def optimise(self):
"""Model-free grid search.
@return: The optimisation results consisting of the parameter vector, function value, iteration count, function count, gradient count, Hessian count, and warnings.
@rtype: tuple of numpy array, float, int, int, int, int, str
"""
# Normal grid search.
if not hasattr(self.opt_params, 'subdivision'):
results = grid(func=self.mf.func,
args=(),
num_incs=self.opt_params.inc,
lower=self.opt_params.lower,
upper=self.opt_params.upper,
A=self.opt_params.A,
b=self.opt_params.b,
verbosity=self.opt_params.verbosity)
# Subdivided grid.
else:
results = grid_point_array(func=self.mf.func,
args=(),
points=self.opt_params.subdivision,
verbosity=self.opt_params.verbosity)
# Unpack the results.
param_vector, func, iter, warning = results
fc = iter
gc = 0.0
hc = 0.0
# Return everything.
return param_vector, func, iter, fc, gc, hc, warning
def optimise(self):
"""Model-free grid search.
@return: The optimisation results consisting of the parameter vector, function value, iteration count, function count, gradient count, Hessian count, and warnings.
@rtype: tuple of numpy array, float, int, int, int, int, str
"""
# Normal grid search.
if not hasattr(self.opt_params, "subdivision"):
results = grid(
func=self.mf.func,
args=(),
num_incs=self.opt_params.inc,
lower=self.opt_params.lower,
upper=self.opt_params.upper,
A=self.opt_params.A,
b=self.opt_params.b,
verbosity=self.opt_params.verbosity,
)
# Subdivided grid.
else:
results = grid_point_array(
func=self.mf.func, args=(), points=self.opt_params.subdivision, verbosity=self.opt_params.verbosity
)
# Unpack the results.
param_vector, func, iter, warning = results
fc = iter
gc = 0.0
hc = 0.0
# Return everything.
return param_vector, func, iter, fc, gc, hc, warning
def run(self, processor, completed):
"""Set up and perform the optimisation."""
# Print out.
if self.verbosity >= 1:
# Individual spin block section.
top = 2
if self.verbosity >= 2:
top += 2
subsection(file=sys.stdout, text="Fitting to the spin block %s"%self.spin_ids, prespace=top)
# Grid search printout.
if search('^[Gg]rid', self.min_algor):
print("Unconstrained grid search size: %s (constraints may decrease this size).\n" % self.grid_size)
# Initialise the function to minimise.
model = Dispersion(model=self.spins[0].model, num_params=self.param_num, num_spins=len(self.spins), num_frq=len(self.fields), exp_types=self.exp_types, values=self.values, errors=self.errors, missing=self.missing, frqs=self.frqs, frqs_H=self.frqs_H, cpmg_frqs=self.cpmg_frqs, spin_lock_nu1=self.spin_lock_nu1, chemical_shifts=self.chemical_shifts, offset=self.offsets, tilt_angles=self.tilt_angles, r1=self.r1, relax_times=self.relax_times, scaling_matrix=self.scaling_matrix)
# Grid search.
if search('^[Gg]rid', self.min_algor):
results = grid(func=model.func, args=(), num_incs=self.inc_new, lower=self.lower_new, upper=self.upper_new, A=self.A, b=self.b, verbosity=self.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, args=(), x0=self.param_vector, min_algor=self.min_algor, min_options=self.min_options, func_tol=self.func_tol, grad_tol=self.grad_tol, maxiter=self.max_iterations, A=self.A, b=self.b, full_output=True, print_flag=self.verbosity)
# Unpack the results.
if results == None:
return
param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results
# Optimisation printout.
if self.verbosity:
print("\nOptimised parameter values:")
for i in range(len(param_vector)):
print("%-20s %25.15f" % (self.param_names[i], param_vector[i]*self.scaling_matrix[i, i]))
# Printout.
if self.sim_index != None:
print("Simulation %s, cluster %s" % (self.sim_index+1, self.spin_ids))
# Create the result command object to send back to the master.
processor.return_object(Disp_result_command(processor=processor, memo_id=self.memo_id, param_vector=param_vector, chi2=chi2, iter_count=iter_count, f_count=f_count, g_count=g_count, h_count=h_count, warning=warning, missing=self.missing, back_calc=model.back_calc, completed=False))
def run(self, processor, completed):
"""Set up and perform the optimisation."""
