def run(self, processor=None, memo=None):
"""Disassemble the model-free optimisation results (on the master).
@param processor: Unused!
@type processor: None
@param memo: The dispersion memo. This holds a lot of the data and objects needed for processing the results from the slave.
@type memo: memo
"""
# Scaling.
if memo.scaling_matrix != None:
param_vector = dot(memo.scaling_matrix, self.param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spins=memo.spins, sim_index=memo.sim_index)
param_conversion(spins=memo.spins, sim_index=memo.sim_index)
# Monte Carlo minimisation statistics.
if memo.sim_index != None:
for spin in memo.spins:
# Chi-squared statistic.
spin.chi2_sim[memo.sim_index] = self.chi2
# Iterations.
spin.iter_sim[memo.sim_index] = self.iter_count
# Function evaluations.
spin.f_count_sim[memo.sim_index] = self.f_count
# Gradient evaluations.
spin.g_count_sim[memo.sim_index] = self.g_count
# Hessian evaluations.
spin.h_count_sim[memo.sim_index] = self.h_count
# Warning.
spin.warning_sim[memo.sim_index] = self.warning
# Normal statistics.
else:
for spin in memo.spins:
# Chi-squared statistic.
spin.chi2 = self.chi2
# Iterations.
spin.iter = self.iter_count
# Function evaluations.
spin.f_count = self.f_count
# Gradient evaluations.
spin.g_count = self.g_count
# Hessian evaluations.
spin.h_count = self.h_count
# Warning.
spin.warning = self.warning
# Store the back-calculated values.
if memo.sim_index == None:
# 1H MMQ flag.
proton_mmq_flag = has_proton_mmq_cpmg()
# Loop over each spin, packing the data.
for si in range(len(memo.spins)):
pack_back_calc_r2eff(spin=memo.spins[si], spin_id=memo.spin_ids[si], si=si, back_calc=self.back_calc, proton_mmq_flag=proton_mmq_flag)
def minimise_r2eff(spins=None, spin_ids=None, min_algor=None, min_options=None, func_tol=None, grad_tol=None, max_iterations=None, constraints=False, scaling_matrix=None, verbosity=0, sim_index=None, lower=None, upper=None, inc=None):
"""Optimise the R2eff model by fitting the 2-parameter exponential curves.
This mimics the R1 and R2 relax_fit analysis.
@keyword spins: The list of spins for the cluster.
@type spins: list of SpinContainer instances
@keyword spin_ids: The list of spin IDs for the cluster.
@type spin_ids: list of str
@keyword min_algor: The minimisation algorithm to use.
@type min_algor: str
@keyword min_options: An array of options to be used by the minimisation algorithm.
@type min_options: array of str
@keyword func_tol: The function tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type func_tol: None or float
@keyword grad_tol: The gradient tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type grad_tol: None or float
@keyword max_iterations: The maximum number of iterations for the algorithm.
@type max_iterations: int
@keyword constraints: If True, constraints are used during optimisation.
@type constraints: bool
@keyword scaling_matrix: The diagonal and square scaling matrix.
@type scaling_matrix: numpy rank-2, float64 array or None
@keyword verbosity: The amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
@keyword sim_index: The index of the simulation to optimise. This should be None if normal optimisation is desired.
@type sim_index: None or int
@keyword lower: The model specific lower bounds of the grid search which must be equal to the number of parameters in the model. This optional argument is only used when doing a grid search.
@type lower: list of numbers
@keyword upper: The model specific upper bounds of the grid search which must be equal to the number of parameters in the model. This optional argument is only used when doing a grid search.
@type upper: list of numbers
@keyword inc: The model specific increments for each dimension of the space for the grid search. The number of elements in the array must equal to the number of parameters in the model. This argument is only used when doing a grid search.
@type inc: list of int
"""
# Check that the C modules have been compiled.
if not C_module_exp_fn:
raise RelaxError("Relaxation curve fitting is not available. Try compiling the C modules on your platform.")
