--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/fit.py	Mon Mar 20 18:30:26 2023 +0000
@@ -0,0 +1,2576 @@
+#!/usr/bin/env python3
+
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Dec  6 15:36:22 2021
+
+@author: rv43
+"""
+
+import logging
+
+from asteval import Interpreter, get_ast_names
+from copy import deepcopy
+from lmfit import Model, Parameters
+from lmfit.model import ModelResult
+from lmfit.models import ConstantModel, LinearModel, QuadraticModel, PolynomialModel,\
+        ExponentialModel, StepModel, RectangleModel, ExpressionModel, GaussianModel,\
+        LorentzianModel
+import numpy as np
+from os import cpu_count, getpid, listdir, mkdir, path
+from re import compile, sub
+from shutil import rmtree
+try:
+    from sympy import diff, simplify
+except:
+    pass
+try:
+    from joblib import Parallel, delayed
+    have_joblib = True
+except:
+    have_joblib = False
+try:
+    import xarray as xr
+    have_xarray = True
+except:
+    have_xarray = False
+
+try:
+    from .general import illegal_value, is_int, is_dict_series, is_index, index_nearest, \
+            almost_equal, quick_plot #, eval_expr
+except:
+    try:
+        from sys import path as syspath
+        syspath.append(f'/nfs/chess/user/rv43/msnctools/msnctools')
+        from general import illegal_value, is_int, is_dict_series, is_index, index_nearest, \
+                almost_equal, quick_plot #, eval_expr
+    except:
+        from general import illegal_value, is_int, is_dict_series, is_index, index_nearest, \
+                almost_equal, quick_plot #, eval_expr
+
+from sys import float_info
+float_min = float_info.min
+float_max = float_info.max
+
+# sigma = fwhm_factor*fwhm
+fwhm_factor = {
+    'gaussian': f'fwhm/(2*sqrt(2*log(2)))',
+    'lorentzian': f'0.5*fwhm',
+    'splitlorentzian': f'0.5*fwhm', # sigma = sigma_r
+    'voight': f'0.2776*fwhm', # sigma = gamma
+    'pseudovoight': f'0.5*fwhm'} # fraction = 0.5
+
+# amplitude = height_factor*height*fwhm
+height_factor = {
+    'gaussian': f'height*fwhm*0.5*sqrt(pi/log(2))',
+    'lorentzian': f'height*fwhm*0.5*pi',
+    'splitlorentzian': f'height*fwhm*0.5*pi', # sigma = sigma_r
+    'voight': f'3.334*height*fwhm', # sigma = gamma
+    'pseudovoight': f'1.268*height*fwhm'} # fraction = 0.5
+
+class Fit:
+    """Wrapper class for lmfit
+    """
+    def __init__(self, y, x=None, models=None, normalize=True, **kwargs):
+        if not isinstance(normalize, bool):
+            raise ValueError(f'Invalid parameter normalize ({normalize})')
+        self._mask = None
+        self._model = None
+        self._norm = None
+        self._normalized = False
+        self._parameters = Parameters()
+        self._parameter_bounds = None
+        self._parameter_norms = {}
+        self._linear_parameters = []
+        self._nonlinear_parameters = []
+        self._result = None
+        self._try_linear_fit = True
+        self._y = None
+        self._y_norm = None
+        self._y_range = None
+        if 'try_linear_fit' in kwargs:
+            try_linear_fit = kwargs.pop('try_linear_fit')
+            if not isinstance(try_linear_fit, bool):
+                illegal_value(try_linear_fit, 'try_linear_fit', 'Fit.fit', raise_error=True)
+            self._try_linear_fit = try_linear_fit
+        if y is not None:
+            if isinstance(y, (tuple, list, np.ndarray)):
+                self._x = np.asarray(x)
+            elif have_xarray and isinstance(y, xr.DataArray):
+                if x is not None:
+                    logging.warning('Ignoring superfluous input x ({x}) in Fit.__init__')
+                if y.ndim != 1:
+                    illegal_value(y.ndim, 'DataArray dimensions', 'Fit:__init__', raise_error=True)
+                self._x = np.asarray(y[y.dims[0]])
+            else:
+                illegal_value(y, 'y', 'Fit:__init__', raise_error=True)
+            self._y = y
+            if self._x.ndim != 1:
+                raise ValueError(f'Invalid dimension for input x ({self._x.ndim})')
+            if self._x.size != self._y.size:
+                raise ValueError(f'Inconsistent x and y dimensions ({self._x.size} vs '+
+                        f'{self._y.size})')
+            if 'mask' in kwargs:
+                self._mask = kwargs.pop('mask')
+            if self._mask is None:
+                y_min = float(self._y.min())
+                self._y_range = float(self._y.max())-y_min
+                if normalize and self._y_range > 0.0:
+                    self._norm = (y_min, self._y_range)
+            else:
+                self._mask = np.asarray(self._mask).astype(bool)
+                if self._x.size != self._mask.size:
+                    raise ValueError(f'Inconsistent x and mask dimensions ({self._x.size} vs '+
+                            f'{self._mask.size})')
+                y_masked = np.asarray(self._y)[~self._mask]
+                y_min = float(y_masked.min())
+                self._y_range = float(y_masked.max())-y_min
+                if normalize and self._y_range > 0.0:
+                    if normalize and self._y_range > 0.0:
+                        self._norm = (y_min, self._y_range)
+        if models is not None:
+            if callable(models) or isinstance(models, str):
+                kwargs = self.add_model(models, **kwargs)
+            elif isinstance(models, (tuple, list)):
+                for model in models:
+                    kwargs = self.add_model(model, **kwargs)
+            self.fit(**kwargs)
+
+    @classmethod
+    def fit_data(cls, y, models, x=None, normalize=True, **kwargs):
+        return(cls(y, x=x, models=models, normalize=normalize, **kwargs))
+
+    @property
+    def best_errors(self):
+        if self._result is None:
+            return(None)
+        return({name:self._result.params[name].stderr for name in sorted(self._result.params)
+                if name != 'tmp_normalization_offset_c'})
+
+    @property
+    def best_fit(self):
+        if self._result is None:
+            return(None)
+        return(self._result.best_fit)
+
+    @property
+    def best_parameters(self):
+        if self._result is None:
+            return(None)
+        parameters = {}
+        for name in sorted(self._result.params):
+            if name != 'tmp_normalization_offset_c':
+                par = self._result.params[name]
+                parameters[name] = {'value': par.value, 'error': par.stderr,
+                        'init_value': par.init_value, 'min': par.min, 'max': par.max,
+                        'vary': par.vary, 'expr': par.expr}
+        return(parameters)
+
+    @property
+    def best_results(self):
+        """Convert the input data array to a data set and add the fit results.
+        """
+        if self._result is None:
+            return(None)
+        if isinstance(self._y, xr.DataArray):
+            best_results = self._y.to_dataset()
+            dims = self._y.dims
+            fit_name = f'{self._y.name}_fit'
+        else:
+            coords = {'x': (['x'], self._x)}
+            dims = ('x')
+            best_results = xr.Dataset(coords=coords)
+            best_results['y'] = (dims, self._y)
+            fit_name = 'y_fit'
+        best_results[fit_name] = (dims, self.best_fit)
+        if self._mask is not None:
+            best_results['mask'] = self._mask
+        best_results.coords['par_names'] = ('peak', [name for name in self.best_values.keys()])
+        best_results['best_values'] = (['par_names'], [v for v in self.best_values.values()])
+        best_results['best_errors'] = (['par_names'], [v for v in self.best_errors.values()])
+        best_results.attrs['components'] = self.components
+        return(best_results)
+
+    @property
+    def best_values(self):
+        if self._result is None:
+            return(None)
+        return({name:self._result.params[name].value for name in sorted(self._result.params)
+                if name != 'tmp_normalization_offset_c'})
+
+    @property
+    def chisqr(self):
+        if self._result is None:
+            return(None)
+        return(self._result.chisqr)
+
+    @property
+    def components(self):
+        components = {}
+        if self._result is None:
+            logging.warning('Unable to collect components in Fit.components')
+            return(components)
+        for component in self._result.components:
+            if 'tmp_normalization_offset_c' in component.param_names:
+                continue
+            parameters = {}
+            for name in component.param_names:
+                par = self._parameters[name]
+                parameters[name] = {'free': par.vary, 'value': self._result.params[name].value}
+                if par.expr is not None:
+                    parameters[name]['expr'] = par.expr
+            expr = None
+            if isinstance(component, ExpressionModel):
+                name = component._name
+                if name[-1] == '_':
+                    name = name[:-1]
+                expr = component.expr
+            else:
+                prefix = component.prefix
+                if len(prefix):
+                    if prefix[-1] == '_':
+                        prefix = prefix[:-1]
+                    name = f'{prefix} ({component._name})'
+                else:
+                    name = f'{component._name}'
+            if expr is None:
+                components[name] = {'parameters': parameters}
+            else:
+                components[name] = {'expr': expr, 'parameters': parameters}
+        return(components)
+
+    @property
+    def covar(self):
+        if self._result is None:
+            return(None)
+        return(self._result.covar)
+
+    @property
+    def init_parameters(self):
+        if self._result is None or self._result.init_params is None:
+            return(None)
+        parameters = {}
+        for name in sorted(self._result.init_params):
+            if name != 'tmp_normalization_offset_c':
+                par = self._result.init_params[name]
+                parameters[name] = {'value': par.value, 'min': par.min, 'max': par.max,
+                        'vary': par.vary, 'expr': par.expr}
+        return(parameters)
+
+    @property
+    def init_values(self):
+        if self._result is None or self._result.init_params is None:
+            return(None)
+        return({name:self._result.init_params[name].value for name in
+                sorted(self._result.init_params) if name != 'tmp_normalization_offset_c'})
+
+    @property
+    def normalization_offset(self):
+        if self._result is None:
+            return(None)
+        if self._norm is None:
+            return(0.0)
+        else:
+            if self._result.init_params is not None:
+                normalization_offset = self._result.init_params['tmp_normalization_offset_c']
+            else:
+                normalization_offset = self._result.params['tmp_normalization_offset_c']
+            return(normalization_offset)
+
+    @property
+    def num_func_eval(self):
+        if self._result is None:
+            return(None)
+        return(self._result.nfev)
+
+    @property
+    def parameters(self):
+        return({name:{'min': par.min, 'max': par.max, 'vary': par.vary, 'expr': par.expr}
+                for name, par in self._parameters.items() if name != 'tmp_normalization_offset_c'})
+
+    @property
+    def redchi(self):
+        if self._result is None:
+            return(None)
+        return(self._result.redchi)
+
+    @property
+    def residual(self):
+        if self._result is None:
+            return(None)
+        return(self._result.residual)
+
+    @property
+    def success(self):
+        if self._result is None:
+            return(None)
+        if not self._result.success:
+#            print(f'ier = {self._result.ier}')
+#            print(f'lmdif_message = {self._result.lmdif_message}')
+#            print(f'message = {self._result.message}')
+#            print(f'nfev = {self._result.nfev}')
+#            print(f'redchi = {self._result.redchi}')
+#            print(f'success = {self._result.success}')
+            if self._result.ier == 0 or self._result.ier == 5:
+                logging.warning(f'ier = {self._result.ier}: {self._result.message}')
+            else:
+                logging.warning(f'ier = {self._result.ier}: {self._result.message}')
+                return(True)
+#            self.print_fit_report()
+#            self.plot()
+        return(self._result.success)
+
+    @property
+    def var_names(self):
+        """Intended to be used with covar
+        """
+        if self._result is None:
+            return(None)
+        return(getattr(self._result, 'var_names', None))
+
+    @property
+    def x(self):
+        return(self._x)
+
+    @property
+    def y(self):
+        return(self._y)
+
+    def print_fit_report(self, result=None, show_correl=False):
