def test_simple(self):
x = np.arange(20, dtype='float32')
#standard normal noise
noise = np.array([-0.76741118, -0.30754369,
0.39950921, -0.46352422, -1.67081778,
0.6595567 , 0.66367639, -2.04388585,
0.8123281 , 1.45977518,
1.21428038, 1.29296866, 0.78028477,
-0.2402853 , -0.21721302,
0.24549405, 0.25987014, -0.90709034,
-1.45688216, -0.31780505])
y = x + noise
expected_lowess = np.array([[ 0. , -0.58337912],
[ 1. , 0.61951246],
[ 2. , 1.82221628],
[ 3. , 3.02536876],
[ 4. , 4.22667951],
[ 5. , 5.42387723],
[ 6. , 6.60834945],
[ 7. , 7.7797691 ],
[ 8. , 8.91824348],
[ 9. , 9.94997506],
[ 10. , 10.89697569],
[ 11. , 11.78746276],
[ 12. , 12.62356492],
[ 13. , 13.41538492],
[ 14. , 14.15745254],
[ 15. , 14.92343948],
[ 16. , 15.70019862],
[ 17. , 16.48167846],
[ 18. , 17.26380699],
[ 19. , 18.0466769 ]])
actual_lowess = lowess(y,x)
assert_almost_equal(expected_lowess, actual_lowess)
[ 4. , 4.22667951],
[ 5. , 5.42387723],
[ 6. , 6.60834945],
[ 7. , 7.7797691 ],
[ 8. , 8.91824348],
[ 9. , 9.94997506],
[ 10. , 10.89697569],
[ 11. , 11.78746276],
[ 12. , 12.62356492],
[ 13. , 13.41538492],
[ 14. , 14.15745254],
[ 15. , 14.92343948],
[ 16. , 15.70019862],
[ 17. , 16.48167846],
[ 18. , 17.26380699],
[ 19. , 18.0466769 ]])
actual_lowess = lo.lowess(y,x)
print actual_lowess
print np.max(np.abs(actual_lowess-expected_lowess))
res0 = lo._lowess_initial_fit(x, y, 4, len(x))
doplot = 1
if doplot:
import matplotlib.pyplot as plt
plt.plot(y, 'o')
plt.plot(actual_lowess[:,1])
plt.plot(expected_lowess[:,1])
plt.plot(res0[0])
plt.show()
plt.subplots_adjust(hspace=0.1)
axes[0].plot(weights_f_kde.support, weights_f_kde.density, label='Female')
axes[0].xaxis.tick_top()
axes[0].legend()
axes[1].plot(weights_m_kde.support, weights_f_kde.density, label='Male')
axes[1].legend()
plt.savefig('weight_density_bysex_subplot.png')
# Scatter plot. Pull weight (both sexes) out as a separate array first, like
# we did with height above.
weights = heights_weights['Weight']
plt.plot(heights, weights, '.k', mew=0, alpha=.1)
plt.savefig('height_weight_scatter.png')
# Lowess smoothing - this seems to be new functionality not yet in docs (as of 0.40, April 2012).
lowess_line = lowess.lowess(weights, heights)
plt.figure(figsize=(13, 9))
plt.plot(heights, weights, '.', mfc='steelblue', mew=0, alpha=.25)
plt.plot(lowess_line[:, 0],
lowess_line[:, 1],
'-',
color='#461B7E',
label="Lowess fit")
plt.legend(loc="upper left")
plt.savefig('height_weight_lowess.png')
# Logistic regression of sex on height and weight
# Sex is coded in the binary variable `male`.
# LHS binary variable
ax2.plot(KSx, KVar, "-o")
ax3 = fig.add_subplot(223)
ax3.plot(x, y, "+")
ax3.plot(KSx, KS2y, "-o")
ax3.set_ylim(-20, 30)
ax4 = fig.add_subplot(224)
ax4.plot(KSx, K2Var, "-o")
fig2 = plt.figure()
ax5 = fig2.add_subplot(111)
ax5.plot(x, y, "+")
ax5.plot(KSConfIntx, KSConfInty, "-o")
from statsmodels.nonparametric import lowess as lo
ys = lo.lowess(y, x)
ax5.plot(ys[:, 0], ys[:, 1], 'b-')
ys2 = lo.lowess(y, x, frac=0.25)
ax5.plot(ys2[:, 0], ys2[:, 1], 'b--', lw=2)
#need to sort for matplolib plot ?