# Loop over the spins.
for si in range(len(spins)):
# Skip deselected spins.
if not spins[si].select:
continue
# Loop over each spectrometer frequency and dispersion point.
for exp_type, frq, offset, point in loop_exp_frq_offset_point():
# The parameter key.
param_key = return_param_key_from_data(exp_type=exp_type, frq=frq, offset=offset, point=point)
# The initial parameter vector.
param_vector = assemble_param_vector(spins=[spins[si]], key=param_key, sim_index=sim_index)
# Diagonal scaling.
if scaling_matrix is not None:
param_vector = dot(inv(scaling_matrix), param_vector)
# Linear constraints.
A, b = None, None
if constraints:
A, b = linear_constraints(spins=[spins[si]], scaling_matrix=scaling_matrix)
# Print out.
if verbosity >= 1:
# Individual spin section.
top = 2
if verbosity >= 2:
top += 2
text = "Fitting to spin %s, frequency %s and dispersion point %s" % (spin_ids[si], frq, point)
subsection(file=sys.stdout, text=text, prespace=top)
# Grid search printout.
if match('^[Gg]rid', min_algor):
result = 1
for x in inc:
result = mul(result, x)
print("Unconstrained grid search size: %s (constraints may decrease this size).\n" % result)
# The peak intensities, errors and times.
values = []
errors = []
times = []
for time in loop_time(exp_type=exp_type, frq=frq, offset=offset, point=point):
values.append(average_intensity(spin=spins[si], exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, sim_index=sim_index))
errors.append(average_intensity(spin=spins[si], exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, error=True))
times.append(time)
# Raise errors if number of time points is less than 2.
if len(times) < 3:
subsection(file=sys.stdout, text="Exponential curve fitting error for point:", prespace=2)
point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (exp_type, frq/1E6, offset, point, len(times))
print(point_info)
raise RelaxError("The data setup points to exponential curve fitting, but only %i time points was found, where 3 time points is minimum. If calculating R2eff values for fixed relaxation time period data, check that a reference intensity has been specified for each offset value."%(len(times)))
# The scaling matrix in a diagonalised list form.
scaling_list = []
if scaling_matrix is None:
for i in range(len(param_vector)):
scaling_list.append(1.0)
else:
for i in range(len(scaling_matrix)):
scaling_list.append(scaling_matrix[i, i])
# Initialise the function to minimise.
model = Relax_fit_opt(model='exp', num_params=len(param_vector), values=values, errors=errors, relax_times=times, scaling_matrix=scaling_list)
# Grid search.
if search('^[Gg]rid', min_algor):
results = grid(func=model.func, args=(), num_incs=inc, lower=lower, upper=upper, A=A, b=b, verbosity=verbosity)
# Unpack the results.
param_vector, chi2, iter_count, warning = results
f_count = iter_count
g_count = 0.0
h_count = 0.0
# Minimisation.
else:
results = generic_minimise(func=model.func, dfunc=model.dfunc, d2func=model.d2func, args=(), x0=param_vector, min_algor=min_algor, min_options=min_options, func_tol=func_tol, grad_tol=grad_tol, maxiter=max_iterations, A=A, b=b, full_output=True, print_flag=verbosity)
# Unpack the results.
if results == None:
return
param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results
# Scaling.
if scaling_matrix is not None:
param_vector = dot(scaling_matrix, param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spins=[spins[si]], key=param_key, sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
spins[si].chi2_sim[sim_index] = chi2
# Iterations.
spins[si].iter_sim[sim_index] = iter_count
# Function evaluations.
spins[si].f_count_sim[sim_index] = f_count
# Gradient evaluations.
spins[si].g_count_sim[sim_index] = g_count
# Hessian evaluations.
spins[si].h_count_sim[sim_index] = h_count
# Warning.
spins[si].warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
spins[si].chi2 = chi2
# Iterations.
spins[si].iter = iter_count
# Function evaluations.
spins[si].f_count = f_count
# Gradient evaluations.
spins[si].g_count = g_count
# Hessian evaluations.
spins[si].h_count = h_count
# Warning.
spins[si].warning = warning
def run(self, processor=None, memo=None):
"""Disassemble the model-free optimisation results (on the master).