+        if result is None:
+            result = self._result
+        if result is not None:
+            print(result.fit_report(show_correl=show_correl))
+
+    def add_parameter(self, **parameter):
+        if not isinstance(parameter, dict):
+            raise ValueError(f'Invalid parameter ({parameter})')
+        if parameter.get('expr') is not None:
+            raise KeyError(f'Illegal "expr" key in parameter {parameter}')
+        name = parameter['name']
+        if not isinstance(name, str):
+            raise ValueError(f'Illegal "name" value ({name}) in parameter {parameter}')
+        if parameter.get('norm') is None:
+            self._parameter_norms[name] = False
+        else:
+            norm = parameter.pop('norm')
+            if self._norm is None:
+                logging.warning(f'Ignoring norm in parameter {name} in '+
+                            f'Fit.add_parameter (normalization is turned off)')
+                self._parameter_norms[name] = False
+            else:
+                if not isinstance(norm, bool):
+                    raise ValueError(f'Illegal "norm" value ({norm}) in parameter {parameter}')
+                self._parameter_norms[name] = norm
+        vary = parameter.get('vary')
+        if vary is not None:
+            if not isinstance(vary, bool):
+                raise ValueError(f'Illegal "vary" value ({vary}) in parameter {parameter}')
+            if not vary:
+                if 'min' in parameter:
+                    logging.warning(f'Ignoring min in parameter {name} in '+
+                            f'Fit.add_parameter (vary = {vary})')
+                    parameter.pop('min')
+                if 'max' in parameter:
+                    logging.warning(f'Ignoring max in parameter {name} in '+
+                            f'Fit.add_parameter (vary = {vary})')
+                    parameter.pop('max')
+        if self._norm is not None and name not in self._parameter_norms:
+            raise ValueError(f'Missing parameter normalization type for paremeter {name}')
+        self._parameters.add(**parameter)
+
+    def add_model(self, model, prefix=None, parameters=None, parameter_norms=None, **kwargs):
+        # Create the new model
+#        print(f'at start add_model:\nself._parameters:\n{self._parameters}')
+#        print(f'at start add_model: kwargs = {kwargs}')
+#        print(f'parameters = {parameters}')
+#        print(f'parameter_norms = {parameter_norms}')
+#        if len(self._parameters.keys()):
+#            print('\nAt start adding model:')
+#            self._parameters.pretty_print()
+#            print(f'parameter_norms:\n{self._parameter_norms}')
+        if prefix is not None and not isinstance(prefix, str):
+            logging.warning('Ignoring illegal prefix: {model} {type(model)}')
+            prefix = None
+        if prefix is None:
+            pprefix = ''
+        else:
+            pprefix = prefix
+        if parameters is not None:
+            if isinstance(parameters, dict):
+                parameters = (parameters, )
+            elif not is_dict_series(parameters):
+                illegal_value(parameters, 'parameters', 'Fit.add_model', raise_error=True)
+            parameters = deepcopy(parameters)
+        if parameter_norms is not None:
+            if isinstance(parameter_norms, dict):
+                parameter_norms = (parameter_norms, )
+            if not is_dict_series(parameter_norms):
+                illegal_value(parameter_norms, 'parameter_norms', 'Fit.add_model', raise_error=True)
+        new_parameter_norms = {}
+        if callable(model):
+            # Linear fit not yet implemented for callable models
+            self._try_linear_fit = False
+            if parameter_norms is None:
+                if parameters is None:
+                    raise ValueError('Either "parameters" or "parameter_norms" is required in '+
+                            f'{model}')
+                for par in parameters:
+                    name = par['name']
+                    if not isinstance(name, str):
+                        raise ValueError(f'Illegal "name" value ({name}) in input parameters')
+                    if par.get('norm') is not None:
+                        norm = par.pop('norm')
+                        if not isinstance(norm, bool):
+                            raise ValueError(f'Illegal "norm" value ({norm}) in input parameters')
+                        new_parameter_norms[f'{pprefix}{name}'] = norm
+            else:
+                for par in parameter_norms:
+                    name = par['name']
+                    if not isinstance(name, str):
+                        raise ValueError(f'Illegal "name" value ({name}) in input parameters')
+                    norm = par.get('norm')
+                    if norm is None or not isinstance(norm, bool):
+                        raise ValueError(f'Illegal "norm" value ({norm}) in input parameters')
+                    new_parameter_norms[f'{pprefix}{name}'] = norm
+            if parameters is not None:
+                for par in parameters:
+                    if par.get('expr') is not None:
+                        raise KeyError(f'Illegal "expr" key ({par.get("expr")}) in parameter '+
+                                f'{name} for a callable model {model}')
+                    name = par['name']
+                    if not isinstance(name, str):
+                        raise ValueError(f'Illegal "name" value ({name}) in input parameters')
+# RV FIX callable model will need partial deriv functions for any linear pars to get the linearized matrix, so for now skip linear solution option
+            newmodel = Model(model, prefix=prefix)
+        elif isinstance(model, str):
+            if model == 'constant':      # Par: c
+                newmodel = ConstantModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}c'] = True
+                self._linear_parameters.append(f'{pprefix}c')
+            elif model == 'linear':      # Par: slope, intercept
+                newmodel = LinearModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}slope'] = True
+                new_parameter_norms[f'{pprefix}intercept'] = True
+                self._linear_parameters.append(f'{pprefix}slope')
+                self._linear_parameters.append(f'{pprefix}intercept')
+            elif model == 'quadratic':   # Par: a, b, c
+                newmodel = QuadraticModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}a'] = True
+                new_parameter_norms[f'{pprefix}b'] = True
+                new_parameter_norms[f'{pprefix}c'] = True
+                self._linear_parameters.append(f'{pprefix}a')
+                self._linear_parameters.append(f'{pprefix}b')
+                self._linear_parameters.append(f'{pprefix}c')
+            elif model == 'gaussian':    # Par: amplitude, center, sigma (fwhm, height)
+                newmodel = GaussianModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}amplitude'] = True
+                new_parameter_norms[f'{pprefix}center'] = False
+                new_parameter_norms[f'{pprefix}sigma'] = False
+                self._linear_parameters.append(f'{pprefix}amplitude')
+                self._nonlinear_parameters.append(f'{pprefix}center')
+                self._nonlinear_parameters.append(f'{pprefix}sigma')
+                # parameter norms for height and fwhm are needed to get correct errors
+                new_parameter_norms[f'{pprefix}height'] = True
+                new_parameter_norms[f'{pprefix}fwhm'] = False
+            elif model == 'lorentzian':    # Par: amplitude, center, sigma (fwhm, height)
+                newmodel = LorentzianModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}amplitude'] = True
+                new_parameter_norms[f'{pprefix}center'] = False
+                new_parameter_norms[f'{pprefix}sigma'] = False
+                self._linear_parameters.append(f'{pprefix}amplitude')
+                self._nonlinear_parameters.append(f'{pprefix}center')
+                self._nonlinear_parameters.append(f'{pprefix}sigma')
+                # parameter norms for height and fwhm are needed to get correct errors
+                new_parameter_norms[f'{pprefix}height'] = True
+                new_parameter_norms[f'{pprefix}fwhm'] = False
+            elif model == 'exponential': # Par: amplitude, decay
+                newmodel = ExponentialModel(prefix=prefix)
+                new_parameter_norms[f'{pprefix}amplitude'] = True
+                new_parameter_norms[f'{pprefix}decay'] = False
+                self._linear_parameters.append(f'{pprefix}amplitude')
+                self._nonlinear_parameters.append(f'{pprefix}decay')
+            elif model == 'step':        # Par: amplitude, center, sigma
+                form = kwargs.get('form')
+                if form is not None:
+                    kwargs.pop('form')
+                if form is None or form not in ('linear', 'atan', 'arctan', 'erf', 'logistic'):
+                    raise ValueError(f'Invalid parameter form for build-in step model ({form})')
+                newmodel = StepModel(prefix=prefix, form=form)
+                new_parameter_norms[f'{pprefix}amplitude'] = True
+                new_parameter_norms[f'{pprefix}center'] = False
+                new_parameter_norms[f'{pprefix}sigma'] = False
+                self._linear_parameters.append(f'{pprefix}amplitude')
+                self._nonlinear_parameters.append(f'{pprefix}center')
+                self._nonlinear_parameters.append(f'{pprefix}sigma')
+            elif model == 'rectangle':   # Par: amplitude, center1, center2, sigma1, sigma2
+                form = kwargs.get('form')
+                if form is not None:
+                    kwargs.pop('form')
+                if form is None or form not in ('linear', 'atan', 'arctan', 'erf', 'logistic'):
+                    raise ValueError('Invalid parameter form for build-in rectangle model '+
+                            f'({form})')
+                newmodel = RectangleModel(prefix=prefix, form=form)
+                new_parameter_norms[f'{pprefix}amplitude'] = True
+                new_parameter_norms[f'{pprefix}center1'] = False
+                new_parameter_norms[f'{pprefix}center2'] = False
+                new_parameter_norms[f'{pprefix}sigma1'] = False
+                new_parameter_norms[f'{pprefix}sigma2'] = False
+                self._linear_parameters.append(f'{pprefix}amplitude')
+                self._nonlinear_parameters.append(f'{pprefix}center1')
+                self._nonlinear_parameters.append(f'{pprefix}center2')
+                self._nonlinear_parameters.append(f'{pprefix}sigma1')
+                self._nonlinear_parameters.append(f'{pprefix}sigma2')
+            elif model == 'expression':  # Par: by expression
+                expr = kwargs['expr']
+                if not isinstance(expr, str):
+                    raise ValueError(f'Illegal "expr" value ({expr}) in {model}')
+                kwargs.pop('expr')
+                if parameter_norms is not None:
+                        logging.warning('Ignoring parameter_norms (normalization determined from '+
+                                'linearity)}')
+                if parameters is not None:
+                    for par in parameters:
+                        if par.get('expr') is not None:
+                            raise KeyError(f'Illegal "expr" key ({par.get("expr")}) in parameter '+
+                                    f'({par}) for an expression model')
+                        if par.get('norm') is not None:
+                            logging.warning(f'Ignoring "norm" key in parameter ({par}) '+
+                                '(normalization determined from linearity)}')
+                            par.pop('norm')
+                        name = par['name']
+                        if not isinstance(name, str):
+                            raise ValueError(f'Illegal "name" value ({name}) in input parameters')
+                ast = Interpreter()
+                expr_parameters = [name for name in get_ast_names(ast.parse(expr))
+                        if name != 'x' and name not in self._parameters
+                        and name not in ast.symtable]
+#                print(f'\nexpr_parameters: {expr_parameters}')
+#                print(f'expr = {expr}')
+                if prefix is None:
+                    newmodel = ExpressionModel(expr=expr)
+                else:
+                    for name in expr_parameters:
+                        expr = sub(rf'\b{name}\b', f'{prefix}{name}', expr)
+                    expr_parameters = [f'{prefix}{name}' for name in expr_parameters]
+#                    print(f'\nexpr_parameters: {expr_parameters}')
+#                    print(f'expr = {expr}')
+                    newmodel = ExpressionModel(expr=expr, name=name)
