From 2910cf2aab842d651925668d44e03d2a23b4199d Mon Sep 17 00:00:00 2001 From: Michael Shirts Date: Sun, 19 Jun 2022 18:59:23 -0600 Subject: [PATCH 1/2] Trying to make MBAR work better adaptively. * Changed the way defaults are set up. * Automatically tries both adaptive and L-BFGS-B if the first one chosen fails. * If multiple solvers are tried, returns the best result. * Makes adaptive more consistent with other methods. --- pymbar/mbar.py | 34 +++++++++---- pymbar/mbar_solvers.py | 111 ++++++++++++++++++++++++++++++----------- 2 files changed, 106 insertions(+), 39 deletions(-) diff --git a/pymbar/mbar.py b/pymbar/mbar.py index f3eace28..73f7aab3 100644 --- a/pymbar/mbar.py +++ b/pymbar/mbar.py @@ -1,9 +1,9 @@ ############################################################################## # pymbar: A Python Library for MBAR # -# Copyright 2017 University of Colorado Boulder -# Copyright 2010-2017 Memorial Sloan-Kettering Cancer Center -# Portions of this software are Copyright (c) 2010-2016 University of Virginia +# Copyright 2016-2022 University of Colorado Boulder +# Copyright 2010-2022 Memorial Sloan-Kettering Cancer Center +# Portions of this software are Copyright (c) 2010-2015 University of Virginia # Portions of this software are Copyright (c) 2006-2007 The Regents of the University of California. All Rights Reserved. # Portions of this software are Copyright (c) 2007-2008 Stanford University and Columbia University. # @@ -43,8 +43,6 @@ from pymbar import mbar_solvers from pymbar.utils import kln_to_kn, kn_to_n, ParameterError, DataError, logsumexp, check_w_normalized -DEFAULT_SOLVER_PROTOCOL = mbar_solvers.DEFAULT_SOLVER_PROTOCOL - # ========================================================================= # MBAR class definition # ========================================================================= @@ -106,9 +104,9 @@ def __init__(self, u_kn, N_k, maximum_iterations=10000, relative_tolerance=1.0e- from above, once ``u_kln`` is phased out. maximum_iterations : int, optional - Set to limit the maximum number of iterations performed (default 1000) + Set to limit the maximum number of iterations performed (default 10000) relative_tolerance : float, optional - Set to determine the relative tolerance convergence criteria (default 1.0e-6) + Set to determine the relative tolerance convergence criteria (default 1.0e-7) verbosity : bool, optional Set to True if verbose debug output is desired (default False) initial_f_k : np.ndarray, float, shape=(K), optional @@ -292,14 +290,32 @@ def __init__(self, u_kn, N_k, maximum_iterations=10000, relative_tolerance=1.0e- print(self.f_k) if solver_protocol is None: - solver_protocol = ({'method': None},) + solver_protocol = mbar_solvers.DEFAULT_SOLVER_PROTOCOL + + # Add backup option if only one method is given + # The backup method is 'adaptive', unless 'adaptive' is already the only method selected. + if len(solver_protocol) == 1: + #Add backup option. + fallback = dict() + if solver_protocol[0]['method'] != 'adaptive': + fallback['method'] = 'adaptive' + print("Adding backup method 'adaptive'") + else: + # the backup method is already adaptive, try l-bfgs-b + fallback['method'] = 'BFGS' + print("Adding backup method 'BFGS'") + solver_protocol = solver_protocol + (fallback,) + + for solver in solver_protocol: if 'options' not in solver: solver['options'] = dict() - solver['options']['maximum_iterations'] = maximum_iterations + if 'maxiter' not in solver['options']: + solver['options']['maxiter'] = maximum_iterations if 'verbose' not in solver['options']: # should add in other ways to get information out of the scipy solvers, not just adaptive, # which might involve passing in different combinations of options, and passing out other strings. + # to be addressed with logging in mbar 4.0. solver['options']['verbose'] = self.verbose self.f_k = mbar_solvers.solve_mbar_for_all_states(self.u_kn, self.N_k, self.f_k, solver_protocol) diff --git a/pymbar/mbar_solvers.py b/pymbar/mbar_solvers.py index 2953ffe0..f786670a 