@param processor: Unused!
@type processor: None
@param memo: The dispersion memo. This holds a lot of the data and objects needed for processing the results from the slave.
@type memo: memo
"""
# Printout.
if memo.sim_index != None:
print("Simulation %s, cluster %s" % (memo.sim_index+1, memo.spin_ids))
# Scaling.
if memo.scaling_matrix is not None:
param_vector = dot(memo.scaling_matrix, self.param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spins=memo.spins, sim_index=memo.sim_index)
param_conversion(spins=memo.spins, sim_index=memo.sim_index)
# Monte Carlo minimisation statistics.
if memo.sim_index != None:
for spin in memo.spins:
# Skip deselected spins.
if not spin.select:
continue
# Chi-squared statistic.
spin.chi2_sim[memo.sim_index] = self.chi2
# Iterations.
spin.iter_sim[memo.sim_index] = self.iter_count
# Function evaluations.
spin.f_count_sim[memo.sim_index] = self.f_count
# Gradient evaluations.
spin.g_count_sim[memo.sim_index] = self.g_count
# Hessian evaluations.
spin.h_count_sim[memo.sim_index] = self.h_count
# Warning.
spin.warning_sim[memo.sim_index] = self.warning
# Normal statistics.
else:
for spin in memo.spins:
# Skip deselected spins.
if not spin.select:
continue
# Chi-squared statistic.
spin.chi2 = self.chi2
# Iterations.
spin.iter = self.iter_count
# Function evaluations.
spin.f_count = self.f_count
# Gradient evaluations.
spin.g_count = self.g_count
# Hessian evaluations.
spin.h_count = self.h_count
# Warning.
spin.warning = self.warning
# Store the back-calculated values.
if memo.sim_index == None:
# 1H MMQ flag.
proton_mmq_flag = has_proton_mmq_cpmg()
# Loop over each spin, packing the data.
si = 0
for spin_index in range(len(memo.spins)):
# Skip deselected spins.
if not memo.spins[spin_index].select:
continue
# Pack the data.
pack_back_calc_r2eff(spin=memo.spins[spin_index], spin_id=memo.spin_ids[spin_index], si=si, back_calc=self.back_calc, proton_mmq_flag=proton_mmq_flag)
# Increment the spin index.
si += 1
def minimise_r2eff(spins=None, spin_ids=None, min_algor=None, min_options=None, func_tol=None, grad_tol=None, max_iterations=None, constraints=False, scaling_matrix=None, verbosity=0, sim_index=None, lower=None, upper=None, inc=None):
"""Optimise the R2eff model by fitting the 2-parameter exponential curves.
This mimics the R1 and R2 relax_fit analysis.
@keyword spins: The list of spins for the cluster.
@type spins: list of SpinContainer instances
@keyword spin_ids: The list of spin IDs for the cluster.
@type spin_ids: list of str
@keyword min_algor: The minimisation algorithm to use.
@type min_algor: str
@keyword min_options: An array of options to be used by the minimisation algorithm.
@type min_options: array of str
@keyword func_tol: The function tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type func_tol: None or float
@keyword grad_tol: The gradient tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type grad_tol: None or float
@keyword max_iterations: The maximum number of iterations for the algorithm.
@type max_iterations: int
@keyword constraints: If True, constraints are used during optimisation.
@type constraints: bool
@keyword scaling_matrix: The diagonal and square scaling matrix.
@type scaling_matrix: numpy rank-2, float64 array or None
@keyword verbosity: The amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
@keyword sim_index: The index of the simulation to optimise. This should be None if normal optimisation is desired.