xind = np.argsort(x)
pmod = smoothers.PolySmoother(5, x[xind])
pmod.fit(y[xind])
yp = pmod(x[xind])
ax5.plot(x[xind], yp, 'k-')
ax5.set_title('Kernel regression, lowess - blue, polysmooth - black')
#plt.show()
axes[0].plot(weights_f_kde.support, weights_f_kde.density, label = 'Female')
axes[0].xaxis.tick_top()
axes[0].legend()
axes[1].plot(weights_m_kde.support, weights_f_kde.density, label = 'Male')
axes[1].legend()
plt.savefig('weight_density_bysex_subplot.png')
# Scatter plot. Pull weight (both sexes) out as a separate array first, like
# we did with height above.
weights = heights_weights['Weight']
plt.plot(heights, weights, '.k', mew = 0, alpha = .1)
plt.savefig('height_weight_scatter.png')
# Lowess smoothing - this seems to be new functionality not yet in docs (as of 0.40, April 2012).
lowess_line = lowess.lowess(weights, heights)
plt.figure(figsize = (13, 9))
plt.plot(heights, weights, '.', mfc = 'steelblue', mew=0, alpha = .25)
plt.plot(lowess_line[:,0], lowess_line[:, 1], '-', color = '#461B7E', label = "Lowess fit")
plt.legend(loc = "upper left")
plt.savefig('height_weight_lowess.png')
# Logistic regression of sex on height and weight
# Sex is coded in the binary variable `male`.
# LHS binary variable
male = (heights_weights['Gender'] == 'Male') * 1
# Matrix of predictor variables: hieght and weight from data frame
# into an Nx2 array.
ax2.plot(KSx, KVar, "-o")
ax3 = fig.add_subplot(223)
ax3.plot(x, y, "+")
ax3.plot(KSx, KS2y, "-o")
ax3.set_ylim(-20, 30)
ax4 = fig.add_subplot(224)
ax4.plot(KSx, K2Var, "-o")
fig2 = plt.figure()
ax5 = fig2.add_subplot(111)
ax5.plot(x, y, "+")
ax5.plot(KSConfIntx, KSConfInty, "-o")
from statsmodels.nonparametric import lowess as lo
ys = lo.lowess(y, x)
ax5.plot(ys[:,0], ys[:,1], 'b-')
ys2 = lo.lowess(y, x, frac=0.25)
ax5.plot(ys2[:,0], ys2[:,1], 'b--', lw=2)
#need to sort for matplolib plot ?