+#                print(f'\nnewmodel = {newmodel.__dict__}')
+#                print(f'params_names = {newmodel._param_names}')
+#                print(f'params_names = {newmodel.param_names}')
+                # Remove already existing names
+                for name in newmodel.param_names.copy():
+                    if name not in expr_parameters:
+                        newmodel._func_allargs.remove(name)
+                        newmodel._param_names.remove(name)
+#                print(f'params_names = {newmodel._param_names}')
+#                print(f'params_names = {newmodel.param_names}')
+            else:
+                raise ValueError(f'Unknown build-in fit model ({model})')
+        else:
+            illegal_value(model, 'model', 'Fit.add_model', raise_error=True)
+
+        # Add the new model to the current one
+#        print('\nBefore adding model:')
+#        print(f'\nnewmodel = {newmodel.__dict__}')
+#        if len(self._parameters):
+#            self._parameters.pretty_print()
+        if self._model is None:
+            self._model = newmodel
+        else:
+            self._model += newmodel
+        new_parameters = newmodel.make_params()
+        self._parameters += new_parameters
+#        print('\nAfter adding model:')
+#        print(f'\nnewmodel = {newmodel.__dict__}')
+#        print(f'\nnew_parameters = {new_parameters}')
+#        self._parameters.pretty_print()
+
+        # Check linearity of expression model paremeters
+        if isinstance(newmodel, ExpressionModel):
+            for name in newmodel.param_names:
+                if not diff(newmodel.expr, name, name):
+                    if name not in self._linear_parameters:
+                        self._linear_parameters.append(name)
+                        new_parameter_norms[name] = True
+#                        print(f'\nADDING {name} TO LINEAR')
+                else:
+                    if name not in self._nonlinear_parameters:
+                        self._nonlinear_parameters.append(name)
+                        new_parameter_norms[name] = False
+#                        print(f'\nADDING {name} TO NONLINEAR')
+#        print(f'new_parameter_norms:\n{new_parameter_norms}')
+
+        # Scale the default initial model parameters
+        if self._norm is not None:
+            for name, norm in new_parameter_norms.copy().items():
+                par = self._parameters.get(name)
+                if par is None:
+                    new_parameter_norms.pop(name)
+                    continue
+                if par.expr is None and norm:
+                    value = par.value*self._norm[1]
+                    _min = par.min
+                    _max = par.max
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min *= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max *= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+#        print('\nAfter norm defaults:')
+#        self._parameters.pretty_print()
+#        print(f'parameters:\n{parameters}')
+#        print(f'all_parameters:\n{list(self.parameters)}')
+#        print(f'new_parameter_norms:\n{new_parameter_norms}')
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+
+        # Initialize the model parameters from parameters
+        if prefix is None:
+            prefix = ""
+        if parameters is not None:
+            for parameter in parameters:
+                name = parameter['name']
+                if not isinstance(name, str):
+                    raise ValueError(f'Illegal "name" value ({name}) in input parameters')
+                if name not in new_parameters:
+                    name = prefix+name
+                    parameter['name'] = name
+                if name not in new_parameters:
+                    logging.warning(f'Ignoring superfluous parameter info for {name}')
+                    continue
+                if name in self._parameters:
+                    parameter.pop('name')
+                    if 'norm' in parameter:
+                        if not isinstance(parameter['norm'], bool):
+                            illegal_value(parameter['norm'], 'norm', 'Fit.add_model',
+                                    raise_error=True)
+                        new_parameter_norms[name] = parameter['norm']
+                        parameter.pop('norm')
+                    if parameter.get('expr') is not None:
+                        if 'value' in parameter:
+                            logging.warning(f'Ignoring value in parameter {name} '+
+                                    f'(set by expression: {parameter["expr"]})')
+                            parameter.pop('value')
+                        if 'vary' in parameter:
+                            logging.warning(f'Ignoring vary in parameter {name} '+
+                                    f'(set by expression: {parameter["expr"]})')
+                            parameter.pop('vary')
+                        if 'min' in parameter:
+                            logging.warning(f'Ignoring min in parameter {name} '+
+                                    f'(set by expression: {parameter["expr"]})')
+                            parameter.pop('min')
+                        if 'max' in parameter:
+                            logging.warning(f'Ignoring max in parameter {name} '+
+                                    f'(set by expression: {parameter["expr"]})')
+                            parameter.pop('max')
+                    if 'vary' in parameter:
+                        if not isinstance(parameter['vary'], bool):
+                            illegal_value(parameter['vary'], 'vary', 'Fit.add_model',
+                                    raise_error=True)
+                        if not parameter['vary']:
+                            if 'min' in parameter:
+                                logging.warning(f'Ignoring min in parameter {name} in '+
+                                        f'Fit.add_model (vary = {parameter["vary"]})')
+                                parameter.pop('min')
+                            if 'max' in parameter:
+                                logging.warning(f'Ignoring max in parameter {name} in '+
+                                        f'Fit.add_model (vary = {parameter["vary"]})')
+                                parameter.pop('max')
+                    self._parameters[name].set(**parameter)
+                    parameter['name'] = name
+                else:
+                    illegal_value(parameter, 'parameter name', 'Fit.model', raise_error=True)
+        self._parameter_norms = {**self._parameter_norms, **new_parameter_norms}
+#        print('\nAfter parameter init:')
+#        self._parameters.pretty_print()
+#        print(f'parameters:\n{parameters}')
+#        print(f'new_parameter_norms:\n{new_parameter_norms}')
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+#        print(f'kwargs:\n{kwargs}')
+
+        # Initialize the model parameters from kwargs
+        for name, value in {**kwargs}.items():
+            full_name = f'{pprefix}{name}'
+            if full_name in new_parameter_norms and isinstance(value, (int, float)):
+                kwargs.pop(name)
+                if self._parameters[full_name].expr is None:
+                    self._parameters[full_name].set(value=value)
+                else:
+                    logging.warning(f'Ignoring parameter {name} in Fit.fit (set by expression: '+
+                            f'{self._parameters[full_name].expr})')
+#        print('\nAfter kwargs init:')
+#        self._parameters.pretty_print()
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+#        print(f'kwargs:\n{kwargs}')
+
+        # Check parameter norms (also need it for expressions to renormalize the errors)
+        if self._norm is not None and (callable(model) or model == 'expression'):
+            missing_norm = False
+            for name in new_parameters.valuesdict():
+                if name not in self._parameter_norms:
+                    print(f'new_parameters:\n{new_parameters.valuesdict()}')
+                    print(f'self._parameter_norms:\n{self._parameter_norms}')
+                    logging.error(f'Missing parameter normalization type for {name} in {model}')
+                    missing_norm = True
+            if missing_norm:
+                raise ValueError
+
+#        print(f'at end add_model:\nself._parameters:\n{list(self.parameters)}')
+#        print(f'at end add_model: kwargs = {kwargs}')
+#        print(f'\nat end add_model: newmodel:\n{newmodel.__dict__}\n')
+        return(kwargs)
+
+    def fit(self, interactive=False, guess=False, **kwargs):
+        # Check inputs
+        if self._model is None:
+            logging.error('Undefined fit model')
+            return
+        if not isinstance(interactive, bool):
+            illegal_value(interactive, 'interactive', 'Fit.fit', raise_error=True)
+        if not isinstance(guess, bool):
+            illegal_value(guess, 'guess', 'Fit.fit', raise_error=True)
+        if 'try_linear_fit' in kwargs:
+            try_linear_fit = kwargs.pop('try_linear_fit')
+            if not isinstance(try_linear_fit, bool):
+                illegal_value(try_linear_fit, 'try_linear_fit', 'Fit.fit', raise_error=True)
+            if not self._try_linear_fit:
+                logging.warning('Ignore superfluous keyword argument "try_linear_fit" (not '+
+                        'yet supported for callable models)')
+            else:
+                self._try_linear_fit = try_linear_fit
+#        if self._result is None:
+#            if 'parameters' in kwargs:
+#                raise ValueError('Invalid parameter parameters ({kwargs["parameters"]})')
+#        else:
+        if self._result is not None:
+            if guess:
+                logging.warning('Ignoring input parameter guess in Fit.fit during refitting')
+                guess = False
+
+        # Check for circular expressions
+        # FIX TODO
+#        for name1, par1 in self._parameters.items():
+#            if par1.expr is not None:
+
+        # Apply mask if supplied:
+        if 'mask' in kwargs:
+            self._mask = kwargs.pop('mask')
+        if self._mask is not None:
+            self._mask = np.asarray(self._mask).astype(bool)
+            if self._x.size != self._mask.size:
+                raise ValueError(f'Inconsistent x and mask dimensions ({self._x.size} vs '+
+                        f'{self._mask.size})')
+
+        # Estimate initial parameters with build-in lmfit guess method (only for a single model)
+#        print(f'\nat start fit: kwargs = {kwargs}')
+#RV        print('\nAt start of fit:')
+#RV        self._parameters.pretty_print()
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+        if guess:
+            if self._mask is None:
+                self._parameters = self._model.guess(self._y, x=self._x)
+            else:
+                self._parameters = self._model.guess(np.asarray(self._y)[~self._mask],
+                        x=self._x[~self._mask])
+#            print('\nAfter guess:')
+#            self._parameters.pretty_print()
+
+        # Add constant offset for a normalized model
+        if self._result is None and self._norm is not None and self._norm[0]:
+            self.add_model('constant', prefix='tmp_normalization_offset_', parameters={'name': 'c',
+                    'value': -self._norm[0], 'vary': False, 'norm': True})
+                    #'value': -self._norm[0]/self._norm[1], 'vary': False, 'norm': False})
+
+        # Adjust existing parameters for refit:
+        if 'parameters' in kwargs:
+            parameters = kwargs.pop('parameters')
+            if isinstance(parameters, dict):
+                parameters = (parameters, )
+            elif not is_dict_series(parameters):
+                illegal_value(parameters, 'parameters', 'Fit.fit', raise_error=True)
+            for par in parameters:
+                name = par['name']
+                if name not in self._parameters:
+                    raise ValueError(f'Unable to match {name} parameter {par} to an existing one')
+                if self._parameters[name].expr is not None:
+                    raise ValueError(f'Unable to modify {name} parameter {par} (currently an '+
+                            'expression)')
+                if par.get('expr') is not None:
+                    raise KeyError(f'Illegal "expr" key in {name} parameter {par}')
+                self._parameters[name].set(vary=par.get('vary'))
+                self._parameters[name].set(min=par.get('min'))
+                self._parameters[name].set(max=par.get('max'))
+                self._parameters[name].set(value=par.get('value'))
+#RV            print('\nAfter adjust:')
+#RV            self._parameters.pretty_print()
+
+        # Apply parameter updates through keyword arguments
+#        print(f'kwargs = {kwargs}')
+#        print(f'parameter_norms = {self._parameter_norms}')