@type sim_index: None or int
@keyword lower: The model specific lower bounds of the grid search which must be equal to the number of parameters in the model. This optional argument is only used when doing a grid search.
@type lower: list of numbers
@keyword upper: The model specific upper bounds of the grid search which must be equal to the number of parameters in the model. This optional argument is only used when doing a grid search.
@type upper: list of numbers
@keyword inc: The model specific increments for each dimension of the space for the grid search. The number of elements in the array must equal to the number of parameters in the model. This argument is only used when doing a grid search.
@type inc: list of int
"""
# Check that the C modules have been compiled.
if not C_module_exp_fn:
raise RelaxError("Relaxation curve fitting is not available. Try compiling the C modules on your platform.")
# Loop over the spins.
for si in range(len(spins)):
# Skip deselected spins.
if not spins[si].select:
continue
# Loop over each spectrometer frequency and dispersion point.
for exp_type, frq, offset, point in loop_exp_frq_offset_point():
# The parameter key.
param_key = return_param_key_from_data(exp_type=exp_type, frq=frq, offset=offset, point=point)
# The initial parameter vector.
param_vector = assemble_param_vector(spins=[spins[si]], key=param_key, sim_index=sim_index)
# Diagonal scaling.
if scaling_matrix is not None:
param_vector = dot(inv(scaling_matrix), param_vector)
# Linear constraints.
A, b = None, None
if constraints:
A, b = linear_constraints(spins=[spins[si]], scaling_matrix=scaling_matrix)
# Print out.
if verbosity >= 1:
# Individual spin section.
top = 2
if verbosity >= 2:
top += 2
text = "Fitting to spin %s, frequency %s and dispersion point %s" % (spin_ids[si], frq, point)
subsection(file=sys.stdout, text=text, prespace=top)
# Grid search printout.
if match('^[Gg]rid', min_algor):
result = 1
for x in inc:
result = mul(result, x)
print("Unconstrained grid search size: %s (constraints may decrease this size).\n" % result)
# The peak intensities, errors and times.
values = []
errors = []
times = []
data_flag = True
for time in loop_time(exp_type=exp_type, frq=frq, offset=offset, point=point):
# Check the peak intensity keys.
int_keys = find_intensity_keys(exp_type=exp_type, frq=frq, offset=offset, point=point, time=time)
peak_intensities = spins[si].peak_intensity
if sim_index != None:
peak_intensities = spins[si].peak_intensity_sim
for i in range(len(int_keys)):
if int_keys[i] not in peak_intensities:
if verbosity:
warn(RelaxWarning("The spin %s peak intensity key '%s' is not present, skipping the optimisation." % (spin_ids[si], int_keys[i])))
data_flag = False
break
if data_flag:
values.append(average_intensity(spin=spins[si], exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, sim_index=sim_index))
errors.append(average_intensity(spin=spins[si], exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, error=True))
times.append(time)
if not data_flag:
continue
# Raise errors if number of time points is less than 2.
if len(times) < 3:
subsection(file=sys.stdout, text="Exponential curve fitting error for point:", prespace=2)
point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (exp_type, frq/1E6, offset, point, len(times))
raise RelaxError("The data setup points to exponential curve fitting, but only %i time points was found, where 3 time points is minimum. If calculating R2eff values for fixed relaxation time period data, check that a reference intensity has been specified for each offset value."%(len(times)))
# The scaling matrix in a diagonalised list form.
scaling_list = []
if scaling_matrix is None:
for i in range(len(param_vector)):
scaling_list.append(1.0)
else:
for i in range(len(scaling_matrix)):
scaling_list.append(scaling_matrix[i, i])
# Initialise the function to minimise.
model = Relax_fit_opt(model='exp', num_params=len(param_vector), values=values, errors=errors, relax_times=times, scaling_matrix=scaling_list)
