def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
# sample a random reversible CTMC rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
distn = mrate.R_to_distn(R)
spectrum = scipy.linalg.eigvalsh(mrate.symmetrized(R))
print >> out, "random reversible CTMC rate matrix:"
print >> out, R
print >> out
print >> out, "stationary distribution:"
print >> out, distn
print >> out
print >> out, "spectrum:"
print >> out, spectrum
print >> out
Q = aggregate(R)
distn = mrate.R_to_distn(Q)
spectrum = scipy.linalg.eigvalsh(mrate.symmetrized(Q))
print >> out, "aggregated rate matrix:"
print >> out, Q
print >> out
print >> out, "stationary distribution:"
print >> out, distn
print >> out
print >> out, "spectrum:"
print >> out, spectrum
print >> out
return out.getvalue()
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
t = fs.divtime
#h = fs.delta
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix
distn = mrate.R_to_distn(R)
spectrum = np.linalg.eigvalsh(mrate.symmetrized(R))
#spectrum, U = np.linalg.eigh(mrate.symmetrized(R))
#spectrum = np.linalg.eigvals(R)
# report some information about the mutual information curve
mi = ctmcmi.get_mutual_information(R, t)
mi_diff = ctmcmi.get_mutual_information_diff(R, t)
mi_diff_b = ctmcmi.get_mutual_information_diff_b(R, t)
mi_diff_c = ctmcmi.get_mutual_information_diff_c(R, t)
print >> out, 'arbitrary large-ish divergence time:'
print >> out, t
print >> out
print >> out, 'randomly sampled reversible rate matrix:'
print >> out, R
print >> out
print >> out, 'stationary distribution:'
print >> out, distn
print >> out
print >> out, 'spectrum of the rate matrix:'
print >> out, spectrum
print >> out
print >> out, 'mutual information at t = %f:' % t
print >> out, mi
print >> out
print >> out, 'mutual information at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.cute_MI_alternate(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_small_approx(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_b(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_d(R, t)
print >> out
print >> out, 'mutual information diff at t = %f:' % t
print >> out, mi_diff
print >> out
print >> out, 'mutual information diff at t = %f (ver. 2):' % t
print >> out, mi_diff_b
print >> out
print >> out, 'mutual information diff at t = %f (ver. 3):' % t
print >> out, mi_diff_c
print >> out
print >> out, 'large t approximation of MI diff at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 2)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 4)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_c(R, t)
print >> out
print >> out, 'log of mutual information at t = %f:' % t
print >> out, math.log(mi)
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of log of mutual information at t = %f:' % t
#print >> out, (math.log(mi_c) - math.log(mi_a)) / (2*h)
#print >> out
print >> out, 'estimated derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, mi_diff / mi
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(
R, t) / ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(
R, t) / ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'twice the relevant eigenvalue:'
print >> out, 2 * spectrum[-2]
print >> out
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of mutual information at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h)
#print >> out
#print >> out, '(estimated derivative of mutual information) /',
#print >> out, '(mutual information) at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h*mi_b)
#print >> out
return out.getvalue()
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix and its re-symmetrization
S = mrate.symmetrized(R)
distn = mrate.R_to_distn(R)
w, U = np.linalg.eigh(S)
D = np.diag(U.T[-1])**2
D_inv = np.diag(np.reciprocal(U.T[-1]))**2
for t in (1.0, 2.0):
P = scipy.linalg.expm(R*t)
M = ndot(D**.5, scipy.linalg.expm(S*t), D**.5)