100644 --- a/pymbar/mbar_solvers.py +++ b/pymbar/mbar_solvers.py @@ -5,14 +5,19 @@ from pymbar.utils import ensure_type, logsumexp, check_w_normalized import warnings -# Below are the recommended default protocols (ordered sequence of minimization algorithms / NLE solvers) for solving the MBAR equations. +# the 'solver_protocol' dictionary is set up to make it possible to wrap around scipy solvers. +# We introduce our our robust solver as well. + # Note: we use tuples instead of lists to avoid accidental mutability. #DEFAULT_SUBSAMPLING_PROTOCOL = (dict(method="L-BFGS-B"), ) # First use BFGS on subsampled data. #DEFAULT_SOLVER_PROTOCOL = (dict(method="hybr"), ) # Then do fmin hybrid on full dataset. # Use Adpative solver as first attempt -DEFAULT_SOLVER_METHOD = "adaptive" -DEFAULT_SOLVER_PROTOCOL = (dict(method=DEFAULT_SOLVER_METHOD,),) +DEFAULT_SOLVER_PROTOCOL = (dict(method="adaptive",),dict(method="L-BFGS-B",)) +# Uses all of the gradient based methods, but not the non-gradient methods +# ["Nelder-Mead", "Powell", "COBYLA"]", +SCIPY_OPTIONS = ["L-BFGS-B", "dogleg", "CG", "BFGS", "Newton-CG", "TNC", "trust-ncg", "trust-krylov", "trust-exact", "SLSQP"] +SCIPY_NOHESS_OPTIONS = ["L-BFGS-B","BFGS","CG","TNC"] # don't pass a hessian to these to avoid warnings to these. def validate_inputs(u_kn, N_k, f_k): """Check types and return inputs for MBAR calculations. @@ -246,7 +251,8 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): options: dictionary of options gamma (float between 0 and 1) - incrementor for NR iterations (default 1.0). Usually not changed now, since adaptively switch. - maximum_iterations (int) - maximum number of Newton-Raphson iterations (default 250: either NR converges or doesn't, pretty quickly) + maxiter (int) - maximum number of Newton-Raphson/self-consistent iterations (default 10000: + either NR converges or doesn't, pretty quickly, but the number of self-consistent iterations can take a while.) verbose (boolean) - verbosity level for debug output NOTES @@ -268,11 +274,12 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): """ # put the defaults here in case we get passed an 'options' dictionary that is only partial options.setdefault('verbose',False) - options.setdefault('maximum_iterations',10000) + options.setdefault('maxiter',10000) options.setdefault('print_warning',False) options.setdefault('gamma',1.0) gamma = options['gamma'] + doneIterating = False if options['verbose'] == True: print("Determining dimensionless free energies by Newton-Raphson / self-consistent iteration.") @@ -286,8 +293,9 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): f_sci = np.zeros(len(f_k), dtype=np.float64) f_nr = np.zeros(len(f_k), dtype=np.float64) + success = False # Perform Newton-Raphson iterations (with sci computed on the way) - for iteration in range(0, options['maximum_iterations']): + for iteration in range(0, options['maxiter']): g = mbar_gradient(u_kn, N_k, f_k) # Objective function gradient H = mbar_hessian(u_kn, N_k, f_k) # Objective function hessian Hinvg = np.linalg.lstsq(H, g, rcond=-1)[0] @@ -331,23 +339,33 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): max_delta = np.max(np.abs(f_k[1:]-f_old[1:])/div) if np.isnan(max_delta) or (max_delta < tol): doneIterating = True + success = True + warn = "Convergence achieved by value of gnorm" break if doneIterating: + if options['verbose']: print('Converged to tolerance of {:e} in {:d} iterations.'.format(max_delta, iteration + 1)) print('Of {:d} iterations, {:d} were Newton-Raphson iterations and {:d} were self-consistent iterations'.format(iteration + 1, nr_iter, sci_iter)) if np.all(f_k == 0.0): # all f_k appear to be zero - print('WARNING: All f_k appear to be zero.') + warn = 'WARNING: All f_k appear to be zero.' + message = warn + success = False else: - print('WARNING: Did not converge to within specified tolerance.') - if options['maximum_iterations'] <= 0: - print("No iterations ran be cause maximum_iterations was <= 0 ({})!".format(options['maximum_iterations'])) + warn = 'WARNING: Did not converge to within specified tolerance.