# Grid search.
if search('^[Gg]rid', min_algor):
results = grid(func=model.func, args=(), num_incs=inc, lower=lower, upper=upper, A=A, b=b, verbosity=verbosity)
# Unpack the results.
param_vector, chi2, iter_count, warning = results
f_count = iter_count
g_count = 0.0
h_count = 0.0
# Minimisation.
else:
results = generic_minimise(func=model.func, dfunc=model.dfunc, d2func=model.d2func, args=(), x0=param_vector, min_algor=min_algor, min_options=min_options, func_tol=func_tol, grad_tol=grad_tol, maxiter=max_iterations, A=A, b=b, full_output=True, print_flag=verbosity)
# Unpack the results.
if results == None:
return
param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results
# Scaling.
if scaling_matrix is not None:
param_vector = dot(scaling_matrix, param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spins=[spins[si]], key=param_key, sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
spins[si].chi2_sim[sim_index] = chi2
# Iterations.
spins[si].iter_sim[sim_index] = iter_count
# Function evaluations.
spins[si].f_count_sim[sim_index] = f_count
# Gradient evaluations.
spins[si].g_count_sim[sim_index] = g_count
# Hessian evaluations.
spins[si].h_count_sim[sim_index] = h_count
# Warning.
spins[si].warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
spins[si].chi2 = chi2
# Iterations.
spins[si].iter = iter_count
# Function evaluations.
spins[si].f_count = f_count
# Gradient evaluations.
spins[si].g_count = g_count
# Hessian evaluations.
spins[si].h_count = h_count
# Warning.
spins[si].warning = warning
def estimate_r2eff(method='minfx',
min_algor='simplex',
c_code=True,
constraints=False,
chi2_jacobian=False,
spin_id=None,
ftol=1e-15,
xtol=1e-15,
maxfev=10000000,
factor=100.0,
verbosity=1):
"""Estimate r2eff and errors by exponential curve fitting with scipy.optimize.leastsq or minfx.
THIS IS ONLY FOR TESTING.
scipy.optimize.leastsq is a wrapper around MINPACK's lmdif and lmder algorithms.
MINPACK is a FORTRAN90 library which solves systems of nonlinear equations, or carries out the least squares minimization of the residual of a set of linear or nonlinear equations.
Errors are calculated by taking the square root of the reported co-variance.
This can be an huge time saving step, when performing model fitting in R1rho.
Errors of R2eff values, are normally estimated by time-consuming Monte-Carlo simulations.
Initial guess for the starting parameter x0 = [r2eff_est, i0_est], is by converting the exponential curve to a linear problem.
Then solving initial guess by linear least squares of: ln(Intensity[j]) = ln(i0) - time[j]* r2eff.
@keyword method: The method to minimise and estimate errors. Options are: 'minfx' or 'scipy.optimize.leastsq'.
@type method: string
@keyword min_algor: The minimisation algorithm
@type min_algor: string
@keyword c_code: If optimise with C code.
@type c_code: bool
@keyword constraints: If constraints should be used.
@type constraints: bool
@keyword chi2_jacobian: If the chi2 Jacobian should be used.
@type chi2_jacobian: bool
@keyword spin_id: The spin identification string.
@type spin_id: str
@keyword ftol: The function tolerance for the relative error desired in the sum of squares, parsed to leastsq.
@type ftol: float
@keyword xtol: The error tolerance for the relative error desired in the approximate solution, parsed to leastsq.
@type xtol: float
@keyword maxfev: The maximum number of function evaluations, parsed to leastsq. If zero, then 100*(N+1) is the maximum function calls. N is the number of elements in x0=[r2eff, i0].
@type maxfev: int
@keyword factor: The initial step bound, parsed to leastsq. It determines the initial step bound (''factor * || diag * x||''). Should be in the interval (0.1, 100).