xind = np.argsort(x)
pmod = smoothers.PolySmoother(5, x[xind])
pmod.fit(y[xind])
yp = pmod(x[xind])
ax5.plot(x[xind], yp, 'k-')
ax5.set_title('Kernel regression, lowess - blue, polysmooth - black')
#plt.show()
0.78028477, -0.2402853, -0.21721302, 0.24549405, 0.25987014, -0.90709034,
-1.45688216, -0.31780505
])
y = x + noise
expected_lowess = np.array([[0., -0.58337912], [1., 0.61951246],
[2., 1.82221628], [3.,
3.02536876], [4., 4.22667951],
[5., 5.42387723], [6.,
6.60834945], [7., 7.7797691],
[8., 8.91824348], [9., 9.94997506],
[10., 10.89697569], [11., 11.78746276],
[12., 12.62356492], [13., 13.41538492],
[14., 14.15745254], [15., 14.92343948],
[16., 15.70019862], [17., 16.48167846],
[18., 17.26380699], [19., 18.0466769]])
actual_lowess = lo.lowess(y, x)
print actual_lowess
print np.max(np.abs(actual_lowess - expected_lowess))
res0 = lo._lowess_initial_fit(x, y, 4, len(x))
doplot = 1
if doplot:
import matplotlib.pyplot as plt
plt.plot(y, 'o')
plt.plot(actual_lowess[:, 1])
plt.plot(expected_lowess[:, 1])
plt.plot(res0[0])
plt.show()
def test_iter(self):
x = np.arange(20, dtype='float32')
#cauchy noise
noise = np.array([ 1.86299605, -0.10816866, 1.87761229,
-3.63442237, 0.30249022,
1.03560416, 0.21163349, 1.14167809,
-0.00368175, -2.08808987,
0.13065417, -1.8052207 , 0.60404596,
-2.30908204, 1.7081412 ,
-0.54633243, -0.93107948, 1.79023999,
1.05822445, -1.04530564])
y = x + noise
expected_lowess_no_iter = np.array([[ 0. , 0.62644797],
[ 1. , 1.5008396 ],
[ 2. , 2.38617613],
[ 3. , 3.27163904],
[ 4. , 4.13972663],
[ 5. , 4.99266138],
[ 6. , 5.90622252],
[ 7. , 6.85414657],
[ 8. , 7.81633577],
[ 9. , 8.6684662 ],
[ 10. , 9.53212147],
[ 11. , 10.46553757],
[ 12. , 11.46969179],
[ 13. , 12.6126706 ],
[ 14. , 13.80804573],
[ 15. , 14.93552186],
[ 16. , 16.04911835],
[ 17. , 17.16049993],
[ 18. , 18.27391721],
[ 19. , 19.38342689]])
expected_lowess_3_iter = np.array([[ 0. , 1.3607733 ],
[ 1. , 2.2062049 ],
[ 2. , 3.04629498],
[ 3. , 3.88158084],
[ 4. , 4.71163579],
[ 5. , 5.54050304],
[ 6. , 6.38645423],
[ 7. , 7.14643561],
[ 8. , 7.94245588],
[ 9. , 8.75675711],
[ 10. , 9.62619136],
[ 11. , 10.55389747],
[ 12. , 11.52718043],
[ 13. , 12.62840261],
[ 14. , 13.80423591],
[ 15. , 14.91812397],
[ 16. , 16.01752637],
[ 17. , 17.11513329],
[ 18. , 18.21651218],
[ 19. , 19.31714769]])
actual_lowess_no_iter = lowess(y,x,it=0)
actual_lowess_3_iter = lowess(y,x,it=3)
assert_almost_equal(expected_lowess_no_iter, actual_lowess_no_iter)
assert_almost_equal(expected_lowess_3_iter, actual_lowess_3_iter)
def test_frac(self):
#linspace from -2*pi to 2*pi with 30 points
x = np.array([-6.28318531, -5.84986218,
-5.41653906, -4.98321593, -4.54989281,
-4.11656968, -3.68324656, -3.24992343,
-2.81660031, -2.38327719,
-1.94995406, -1.51663094, -1.08330781,
-0.64998469, -0.21666156,
0.21666156, 0.64998469, 1.08330781,
1.51663094, 1.94995406,
2.38327719, 2.81660031, 3.24992343,
3.68324656, 4.11656968,