\n' + if options['maxiter'] <= 0: + warn += "No iterations ran because maximum_iterations was <= 0 ({})!".format(options['maxiter']) else: - print('max_delta = {:e}, tol = {:e}, maximum_iterations = {:d}, iterations completed = {:d}'.format(max_delta,tol, options['maximum_iterations'], iteration)) - return f_k + warn += 'max_delta = {:e}, tol = {:e}, maximum_iterations = {:d}, iterations completed = {:d}'.format(max_delta,tol, options['maxiter'], iteration) + + results = dict() + results['success'] = success + results['message'] = warn + results['x'] = f_k + return results def precondition_u_kn(u_kn, N_k, f_k): """Subtract a sample-dependent constant from u_kn to improve precision @@ -380,7 +398,7 @@ def precondition_u_kn(u_kn, N_k, f_k): return u_kn -def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method="hybr", tol=1E-12, options=None): +def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", tol=1E-12, options=None): """Solve MBAR self-consistent equations using some form of equation solver. Parameters @@ -392,7 +410,7 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method="hybr", tol=1 The number of samples in each state for the nonempty states f_k_nonzero : np.ndarray, shape=(n_states), dtype='float' The reduced free energies for the nonempty states - method : str, optional, default="hybr" + method : str, optional, "adaptive" The optimization routine to use. This can be any of the methods available via scipy.optimize.minimize() or scipy.optimize.root(). tol : float, optional, default=1E-14 @@ -435,15 +453,16 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method="hybr", tol=1 hess = lambda x: mbar_hessian(u_kn_nonzero, N_k_nonzero, pad(x))[1:][:, 1:] # Hessian of objective function with warnings.catch_warnings(record=True) as w: - if method in ["L-BFGS-B", "dogleg", "CG", "BFGS", "Newton-CG", "TNC", "trust-ncg", "SLSQP"]: - if method in ["L-BFGS-B", "CG"]: + if method in SCIPY_OPTIONS: + if method in SCIPY_NOHESS_OPTIONS: hess = None # To suppress warning from passing a hessian function. results = scipy.optimize.minimize(grad_and_obj, f_k_nonzero[1:], jac=True, hess=hess, method=method, tol=tol, options=options) f_k_nonzero = pad(results["x"]) elif method == 'adaptive': results = adaptive(u_kn_nonzero, N_k_nonzero, f_k_nonzero, tol=tol, options=options) - f_k_nonzero = results # they are the same for adaptive, until we decide to return more. + f_k_nonzero = results["x"] else: + # find the root in the gradient. Not sure how well this has been tested . . . ? results = scipy.optimize.root(grad, f_k_nonzero[1:], jac=hess, method=method, tol=tol, options=options) f_k_nonzero = pad(results["x"]) @@ -460,7 +479,7 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method="hybr", tol=1 # Ensure MBAR solved correctly w_nk_check = mbar_W_nk(u_kn_nonzero, N_k_nonzero, f_k_nonzero) check_w_normalized(w_nk_check, N_k_nonzero) - print("MBAR weights converged within tolerance, despite the SciPy Warnings. Please validate your results.") + print("MBAR weights converged within tolerance, despite the SciPy Warnings. However, please validate your results.") return f_k_nonzero, results @@ -498,24 +517,56 @@ def solve_mbar(u_kn_nonzero, N_k_nonzero, f_k_nonzero, solver_protocol=None): by subtracting off the first component of f_k and fixing that component to be zero. - This function calls `solve_mbar_once()` multiple times to achieve - converged results. Generally, a single call to solve_mbar_once() - will not give fully converged answers because of limited numerical precision. + This function calls `solve_mbar_once()`. Usually, a single call + will converge to the correct answer. However, there are a number + specific cases that may succeed or fail with a specific algorithm. + + The default case is to use the adaptive solver, which alternates + between N-R iteration and self-consistent iteration, depending on + which has the the lowest gradient. If the adaptive solver fails, + it then