@type factor: float
@keyword verbosity: The amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
"""
# Perform checks.
check_model_type(model=MODEL_R2EFF)
# Check that the C modules have been compiled.
if not C_module_exp_fn and method == 'minfx':
raise RelaxError(
"Relaxation curve fitting is not available. Try compiling the C modules on your platform."
)
# Set class scipy setting.
E = Exp(verbosity=verbosity)
E.set_settings_leastsq(ftol=ftol, xtol=xtol, maxfev=maxfev, factor=factor)
# Check if intensity errors have already been calculated by the user.
precalc = True
for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(
selection=spin_id, full_info=True, return_id=True,
skip_desel=True):
# No structure.
if not hasattr(cur_spin, 'peak_intensity_err'):
precalc = False
break
# Determine if a spectrum ID is missing from the list.
for id in cdp.spectrum_ids:
if id not in cur_spin.peak_intensity_err:
precalc = False
break
# Loop over the spins.
for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(
selection=spin_id, full_info=True, return_id=True,
skip_desel=True):
# Generate spin string.
spin_string = generate_spin_string(spin=cur_spin,
mol_name=mol_name,
res_num=resi,
res_name=resn)
# Print information.
if E.verbosity >= 1:
# Individual spin block section.
top = 2
if E.verbosity >= 2:
top += 2
subsection(file=sys.stdout,
text="Fitting with %s to: %s" % (method, spin_string),
prespace=top)
if method == 'minfx':
subsection(
file=sys.stdout,
text=
"min_algor='%s', c_code=%s, constraints=%s, chi2_jacobian?=%s"
% (min_algor, c_code, constraints, chi2_jacobian),
prespace=0)
# Loop over each spectrometer frequency and dispersion point.
for exp_type, frq, offset, point, ei, mi, oi, di in loop_exp_frq_offset_point(
return_indices=True):
# The parameter key.
param_key = return_param_key_from_data(exp_type=exp_type,
frq=frq,
offset=offset,
point=point)
# The peak intensities, errors and times.
values = []
errors = []
times = []
for time in loop_time(exp_type=exp_type,
frq=frq,
offset=offset,
point=point):
values.append(
average_intensity(spin=cur_spin,
exp_type=exp_type,
frq=frq,
offset=offset,
point=point,
time=time))
errors.append(
average_intensity(spin=cur_spin,
exp_type=exp_type,
frq=frq,
offset=offset,
point=point,
time=time,
error=True))
times.append(time)
# Convert to numpy array.
values = asarray(values)
errors = asarray(errors)
times = asarray(times)
# Initialise data.
E.setup_data(values=values, errors=errors, times=times)
# Get the result based on method.
if method == 'scipy.optimize.leastsq':
# Acquire results.
results = minimise_leastsq(E=E)
elif method == 'minfx':
# Set settings.
E.set_settings_minfx(min_algor=min_algor,
c_code=c_code,
chi2_jacobian=chi2_jacobian,
constraints=constraints)
# Acquire results.
results = minimise_minfx(E=E)
else:
raise RelaxError(
"Method for minimisation not known. Try setting: method='scipy.optimize.leastsq'."
)
# Unpack results
param_vector, param_vector_error, chi2, iter_count, f_count, g_count, h_count, warning = results
# Extract values.
r2eff = param_vector[0]
i0 = param_vector[1]
r2eff_err = param_vector_error[0]
i0_err = param_vector_error[1]
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector,
spins=[cur_spin],
key=param_key)
# Errors.
if not hasattr(cur_spin, 'r2eff_err'):
setattr(cur_spin, 'r2eff_err',
deepcopy(getattr(cur_spin, 'r2eff')))
if not hasattr(cur_spin, 'i0_err'):
setattr(cur_spin, 'i0_err', deepcopy(getattr(cur_spin, 'i0')))