# Print out.
if self.verbosity >= 1:
# Individual spin block section.
top = 2
if self.verbosity >= 2:
top += 2
subsection(file=sys.stdout, text="Fitting to the spin block %s"%self.spin_ids, prespace=top)
# Grid search printout.
if search('^[Gg]rid', self.min_algor):
result = 1
for x in self.inc:
result = mul(result, x)
print("Unconstrained grid search size: %s (constraints may decrease this size).\n" % result)
# Initialise the function to minimise.
model = Dispersion(model=self.spins[0].model, num_params=self.param_num, num_spins=count_spins(self.spins), num_frq=len(self.fields), exp_types=self.exp_types, values=self.values, errors=self.errors, missing=self.missing, frqs=self.frqs, frqs_H=self.frqs_H, cpmg_frqs=self.cpmg_frqs, spin_lock_nu1=self.spin_lock_nu1, chemical_shifts=self.chemical_shifts, offset=self.offsets, tilt_angles=self.tilt_angles, r1=self.r1, relax_times=self.relax_times, scaling_matrix=self.scaling_matrix, r1_fit=self.r1_fit)
# Grid search.
if search('^[Gg]rid', self.min_algor):
results = grid(func=model.func, args=(), num_incs=self.inc, lower=self.lower, upper=self.upper, A=self.A, b=self.b, verbosity=self.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, args=(), x0=self.param_vector, min_algor=self.min_algor, min_options=self.min_options, func_tol=self.func_tol, grad_tol=self.grad_tol, maxiter=self.max_iterations, A=self.A, b=self.b, full_output=True, print_flag=self.verbosity)
# Unpack the results.
if results == None:
return
param_vector, chi2, iter_count, f_count, g_count, h_count, warning = results
# Optimisation printout.
if self.verbosity:
print("\nOptimised parameter values:")
for i in range(len(param_vector)):
print("%-20s %25.15f" % (self.param_names[i], param_vector[i]*self.scaling_matrix[i, i]))
# Create the result command object to send back to the master.
processor.return_object(Disp_result_command(processor=processor, memo_id=self.memo_id, param_vector=param_vector, chi2=chi2, iter_count=iter_count, f_count=f_count, g_count=g_count, h_count=h_count, warning=warning, missing=self.missing, back_calc=model.get_back_calc(), completed=False))
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 minimise(self, min_algor=None, min_options=None, func_tol=None, grad_tol=None, max_iterations=None, constraints=False, scaling=True, verbosity=0, sim_index=None, lower=None, upper=None, inc=None):
"""Relaxation curve fitting minimisation method.
@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: If True, diagonal scaling is enabled during optimisation to allow the problem to be better conditioned.
@type scaling: bool
@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 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: array of numbers
@keyword upper: The 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: array of numbers
@keyword inc: The 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: array of int
"""
# Test if sequence data is loaded.
if not exists_mol_res_spin_data():
raise RelaxNoSequenceError
# Loop over the sequence.
for spin, mol_name, res_num, res_name in spin_loop(full_info=True):
# Skip deselected spins.
if not spin.select:
continue
# Skip spins which have no data.
if not hasattr(spin, 'intensities'):
continue
# Create the initial parameter vector.
param_vector = self._assemble_param_vector(spin=spin)
# Diagonal scaling.
scaling_matrix = self._assemble_scaling_matrix(spin=spin, scaling=scaling)
if len(scaling_matrix):
param_vector = dot(inv(scaling_matrix), param_vector)
# Get the grid search minimisation options.
if match('^[Gg]rid', min_algor):
inc, lower_new, upper_new = self._grid_search_setup(spin=spin, param_vector=param_vector, lower=lower, upper=upper, inc=inc, scaling_matrix=scaling_matrix)
# Linear constraints.
if constraints:
A, b = self._linear_constraints(spin=spin, scaling_matrix=scaling_matrix)
else:
A, b = None, None
# Print out.
if verbosity >= 1:
# Get the spin id string.
spin_id = generate_spin_id_unique(mol_name=mol_name, res_num=res_num, res_name=res_name, spin_num=spin.num, spin_name=spin.name)
# Individual spin printout.
if verbosity >= 2:
print("\n\n")
string = "Fitting to spin " + repr(spin_id)
print("\n\n" + string)
print(len(string) * '~')
