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_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_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_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))