def build_FI_trace_term():
cov_matrix = eqns2l.matrix_sigmadata(c1, koff, c2, koff2)
cov_matrix_inv = np.linalg.inv(cov_matrix)
dcov_dtheta_idx_dict = {0: build_dcov_dtheta_idx(0),
1: build_dcov_dtheta_idx(1),
2: build_dcov_dtheta_idx(2),
3: build_dcov_dtheta_idx(3)}
def compute_trace(n, m):
arr = np.linalg.multi_dot([cov_matrix_inv,
dcov_dtheta_idx_dict[n],
cov_matrix_inv,
dcov_dtheta_idx_dict[m]])
return np.trace(arr)
FI_trace_term = np.zeros((4, 4))
for n in range(4):
for m in range(4):
FI_trace_term[n, m] = 0.5 * compute_trace(n, m)
return FI_trace_term
def __sigmaEst__(c1, koff, c2, koff2, add_trace_term=True):
# eqns2l are the equations imported from Mathematica and turned into matrices (function of c1,c2,koff,koff2)
A = eqns2l.matrix_dmudthetaInv(c1, koff, c2, koff2)
B = eqns2l.matrix_sigmadata(c1, koff, c2, koff2)
Atrans = np.transpose(A)
def build_dcov_dtheta_idx(theta_idx):
label_data = {0: 'N1', 1: 'M1', 2: 'N2', 3: 'M2'}
label_theta = {0: 'c1', 1: 'koff', 2: 'c2', 3: 'koff2'}
def fetch_eqn(i, j):
if j > i:
method_to_call = getattr(eqns2l,
'Cov%s%sd%s' % (label_data[i], label_data[j], label_theta[theta_idx]))
else:
method_to_call = getattr(eqns2l,
'Cov%s%sd%s' % (label_data[j], label_data[i], label_theta[theta_idx]))
return method_to_call
dcov_dtheta_idx = np.zeros((4, 4))
for i in range(4):
for j in range(4):
dcov_dtheta_idx[i, j] = fetch_eqn(i, j)(c1, koff, c2, koff2)
return dcov_dtheta_idx
def build_FI_trace_term():
cov_matrix = eqns2l.matrix_sigmadata(c1, koff, c2, koff2)
cov_matrix_inv = np.linalg.inv(cov_matrix)
dcov_dtheta_idx_dict = {0: build_dcov_dtheta_idx(0),
1: build_dcov_dtheta_idx(1),
2: build_dcov_dtheta_idx(2),
3: build_dcov_dtheta_idx(3)}
def compute_trace(n, m):
arr = np.linalg.multi_dot([cov_matrix_inv,
dcov_dtheta_idx_dict[n],
cov_matrix_inv,
dcov_dtheta_idx_dict[m]])
return np.trace(arr)
FI_trace_term = np.zeros((4, 4))
for n in range(4):
for m in range(4):
FI_trace_term[n, m] = 0.5 * compute_trace(n, m)
return FI_trace_term
error_matrix = np.linalg.multi_dot([A, B, Atrans])
if add_trace_term:
# idea is to invert the matrix above, add the trace term, then invert the whole thing
FI_term_base = np.linalg.inv(error_matrix)
FI_term_trace = build_FI_trace_term()
FI_full = FI_term_base + FI_term_trace
error_matrix = np.linalg.inv(FI_full)
# use to make the entries relative estimates
rel = np.array([[c1 * c1, c1 * koff, c1 * c2, c1 * koff2], [koff * c1, koff * koff, koff * c2, koff * koff2],
[c2 * c1, c2 * koff, c2 * c2, c2 * koff2], [koff2 * c1, koff2 * koff, koff2 * c2, koff2 * koff2]])
relErrorMatrix = np.divide(error_matrix, rel)
return error_matrix, np.linalg.det(error_matrix), relErrorMatrix, np.linalg.det(error_matrix)/(c1**2 * c2**2 * koff**2 * koff2**2)
def __sigmaData__(c1, koff, c2, koff2):
""" Create the matrix from exported mathematica expressions """
return eqns2l.matrix_sigmadata(c1, koff, c2, koff2), np.linalg.det(eqns2l.matrix_sigmadata(c1, koff, c2, koff2))