# Initialise the function to minimise.
######################################
# The keys.
keys = list(spin.intensities.keys())
# The peak intensities and times.
values = []
errors = []
times = []
for key in keys:
# The values.
if sim_index == None:
values.append(spin.intensities[key])
else:
values.append(spin.sim_intensities[sim_index][key])
# The errors.
errors.append(spin.intensity_err[key])
# The relaxation times.
times.append(cdp.relax_times[key])
# The scaling matrix in a diagonalised list form.
scaling_list = []
for i in range(len(scaling_matrix)):
scaling_list.append(scaling_matrix[i, i])
setup(num_params=len(spin.params), num_times=len(values), values=values, sd=errors, relax_times=times, scaling_matrix=scaling_list)
# Setup the minimisation algorithm when constraints are present.
################################################################
if constraints and not match('^[Gg]rid', min_algor):
algor = min_options[0]
else:
algor = min_algor
# Levenberg-Marquardt minimisation.
###################################
if match('[Ll][Mm]$', algor) or match('[Ll]evenburg-[Mm]arquardt$', algor):
# Reconstruct the error data structure.
lm_error = zeros(len(spin.relax_times), float64)
index = 0
for k in range(len(spin.relax_times)):
lm_error[index:index+len(relax_error[k])] = relax_error[k]
index = index + len(relax_error[k])
min_options = min_options + (self.relax_fit.lm_dri, lm_error)
# Minimisation.
###############
# Grid search.
if search('^[Gg]rid', min_algor):
results = grid(func=self._func, args=(), num_incs=inc, lower=lower_new, upper=upper_new, 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=self._func, dfunc=self._dfunc, d2func=self._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:
param_vector = dot(scaling_matrix, param_vector)
# Disassemble the parameter vector.
self._disassemble_param_vector(param_vector=param_vector, spin=spin, sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
spin.chi2_sim[sim_index] = chi2
# Iterations.
spin.iter_sim[sim_index] = iter_count
# Function evaluations.
spin.f_count_sim[sim_index] = f_count
# Gradient evaluations.
spin.g_count_sim[sim_index] = g_count
# Hessian evaluations.
spin.h_count_sim[sim_index] = h_count
# Warning.
spin.warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
spin.chi2 = chi2
# Iterations.
spin.iter = iter_count
# Function evaluations.
spin.f_count = f_count
# Gradient evaluations.
spin.g_count = g_count
# Hessian evaluations.
spin.h_count = h_count
# Warning.
spin.warning = warning
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 minimise(self, 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):
"""Minimisation function.
@param min_algor: The minimisation algorithm to use.
@type min_algor: str
@param min_options: An array of options to be used by the minimisation algorithm.
@type min_options: array of str
@param func_tol: The function tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type func_tol: None or float
@param grad_tol: The gradient tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type grad_tol: None or float
@param max_iterations: The maximum number of iterations for the algorithm.
@type max_iterations: int
@param constraints: If True, constraints are used during optimisation.
@type constraints: bool
@keyword scaling_matrix: The per-model list of diagonal and square scaling matrices.