+        for name in set(self._parameters) & set(kwargs):
+            value = kwargs.pop(name)
+            if self._parameters[name].expr is None:
+                self._parameters[name].set(value=value)
+            else:
+                logging.warning(f'Ignoring parameter {name} in Fit.fit (set by expression: '+
+                        f'{self._parameters[name].expr})')
+
+        # Check for uninitialized parameters
+        for name, par in self._parameters.items():
+            if par.expr is None:
+                value = par.value
+                if value is None or np.isinf(value) or np.isnan(value):
+                    if interactive:
+                        value = input_num(f'Enter an initial value for {name}', default=1.0)
+                    else:
+                        value = 1.0
+                    if self._norm is None or name not in self._parameter_norms:
+                        self._parameters[name].set(value=value)
+                    elif self._parameter_norms[name]:
+                        self._parameters[name].set(value=value*self._norm[1])
+
+        # Check if model is linear
+        try:
+            linear_model = self._check_linearity_model()
+        except:
+            linear_model = False
+#        print(f'\n\n--------> linear_model = {linear_model}\n')
+        if kwargs.get('check_only_linearity') is not None:
+            return(linear_model)
+
+        # Normalize the data and initial parameters
+#RV        print('\nBefore normalization:')
+#RV        self._parameters.pretty_print()
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+        self._normalize()
+#        print(f'norm = {self._norm}') 
+#RV        print('\nAfter normalization:')
+#RV        self._parameters.pretty_print()
+#        self.print_fit_report()
+#        print(f'parameter_norms:\n{self._parameter_norms}')
+
+        if linear_model:
+            # Perform a linear fit by direct matrix solution with numpy
+            try:
+                if self._mask is None:
+                    self._fit_linear_model(self._x, self._y_norm)
+                else:
+                    self._fit_linear_model(self._x[~self._mask],
+                            np.asarray(self._y_norm)[~self._mask])
+            except:
+                linear_model = False
+        if not linear_model:
+            # Perform a non-linear fit with lmfit
+            # Prevent initial values from sitting at boundaries
+            self._parameter_bounds = {name:{'min': par.min, 'max': par.max} for name, par in
+                    self._parameters.items() if par.vary}
+            for par in self._parameters.values():
+                if par.vary:
+                    par.set(value=self._reset_par_at_boundary(par, par.value))
+#            print('\nAfter checking boundaries:')
+#            self._parameters.pretty_print()
+
+            # Perform the fit
+#            fit_kws = None
+#            if 'Dfun' in kwargs:
+#                fit_kws = {'Dfun': kwargs.pop('Dfun')}
+#            self._result = self._model.fit(self._y_norm, self._parameters, x=self._x,
+#                    fit_kws=fit_kws, **kwargs)
+            if self._mask is None:
+                self._result = self._model.fit(self._y_norm, self._parameters, x=self._x, **kwargs)
+            else:
+                self._result = self._model.fit(np.asarray(self._y_norm)[~self._mask],
+                        self._parameters, x=self._x[~self._mask], **kwargs)
+#RV        print('\nAfter fit:')
+#        print(f'\nself._result ({self._result}):\n\t{self._result.__dict__}')
+#RV        self._parameters.pretty_print()
+#        self.print_fit_report()
+
+        # Set internal parameter values to fit results upon success
+        if self.success:
+            for name, par in self._parameters.items():
+                if par.expr is None and par.vary:
+                    par.set(value=self._result.params[name].value)
+#            print('\nAfter update parameter values:')
+#            self._parameters.pretty_print()
+
+        # Renormalize the data and results
+        self._renormalize()
+#RV        print('\nAfter renormalization:')
+#RV        self._parameters.pretty_print()
+#        self.print_fit_report()
+
+    def plot(self, y=None, y_title=None, result=None, skip_init=False, plot_comp_legends=False,
+            plot_residual=False, plot_masked_data=True, **kwargs):
+        if result is None:
+            result = self._result
+        if result is None:
+            return
+        plots = []
+        legend = []
+        if self._mask is None:
+            mask = np.zeros(self._x.size).astype(bool)
+            plot_masked_data = False
+        else:
+            mask = self._mask
+        if y is not None:
+            if not isinstance(y, (tuple, list, np.ndarray)):
+                illegal_value(y, 'y', 'Fit.plot')
+            if len(y) != len(self._x):
+                logging.warning('Ignoring parameter y in Fit.plot (wrong dimension)')
+                y = None
+        if y is not None:
+            if y_title is None or not isinstance(y_title, str):
+                y_title = 'data'
+            plots += [(self._x, y, '.')]
+            legend += [y_title]
+        if self._y is not None:
+            plots += [(self._x, np.asarray(self._y), 'b.')]
+            legend += ['data']
+            if plot_masked_data:
+                plots += [(self._x[mask], np.asarray(self._y)[mask], 'bx')]
+                legend += ['masked data']
+        if isinstance(plot_residual, bool) and plot_residual:
+            plots += [(self._x[~mask], result.residual, 'k-')]
+            legend += ['residual']
+        plots += [(self._x[~mask], result.best_fit, 'k-')]
+        legend += ['best fit']
+        if not skip_init and hasattr(result, 'init_fit'):
+            plots += [(self._x[~mask], result.init_fit, 'g-')]
+            legend += ['init']
+        components = result.eval_components(x=self._x[~mask])
+        num_components = len(components)
+        if 'tmp_normalization_offset_' in components:
+            num_components -= 1
+        if num_components > 1:
+            eval_index = 0
+            for modelname, y in components.items():
+                if modelname == 'tmp_normalization_offset_':
+                    continue
+                if modelname == '_eval':
+                    modelname = f'eval{eval_index}'
+                if len(modelname) > 20:
+                    modelname = f'{modelname[0:16]} ...'
+                if isinstance(y, (int, float)):
+                    y *= np.ones(self._x[~mask].size)
+                plots += [(self._x[~mask], y, '--')]
+                if plot_comp_legends:
+                    if modelname[-1] == '_':
+                        legend.append(modelname[:-1])
+                    else:
+                        legend.append(modelname)
+        title = kwargs.get('title')
+        if title is not None:
+            kwargs.pop('title')
+        quick_plot(tuple(plots), legend=legend, title=title, block=True, **kwargs)
+
+    @staticmethod
+    def guess_init_peak(x, y, *args, center_guess=None, use_max_for_center=True):
+        """ Return a guess for the initial height, center and fwhm for a peak
+        """
+#        print(f'\n\nargs = {args}')
+#        print(f'center_guess = {center_guess}')
+#        quick_plot(x, y, vlines=center_guess, block=True)
+        center_guesses = None
+        x = np.asarray(x)
+        y = np.asarray(y)
+        if len(x) != len(y):
+            logging.error(f'Invalid x and y lengths ({len(x)}, {len(y)}), skip initial guess')
+            return(None, None, None)
+        if isinstance(center_guess, (int, float)):
+            if len(args):
+                logging.warning('Ignoring additional arguments for single center_guess value')
+            center_guesses = [center_guess]
+        elif isinstance(center_guess, (tuple, list, np.ndarray)):
+            if len(center_guess) == 1:
+                logging.warning('Ignoring additional arguments for single center_guess value')
+                if not isinstance(center_guess[0], (int, float)):
+                    raise ValueError(f'Invalid parameter center_guess ({type(center_guess[0])})')
+                center_guess = center_guess[0]
+            else:
+                if len(args) != 1:
+                    raise ValueError(f'Invalid number of arguments ({len(args)})')
+                n = args[0]
+                if not is_index(n, 0, len(center_guess)):
+                    raise ValueError('Invalid argument')
+                center_guesses = center_guess
+                center_guess = center_guesses[n]
+        elif center_guess is not None:
+            raise ValueError(f'Invalid center_guess type ({type(center_guess)})')
+#        print(f'x = {x}')
+#        print(f'y = {y}')
+#        print(f'center_guess = {center_guess}')
+
+        # Sort the inputs
+        index = np.argsort(x)
+        x = x[index]
+        y = y[index]
+        miny = y.min()
+#        print(f'miny = {miny}')
+#        print(f'x_range = {x[0]} {x[-1]} {len(x)}')
+#        print(f'y_range = {y[0]} {y[-1]} {len(y)}')
+#        quick_plot(x, y, vlines=center_guess, block=True)
+
+#        xx = x
+#        yy = y
+        # Set range for current peak
+#        print(f'n = {n}')
+#        print(f'center_guesses = {center_guesses}')
+        if center_guesses is not None:
+            if len(center_guesses) > 1:
+                index = np.argsort(center_guesses)
+                n = list(index).index(n)
+#                print(f'n = {n}')
+#                print(f'index = {index}')
+                center_guesses = np.asarray(center_guesses)[index]
+#                print(f'center_guesses = {center_guesses}')
+            if n == 0:
+               low = 0
+               upp = index_nearest(x, (center_guesses[0]+center_guesses[1])/2)
+            elif n == len(center_guesses)-1:
+               low = index_nearest(x, (center_guesses[n-1]+center_guesses[n])/2)
+               upp = len(x)
+            else:
+               low = index_nearest(x, (center_guesses[n-1]+center_guesses[n])/2)
+               upp = index_nearest(x, (center_guesses[n]+center_guesses[n+1])/2)
+#            print(f'low = {low}')
+#            print(f'upp = {upp}')
+            x = x[low:upp]
+            y = y[low:upp]
+#            quick_plot(x, y, vlines=(x[0], center_guess, x[-1]), block=True)
+
+        # Estimate FHHM
+        maxy = y.max()
+#        print(f'x_range = {x[0]} {x[-1]} {len(x)}')
+#        print(f'y_range = {y[0]} {y[-1]} {len(y)} {miny} {maxy}')
+#        print(f'center_guess = {center_guess}')
+        if center_guess is None:
+            center_index = np.argmax(y)
+            center = x[center_index]
+            height = maxy-miny
+        else:
+            if use_max_for_center:
+                center_index = np.argmax(y)
+                center = x[center_index]
+                if center_index < 0.1*len(x) or center_index > 0.9*len(x):
+                    center_index = index_nearest(x, center_guess)
+                    center = center_guess
+            else:
+                center_index = index_nearest(x, center_guess)
+                center = center_guess
+            height = y[center_index]-miny
+#        print(f'center_index = {center_index}')
+#        print(f'center = {center}')
+#        print(f'height = {height}')
+        half_height = miny+0.5*height
+#        print(f'half_height = {half_height}')
+        fwhm_index1 = 0
+        for i in range(center_index, fwhm_index1, -1):
+            if y[i] < half_height:
+                fwhm_index1 = i
+                break
+#        print(f'fwhm_index1 = {fwhm_index1} {x[fwhm_index1]}')
+        fwhm_index2 = len(x)-1
+        for i in range(center_index, fwhm_index2):
+            if y[i] < half_height:
+                fwhm_index2 = i
+                break
+#        print(f'fwhm_index2 = {fwhm_index2} {x[fwhm_index2]}')
+#        quick_plot((x,y,'o'), vlines=(x[fwhm_index1], center, x[fwhm_index2]), block=True)
+        if fwhm_index1 == 0 and fwhm_index2 < len(x)-1:
+            fwhm = 2*(x[fwhm_index2]-center)
+        elif fwhm_index1 > 0 and fwhm_index2 == len(x)-1:
+            fwhm = 2*(center-x[fwhm_index1])
+        else:
+            fwhm = x[fwhm_index2]-x[fwhm_index1]
+#        print(f'fwhm_index1 = {fwhm_index1} {x[fwhm_index1]}')
+#        print(f'fwhm_index2 = {fwhm_index2} {x[fwhm_index2]}')
+#        print(f'fwhm = {fwhm}')
+
+        # Return height, center and FWHM
+#        quick_plot((x,y,'o'), (xx,yy), vlines=(x[fwhm_index1], center, x[fwhm_index2]), block=True)
+        return(height, center, fwhm)
+
+    def _check_linearity_model(self):
+        """Identify the linearity of all model parameters and check if the model is linear or not
+        """
+        if not self._try_linear_fit:
