def test_rank_square(self):
#Ranks of square matrices
x = [[1.0, 2.0, 3.0, 4.0], [-5.0, -2.0, -1.0, 0.0]]
self.assertEqual(svd.rank(mmul(transpose(x), x)), 2)
x = [[1.0, 2.0, 3.0, 4.0]]
self.assertEqual(svd.rank(mmul(transpose(x), x)), 1)
x = [[1.0, 2.0, 3.0, 4.0], [1.0, 0.0, 0.0, 0.0],
[-5.0, -2.0, -1.0, 0.0]]
self.assertEqual(svd.rank(mmul(transpose(x), x)), 3)
def test_rank_square(self):
#Ranks of square matrices
x = [[1.0, 2.0, 3.0, 4.0],
[-5.0, -2.0, -1.0, 0.0]]
self.assertEqual( svd.rank( mmul( transpose(x), x) ),
2 )
x = [[1.0, 2.0, 3.0, 4.0] ]
self.assertEqual( svd.rank( mmul( transpose(x), x) ),
1 )
x = [[1.0, 2.0, 3.0, 4.0],
[1.0, 0.0,0.0,0.0],
[-5.0, -2.0, -1.0, 0.0]]
self.assertEqual( svd.rank( mmul( transpose(x), x) ),
3 )
def test_pinv_full_rank(self):
"""First check pinv on the matrices of full rank, when PINV is the same as INV"""
M = [[1.0, 2.0, 3.0, 4.0], [3.0, 5.0, -1.0, 0.0],
[2.0, -2.0, 1.0, 1.0], [-5.0, -2.0, -1.0, 0.0]]
self.assertEqual(svd.rank(M), 4) #Rank is full
#print (svd.svd(M)[1])
IM = svd.pinv(M)
#print (svd.svd(IM)[1])
IIM = svd.pinv(IM)
#print ("----")
#print (show_mat( mat_diff( M, IIM )))
#print (show_mat( mmul(M, IM) ) )
self.assertTrue(mat_eq(mmul(M, IM), eye(4), 1e-5)) #Inverse is right
self.assertTrue(mat_eq(M, IIM,
1e-5)) #double pinv is the same as original
def test_pinv_full_rank(self):
"""First check pinv on the matrices of full rank, when PINV is the same as INV"""
M = [[1.0, 2.0, 3.0, 4.0],
[3.0, 5.0, -1.0, 0.0],
[2.0, -2.0, 1.0, 1.0],
[-5.0, -2.0, -1.0, 0.0]]
self.assertEqual( svd.rank(M), 4 ) #Rank is full
#print (svd.svd(M)[1])
IM = svd.pinv(M)
#print (svd.svd(IM)[1])
IIM = svd.pinv(IM)
#print ("----")
#print (show_mat( mat_diff( M, IIM )))
#print (show_mat( mmul(M, IM) ) )
self.assertTrue( mat_eq( mmul(M, IM),
eye(4),
1e-5 ) ) #Inverse is right
self.assertTrue( mat_eq( M, IIM, 1e-5 ) ) #double pinv is the same as original