@type scaling_matrix: list of numpy rank-2, float64 array or list of None
@param verbosity: A flag specifying the amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
@param 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 per-model 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 lists of numbers
@keyword upper: The per-model 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 lists of numbers
@keyword inc: The per-model 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 lists of int
"""
# Set up the target function for direct calculation.
model, param_vector, data_types = target_fn_setup(sim_index=sim_index, scaling_matrix=scaling_matrix[0], verbosity=verbosity)
# Nothing to do!
if not len(param_vector):
warn(RelaxWarning("The model has no parameters, minimisation cannot be performed."))
return
# Right, constraints cannot be used for the 'fixed' model.
if constraints and cdp.model == 'fixed':
if verbosity:
warn(RelaxWarning("Turning constraints off. These cannot be used for the 'fixed' model."))
constraints = False
# Pop out the Method of Multipliers algorithm.
if min_algor == 'Method of Multipliers':
min_algor = min_options[0]
min_options = min_options[1:]
# And constraints absolutely must be used for the 'population' model.
if not constraints and cdp.model == 'population':
warn(RelaxWarning("Turning constraints on. These absolutely must be used for the 'population' model."))
constraints = True
# Add the Method of Multipliers algorithm.
min_options = (min_algor,) + min_options
min_algor = 'Method of Multipliers'
# Disallow Newton optimisation and other Hessian optimisers for the paramagnetic centre position optimisation (the PCS Hessian is not yet implemented).
if hasattr(cdp, 'paramag_centre_fixed') and not cdp.paramag_centre_fixed:
if min_algor in ['newton']:
raise RelaxError("For the paramagnetic centre position, as the Hessians are not yet implemented Newton optimisation cannot be performed.")
# Linear constraints.
A, b = None, None
if constraints:
A, b = linear_constraints(data_types=data_types, scaling_matrix=scaling_matrix[0])
# Grid search.
if search('^[Gg]rid', min_algor):
# The search.
results = grid(func=model.func, args=(), num_incs=inc[0], lower=lower[0], upper=upper[0], A=A, b=b, verbosity=verbosity)
# Unpack the results.
param_vector, func, 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=1, print_flag=verbosity)
# Unpack the results.
if results == None:
return
param_vector, func, iter_count, f_count, g_count, h_count, warning = results
# Catch infinite chi-squared values.
if isInf(func):
raise RelaxInfError('chi-squared')
# Catch chi-squared values of NaN.
if isNaN(func):
raise RelaxNaNError('chi-squared')
# Make a last function call to update the back-calculated RDC and PCS structures to the optimal values.
chi2 = model.func(param_vector)
# Scaling.
if scaling_matrix[0] is not None:
param_vector = dot(scaling_matrix[0], param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, data_types=data_types, sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
cdp.chi2_sim[sim_index] = func
# Iterations.
cdp.iter_sim[sim_index] = iter_count
# Function evaluations.
cdp.f_count_sim[sim_index] = f_count
# Gradient evaluations.
cdp.g_count_sim[sim_index] = g_count
# Hessian evaluations.
cdp.h_count_sim[sim_index] = h_count
# Warning.
cdp.warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
cdp.chi2 = func
# Iterations.
cdp.iter = iter_count
# Function evaluations.
cdp.f_count = f_count
# Gradient evaluations.
cdp.g_count = g_count
# Hessian evaluations.
cdp.h_count = h_count
# Warning.
cdp.warning = warning
# Statistical analysis.
if 'rdc' in data_types or 'pcs' in data_types:
# Get the final back calculated data (for the Q factor and
minimise_bc_data(model, sim_index=sim_index)
# Calculate the RDC Q factors.
if 'rdc' in data_types:
rdc.q_factors(sim_index=sim_index, verbosity=verbosity)
# Calculate the PCS Q factors.
if 'pcs' in data_types:
pcs.q_factors(sim_index=sim_index, verbosity=verbosity)
def minimise(self,
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):
"""Minimisation function.
@param min_algor: The minimisation algorithm to use.
@type min_algor: str
@param min_options: An array of options to be used by the minimisation algorithm.
@type min_options: array of str
@param func_tol: The function tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type func_tol: None or float
@param grad_tol: The gradient tolerance which, when reached, terminates optimisation. Setting this to None turns of the check.
@type grad_tol: None or float
@param max_iterations: The maximum number of iterations for the algorithm.
@type max_iterations: int
@param constraints: If True, constraints are used during optimisation.
@type constraints: bool
@keyword scaling_matrix: The per-model list of diagonal and square scaling matrices.