M_star = ndot(D_inv**.5, scipy.linalg.expm(S*t), D_inv**.5)
M_star_log = np.log(M_star)
M_star_log_w, M_star_log_U = np.linalg.eigh(M_star_log)
E = M * np.log(M_star)
E_w, E_U = np.linalg.eigh(E)
print >> out, 't:'
print >> out, t
print >> out
print >> out, 'randomly sampled rate matrix R'
print >> out, R
print >> out
print >> out, 'symmetrized matrix S'
print >> out, S
print >> out
print >> out, 'stationary distribution diagonal D'
print >> out, D
print >> out
print >> out, 'R = D^-1/2 S D^1/2'
print >> out, ndot(D_inv**.5, S, D**.5)
print >> out
print >> out, 'probability matrix e^(R*t) = P'
print >> out, P
print >> out
print >> out, 'P = D^-1/2 e^(S*t) D^1/2'
print >> out, ndot(D_inv**.5, scipy.linalg.expm(S*t), D**.5)
print >> out
print >> out, 'pairwise distribution matrix M'
print >> out, 'M = D^1/2 e^(S*t) D^1/2'
print >> out, M
print >> out
print >> out, 'sum of entries of M'
print >> out, np.sum(M)
print >> out
print >> out, 'M_star = D^-1/2 e^(S*t) D^-1/2'
print >> out, M_star
print >> out
print >> out, 'entrywise logarithm logij(M_star)'
print >> out, np.log(M_star)
print >> out
print >> out, 'Hadamard product M o logij(M_star) = E'
print >> out, E
print >> out
print >> out, 'spectrum of M:'
print >> out, np.linalg.eigvalsh(M)
print >> out
print >> out, 'spectrum of logij(M_star):'
print >> out, M_star_log_w
print >> out
print >> out, 'corresponding eigenvectors of logij(M_star) as columns:'
print >> out, M_star_log_U
print >> out
print >> out, 'spectrum of E:'
print >> out, E_w
print >> out
print >> out, 'corresponding eigenvectors of E as columns:'
print >> out, E_U
print >> out
print >> out, 'entrywise square roots of stationary distribution:'
print >> out, np.sqrt(v)
print >> out
print >> out, 'sum of entries of E:'
print >> out, np.sum(E)
print >> out
print >> out, 'mutual information:'
print >> out, ctmcmi.get_mutual_information(R, t)
print >> out
print >> out
return out.getvalue()
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix and its re-symmetrization
S = mrate.symmetrized(R)
distn = mrate.R_to_distn(R)
w, U = np.linalg.eigh(S)
D = np.diag(U.T[-1])**2
D_inv = np.diag(np.reciprocal(U.T[-1]))**2
for t in (1.0, 2.0):
P = scipy.linalg.expm(R * t)
M = ndot(D**.5, scipy.linalg.expm(S * t), D**.5)
M_star = ndot(D_inv**.5, scipy.linalg.expm(S * t), D_inv**.5)
M_star_log = np.log(M_star)
M_star_log_w, M_star_log_U = np.linalg.eigh(M_star_log)
E = M * np.log(M_star)
E_w, E_U = np.linalg.eigh(E)
print >> out, 't:'
print >> out, t
print >> out
print >> out, 'randomly sampled rate matrix R'
print >> out, R
print >> out
print >> out, 'symmetrized matrix S'
print >> out, S
print >> out
print >> out, 'stationary distribution diagonal D'
print >> out, D
print >> out
print >> out, 'R = D^-1/2 S D^1/2'
print >> out, ndot(D_inv**.5, S, D**.5)
print >> out
print >> out, 'probability matrix e^(R*t) = P'
print >> out, P
print >> out
print >> out, 'P = D^-1/2 e^(S*t) D^1/2'
print >> out, ndot(D_inv**.5, scipy.linalg.expm(S * t), D**.5)
print >> out
print >> out, 'pairwise distribution matrix M'
print >> out, 'M = D^1/2 e^(S*t) D^1/2'
print >> out, M
print >> out
print >> out, 'sum of entries of M'
print >> out, np.sum(M)
print >> out
print >> out, 'M_star = D^-1/2 e^(S*t) D^-1/2'
print >> out, M_star
print >> out
print >> out, 'entrywise logarithm logij(M_star)'
print >> out, np.log(M_star)
print >> out
print >> out, 'Hadamard product M o logij(M_star) = E'
print >> out, E
print >> out
print >> out, 'spectrum of M:'
print >> out, np.linalg.eigvalsh(M)
print >> out
print >> out, 'spectrum of logij(M_star):'
print >> out, M_star_log_w
print >> out
print >> out, 'corresponding eigenvectors of logij(M_star) as columns:'
print >> out, M_star_log_U
print >> out
print >> out, 'spectrum of E:'
print >> out, E_w
print >> out
print >> out, 'corresponding eigenvectors of E as columns:'
print >> out, E_U
print >> out