+            logging.info('Skip linearity check (not yet supported for callable models)')
+            return(False)
+        free_parameters = [name for name, par in self._parameters.items() if par.vary]
+        for component in self._model.components:
+            if 'tmp_normalization_offset_c' in component.param_names:
+                continue
+            if isinstance(component, ExpressionModel):
+                for name in free_parameters:
+                    if diff(component.expr, name, name):
+#                        print(f'\t\t{component.expr} is non-linear in {name}')
+                        self._nonlinear_parameters.append(name)
+                        if name in self._linear_parameters:
+                            self._linear_parameters.remove(name)
+            else:
+                model_parameters = component.param_names.copy()
+                for basename, hint in component.param_hints.items():
+                    name = f'{component.prefix}{basename}'
+                    if hint.get('expr') is not None:
+                        model_parameters.remove(name)
+                for name in model_parameters:
+                    expr = self._parameters[name].expr
+                    if expr is not None:
+                        for nname in free_parameters:
+                            if name in self._nonlinear_parameters:
+                                if diff(expr, nname):
+#                                    print(f'\t\t{component} is non-linear in {nname} (through {name} = "{expr}")')
+                                    self._nonlinear_parameters.append(nname)
+                                    if nname in self._linear_parameters:
+                                        self._linear_parameters.remove(nname)
+                            else:
+                                assert(name in self._linear_parameters)
+#                                print(f'\n\nexpr ({type(expr)}) = {expr}\nnname ({type(nname)}) = {nname}\n\n')
+                                if diff(expr, nname, nname):
+#                                    print(f'\t\t{component} is non-linear in {nname} (through {name} = "{expr}")')
+                                    self._nonlinear_parameters.append(nname)
+                                    if nname in self._linear_parameters:
+                                        self._linear_parameters.remove(nname)
+#        print(f'\nfree parameters:\n\t{free_parameters}')
+#        print(f'linear parameters:\n\t{self._linear_parameters}')
+#        print(f'nonlinear parameters:\n\t{self._nonlinear_parameters}\n')
+        if any(True for name in self._nonlinear_parameters if self._parameters[name].vary):
+            return(False)
+        return(True)
+
+    def _fit_linear_model(self, x, y):
+        """Perform a linear fit by direct matrix solution with numpy
+        """
+        # Construct the matrix and the free parameter vector
+#        print(f'\nparameters:')
+#        self._parameters.pretty_print()
+#        print(f'\nparameter_norms:\n\t{self._parameter_norms}')
+#        print(f'\nlinear_parameters:\n\t{self._linear_parameters}')
+#        print(f'nonlinear_parameters:\n\t{self._nonlinear_parameters}')
+        free_parameters = [name for name, par in self._parameters.items() if par.vary]
+#        print(f'free parameters:\n\t{free_parameters}\n')
+        expr_parameters = {name:par.expr for name, par in self._parameters.items()
+                if par.expr is not None}
+        model_parameters = []
+        for component in self._model.components:
+            if 'tmp_normalization_offset_c' in component.param_names:
+                continue
+            model_parameters += component.param_names
+            for basename, hint in component.param_hints.items():
+                name = f'{component.prefix}{basename}'
+                if hint.get('expr') is not None:
+                    expr_parameters.pop(name)
+                    model_parameters.remove(name)
+#        print(f'expr parameters:\n{expr_parameters}')
+#        print(f'model parameters:\n\t{model_parameters}\n')
+        norm = 1.0
+        if self._normalized:
+            norm = self._norm[1]
+#        print(f'\n\nself._normalized = {self._normalized}\nnorm = {norm}\nself._norm = {self._norm}\n')
+        # Add expression parameters to asteval
+        ast = Interpreter()
+#        print(f'Adding to asteval sym table:')
+        for name, expr in expr_parameters.items():
+#            print(f'\tadding {name} {expr}')
+            ast.symtable[name] = expr
+        # Add constant parameters to asteval
+        # (renormalize to use correctly in evaluation of expression models)
+        for name, par in self._parameters.items():
+            if par.expr is None and not par.vary:
+                if self._parameter_norms[name]:
+#                    print(f'\tadding {name} {par.value*norm}')
+                    ast.symtable[name] = par.value*norm
+                else:
+#                    print(f'\tadding {name} {par.value}')
+                    ast.symtable[name] = par.value
+        A = np.zeros((len(x), len(free_parameters)), dtype='float64')
+        y_const = np.zeros(len(x), dtype='float64')
+        have_expression_model = False
+        for component in self._model.components:
+            if isinstance(component, ConstantModel):
+                name = component.param_names[0]
+#                print(f'\nConstant model: {name} {self._parameters[name]}\n')
+                if name in free_parameters:
+#                    print(f'\t\t{name} is a free constant set matrix column {free_parameters.index(name)} to 1.0')
+                    A[:,free_parameters.index(name)] = 1.0
+                else:
+                    if self._parameter_norms[name]:
+                        delta_y_const = self._parameters[name]*np.ones(len(x))
+                    else:
+                        delta_y_const = (self._parameters[name]*norm)*np.ones(len(x))
+                    y_const += delta_y_const
+#                    print(f'\ndelta_y_const ({type(delta_y_const)}):\n{delta_y_const}\n')
+            elif isinstance(component, ExpressionModel):
+                have_expression_model = True
+                const_expr = component.expr
+#                print(f'\nExpression model:\nconst_expr: {const_expr}\n')
+                for name in free_parameters:
+                    dexpr_dname = diff(component.expr, name)
+                    if dexpr_dname:
+                        const_expr = f'{const_expr}-({str(dexpr_dname)})*{name}'
+#                        print(f'\tconst_expr: {const_expr}')
+                        if not self._parameter_norms[name]:
+                            dexpr_dname = f'({dexpr_dname})/{norm}'
+#                        print(f'\t{component.expr} is linear in {name}\n\t\tadd "{str(dexpr_dname)}" to matrix as column {free_parameters.index(name)}')
+                        fx = [(lambda _: ast.eval(str(dexpr_dname)))(ast(f'x={v}')) for v in x]
+#                        print(f'\tfx:\n{fx}')
+                        if len(ast.error):
+                            raise ValueError(f'Unable to evaluate {dexpr_dname}')
+                        A[:,free_parameters.index(name)] += fx
+#                        if self._parameter_norms[name]:
+#                            print(f'\t\t{component.expr} is linear in {name} add "{str(dexpr_dname)}" to matrix as column {free_parameters.index(name)}')
+#                            A[:,free_parameters.index(name)] += fx
+#                        else:
+#                            print(f'\t\t{component.expr} is linear in {name} add "({str(dexpr_dname)})/{norm}" to matrix as column {free_parameters.index(name)}')
+#                            A[:,free_parameters.index(name)] += np.asarray(fx)/norm
+                # FIX: find another solution if expr not supported by simplify
+                const_expr = str(simplify(f'({const_expr})/{norm}'))
+#                print(f'\nconst_expr: {const_expr}')
+                delta_y_const = [(lambda _: ast.eval(const_expr))(ast(f'x = {v}')) for v in x]
+                y_const += delta_y_const
+#                print(f'\ndelta_y_const ({type(delta_y_const)}):\n{delta_y_const}\n')
+                if len(ast.error):
+                    raise ValueError(f'Unable to evaluate {const_expr}')
+            else:
+                free_model_parameters = [name for name in component.param_names
+                        if name in free_parameters or name in expr_parameters]
+#                print(f'\nBuild-in model ({component}):\nfree_model_parameters: {free_model_parameters}\n')
+                if not len(free_model_parameters):
+                    y_const += component.eval(params=self._parameters, x=x)
+                elif isinstance(component, LinearModel):
+                    if f'{component.prefix}slope' in free_model_parameters:
+                        A[:,free_parameters.index(f'{component.prefix}slope')] = x
+                    else:
+                        y_const += self._parameters[f'{component.prefix}slope'].value*x
+                    if f'{component.prefix}intercept' in free_model_parameters:
+                        A[:,free_parameters.index(f'{component.prefix}intercept')] = 1.0
+                    else:
+                        y_const += self._parameters[f'{component.prefix}intercept'].value* \
+                                np.ones(len(x))
+                elif isinstance(component, QuadraticModel):
+                    if f'{component.prefix}a' in free_model_parameters:
+                        A[:,free_parameters.index(f'{component.prefix}a')] = x**2
+                    else:
+                        y_const += self._parameters[f'{component.prefix}a'].value*x**2
+                    if f'{component.prefix}b' in free_model_parameters:
+                        A[:,free_parameters.index(f'{component.prefix}b')] = x
+                    else:
+                        y_const += self._parameters[f'{component.prefix}b'].value*x
+                    if f'{component.prefix}c' in free_model_parameters:
+                        A[:,free_parameters.index(f'{component.prefix}c')] = 1.0
+                    else:
+                        y_const += self._parameters[f'{component.prefix}c'].value*np.ones(len(x))
+                else:
+                    # At this point each build-in model must be strictly proportional to each linear
+                    #   model parameter. Without this assumption, the model equation is needed
+                    #   For the current build-in lmfit models, this can only ever be the amplitude
+                    assert(len(free_model_parameters) == 1)
+                    name = f'{component.prefix}amplitude'
+                    assert(free_model_parameters[0] == name)
+                    assert(self._parameter_norms[name])
+                    expr = self._parameters[name].expr
+                    if expr is None:
+#                        print(f'\t{component} is linear in {name} add to matrix as column {free_parameters.index(name)}')
+                        parameters = deepcopy(self._parameters)
+                        parameters[name].set(value=1.0)
+                        index = free_parameters.index(name)
+                        A[:,free_parameters.index(name)] += component.eval(params=parameters, x=x)
+                    else:
+                        const_expr = expr
+#                        print(f'\tconst_expr: {const_expr}')
+                        parameters = deepcopy(self._parameters)
+                        parameters[name].set(value=1.0)
+                        dcomp_dname = component.eval(params=parameters, x=x)
+#                        print(f'\tdcomp_dname ({type(dcomp_dname)}):\n{dcomp_dname}')
+                        for nname in free_parameters:
+                            dexpr_dnname =  diff(expr, nname)
+                            if dexpr_dnname:
+                                assert(self._parameter_norms[name])
+#                                print(f'\t\td({expr})/d{nname} = {dexpr_dnname}')
+#                                print(f'\t\t{component} is linear in {nname} (through {name} = "{expr}", add to matrix as column {free_parameters.index(nname)})')
+                                fx = np.asarray(dexpr_dnname*dcomp_dname, dtype='float64')
+#                                print(f'\t\tfx ({type(fx)}): {fx}')
+#                                print(f'free_parameters.index({nname}): {free_parameters.index(nname)}')
+                                if self._parameter_norms[nname]:
+                                    A[:,free_parameters.index(nname)] += fx
+                                else:
+                                    A[:,free_parameters.index(nname)] += fx/norm
+                                const_expr = f'{const_expr}-({dexpr_dnname})*{nname}'
+#                                print(f'\t\tconst_expr: {const_expr}')