@type scaling_matrix: list of numpy rank-2, float64 array or list of None
@param verbosity: A flag specifying the amount of information to print. The higher the value, the greater the verbosity.
@type verbosity: int
@param 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 per-model 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 lists of numbers
@keyword upper: The per-model 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 lists of numbers
@keyword inc: The per-model 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 lists of int
"""
# Set up the target function for direct calculation.
model, param_vector, data_types = target_fn_setup(
sim_index=sim_index,
scaling_matrix=scaling_matrix[0],
verbosity=verbosity)
# Nothing to do!
if not len(param_vector):
warn(
RelaxWarning(
"The model has no parameters, minimisation cannot be performed."
))
return
# Right, constraints cannot be used for the 'fixed' model.
if constraints and cdp.model == 'fixed':
if verbosity:
warn(
RelaxWarning(
"Turning constraints off. These cannot be used for the 'fixed' model."
))
constraints = False
# Pop out the Method of Multipliers algorithm.
if min_algor == 'Method of Multipliers':
min_algor = min_options[0]
min_options = min_options[1:]
# And constraints absolutely must be used for the 'population' model.
if not constraints and cdp.model == 'population':
warn(
RelaxWarning(
"Turning constraints on. These absolutely must be used for the 'population' model."
))
constraints = True
# Add the Method of Multipliers algorithm.
min_options = (min_algor, ) + min_options
min_algor = 'Method of Multipliers'
# Disallow Newton optimisation and other Hessian optimisers for the paramagnetic centre position optimisation (the PCS Hessian is not yet implemented).
if hasattr(cdp,
'paramag_centre_fixed') and not cdp.paramag_centre_fixed:
if min_algor in ['newton']:
raise RelaxError(
"For the paramagnetic centre position, as the Hessians are not yet implemented Newton optimisation cannot be performed."
)
# Linear constraints.
A, b = None, None
if constraints:
A, b = linear_constraints(data_types=data_types,
scaling_matrix=scaling_matrix[0])
# Grid search.
if search('^[Gg]rid', min_algor):
# The search.
results = grid(func=model.func,
args=(),
num_incs=inc[0],
lower=lower[0],
upper=upper[0],
A=A,
b=b,
verbosity=verbosity)
# Unpack the results.
param_vector, func, 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=1,
print_flag=verbosity)
# Unpack the results.
if results == None:
return
param_vector, func, iter_count, f_count, g_count, h_count, warning = results
# Catch infinite chi-squared values.
if isInf(func):
raise RelaxInfError('chi-squared')
# Catch chi-squared values of NaN.
if isNaN(func):
raise RelaxNaNError('chi-squared')
# Make a last function call to update the back-calculated RDC and PCS structures to the optimal values.
chi2 = model.func(param_vector)
# Scaling.
if scaling_matrix[0] is not None:
param_vector = dot(scaling_matrix[0], param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector,
data_types=data_types,
sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
cdp.chi2_sim[sim_index] = func
# Iterations.
cdp.iter_sim[sim_index] = iter_count
# Function evaluations.
cdp.f_count_sim[sim_index] = f_count
# Gradient evaluations.
cdp.g_count_sim[sim_index] = g_count
# Hessian evaluations.
cdp.h_count_sim[sim_index] = h_count
# Warning.
cdp.warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
cdp.chi2 = func
# Iterations.
cdp.iter = iter_count
# Function evaluations.
cdp.f_count = f_count
# Gradient evaluations.
cdp.g_count = g_count
# Hessian evaluations.
cdp.h_count = h_count
# Warning.
cdp.warning = warning
# Statistical analysis.
if 'rdc' in data_types or 'pcs' in data_types:
# Get the final back calculated data (for the Q factor and
minimise_bc_data(model, sim_index=sim_index)
# Calculate the RDC Q factors.
if 'rdc' in data_types:
rdc.q_factors(sim_index=sim_index, verbosity=verbosity)
# Calculate the PCS Q factors.
if 'pcs' in data_types:
pcs.q_factors(sim_index=sim_index, verbosity=verbosity)
def minimise(self, 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):
"""Relaxation curve fitting minimisation method.