print >> out, 'entrywise square roots of stationary distribution:'
print >> out, np.sqrt(v)
print >> out
print >> out, 'sum of entries of E:'
print >> out, np.sum(E)
print >> out
print >> out, 'mutual information:'
print >> out, ctmcmi.get_mutual_information(R, t)
print >> out
print >> out
return out.getvalue()
def get_response_content(fs):
out = StringIO()
np.set_printoptions(linewidth=200)
# get the user defined variables
n = fs.nstates
t = fs.divtime
#h = fs.delta
# sample a random rate matrix
v = divtime.sample_distribution(n)
S = divtime.sample_symmetric_rate_matrix(n)
R = mrate.to_gtr_halpern_bruno(S, v)
# get some properties of the rate matrix
distn = mrate.R_to_distn(R)
spectrum = np.linalg.eigvalsh(mrate.symmetrized(R))
#spectrum, U = np.linalg.eigh(mrate.symmetrized(R))
#spectrum = np.linalg.eigvals(R)
# report some information about the mutual information curve
mi = ctmcmi.get_mutual_information(R, t)
mi_diff = ctmcmi.get_mutual_information_diff(R, t)
mi_diff_b = ctmcmi.get_mutual_information_diff_b(R, t)
mi_diff_c = ctmcmi.get_mutual_information_diff_c(R, t)
print >> out, 'arbitrary large-ish divergence time:'
print >> out, t
print >> out
print >> out, 'randomly sampled reversible rate matrix:'
print >> out, R
print >> out
print >> out, 'stationary distribution:'
print >> out, distn
print >> out
print >> out, 'spectrum of the rate matrix:'
print >> out, spectrum
print >> out
print >> out, 'mutual information at t = %f:' % t
print >> out, mi
print >> out
print >> out, 'mutual information at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.cute_MI_alternate(R, t)
print >> out
print >> out, 'large t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_small_approx(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_b(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 3):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_c(R, t)
print >> out
print >> out, 'small t approximation of MI at t = %f (ver. 4):' % t
print >> out, ctmcmi.get_mutual_information_small_approx_d(R, t)
print >> out
print >> out, 'mutual information diff at t = %f:' % t
print >> out, mi_diff
print >> out
print >> out, 'mutual information diff at t = %f (ver. 2):' % t
print >> out, mi_diff_b
print >> out
print >> out, 'mutual information diff at t = %f (ver. 3):' % t
print >> out, mi_diff_c
print >> out
print >> out, 'large t approximation of MI diff at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 2)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R, t)
print >> out
print >> out, 'large t approximation of MI diff at t = %f: (ver. 4)' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_c(R, t)
print >> out
print >> out, 'log of mutual information at t = %f:' % t
print >> out, math.log(mi)
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of log of mutual information at t = %f:' % t
#print >> out, (math.log(mi_c) - math.log(mi_a)) / (2*h)
#print >> out
print >> out, 'estimated derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, mi_diff / mi
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f:' % t
print >> out, ctmcmi.get_mutual_information_diff_approx(R,
t) / ctmcmi.get_mutual_information_approx(R, t)
print >> out
print >> out, 'large t approximation of derivative of log of MI',
print >> out, 'at t = %f (ver. 2):' % t
print >> out, ctmcmi.get_mutual_information_diff_approx_b(R,
t) / ctmcmi.get_mutual_information_approx_b(R, t)
print >> out
print >> out, 'twice the relevant eigenvalue:'
print >> out, 2 * spectrum[-2]
print >> out
print >> out
#print >> out, 'estimated derivative',
#print >> out, 'of mutual information at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h)
#print >> out
#print >> out, '(estimated derivative of mutual information) /',
#print >> out, '(mutual information) at t = %f:' % t
#print >> out, (mi_c - mi_a) / (2*h*mi_b)
#print >> out
return out.getvalue()