def test_CF(self):
# quartimax
out = self.get_quartimax_example_derivative_free()
A, table_required, L_required = out
vgQ = lambda L=None, A=None, T=None: CF_objective(
L=L, A=A, T=T, kappa=0, rotation_method='orthogonal',
return_gradient=True)
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
# quartimax derivative free
ff = lambda L=None, A=None, T=None: CF_objective(
L=L, A=A, T=T, kappa=0, rotation_method='orthogonal',
return_gradient=False)
L, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal')
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
# varimax
p, k = A.shape
vgQ = lambda L=None, A=None, T=None: orthomax_objective(
L=L, A=A, T=T, gamma=1, return_gradient=True)
L_vm, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
vgQ = lambda L=None, A=None, T=None: CF_objective(
L=L, A=A, T=T, kappa=1/p, rotation_method='orthogonal',
return_gradient=True)
L_CF, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
ff = lambda L=None, A=None, T=None: CF_objective(
L=L, A=A, T=T, kappa=1/p, rotation_method='orthogonal',
return_gradient=False)
L_CF_df, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal')
self.assertTrue(np.allclose(L_vm, L_CF, atol=1e-05))
self.assertTrue(np.allclose(L_CF, L_CF_df, atol=1e-05))
def test_oblimin(self):
# quartimin
A, table_required, L_required = self.get_quartimin_example()
vgQ = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=0, rotation_method='oblique')
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique')
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
# quartimin derivative free
ff = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=0, rotation_method='oblique',
return_gradient=False)
L, phi, T, table = GPA(A, ff=ff, rotation_method='oblique')
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
# biquartimin
A, table_required, L_required = self.get_biquartimin_example()
vgQ = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=1/2, rotation_method='oblique')
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique')
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
# quartimin derivative free
out = self.get_biquartimin_example_derivative_free()
A, table_required, L_required = out
ff = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=1/2, rotation_method='oblique',
return_gradient=False)
L, phi, T, table = GPA(A, ff=ff, rotation_method='oblique')
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
def test_equivalence_orthomax_oblimin(self):
"""
These criteria should be equivalent when restricted to orthogonal
rotation.
See Hartman 1976 page 299.
"""
A = self.get_A()
gamma = 0 # quartimax
vgQ = lambda L=None, A=None, T=None: orthomax_objective(
L=L, A=A, T=T, gamma=gamma, return_gradient=True)
L_orthomax, phi, T, table = GPA(
A, vgQ=vgQ, rotation_method='orthogonal')
vgQ = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=gamma, rotation_method='orthogonal',
return_gradient=True)
L_oblimin, phi2, T2, table2 = GPA(A, vgQ=vgQ,
rotation_method='orthogonal')
self.assertTrue(np.allclose(L_orthomax, L_oblimin, atol=1e-05))
gamma = 1 # varimax
vgQ = lambda L=None, A=None, T=None: orthomax_objective(
L=L, A=A, T=T, gamma=gamma, return_gradient=True)
L_orthomax, phi, T, table = GPA(
A, vgQ=vgQ, rotation_method='orthogonal')
vgQ = lambda L=None, A=None, T=None: oblimin_objective(
L=L, A=A, T=T, gamma=gamma, rotation_method='orthogonal',
return_gradient=True)
L_oblimin, phi2, T2, table2 = GPA(
A, vgQ=vgQ, rotation_method='orthogonal')
self.assertTrue(np.allclose(L_orthomax, L_oblimin, atol=1e-05))
def test_orthogonal_partial_target(self):
"""
Rotation towards target matrix example
http://www.stat.ucla.edu/research/gpa
"""
A = self.get_A()
H = self.str2matrix("""
.8 -.3
.8 -.4
.7 -.4
.9 -.4
.8 .5
.6 .4
.5 .4
.6 .3
""")
W = self.str2matrix("""
1 0
0 1
0 0
1 1
1 0
1 0
0 1
1 0
""")
vgQ = lambda L=None, A=None, T=None: vgQ_partial_target(
H, W, L=L, A=A, T=T)
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
table_required = self.str2matrix("""
0.00000 0.02559 -0.84194 1.00000
1.00000 0.02203 -1.27116 0.25000
2.00000 0.02154 -1.71198 0.25000
3.00000 0.02148 -2.15713 0.25000
4.00000 0.02147 -2.60385 0.25000
5.00000 0.02147 -3.05114 0.25000
6.00000 0.02147 -3.49863 0.25000
7.00000 0.02147 -3.94619 0.25000
8.00000 0.02147 -4.39377 0.25000
