def test_transition_matrices():
nspins = 11
n = 2**nspins
T_old = transition_matrix(n)
T_dense = transition_matrix2(n)
T_sparse = transition_matrix_sparse(n)
assert np.array_equal(T_old.todense(), T_dense)
assert np.array_equal(T_old.todense(), T_sparse.todense())
def test_dot_speed():
# Test suggests .dot has a modest speed advantage.
# 10000 runs: 276s/298s/252s spin-8 star/at/dot
E, V = np.linalg.eigh(H8_MATRIX)
Vcol = csc_matrix(V)
Vrow = csr_matrix(Vcol.T)
T = transition_matrix(2**8)
intensity_matrices = [
f(Vrow, T, Vcol, 1).todense() for f in [istar, iat, idot]
]
for i in range(2):
assert np.allclose(intensity_matrices[i], intensity_matrices[i + 1])
def simsignals(H, nspins):
"""
Calculates the eigensolution of the spin Hamiltonian H and, using it,
returns the allowed transitions as list of (frequency, intensity) tuples.
Parameters
---------
H : ndarray
the spin Hamiltonian.
nspins : int
the number of nuclei in the spin system.
Returns
-------
spectrum : [(float, float)...]
a list of (frequency, intensity) tuples.
"""
"""The original simsignals."""
# This routine was optimized for speed by vectorizing the intensity
# calculations, replacing a nested-for signal-by-signal calculation.
# Considering that hamiltonian was dramatically faster when refactored to
# use arrays instead of sparse matrices, consider an array refactor to this
# function as well.
# The eigensolution calculation apparently must be done on a dense matrix,
# because eig functions on sparse matrices can't return all answers?!
# Using eigh so that answers have only real components and no residual small
# unreal components b/c of rounding errors
E, V = np.linalg.eigh(H) # V will be eigenvectors, v will be frequencies
# 2019-04-27: the statement below may be wrong. May be entirely real already
# Eigh still leaves residual 0j terms, so:
V = np.asmatrix(V.real)
# Calculate signal intensities
Vcol = csc_matrix(V)
Vrow = csr_matrix(Vcol.T)
m = 2**nspins
T = transition_matrix(m)
I = Vrow * T * Vcol
I = np.square(I.todense())
spectrum = []
for i in range(m - 1):
for j in range(i + 1, m):
if I[i, j] > 0.01: # consider making this minimum intensity
# cutoff a function arg, for flexibility
v = abs(E[i] - E[j])
spectrum.append((v, I[i, j]))
return spectrum
def test_matrix_multiplication():
"""A sanity test that all three versions of matrix multiplication are
identical.
"""
E, V = np.linalg.eigh(H_RIOUX)
Vcol = csc_matrix(V)
Vrow = csr_matrix(Vcol.T)
T = transition_matrix(8)
Istar = Vrow * T * Vcol
Iat = Vrow @ T @ Vcol
Idot = Vrow.dot(T.dot(Vcol))
assert np.allclose(Istar.todense(), Iat.todense())
assert np.allclose(Istar.todense(), Idot.todense())
def new_simsignals(H, nspins):
"""Taking lessons from test results to create a faster simsignals
function.
"""
m = 2**nspins
E, V = np.linalg.eigh(H)
T = transition_matrix(m)
I = np.square(V.T.dot(T.dot(V)))
spectrum = []
for i in range(m - 1):
for j in range(i + 1, m):
if I[i, j] > 0.01: # consider making this minimum intensity
# cutoff a function arg, for flexibility
v = abs(E[i] - E[j])
spectrum.append((v, I[i, j]))
return spectrum
def test_new_matrix_simsignals():
# Testing with H11_MATRIX: dense is MUCH faster!
# e.g. 13.8 vs. 13.6 vs. 0.28 s original/norow/dense
# H11_NDARRAY 22.9 / 23.2 / 0.57 s
n = 1
nspins = 11
E, V = np.linalg.eigh(H11_NDARRAY)
T = transition_matrix(2**nspins)
test_functions = [
original_intensity_matrix, norow_intensity_matrix,
dense_intensity_matrix
]
intensity_matrices = []
intensity_matrices.append((original_intensity_matrix(V, T, n).todense()))
intensity_matrices.append((norow_intensity_matrix(V, T, n).todense()))
intensity_matrices.append(dense_intensity_matrix(V, T, n))
assert np.allclose(intensity_matrices[0], intensity_matrices[1])
assert np.allclose(intensity_matrices[1], intensity_matrices[2])
def test_tm():
t_old = transition_matrix(2**11)
t_new = cache_tm(2**11)
assert np.array_equal(t_old.todense(), t_new.todense())
def test_cache_tm():
T1 = transition_matrix(2**3)
T2 = cache_tm(2**3)
assert np.array_equal(T1.todense(), T2.todense())