+                        const_expr = str(simplify(f'({const_expr})/{norm}'))
+#                        print(f'\tconst_expr: {const_expr}')
+                        fx = [(lambda _: ast.eval(const_expr))(ast(f'x = {v}')) for v in x]
+#                        print(f'\tfx: {fx}')
+                        delta_y_const = np.multiply(fx, dcomp_dname)
+                        y_const += delta_y_const
+#                        print(f'\ndelta_y_const ({type(delta_y_const)}):\n{delta_y_const}\n')
+#            print(A)
+#            print(y_const)
+        solution, residual, rank, s = np.linalg.lstsq(A, y-y_const, rcond=None)
+#        print(f'\nsolution ({type(solution)} {solution.shape}):\n\t{solution}')
+#        print(f'\nresidual ({type(residual)} {residual.shape}):\n\t{residual}')
+#        print(f'\nrank ({type(rank)} {rank.shape}):\n\t{rank}')
+#        print(f'\ns ({type(s)} {s.shape}):\n\t{s}\n')
+
+        # Assemble result (compensate for normalization in expression models)
+        for name, value in zip(free_parameters, solution):
+            self._parameters[name].set(value=value)
+        if self._normalized and (have_expression_model or len(expr_parameters)):
+            for name, norm in self._parameter_norms.items():
+                par = self._parameters[name]
+                if par.expr is None and norm:
+                    self._parameters[name].set(value=par.value*self._norm[1])
+#        self._parameters.pretty_print()
+#        print(f'\nself._parameter_norms:\n\t{self._parameter_norms}')
+        self._result = ModelResult(self._model, deepcopy(self._parameters))
+        self._result.best_fit = self._model.eval(params=self._parameters, x=x)
+        if self._normalized and (have_expression_model or len(expr_parameters)):
+            if 'tmp_normalization_offset_c' in self._parameters:
+                offset = self._parameters['tmp_normalization_offset_c']
+            else:
+                offset = 0.0
+            self._result.best_fit = (self._result.best_fit-offset-self._norm[0])/self._norm[1]
+            if self._normalized:
+                for name, norm in self._parameter_norms.items():
+                    par = self._parameters[name]
+                    if par.expr is None and norm:
+                        value = par.value/self._norm[1]
+                        self._parameters[name].set(value=value)
+                        self._result.params[name].set(value=value)
+#        self._parameters.pretty_print()
+        self._result.residual = self._result.best_fit-y
+        self._result.components = self._model.components
+        self._result.init_params = None
+#        quick_plot((x, y, '.'), (x, y_const, 'g'), (x, self._result.best_fit, 'k'), (x, self._result.residual, 'r'), block=True)
+
+    def _normalize(self):
+        """Normalize the data and initial parameters
+        """
+        if self._normalized:
+            return
+        if self._norm is None:
+            if self._y is not None and self._y_norm is None:
+                self._y_norm = np.asarray(self._y)
+        else:
+            if self._y is not None and self._y_norm is None:
+                self._y_norm = (np.asarray(self._y)-self._norm[0])/self._norm[1]
+            self._y_range = 1.0
+            for name, norm in self._parameter_norms.items():
+                par = self._parameters[name]
+                if par.expr is None and norm:
+                    value = par.value/self._norm[1]
+                    _min = par.min
+                    _max = par.max
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min /= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max /= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+            self._normalized = True
+
+    def _renormalize(self):
+        """Renormalize the data and results
+        """
+        if self._norm is None or not self._normalized:
+            return
+        self._normalized = False
+        for name, norm in self._parameter_norms.items():
+            par = self._parameters[name]
+            if par.expr is None and norm:
+                value = par.value*self._norm[1]
+                _min = par.min
+                _max = par.max
+                if not np.isinf(_min) and abs(_min) != float_min:
+                    _min *= self._norm[1]
+                if not np.isinf(_max) and abs(_max) != float_min:
+                    _max *= self._norm[1]
+                par.set(value=value, min=_min, max=_max)
+        if self._result is None:
+            return
+        self._result.best_fit = self._result.best_fit*self._norm[1]+self._norm[0]
+        for name, par in self._result.params.items():
+            if self._parameter_norms.get(name, False):
+                if par.stderr is not None:
+                    par.stderr *= self._norm[1]
+                if par.expr is None:
+                    _min = par.min
+                    _max = par.max
+                    value = par.value*self._norm[1]
+                    if par.init_value is not None:
+                        par.init_value *= self._norm[1]
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min *= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max *= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+        if hasattr(self._result, 'init_fit'):
+            self._result.init_fit = self._result.init_fit*self._norm[1]+self._norm[0]
+        if hasattr(self._result, 'init_values'):
+            init_values = {}
+            for name, value in self._result.init_values.items():
+                if name not in self._parameter_norms or self._parameters[name].expr is not None:
+                    init_values[name] = value
+                elif self._parameter_norms[name]:
+                    init_values[name] = value*self._norm[1]
+            self._result.init_values = init_values
+            for name, par in self._result.init_params.items():
+                if par.expr is None and self._parameter_norms.get(name, False):
+                    value = par.value
+                    _min = par.min
+                    _max = par.max
+                    value *= self._norm[1]
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min *= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max *= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+                par.init_value = par.value
+        # Don't renormalize chisqr, it has no useful meaning in physical units
+        #self._result.chisqr *= self._norm[1]*self._norm[1]
+        if self._result.covar is not None:
+            for i, name in enumerate(self._result.var_names):
+                if self._parameter_norms.get(name, False):
+                    for j in range(len(self._result.var_names)):
+                        if self._result.covar[i,j] is not None:
+                            self._result.covar[i,j] *= self._norm[1]
+                        if self._result.covar[j,i] is not None:
+                            self._result.covar[j,i] *= self._norm[1]
+        # Don't renormalize redchi, it has no useful meaning in physical units
+        #self._result.redchi *= self._norm[1]*self._norm[1]
+        if self._result.residual is not None:
+            self._result.residual *= self._norm[1]
+
+    def _reset_par_at_boundary(self, par, value):
+        assert(par.vary)
+        name = par.name
+        _min = self._parameter_bounds[name]['min']
+        _max = self._parameter_bounds[name]['max']
+        if np.isinf(_min):
+            if not np.isinf(_max):
+                if self._parameter_norms.get(name, False):
+                    upp = _max-0.1*self._y_range
+                elif _max == 0.0:
+                    upp = _max-0.1
+                else:
+                    upp = _max-0.1*abs(_max)
+                if value >= upp:
+                    return(upp)
+        else:
+            if np.isinf(_max):
+                if self._parameter_norms.get(name, False):
+                    low = _min+0.1*self._y_range
+                elif _min == 0.0:
+                    low = _min+0.1
+                else:
+                    low = _min+0.1*abs(_min)
+                if value <= low:
+                    return(low)
+            else:
+                low = 0.9*_min+0.1*_max
+                upp = 0.1*_min+0.9*_max
+                if value <= low:
+                    return(low)
+                elif value >= upp:
+                    return(upp)
+        return(value)
+
+
+class FitMultipeak(Fit):
+    """Fit data with multiple peaks
+    """
+    def __init__(self, y, x=None, normalize=True):
+        super().__init__(y, x=x, normalize=normalize)
+        self._fwhm_max = None
+        self._sigma_max = None
+
+    @classmethod
+    def fit_multipeak(cls, y, centers, x=None, normalize=True, peak_models='gaussian',
+            center_exprs=None, fit_type=None, background_order=None, background_exp=False,
+            fwhm_max=None, plot_components=False):
+        """Make sure that centers and fwhm_max are in the correct units and consistent with expr
+           for a uniform fit (fit_type == 'uniform')
+        """
+        fit = cls(y, x=x, normalize=normalize)
+        success = fit.fit(centers, fit_type=fit_type, peak_models=peak_models, fwhm_max=fwhm_max,
+                center_exprs=center_exprs, background_order=background_order,
+                background_exp=background_exp, plot_components=plot_components)
+        if success:
+            return(fit.best_fit, fit.residual, fit.best_values, fit.best_errors, fit.redchi, \
+                    fit.success)
+        else:
+            return(np.array([]), np.array([]), {}, {}, float_max, False)
+
+    def fit(self, centers, fit_type=None, peak_models=None, center_exprs=None, fwhm_max=None,
+                background_order=None, background_exp=False, plot_components=False,
+                param_constraint=False):
+        self._fwhm_max = fwhm_max
+        # Create the multipeak model
+        self._create_model(centers, fit_type, peak_models, center_exprs, background_order,
+                background_exp, param_constraint)
+
+        # RV: Obsolete Normalize the data and results
+#        print('\nBefore fit before normalization in FitMultipeak:')
+#        self._parameters.pretty_print()
+#        self._normalize()
+#        print('\nBefore fit after normalization in FitMultipeak:')
+#        self._parameters.pretty_print()
+
+        # Perform the fit
+        try:
+            if param_constraint:
+                super().fit(fit_kws={'xtol': 1.e-5, 'ftol': 1.e-5, 'gtol': 1.e-5})
+            else:
+                super().fit()
+        except:
+            return(False)
+
+        # Check for valid fit parameter results
+        fit_failure = self._check_validity()
+        success = True
+        if fit_failure:
+            if param_constraint:
+                logging.warning('  -> Should not happen with param_constraint set, fail the fit')
+                success = False
+            else:
+                logging.info('  -> Retry fitting with constraints')
+                self.fit(centers, fit_type, peak_models, center_exprs, fwhm_max=fwhm_max,
+                        background_order=background_order, background_exp=background_exp,
+                        plot_components=plot_components, param_constraint=True)
+        else:
+            # RV: Obsolete Renormalize the data and results
+#            print('\nAfter fit before renormalization in FitMultipeak:')
+#            self._parameters.pretty_print()
+#            self.print_fit_report()
+#            self._renormalize()
+#            print('\nAfter fit after renormalization in FitMultipeak:')
+#            self._parameters.pretty_print()
+#            self.print_fit_report()
+
+            # Print report and plot components if requested
+            if plot_components:
+                self.print_fit_report()
+                self.plot()
+
+        return(success)
+
+    def _create_model(self, centers, fit_type=None, peak_models=None, center_exprs=None,
+                background_order=None, background_exp=False, param_constraint=False):
+        """Create the multipeak model
+        """
+        if isinstance(centers, (int, float)):
+            centers = [centers]
+        num_peaks = len(centers)
+        if peak_models is None:
+            peak_models = num_peaks*['gaussian']
+        elif isinstance(peak_models, str):
+            peak_models = num_peaks*[peak_models]
+        if len(peak_models) != num_peaks:
+            raise ValueError(f'Inconsistent number of peaks in peak_models ({len(peak_models)} vs '+
+                    f'{num_peaks})')
+        if num_peaks == 1:
+            if fit_type is not None:
+                logging.debug('Ignoring fit_type input for fitting one peak')
+            fit_type = None
+            if center_exprs is not None:
+                logging.debug('Ignoring center_exprs input for fitting one peak')
+                center_exprs = None
+        else:
+            if fit_type == 'uniform':
+                if center_exprs is None:
+                    center_exprs = [f'scale_factor*{cen}' for cen in centers]
+                if len(center_exprs) != num_peaks:
+                    raise ValueError(f'Inconsistent number of peaks in center_exprs '+
+                            f'({len(center_exprs)} vs {num_peaks})')
+            elif fit_type == 'unconstrained' or fit_type is None:
+                if center_exprs is not None:
+                    logging.warning('Ignoring center_exprs input for unconstrained fit')
+                    center_exprs = None
+            else:
+                raise ValueError(f'Invalid fit_type in fit_multigaussian {fit_type}')
+        self._sigma_max = None
+        if param_constraint:
+            min_value = float_min
+            if self._fwhm_max is not None:
+                self._sigma_max = np.zeros(num_peaks)
+        else:
+            min_value = None
+
+        # Reset the fit
+        self._model = None
+        self._parameters = Parameters()
+        self._result = None
+
+        # Add background model
+        if background_order is not None:
+            if background_order == 0:
+                self.add_model('constant', prefix='background', parameters=
+                        {'name': 'c', 'value': float_min, 'min': min_value})
+            elif background_order == 1:
+                self.add_model('linear', prefix='background', slope=0.0, intercept=0.0)
+            elif background_order == 2:
+                self.add_model('quadratic', prefix='background', a=0.0, b=0.0, c=0.0)
+            else:
+                raise ValueError(f'Invalid parameter background_order ({background_order})')
+        if background_exp:
+            self.add_model('exponential', prefix='background', parameters=(
+                        {'name': 'amplitude', 'value': float_min, 'min': min_value},
+                        {'name': 'decay', 'value': float_min, 'min': min_value}))
+
+        # Add peaks and guess initial fit parameters
+        ast = Interpreter()
+        if num_peaks == 1:
+            height_init, cen_init, fwhm_init = self.guess_init_peak(self._x, self._y)
+            if self._fwhm_max is not None and fwhm_init > self._fwhm_max:
+                fwhm_init = self._fwhm_max
+            ast(f'fwhm = {fwhm_init}')
+            ast(f'height = {height_init}')
+            sig_init = ast(fwhm_factor[peak_models[0]])
+            amp_init = ast(height_factor[peak_models[0]])
+            sig_max = None
+            if self._sigma_max is not None:
+                ast(f'fwhm = {self._fwhm_max}')
+                sig_max = ast(fwhm_factor[peak_models[0]])
+                self._sigma_max[0] = sig_max
+            self.add_model(peak_models[0], parameters=(
+                    {'name': 'amplitude', 'value': amp_init, 'min': min_value},
+                    {'name': 'center', 'value': cen_init, 'min': min_value},
+                    {'name': 'sigma', 'value': sig_init, 'min': min_value, 'max': sig_max}))
+        else:
+            if fit_type == 'uniform':
+                self.add_parameter(name='scale_factor', value=1.0)
+            for i in range(num_peaks):
+                height_init, cen_init, fwhm_init = self.guess_init_peak(self._x, self._y, i,
+                        center_guess=centers)
+                if self._fwhm_max is not None and fwhm_init > self._fwhm_max:
+                    fwhm_init = self._fwhm_max
+                ast(f'fwhm = {fwhm_init}')
+                ast(f'height = {height_init}')
+                sig_init = ast(fwhm_factor[peak_models[i]])
+                amp_init = ast(height_factor[peak_models[i]])
+                sig_max = None
+                if self._sigma_max is not None:
+                    ast(f'fwhm = {self._fwhm_max}')
+                    sig_max = ast(fwhm_factor[peak_models[i]])
+                    self._sigma_max[i] = sig_max
+                if fit_type == 'uniform':
+                    self.add_model(peak_models[i], prefix=f'peak{i+1}_', parameters=(
+                            {'name': 'amplitude', 'value': amp_init, 'min': min_value},
+                            {'name': 'center', 'expr': center_exprs[i]},
+                            {'name': 'sigma', 'value': sig_init, 'min': min_value,
+                            'max': sig_max}))
+                else:
+                    self.add_model('gaussian', prefix=f'peak{i+1}_', parameters=(
+                            {'name': 'amplitude', 'value': amp_init, 'min': min_value},
+                            {'name': 'center', 'value': cen_init, 'min': min_value},
+                            {'name': 'sigma', 'value': sig_init, 'min': min_value,
+                            'max': sig_max}))
+
+    def _check_validity(self):
+        """Check for valid fit parameter results
+        """
+        fit_failure = False
+        index = compile(r'\d+')
+        for name, par in self.best_parameters.items():
+            if 'background' in name:
+#                if ((name == 'backgroundc' and par['value'] <= 0.0) or
+#                        (name.endswith('amplitude') and par['value'] <= 0.0) or
+                 if ((name.endswith('amplitude') and par['value'] <= 0.0) or
+                        (name.endswith('decay') and par['value'] <= 0.0)):
+                    logging.info(f'Invalid fit result for {name} ({par["value"]})')
+                    fit_failure = True
+            elif (((name.endswith('amplitude') or name.endswith('height')) and
+                    par['value'] <= 0.0) or
+                    ((name.endswith('sigma') or name.endswith('fwhm')) and par['value'] <= 0.0) or
+                    (name.endswith('center') and par['value'] <= 0.0) or
+                    (name == 'scale_factor' and par['value'] <= 0.0)):
+                logging.info(f'Invalid fit result for {name} ({par["value"]})')
+                fit_failure = True
+            if name.endswith('sigma') and self._sigma_max is not None:
+                if name == 'sigma':
+                    sigma_max = self._sigma_max[0]
+                else:
+                    sigma_max = self._sigma_max[int(index.search(name).group())-1]
+                if par['value'] > sigma_max:
+                    logging.info(f'Invalid fit result for {name} ({par["value"]})')
+                    fit_failure = True
+                elif par['value'] == sigma_max:
+                    logging.warning(f'Edge result on for {name} ({par["value"]})')
+            if name.endswith('fwhm') and self._fwhm_max is not None:
+                if par['value'] > self._fwhm_max:
+                    logging.info(f'Invalid fit result for {name} ({par["value"]})')
+                    fit_failure = True
+                elif par['value'] == self._fwhm_max:
+                    logging.warning(f'Edge result on for {name} ({par["value"]})')
+        return(fit_failure)
+
+
+class FitMap(Fit):
+    """Fit a map of data
+    """
+    def __init__(self, ymap, x=None, models=None, normalize=True, transpose=None, **kwargs):
+        super().__init__(None)
+        self._best_errors = None
+        self._best_fit = None
+        self._best_parameters = None
+        self._best_values = None
+        self._inv_transpose = None
+        self._max_nfev = None
+        self._memfolder = None
+        self._new_parameters = None
+        self._out_of_bounds = None
+        self._plot = False
+        self._print_report = False
+        self._redchi = None
+        self._redchi_cutoff = 0.1
+        self._skip_init = True
+        self._success = None
+        self._transpose = None
+        self._try_no_bounds = True
+
+        # At this point the fastest index should always be the signal dimension so that the slowest 
+        #    ndim-1 dimensions are the map dimensions
+        if isinstance(ymap, (tuple, list, np.ndarray)):
+            self._x = np.asarray(x)
+        elif have_xarray and isinstance(ymap, xr.DataArray):
+            if x is not None:
+                logging.warning('Ignoring superfluous input x ({x}) in Fit.__init__')
+            self._x = np.asarray(ymap[ymap.dims[-1]])
+        else:
+            illegal_value(ymap, 'ymap', 'FitMap:__init__', raise_error=True)
+        self._ymap = ymap
+
+        # Verify the input parameters
+        if self._x.ndim != 1:
+            raise ValueError(f'Invalid dimension for input x {self._x.ndim}')
+        if self._ymap.ndim < 2:
+            raise ValueError('Invalid number of dimension of the input dataset '+
+                    f'{self._ymap.ndim}')
+        if self._x.size != self._ymap.shape[-1]:
+            raise ValueError(f'Inconsistent x and y dimensions ({self._x.size} vs '+
+                    f'{self._ymap.shape[-1]})')
+        if not isinstance(normalize, bool):
+            logging.warning(f'Invalid value for normalize ({normalize}) in Fit.__init__: '+
+                    'setting normalize to True')
+            normalize = True
+        if isinstance(transpose, bool) and not transpose:
+            transpose = None
+        if transpose is not None and self._ymap.ndim < 3:
+            logging.warning(f'Transpose meaningless for {self._ymap.ndim-1}D data maps: ignoring '+
+                    'transpose')
+        if transpose is not None:
+            if self._ymap.ndim == 3 and isinstance(transpose, bool) and transpose:
+                self._transpose = (1, 0)
+            elif not isinstance(transpose, (tuple, list)):
+                logging.warning(f'Invalid data type for transpose ({transpose}, '+
+                        f'{type(transpose)}) in Fit.__init__: setting transpose to False')
+            elif len(transpose) != self._ymap.ndim-1:
+                logging.warning(f'Invalid dimension for transpose ({transpose}, must be equal to '+
+                        f'{self._ymap.ndim-1}) in Fit.__init__: setting transpose to False')
+            elif any(i not in transpose for i in range(len(transpose))):
+                logging.warning(f'Invalid index in transpose ({transpose}) '+
+                        f'in Fit.__init__: setting transpose to False')
+            elif not all(i==transpose[i] for i in range(self._ymap.ndim-1)):
+                self._transpose = transpose
+            if self._transpose is not None:
+                self._inv_transpose = tuple(self._transpose.index(i)
+                        for i in range(len(self._transpose)))
+
+        # Flatten the map (transpose if requested)
+        # Store the flattened map in self._ymap_norm, whether normalized or not
+        if self._transpose is not None:
+            self._ymap_norm = np.transpose(np.asarray(self._ymap), list(self._transpose)+
+                    [len(self._transpose)])
+        else:
+            self._ymap_norm = np.asarray(self._ymap)
+        self._map_dim = int(self._ymap_norm.size/self._x.size)
+        self._map_shape = self._ymap_norm.shape[:-1]
+        self._ymap_norm = np.reshape(self._ymap_norm, (self._map_dim, self._x.size))
+
+        # Check if a mask is provided
+        if 'mask' in kwargs:
+            self._mask = kwargs.pop('mask')
+        if self._mask is None:
+            ymap_min = float(self._ymap_norm.min())
+            ymap_max = float(self._ymap_norm.max())
+        else:
+            self._mask = np.asarray(self._mask).astype(bool)
+            if self._x.size != self._mask.size:
+                raise ValueError(f'Inconsistent mask dimension ({self._x.size} vs '+
+                        f'{self._mask.size})')
+            ymap_masked = np.asarray(self._ymap_norm)[:,~self._mask]
+            ymap_min = float(ymap_masked.min())
+            ymap_max = float(ymap_masked.max())
+
+        # Normalize the data
+        self._y_range = ymap_max-ymap_min
+        if normalize and self._y_range > 0.0:
+            self._norm = (ymap_min, self._y_range)
+            self._ymap_norm = (self._ymap_norm-self._norm[0])/self._norm[1]
+        else:
+            self._redchi_cutoff *= self._y_range**2
+        if models is not None:
+            if callable(models) or isinstance(models, str):
+                kwargs = self.add_model(models, **kwargs)
+            elif isinstance(models, (tuple, list)):
+                for model in models:
+                    kwargs = self.add_model(model, **kwargs)
+            self.fit(**kwargs)
+
+    @classmethod
+    def fit_map(cls, ymap, models, x=None, normalize=True, **kwargs):
+        return(cls(ymap, x=x, models=models, normalize=normalize, **kwargs))
+
+    @property
+    def best_errors(self):
+        return(self._best_errors)
+
+    @property
+    def best_fit(self):
+        return(self._best_fit)
+
+    @property
+    def best_results(self):
+        """Convert the input data array to a data set and add the fit results.