@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 per-model list of diagonal and square scaling matrices.
@type scaling_matrix: list of numpy rank-2, float64 array or list of 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 per-model 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 lists of numbers
@keyword upper: The per-model 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 lists of numbers
@keyword inc: The per-model 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 lists of int
"""
# Checks.
check_mol_res_spin_data()
# Loop over the sequence.
model_index = 0
for spin, spin_id in self.model_loop():
# Skip deselected spins.
if not spin.select:
continue
# Skip spins which have no data.
if not hasattr(spin, 'peak_intensity'):
continue
# Create the initial parameter vector.
param_vector = assemble_param_vector(spin=spin)
# Diagonal scaling.
if scaling_matrix[model_index] is not None:
param_vector = dot(inv(scaling_matrix[model_index]), param_vector)
# Linear constraints.
if constraints:
A, b = linear_constraints(spin=spin, scaling_matrix=scaling_matrix[model_index])
else:
A, b = None, None
# Print out.
if verbosity >= 1:
# Individual spin printout.
if verbosity >= 2:
print("\n\n")
string = "Fitting to spin " + repr(spin_id)
print("\n\n" + string)
print(len(string) * '~')
# Initialise the function to minimise.
######################################
# The peak intensities and times.
values = []
errors = []
times = []
for key in spin.peak_intensity:
# The values.
if sim_index == None:
values.append(spin.peak_intensity[key])
else:
values.append(spin.peak_intensity_sim[sim_index][key])
# The errors.
errors.append(spin.peak_intensity_err[key])
# The relaxation times.
times.append(cdp.relax_times[key])
# The scaling matrix in a diagonalised list form.
scaling_list = []
if scaling_matrix[model_index] is None:
for i in range(len(param_vector)):
scaling_list.append(1.0)
else:
for i in range(len(scaling_matrix[model_index])):
scaling_list.append(scaling_matrix[model_index][i, i])
# Set up the target function.
model = Relax_fit_opt(model=spin.model, num_params=len(spin.params), values=values, errors=errors, relax_times=times, scaling_matrix=scaling_list)
# Setup the minimisation algorithm when constraints are present.
################################################################
if constraints and not match('^[Gg]rid', min_algor):
algor = min_options[0]
else:
algor = min_algor
# Levenberg-Marquardt minimisation.
###################################
if match('[Ll][Mm]$', algor) or match('[Ll]evenburg-[Mm]arquardt$', algor):
# Reconstruct the error data structure.
lm_error = zeros(len(spin.relax_times), float64)
index = 0
for k in range(len(spin.relax_times)):
lm_error[index:index+len(relax_error[k])] = relax_error[k]
index = index + len(relax_error[k])
min_options = min_options + (self.relax_fit.lm_dri, lm_error)
# Minimisation.
###############
# Grid search.
if search('^[Gg]rid', min_algor):
results = grid(func=model.func, args=(), num_incs=inc[model_index], lower=lower[model_index], upper=upper[model_index], 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[model_index] is not None:
param_vector = dot(scaling_matrix[model_index], param_vector)
# Disassemble the parameter vector.
disassemble_param_vector(param_vector=param_vector, spin=spin, sim_index=sim_index)
# Monte Carlo minimisation statistics.
if sim_index != None:
# Chi-squared statistic.
spin.chi2_sim[sim_index] = chi2
# Iterations.
spin.iter_sim[sim_index] = iter_count
# Function evaluations.
spin.f_count_sim[sim_index] = f_count
# Gradient evaluations.
spin.g_count_sim[sim_index] = g_count
# Hessian evaluations.
spin.h_count_sim[sim_index] = h_count
# Warning.
spin.warning_sim[sim_index] = warning
# Normal statistics.
else:
# Chi-squared statistic.
spin.chi2 = chi2
# Iterations.
spin.iter = iter_count
# Function evaluations.
spin.f_count = f_count
# Gradient evaluations.
spin.g_count = g_count
# Hessian evaluations.
spin.h_count = h_count
# Warning.
spin.warning = warning
# Increment the model index.
model_index += 1