tries the BFGS algorithm. If one starts with BFSG, + then it changes to adaptive if BFGS fails.. Currently, it restarts + with whatever the initialized values are when it switches algorithms, + with the assumption that if it is failing, the current guess + may not be a workable starting point. + Each call to `solve_mbar_once()` re-conditions the nonlinear equations using the current guess. + """ - if solver_protocol is None: - solver_protocol = DEFAULT_SOLVER_PROTOCOL - for protocol in solver_protocol: - if protocol['method'] is None: - protocol['method'] = DEFAULT_SOLVER_METHOD + all_fks = [] all_results = [] - for k, options in enumerate(solver_protocol): - f_k_nonzero, results = solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, **options) + all_gnorms = [] + success = False + for k, solver in enumerate(solver_protocol): + print(f"Trying solution with solver {solver['method']}") + f_k_nonzero_result, results = solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, **solver) + all_fks.append(f_k_nonzero_result) all_results.append(results) - all_results.append(("Final gradient norm: %.3g" % np.linalg.norm(mbar_gradient(u_kn_nonzero, N_k_nonzero, f_k_nonzero)))) - return f_k_nonzero, all_results + all_gnorms.append(np.linalg.norm(mbar_gradient(u_kn_nonzero, N_k_nonzero, f_k_nonzero_result))) + + if results["success"] == True: + success = True + best_gnorm = all_gnorms[-1] + break + else: + print(f"Failed to reach a solution to within tolerance with {solver['method']}: trying next method") + + if success is True: + print("Solution found within tolerance!") + else: + i_best_gnorm = np.argmin(all_gnorms) + print("No solution found to within tolerance.") + best_method = solver_protocol[i_best_gnorm]['method'] + print(f"The solution with the smallest lowest gradient norm is {best_method}") + best_gnorm = all_gnorm[i_best_gnorm] + f_k_nonzero_result = all_fks[i_best_ngnorm] + print("Please exercise caution with this solution and consider alternative methods or a different tolerance") + + print(f"Final gradient norm: {best_gnorm:.3g}") + + return f_k_nonzero_result, all_results def solve_mbar_for_all_states(u_kn, N_k, f_k, solver_protocol): From 4be3ac85f0439abc7a8212d16e937252a10b3cbf Mon Sep 17 00:00:00 2001 From: Michael Shirts Date: Tue, 21 Jun 2022 09:48:29 -0600 Subject: [PATCH 2/2] More changes in adaptive solving --- pymbar/mbar.py | 2 ++ pymbar/mbar_solvers.py | 62 ++++++++++++++++++++---------------------- pymbar/utils.py | 8 +++--- 3 files changed, 36 insertions(+), 36 deletions(-) diff --git a/pymbar/mbar.py b/pymbar/mbar.py index 73f7aab3..549ae779 100644 --- a/pymbar/mbar.py +++ b/pymbar/mbar.py @@ -310,6 +310,8 @@ def __init__(self, u_kn, N_k, maximum_iterations=10000, relative_tolerance=1.0e- for solver in solver_protocol: if 'options' not in solver: solver['options'] = dict() + if 'continuation' not in solver: + solver['continuation'] = None if 'maxiter' not in solver['options']: solver['options']['maxiter'] = maximum_iterations if 'verbose' not in solver['options']: diff --git a/pymbar/mbar_solvers.py b/pymbar/mbar_solvers.py index f786670a..82b41b29 100644 --- a/pymbar/mbar_solvers.py +++ b/pymbar/mbar_solvers.py @@ -9,15 +9,13 @@ # We introduce our our robust solver as well. # Note: we use tuples instead of lists to avoid accidental mutability. -#DEFAULT_SUBSAMPLING_PROTOCOL = (dict(method="L-BFGS-B"), ) # First use BFGS on subsampled data. -#DEFAULT_SOLVER_PROTOCOL = (dict(method="hybr"), ) # Then do fmin hybrid on full dataset. -# Use Adpative solver as first attempt - -DEFAULT_SOLVER_PROTOCOL = (dict(method="adaptive",),dict(method="L-BFGS-B",)) +#DEFAULT_SOLVER_PROTOCOL = (dict(method="adaptive",),dict(method="L-BFGS-B",)) +DEFAULT_SOLVER_PROTOCOL = (dict(method="BFGS",continuation=True),dict(method="adaptive",)) # Uses all of the gradient based methods, but not the non-gradient methods # ["Nelder-Mead", "Powell", "COBYLA"]", -SCIPY_OPTIONS = ["L-BFGS-B", "dogleg", "CG", "BFGS", "Newton-CG", "TNC", "trust-ncg", "trust-krylov", "trust-exact", "SLSQP"] -SCIPY_NOHESS_OPTIONS = ["L-BFGS-B","BFGS","CG","TNC"] # don't pass a hessian to these to avoid warnings to these. +scipy_minimize_options = ["L-BFGS-B", "dogleg", "CG", "BFGS", "Newton-CG", "TNC", "trust-ncg", "trust-krylov", "trust-exact", "SLSQP"] +scipy_nohess_options = ["L-BFGS-B","BFGS","CG","TNC","SLSQP"] # don't pass a hessian to these to avoid warnings to these. +scipy_root_options = ['hybr','lm'] # only use root options with the hessian. def validate_inputs(u_kn, N_k, f_k): """Check types and return inputs for MBAR calculations. @@ -247,7 +245,7 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): Is slower than NR since it calculates the log norms twice each iteration. OPTIONAL ARGUMENTS - tol (float between 0 and 1) - relative tolerance for convergence (default 1.0e-12) + tol (float between 0 and 1) - relative tolerance for convergence (default 1.0e-8) options: dictionary of options gamma (float between 0 and 1) - incrementor for NR iterations (default 1.0). Usually not changed now, since adaptively switch. @@ -279,12 +277,12 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): options.setdefault('gamma',1.0) gamma = options['gamma'] - + doneIterating = False if options['verbose'] == True: print("Determining dimensionless free energies by Newton-Raphson / self-consistent iteration.") - if tol < 1.5e-15: + if tol < 1.5e-8: print("Tolerance may be too close to machine precision to converge.") # keep track of Newton-Raphson and self-consistent iterations nr_iter = 0 @@ -306,11 +304,11 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): f_sci = self_consistent_update(u_kn, N_k, f_k) f_sci = f_sci - f_sci[0] # zero out the minimum g_sci = mbar_gradient(u_kn, N_k, f_sci) - gnorm_sci = np.dot(g_sci, g_sci) + gnorm_sci = np.sqrt(np.dot(g_sci, g_sci)) # newton raphson gradient norm and saved log sums. g_nr = mbar_gradient(u_kn, N_k, f_nr) - gnorm_nr = np.dot(g_nr, g_nr) + gnorm_nr = np.sqrt(np.dot(g_nr, g_nr)) # we could save the gradient, for the next round, but it's not too expensive to # compute since we are doing the Hessian anyway. @@ -340,7 +338,7 @@ def adaptive(u_kn, N_k, f_k, tol = 1.0e-12, options = None): if np.isnan(max_delta) or (max_delta < tol): doneIterating = True success = True - warn = "Convergence achieved by value of gnorm" + warn = "Convergence achieved by change in f with respect to previous guess." break if doneIterating: @@ -398,7 +396,7 @@ def precondition_u_kn(u_kn, N_k, f_k): return u_kn -def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", tol=1E-12, options=None): +def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", tol=1E-12, continuation=None, options=None): """Solve MBAR self-consistent equations using some form of equation solver. Parameters @@ -410,16 +408,7 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", The number of samples in each state for the nonempty states f_k_nonzero : np.ndarray, shape=(n_states), dtype='float' The reduced free energies for the nonempty states - method : str, optional, "adaptive" - The optimization routine to use. This can be any of the methods - available via scipy.optimize.minimize() or scipy.optimize.root(). - tol : float, optional, default=1E-14 - The convergance tolerance for minimize() or root() - verbose: bool - Whether to print information about the solution method. - options: dict, optional, default=None - Optional dictionary of algorithm-specific parameters. See - scipy.optimize.root or scipy.optimize.minimize for details. + solver: dict of solver options Returns ------- @@ -440,6 +429,7 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", For fast but precise convergence, we recommend calling this function multiple times to polish the result. `solve_mbar()` facilitates this. """ + u_kn_nonzero, N_k_nonzero, f_k_nonzero = validate_inputs(u_kn_nonzero, N_k_nonzero, f_k_nonzero) f_k_nonzero = f_k_nonzero - f_k_nonzero[0] # Work with reduced dimensions with f_k[0] := 0 u_kn_nonzero = precondition_u_kn(u_kn_nonzero, N_k_nonzero, f_k_nonzero) @@ -453,19 +443,21 @@ def solve_mbar_once(u_kn_nonzero, N_k_nonzero, f_k_nonzero, method = "adaptive", hess = lambda x: mbar_hessian(u_kn_nonzero, N_k_nonzero, pad(x))[1:][:, 1:] # Hessian of objective function with warnings.catch_warnings(record=True) as w: - if method in SCIPY_OPTIONS: - if method in SCIPY_NOHESS_OPTIONS: + if method in scipy_minimize_options: + if method in scipy_nohess_options: hess = None # To suppress warning from passing a hessian function. results = scipy.optimize.minimize(grad_and_obj, f_k_nonzero[1:], jac=True, hess=hess, method=method, tol=tol, options=options) f_k_nonzero = pad(results["x"]) elif method == 'adaptive': results = adaptive(u_kn_nonzero, N_k_nonzero, f_k_nonzero, tol=tol, options=options) f_k_nonzero = results["x"] - else: + elif method in scipy_root_options: # find the root in the gradient. Not sure how well this has been tested . . . ? results = scipy.optimize.root(grad, f_k_nonzero[1:], jac=hess, method=method, tol=tol, options=options) f_k_nonzero = pad(results["x"]) - + else: + raise ParameterError(f"Method {method} for solution of free energies not recognized") + # If there were runtime warnings, show the messages if len(w) > 0: can_ignore = True @@ -535,6 +527,8 @@ def solve_mbar(u_kn_nonzero, N_k_nonzero, f_k_nonzero, solver_protocol=None): """ + import pdb + pdb.set_trace() all_fks = [] all_results = [] all_gnorms = [] @@ -552,6 +546,10 @@ def solve_mbar(u_kn_nonzero, N_k_nonzero, f_k_nonzero, solver_protocol=None): break else: print(f"Failed to reach a solution to within tolerance with {solver['method']}: trying next method") + print(all_gnorms[-1]) + if solver["continuation"]: + f_k_nonzero = f_k_nonzero_result + print("Will continue with results from previous method") if success is True: print("Solution found within tolerance!") @@ -559,10 +557,10 @@ def solve_mbar(u_kn_nonzero, N_k_nonzero, f_k_nonzero, solver_protocol=None): i_best_gnorm = np.argmin(all_gnorms) print("No solution found to within tolerance.") best_method = solver_protocol[i_best_gnorm]['method'] - print(f"The solution with the smallest lowest gradient norm is {best_method}") - best_gnorm = all_gnorm[i_best_gnorm] - f_k_nonzero_result = all_fks[i_best_ngnorm] - print("Please exercise caution with this solution and consider alternative methods or a different tolerance") + print(f"The solution with the smallest gradient norm is {best_method}") + best_gnorm = all_gnorms[i_best_gnorm] + f_k_nonzero_result = all_fks[i_best_gnorm] + print("Please exercise caution with this solution and consider alternative methods or a different tolerance.") print(f"Final gradient norm: {best_gnorm:.3g}") diff --git a/pymbar/utils.py b/pymbar/utils.py index a44f294c..7ce3d6d0 100644 --- a/pymbar/utils.py +++ b/pymbar/utils.py @@ -356,8 +356,8 @@ def check_w_normalized(W, N_k, tolerance = 1.0e-4): which_badcolumns = np.arange(K)[badcolumns] firstbad = which_badcolumns[0] raise ParameterError( - 'Warning: Should have \sum_n W_nk = 1. Actual column sum for state %d was %f. %d other columns have similar problems' % - (firstbad, column_sums[firstbad], np.sum(badcolumns))) + 'Warning: Should have \sum_n W_nk = 1. Actual column sum for state %d was %f. %d other columns have similar problems.' % + (firstbad, column_sums[firstbad], np.sum(badcolumns)) + ' This generally indicates the free energies are not converged.') row_sums = np.sum(W * N_k, axis=1) badrows = (np.abs(row_sums - 1) > tolerance) @@ -365,8 +365,8 @@ def check_w_normalized(W, N_k, tolerance = 1.0e-4): which_badrows = np.arange(N)[badrows] firstbad = which_badrows[0] raise ParameterError( - 'Warning: Should have \sum_k N_k W_nk = 1. Actual row sum for sample %d was %f. %d other rows have similar problems' % - (firstbad, row_sums[firstbad], np.sum(badrows))) + 'Warning: Should have \sum_k N_k W_nk = 1. Actual row sum for sample %d was %f. %d other rows have similar problems.' % + (firstbad, row_sums[firstbad], np.sum(badrows)) + ' This generally indicates the free energies are not converged.') return