9.00000 0.02147 -4.84137 0.25000
10.00000 0.02147 -5.28897 0.25000
""")
L_required = self.str2matrix("""
0.84526 -0.36228
0.83621 -0.43571
0.79528 -0.43836
0.81349 -0.36857
0.76525 0.53122
0.65303 0.48467
0.57565 0.46754
0.63308 0.35876
""")
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
ff = lambda L=None, A=None, T=None: ff_partial_target(
H, W, L=L, A=A, T=T)
L2, phi, T2, table = GPA(A, ff=ff, rotation_method='orthogonal')
self.assertTrue(np.allclose(L, L2, atol=1e-05))
self.assertTrue(np.allclose(T, T2, atol=1e-05))
def test_orthomax(self):
"""
Quartimax example
http://www.stat.ucla.edu/research/gpa
"""
A = self.get_A()
vgQ = lambda L=None, A=None, T=None: orthomax_objective(
L=L, A=A, T=T, gamma=0, return_gradient=True)
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
table_required = self.str2matrix("""
0.00000 -0.72073 -0.65498 1.00000
1.00000 -0.88561 -0.34614 2.00000
2.00000 -1.01992 -1.07152 1.00000
3.00000 -1.02237 -1.51373 0.50000
4.00000 -1.02269 -1.96205 0.50000
5.00000 -1.02273 -2.41116 0.50000
6.00000 -1.02273 -2.86037 0.50000
7.00000 -1.02273 -3.30959 0.50000
8.00000 -1.02273 -3.75881 0.50000
9.00000 -1.02273 -4.20804 0.50000
10.00000 -1.02273 -4.65726 0.50000
11.00000 -1.02273 -5.10648 0.50000
""")
L_required = self.str2matrix("""
0.89876 0.19482
0.93394 0.12974
0.90213 0.10386
0.87651 0.17128
0.31558 0.87647
0.25113 0.77349
0.19801 0.71468
0.30786 0.65933
""")
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
# oblimin criterion gives same result
vgQ = lambda L=None, A=None, T=None: oblimin_objective(
L=L,
A=A,
T=T,
gamma=0,
rotation_method='orthogonal',
return_gradient=True)
L_oblimin, phi2, T2, table2 = GPA(A,
vgQ=vgQ,
rotation_method='orthogonal')
self.assertTrue(np.allclose(L, L_oblimin, atol=1e-05))
# derivative free quartimax
out = self.get_quartimax_example_derivative_free()
A, table_required, L_required = out
ff = lambda L=None, A=None, T=None: orthomax_objective(
L=L, A=A, T=T, gamma=0, return_gradient=False)
L, phi, T, table = GPA(A, ff=ff, rotation_method='orthogonal')
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
def test_orthogonal_target(self):
"""
Rotation towards target matrix example
http://www.stat.ucla.edu/research/gpa
"""
A = self.get_A()
H = self.str2matrix("""
.8 -.3
.8 -.4
.7 -.4
.9 -.4
.8 .5
.6 .4
.5 .4
.6 .3
""")
vgQ = lambda L=None, A=None, T=None: vgQ_target(H, L=L, A=A, T=T)
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
table_required = self.str2matrix("""
0.00000 0.05925 -0.61244 1.00000
1.00000 0.05444 -1.14701 0.12500
2.00000 0.05403 -1.68194 0.12500
3.00000 0.05399 -2.21689 0.12500
4.00000 0.05399 -2.75185 0.12500
5.00000 0.05399 -3.28681 0.12500
6.00000 0.05399 -3.82176 0.12500
7.00000 0.05399 -4.35672 0.12500
8.00000 0.05399 -4.89168 0.12500
9.00000 0.05399 -5.42664 0.12500
""")
L_required = self.str2matrix("""
0.84168 -0.37053
0.83191 -0.44386
0.79096 -0.44611
0.80985 -0.37650
0.77040 0.52371
0.65774 0.47826
0.58020 0.46189
0.63656 0.35255
""")
self.assertTrue(np.allclose(table, table_required, atol=1e-05))
self.assertTrue(np.allclose(L, L_required, atol=1e-05))
ff = lambda L=None, A=None, T=None: ff_target(H, L=L, A=A, T=T)
L2, phi, T2, table = GPA(A, ff=ff, rotation_method='orthogonal')
self.assertTrue(np.allclose(L, L2, atol=1e-05))
self.assertTrue(np.allclose(T, T2, atol=1e-05))
vgQ = lambda L=None, A=None, T=None: vgQ_target(
H, L=L, A=A, T=T, rotation_method='oblique')
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='oblique')
ff = lambda L=None, A=None, T=None: ff_target(
H, L=L, A=A, T=T, rotation_method='oblique')
L2, phi, T2, table = GPA(A, ff=ff, rotation_method='oblique')
self.assertTrue(np.allclose(L, L2, atol=1e-05))
self.assertTrue(np.allclose(T, T2, atol=1e-05))
def test_orthogonal_target(self):
"""
Rotation towards target matrix example
http://www.stat.ucla.edu/research/gpa
"""
A = self.str2matrix("""
.830 -.396
.818 -.469
.777 -.470
.798 -.401
.786 .500
.672 .458
.594 .444
.647 .333
""")
H = self.str2matrix("""
.8 -.3
.8 -.4
.7 -.4
.9 -.4
.8 .5
.6 .4
.5 .4
.6 .3
""")
vgQ = lambda L=None, A=None, T=None: vgQ_target(H, L=L, A=A, T=T)
L, phi, T, table = GPA(A, vgQ=vgQ, rotation_method='orthogonal')
T_analytic = target_rotation(A, H)
self.assertTrue(np.allclose(T, T_analytic, atol=1e-05))