4.54989281, 4.98321593, 5.41653906,
5.84986218, 6.28318531],
dtype='float32')
#normal noise
noise = np.array([ 1.62379338, -1.11849371, 1.60085673,
0.41996348, 0.70896754,
0.19271408, 0.04972776, -0.22411356,
0.18154882, -0.63651971,
0.64942414, -2.26509826, 0.80018964,
0.89826857, -0.09136105,
0.80482898, 1.54504686, -1.23734643,
-1.16572754, 0.28027691,
-0.85191583, 0.20417445, 0.61034806,
0.68297375, 1.45707167,
0.45157072, -1.13669622, -0.08552254,
-0.28368514, -0.17326155])
y = np.sin(x) + noise
expected_lowess_23 = np.array([[ -6.28318548e+00, 1.85879646e+00],
[ -5.84986210e+00, 1.66545513e+00],
[ -5.41653919e+00, 1.47654627e+00],
[ -4.98321581e+00, 1.29359535e+00],
[ -4.54989290e+00, 1.11753312e+00],
[ -4.11656952e+00, 9.48760031e-01],
[ -3.68324661e+00, 7.86602333e-01],
[ -3.24992347e+00, 6.29003517e-01],
[ -2.81660032e+00, 4.72212611e-01],
[ -2.38327718e+00, 3.12269779e-01],
[ -1.94995403e+00, 2.10972652e-01],
[ -1.51663089e+00, 1.30637140e-01],
[ -1.08330786e+00, 7.40090948e-02],
[ -6.49984717e-01, 4.52736083e-02],
[ -2.16661558e-01, 4.75763268e-02],
[ 2.16661558e-01, 7.63986832e-02],
[ 6.49984717e-01, 1.19888748e-01],
[ 1.08330786e+00, 1.58644711e-01],
[ 1.51663089e+00, 1.79693123e-01],
[ 1.94995403e+00, 1.74680415e-01],
[ 2.38327718e+00, 1.44171836e-01],
[ 2.81660032e+00, 7.04760114e-02],
[ 3.24992347e+00, 2.44342733e-03],
[ 3.68324661e+00, -6.24431808e-02],
[ 4.11656952e+00, -1.27504921e-01],
[ 4.54989290e+00, -1.94864501e-01],
[ 4.98321581e+00, -2.66005721e-01],
[ 5.41653919e+00, -3.41494321e-01],
[ 5.84986210e+00, -4.21172959e-01],
[ 6.28318548e+00, -5.04237292e-01]])
expected_lowess_15 = np.array([[ -6.28318548e+00, 1.65774825e+00],
[ -5.84986210e+00, 1.63964795e+00],
[ -5.41653919e+00, 1.62809791e+00],
[ -4.98321581e+00, 1.64839187e+00],
[ -4.54989290e+00, 1.35052489e+00],
[ -4.11656952e+00, 9.93959944e-01],
[ -3.68324661e+00, 5.46400659e-01],
[ -3.24992347e+00, 1.04275107e-01],
[ -2.81660032e+00, -1.38801715e-01],
[ -2.38327718e+00, -2.50771029e-01],
[ -1.94995403e+00, -2.46649407e-01],
[ -1.51663089e+00, -1.70098614e-01],
[ -1.08330786e+00, 5.71349520e-03],
[ -6.49984717e-01, 2.22985781e-01],
[ -2.16661558e-01, 5.64203458e-01],
[ 2.16661558e-01, 4.33321361e-01],
[ 6.49984717e-01, 3.52990770e-01],
[ 1.08330786e+00, 2.24004384e-02],
[ 1.51663089e+00, -2.14066736e-01],
[ 1.94995403e+00, -6.12592369e-02],
[ 2.38327718e+00, 1.28970397e-01],
[ 2.81660032e+00, 2.87401733e-01],
[ 3.24992347e+00, 3.64551907e-01],
[ 3.68324661e+00, 2.11244778e-01],
[ 4.11656952e+00, -9.71116261e-02],
[ 4.54989290e+00, -3.64730683e-01],
[ 4.98321581e+00, -6.05243177e-01],
[ 5.41653919e+00, -6.91780300e-01],
[ 5.84986210e+00, -5.42520396e-01],
[ 6.28318548e+00, -3.23807686e-01]])
actual_lowess_23 = lowess(y,x,frac=2./3)
actual_lowess_15 = lowess(y,x,frac=1./5)
assert_almost_equal(expected_lowess_23, actual_lowess_23)
assert_almost_equal(expected_lowess_15, actual_lowess_15)