def test_full_both(self):
# contraction over both full
T = np.random.random((3, 4, 5))
U = np.random.random((3, 4, 5))
TU = np.tensordot(T, U, axes=([0, 1, 2], [0, 1, 2]))
T_tt = TT(np.reshape(T, (3, 4, 5, 1, 1, 1)))
U_tt = TT(np.reshape(U, (3, 4, 5, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# operator
T_tt = rand([2, 3, 4], [5, 6, 7], ranks=2)
U_tt = rand([2, 3, 4], [5, 6, 7], ranks=3)
T = T_tt.full()
U = U_tt.full()
TU = np.tensordot(T, U, axes=([0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5]))
T_tt.tensordot(U_tt, 3, overwrite=True)
TU_back = T_tt.full()
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
def test_exceptions(self):
T = np.random.random((2, 3, 4, 5))
U = np.random.random((5, 6, 7))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (5, 6, 7, 1, 1, 1)))
with self.assertRaises(ValueError):
T_tt.tensordot(U_tt, 1, mode='bla')
with self.assertRaises(ValueError):
T_tt.tensordot(U_tt, 1, mode='last-last')
with self.assertRaises(ValueError):
T_tt.tensordot(U_tt, 1, mode='firs-last')
with self.assertRaises(ValueError):
T_tt.tensordot(U_tt, 1, mode='first-first')
def simple_test_case():
# initialize random tensors
T = np.random.random((2, 3, 4, 5))
U = np.random.random((4, 5, 6))
# calculate tensordot using numpy
TU = np.tensordot(T, U, axes=([2, 3], [0, 1]))
# convert to TT format
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
print('T:')
print(T_tt)
U_tt = TT(np.reshape(U, (4, 5, 6, 1, 1, 1)))
print('\n\nU:')
print(U_tt)
# calculate tensordot in TT format
TU_back = T_tt.tensordot(U_tt, 2)
print('\n\ntensordot <T,U>:')
print(TU_back)
# convert back to full tensor format and compare the results
TU_back = np.squeeze(TU_back.full())
print('\n\nerror: {}'.format(np.linalg.norm(TU_back - TU)))
def test_1_axis(self):
# test contraction over 1 axis
# last-first contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((5, 6, 7))
TU = np.tensordot(T, U, axes=([3], [0]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (5, 6, 7, 1, 1, 1)))
TU_back = T_tt.tensordot(U_tt, 1)
TU_back = np.squeeze(TU_back.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-last contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((6, 7, 5))
TU = np.tensordot(T, U, axes=([3], [2]))
TU = np.transpose(TU, [0, 1, 2, 4, 3])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (6, 7, 5, 1, 1, 1)))
T_tt.tensordot(U_tt, 1, mode='last-last', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-last contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((6, 7, 2))
TU = np.tensordot(T, U, axes=([0], [2]))
TU = np.transpose(TU, [3, 4, 0, 1, 2])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (6, 7, 2, 1, 1, 1)))
T_tt.tensordot(U_tt, 1, mode='first-last', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-first contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((2, 6, 7))
TU = np.tensordot(T, U, axes=([0], [0]))
TU = np.transpose(TU, [4, 3, 0, 1, 2])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (2, 6, 7, 1, 1, 1)))
T_tt.tensordot(U_tt, 1, mode='first-first', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-first contraction for operator
T_tt = rand([2, 3, 4], [5, 6, 7], ranks=3)
U_tt = rand([4, 8, 9], [7, 8, 9], ranks=2)
T = T_tt.full()
U = U_tt.full()
TU = np.tensordot(T, U, axes=([2, 5], [0, 3]))
TU = np.transpose(TU, [0, 1, 4, 5, 2, 3, 6, 7])
T_tt.tensordot(U_tt, 1, overwrite=True)
TU_back = T_tt.full()
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
def test_full_other(self):
# contraction over full U
# last-first contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((3, 4, 5))
TU = np.tensordot(T, U, axes=([1, 2, 3], [0, 1, 2]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (3, 4, 5, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-last contraction
T = np.random.random((2, 3, 4, 5, 6))
U = np.random.random((4, 5, 6))
TU = np.tensordot(T, U, axes=([2, 3, 4], [0, 1, 2]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 6, 1, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (4, 5, 6, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, mode='last-last', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-last contraction
T = np.random.random((2, 3, 4, 5, 6))
U = np.random.random((2, 3, 4))
TU = np.tensordot(T, U, axes=([0, 1, 2], [0, 1, 2]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 6, 1, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (2, 3, 4, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, mode='first-last', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-first contraction
T = np.random.random((2, 3, 4, 5, 6))
U = np.random.random((2, 3, 4))
TU = np.tensordot(T, U, axes=([0, 1, 2], [0, 1, 2]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 6, 1, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (2, 3, 4, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, mode='first-first', overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-first contraction for operator
T_tt = rand([2, 3, 4, 5], [5, 6, 7, 8], ranks=2)
U_tt = rand([4, 5], [7, 8], ranks=3)
T = T_tt.full()
U = U_tt.full()
TU = np.tensordot(T, U, axes=([2, 3, 6, 7], [0, 1, 2, 3]))
T_tt.tensordot(U_tt, 2, overwrite=True)
TU_back = T_tt.full()
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
def test_multiple_axes(self):
# contraction over multiple axis
# last-first contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((3, 4, 5, 6, 7))
TU = np.tensordot(T, U, axes=([1, 2, 3], [0, 1, 2]))
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (3, 4, 5, 6, 7, 1, 1, 1, 1, 1)))
T_tt.tensordot(U_tt, 3, overwrite=True)
TU_back = np.squeeze(T_tt.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-last contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((6, 7, 4, 5))
TU = np.tensordot(T, U, axes=([2, 3], [2, 3]))
TU = np.transpose(TU, [0, 1, 3, 2])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (6, 7, 4, 5, 1, 1, 1, 1)))
TU_back = T_tt.tensordot(U_tt, 2, mode='last-last')
TU_back = np.squeeze(TU_back.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-last contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((6, 7, 2, 3))
TU = np.tensordot(T, U, axes=([0, 1], [2, 3]))
TU = np.transpose(TU, [2, 3, 0, 1])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (6, 7, 2, 3, 1, 1, 1, 1)))
TU_back = T_tt.tensordot(U_tt, 2, mode='first-last')
TU_back = np.squeeze(TU_back.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# first-first contraction
T = np.random.random((2, 3, 4, 5))
U = np.random.random((2, 3, 6, 7))
TU = np.tensordot(T, U, axes=([0, 1], [0, 1]))
TU = np.transpose(TU, [3, 2, 0, 1])
T_tt = TT(np.reshape(T, (2, 3, 4, 5, 1, 1, 1, 1)))
U_tt = TT(np.reshape(U, (2, 3, 6, 7, 1, 1, 1, 1)))
TU_back = T_tt.tensordot(U_tt, 2, mode='first-first')
TU_back = np.squeeze(TU_back.full())
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
# last-last contraction for operator
T_tt = rand([3, 4, 5], [6, 7, 8], ranks=3)
U_tt = rand([8, 9, 4, 5], [2, 3, 7, 8], ranks=2)
T = T_tt.full()
U = U_tt.full()
TU = np.tensordot(T, U, axes=([1, 2, 4, 5], [2, 3, 6, 7]))
TU = np.transpose(TU, [0, 3, 2, 1, 5, 4])
T_tt.tensordot(U_tt, 2, mode='last-last', overwrite=True)
TU_back = T_tt.full()
error = np.linalg.norm(TU_back - TU)
self.assertLess(error, self.tol)
