.1)
def test_roots_1_1():
# Test 1.1
f = lambda x,y: 144*(x**4+y**4)-225*(x**2+y**2) + 350*x**2*y**2+81
g = lambda x,y: y-x**6
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_1.1.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_1.1.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 1.1, cheb_roots=chebfun_roots)
def test_roots_3_1():
# Test 3.1
f = lambda x,y: ((x-.3)**2+2*(y+0.3)**2-1)
g = lambda x,y: ((x-.49)**2+(y+.5)**2-1)*((x+0.5)**2+(y+0.5)**2-1)*((x-1)**2+(y-0.5)**2-1)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_3.1.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_3.1.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 3.1, cheb_roots=chebfun_roots, tol=2.220446049250313e-11)
def test_roots_2_5():
# Test 2.5
f = lambda x,y: 2*y*np.cos(y**2)*np.cos(2*x)-np.cos(y)
g = lambda x,y: 2*np.sin(y**2)*np.sin(2*x)-np.sin(x)
start = time()
yroots = solve([f,g],[-4,-4],[4,4], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_2.5.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_2.5.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 2.5, cheb_roots=chebfun_roots, tol=2.220446049250313e-12)
def test_roots_2_4():
# Test 2.4
f = lambda x,y: np.exp(x-2*x**2-y**2)*np.sin(10*(x+y+x*y**2))
g = lambda x,y: np.exp(-x+2*y**2+x*y**2)*np.sin(10*(x-y-2*x*y**2))
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_2.4.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_2.4.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 2.4, cheb_roots=chebfun_roots)
def test_roots_2_3():
# Test 2.3
f = lambda x,y: np.sin(4*(x + y/10 + np.pi/10))
g = lambda x,y: np.cos(2*(x-2*y+ np.pi/7))
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_2.3.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_2.3.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 2.3, cheb_roots=chebfun_roots)
def test_roots_2_1():
# Test 2.1
f = lambda x,y: np.cos(10*x*y)
g = lambda x,y: x + y**2
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_2.1.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_2.1.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 2.1, cheb_roots=chebfun_roots)
def test_roots_8_2():
# Test 8.2
f = lambda x,y: np.sin(10*x-y/10) + y
g = lambda x,y: np.cos(10*y-x/10) - x
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_8.2.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_8.2.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 8.2, cheb_roots=chebfun_roots)
def test_roots_9_2():
# Test 9.2
f = lambda x,y: x**2+y**2-.49**2
g = lambda x,y: (x-.1)*(x*y - .2)
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_9.2.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_9.2.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 9.2, cheb_roots=chebfun_roots)
def test_roots_1_3():
# Test 1.3
f = lambda x,y: y**2-x**3
g = lambda x,y: (y+.1)**3-(x-.1)**2
start = time()
yroots = solve([f,g],[-1,-1],[1,1], plot=False)
t = time() - start
actual_roots = np.load('Polished_results/polished_1.3.npy')
chebfun_roots = np.loadtxt('Chebfun_results/test_roots_1.3.csv', delimiter=',')
return t, verbose_pass_or_fail([f,g], yroots, actual_roots, 1.3, cheb_roots=chebfun_roots)