# Set error.
cur_spin.r2eff_err[param_key] = r2eff_err
cur_spin.i0_err[param_key] = i0_err
# Chi-squared statistic.
cur_spin.chi2 = chi2
# Iterations.
cur_spin.f_count = f_count
# Warning.
cur_spin.warning = warning
# Print information.
print_strings = []
if E.verbosity >= 1:
# Add print strings.
point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (
exp_type, frq / 1E6, offset, point, len(times))
print_strings.append(point_info)
par_info = "r2eff=%3.3f r2eff_err=%3.4f, i0=%6.1f, i0_err=%3.4f, chi2=%3.3f.\n" % (
r2eff, r2eff_err, i0, i0_err, chi2)
print_strings.append(par_info)
if E.verbosity >= 2:
time_info = ', '.join(map(str, times))
print_strings.append('For time array: ' + time_info +
'.\n\n')
# Print info
if len(print_strings) > 0:
for print_string in print_strings:
print(print_string),
def estimate_r2eff(method='minfx', min_algor='simplex', c_code=True, constraints=False, chi2_jacobian=False, spin_id=None, ftol=1e-15, xtol=1e-15, maxfev=10000000, factor=100.0, verbosity=1):
"""Estimate r2eff and errors by exponential curve fitting with scipy.optimize.leastsq or minfx.
THIS IS ONLY FOR TESTING.
scipy.optimize.leastsq is a wrapper around MINPACK's lmdif and lmder algorithms.
MINPACK is a FORTRAN90 library which solves systems of nonlinear equations, or carries out the least squares minimization of the residual of a set of linear or nonlinear equations.
Errors are calculated by taking the square root of the reported co-variance.
This can be an huge time saving step, when performing model fitting in R1rho.
Errors of R2eff values, are normally estimated by time-consuming Monte-Carlo simulations.
Initial guess for the starting parameter x0 = [r2eff_est, i0_est], is by converting the exponential curve to a linear problem.
Then solving initial guess by linear least squares of: ln(Intensity[j]) = ln(i0) - time[j]* r2eff.
@keyword method: The method to minimise and estimate errors. Options are: 'minfx' or 'scipy.optimize.leastsq'.
@type method: string
@keyword min_algor: The minimisation algorithm
@type min_algor: string
@keyword c_code: If optimise with C code.
@type c_code: bool
@keyword constraints: If constraints should be used.
@type constraints: bool
@keyword chi2_jacobian: If the chi2 Jacobian should be used.
@type chi2_jacobian: bool
@keyword spin_id: The spin identification string.
@type spin_id: str
@keyword ftol: The function tolerance for the relative error desired in the sum of squares, parsed to leastsq.
@type ftol: float
@keyword xtol: The error tolerance for the relative error desired in the approximate solution, parsed to leastsq.
@type xtol: float
@keyword maxfev: The maximum number of function evaluations, parsed to leastsq. If zero, then 100*(N+1) is the maximum function calls. N is the number of elements in x0=[r2eff, i0].
@type maxfev: int
@keyword factor: The initial step bound, parsed to leastsq. It determines the initial step bound (''factor * || diag * x||''). Should be in the interval (0.1, 100).
@type factor: float
@keyword verbosity: The amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
"""
# Perform checks.
check_model_type(model=MODEL_R2EFF)
# Check that the C modules have been compiled.
if not C_module_exp_fn and method == 'minfx':
raise RelaxError("Relaxation curve fitting is not available. Try compiling the C modules on your platform.")
# Set class scipy setting.
E = Exp(verbosity=verbosity)
E.set_settings_leastsq(ftol=ftol, xtol=xtol, maxfev=maxfev, factor=factor)
# Check if intensity errors have already been calculated by the user.
precalc = True
for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(selection=spin_id, full_info=True, return_id=True, skip_desel=True):
# No structure.
if not hasattr(cur_spin, 'peak_intensity_err'):
precalc = False
break
# Determine if a spectrum ID is missing from the list.
for id in cdp.spectrum_ids:
if id not in cur_spin.peak_intensity_err:
precalc = False
break
# Loop over the spins.
for cur_spin, mol_name, resi, resn, cur_spin_id in spin_loop(selection=spin_id, full_info=True, return_id=True, skip_desel=True):
# Generate spin string.
spin_string = generate_spin_string(spin=cur_spin, mol_name=mol_name, res_num=resi, res_name=resn)
# Print information.
if E.verbosity >= 1:
# Individual spin block section.
top = 2
if E.verbosity >= 2:
top += 2
subsection(file=sys.stdout, text="Fitting with %s to: %s"%(method, spin_string), prespace=top)
if method == 'minfx':
subsection(file=sys.stdout, text="min_algor='%s', c_code=%s, constraints=%s, chi2_jacobian?=%s"%(min_algor, c_code, constraints, chi2_jacobian), prespace=0)
# Loop over each spectrometer frequency and dispersion point.
for exp_type, frq, offset, point, ei, mi, oi, di in loop_exp_frq_offset_point(return_indices=True):
# The parameter key.
param_key = return_param_key_from_data(exp_type=exp_type, frq=frq, offset=offset, point=point)
# The peak intensities, errors and times.
values = []
errors = []
times = []
for time in loop_time(exp_type=exp_type, frq=frq, offset=offset, point=point):
values.append(average_intensity(spin=cur_spin, exp_type=exp_type, frq=frq, offset=offset, point=point, time=time))
errors.append(average_intensity(spin=cur_spin, exp_type=exp_type, frq=frq, offset=offset, point=point, time=time, error=True))
times.append(time)
# Convert to numpy array.
values = asarray(values)
errors = asarray(errors)
times = asarray(times)
# Initialise data.
E.setup_data(values=values, errors=errors, times=times)
# Get the result based on method.
if method == 'scipy.optimize.leastsq':
# Acquire results.
results = minimise_leastsq(E=E)
elif method == 'minfx':
# Set settings.
E.set_settings_minfx(min_algor=min_algor, c_code=c_code, chi2_jacobian=chi2_jacobian, constraints=constraints)
# Acquire results.
results = minimise_minfx(E=E)
else:
raise RelaxError("Method for minimisation not known. Try setting: method='scipy.optimize.leastsq'.")
# Unpack results
param_vector, param_vector_error, chi2, iter_count, f_count, g_count, h_count, warning = results
# Extract values.
r2eff = param_vector[0]
i0 = param_vector[1]
r2eff_err = param_vector_error[0]
i0_err = param_vector_error[1]
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spins=[cur_spin], key=param_key)
# Errors.
if not hasattr(cur_spin, 'r2eff_err'):
setattr(cur_spin, 'r2eff_err', deepcopy(getattr(cur_spin, 'r2eff')))
if not hasattr(cur_spin, 'i0_err'):
setattr(cur_spin, 'i0_err', deepcopy(getattr(cur_spin, 'i0')))
# Set error.
cur_spin.r2eff_err[param_key] = r2eff_err
cur_spin.i0_err[param_key] = i0_err
# Chi-squared statistic.
cur_spin.chi2 = chi2
# Iterations.
cur_spin.f_count = f_count
# Warning.
cur_spin.warning = warning
# Print information.
print_strings = []
if E.verbosity >= 1:
# Add print strings.
point_info = "%s at %3.1f MHz, for offset=%3.3f ppm and dispersion point %-5.1f, with %i time points." % (exp_type, frq/1E6, offset, point, len(times))
print_strings.append(point_info)
par_info = "r2eff=%3.3f r2eff_err=%3.4f, i0=%6.1f, i0_err=%3.4f, chi2=%3.3f.\n" % ( r2eff, r2eff_err, i0, i0_err, chi2)
print_strings.append(par_info)
if E.verbosity >= 2:
time_info = ', '.join(map(str, times))
print_strings.append('For time array: '+time_info+'.\n\n')
# Print info
if len(print_strings) > 0:
for print_string in print_strings:
print(print_string),