+        """
+        if self.best_values is None or self.best_errors is None or self.best_fit is None:
+            return(None)
+        if not have_xarray:
+            logging.warning('Unable to load xarray module')
+            return(None)
+        best_values = self.best_values
+        best_errors = self.best_errors
+        if isinstance(self._ymap, xr.DataArray):
+            best_results = self._ymap.to_dataset()
+            dims = self._ymap.dims
+            fit_name = f'{self._ymap.name}_fit'
+        else:
+            coords = {f'dim{n}_index':([f'dim{n}_index'], range(self._ymap.shape[n]))
+                    for n in range(self._ymap.ndim-1)}
+            coords['x'] = (['x'], self._x)
+            dims = list(coords.keys())
+            best_results = xr.Dataset(coords=coords)
+            best_results['y'] = (dims, self._ymap)
+            fit_name = 'y_fit'
+        best_results[fit_name] = (dims, self.best_fit)
+        if self._mask is not None:
+            best_results['mask'] = self._mask
+        for n in range(best_values.shape[0]):
+            best_results[f'{self._best_parameters[n]}_values'] = (dims[:-1], best_values[n])
+            best_results[f'{self._best_parameters[n]}_errors'] = (dims[:-1], best_errors[n])
+        best_results.attrs['components'] = self.components
+        return(best_results)
+
+    @property
+    def best_values(self):
+        return(self._best_values)
+
+    @property
+    def chisqr(self):
+        logging.warning('property chisqr not defined for fit.FitMap')
+        return(None)
+
+    @property
+    def components(self):
+        components = {}
+        if self._result is None:
+            logging.warning('Unable to collect components in FitMap.components')
+            return(components)
+        for component in self._result.components:
+            if 'tmp_normalization_offset_c' in component.param_names:
+                continue
+            parameters = {}
+            for name in component.param_names:
+                if self._parameters[name].vary:
+                    parameters[name] = {'free': True}
+                elif self._parameters[name].expr is not None:
+                    parameters[name] = {'free': False, 'expr': self._parameters[name].expr}
+                else:
+                    parameters[name] = {'free': False, 'value': self.init_parameters[name]['value']}
+            expr = None
+            if isinstance(component, ExpressionModel):
+                name = component._name
+                if name[-1] == '_':
+                    name = name[:-1]
+                expr = component.expr
+            else:
+                prefix = component.prefix
+                if len(prefix):
+                    if prefix[-1] == '_':
+                        prefix = prefix[:-1]
+                    name = f'{prefix} ({component._name})'
+                else:
+                    name = f'{component._name}'
+            if expr is None:
+                components[name] = {'parameters': parameters}
+            else:
+                components[name] = {'expr': expr, 'parameters': parameters}
+        return(components)
+
+    @property
+    def covar(self):
+        logging.warning('property covar not defined for fit.FitMap')
+        return(None)
+
+    @property
+    def max_nfev(self):
+        return(self._max_nfev)
+
+    @property
+    def num_func_eval(self):
+        logging.warning('property num_func_eval not defined for fit.FitMap')
+        return(None)
+
+    @property
+    def out_of_bounds(self):
+        return(self._out_of_bounds)
+
+    @property
+    def redchi(self):
+        return(self._redchi)
+
+    @property
+    def residual(self):
+        if self.best_fit is None:
+            return(None)
+        if self._mask is None:
+            return(np.asarray(self._ymap)-self.best_fit)
+        else:
+            ymap_flat = np.reshape(np.asarray(self._ymap), (self._map_dim, self._x.size))
+            ymap_flat_masked = ymap_flat[:,~self._mask]
+            ymap_masked = np.reshape(ymap_flat_masked,
+                    list(self._map_shape)+[ymap_flat_masked.shape[-1]])
+            return(ymap_masked-self.best_fit)
+
+    @property
+    def success(self):
+        return(self._success)
+
+    @property
+    def var_names(self):
+        logging.warning('property var_names not defined for fit.FitMap')
+        return(None)
+
+    @property
+    def y(self):
+        logging.warning('property y not defined for fit.FitMap')
+        return(None)
+
+    @property
+    def ymap(self):
+        return(self._ymap)
+
+    def best_parameters(self, dims=None):
+        if dims is None:
+            return(self._best_parameters)
+        if not isinstance(dims, (list, tuple)) or len(dims) != len(self._map_shape):
+            illegal_value(dims, 'dims', 'FitMap.best_parameters', raise_error=True)
+        if self.best_values is None or self.best_errors is None:
+            logging.warning(f'Unable to obtain best parameter values for dims = {dims} in '+
+                    'FitMap.best_parameters')
+            return({})
+        # Create current parameters
+        parameters = deepcopy(self._parameters)
+        for n, name in enumerate(self._best_parameters):
+            if self._parameters[name].vary:
+                parameters[name].set(value=self.best_values[n][dims])
+            parameters[name].stderr = self.best_errors[n][dims]
+        parameters_dict = {}
+        for name in sorted(parameters):
+            if name != 'tmp_normalization_offset_c':
+                par = parameters[name]
+                parameters_dict[name] = {'value': par.value, 'error': par.stderr,
+                        'init_value': self.init_parameters[name]['value'], 'min': par.min,
+                        'max': par.max, 'vary': par.vary, 'expr': par.expr}
+        return(parameters_dict)
+
+    def freemem(self):
+        if self._memfolder is None:
+            return
+        try:
+            rmtree(self._memfolder)
+            self._memfolder = None
+        except:
+            logging.warning('Could not clean-up automatically.')
+
+    def plot(self, dims, y_title=None, plot_residual=False, plot_comp_legends=False,
+            plot_masked_data=True):
+        if not isinstance(dims, (list, tuple)) or len(dims) != len(self._map_shape):
+            illegal_value(dims, 'dims', 'FitMap.plot', raise_error=True)
+        if self._result is None or self.best_fit is None or self.best_values is None:
+            logging.warning(f'Unable to plot fit for dims = {dims} in FitMap.plot')
+            return
+        if y_title is None or not isinstance(y_title, str):
+            y_title = 'data'
+        if self._mask is None:
+            mask = np.zeros(self._x.size).astype(bool)
+            plot_masked_data = False
+        else:
+            mask = self._mask
+        plots = [(self._x, np.asarray(self._ymap[dims]), 'b.')]
+        legend = [y_title]
+        if plot_masked_data:
+            plots += [(self._x[mask], np.asarray(self._ymap)[(*dims,mask)], 'bx')]
+            legend += ['masked data']
+        plots += [(self._x[~mask], self.best_fit[dims], 'k-')]
+        legend += ['best fit']
+        if plot_residual:
+            plots += [(self._x[~mask], self.residual[dims], 'k--')]
+            legend += ['residual']
+        # Create current parameters
+        parameters = deepcopy(self._parameters)
+        for name in self._best_parameters:
+            if self._parameters[name].vary:
+                parameters[name].set(value=
+                        self.best_values[self._best_parameters.index(name)][dims])
+        for component in self._result.components:
+            if 'tmp_normalization_offset_c' in component.param_names:
+                continue
+            if isinstance(component, ExpressionModel):
+                prefix = component._name
+                if prefix[-1] == '_':
+                    prefix = prefix[:-1]
+                modelname = f'{prefix}: {component.expr}'
+            else:
+                prefix = component.prefix
+                if len(prefix):
+                    if prefix[-1] == '_':
+                        prefix = prefix[:-1]
+                    modelname = f'{prefix} ({component._name})'
+                else:
+                    modelname = f'{component._name}'
+            if len(modelname) > 20:
+                modelname = f'{modelname[0:16]} ...'
+            y = component.eval(params=parameters, x=self._x[~mask])
+            if isinstance(y, (int, float)):
+                y *= np.ones(self._x[~mask].size)
+            plots += [(self._x[~mask], y, '--')]
+            if plot_comp_legends:
+                legend.append(modelname)
+        quick_plot(tuple(plots), legend=legend, title=str(dims), block=True)
+
+    def fit(self, **kwargs):
+#        t0 = time()
+        # Check input parameters
+        if self._model is None:
+            logging.error('Undefined fit model')
+        if 'num_proc' in kwargs:
+            num_proc = kwargs.pop('num_proc')
+            if not is_int(num_proc, ge=1):
+                illegal_value(num_proc, 'num_proc', 'FitMap.fit', raise_error=True)
+        else:
+            num_proc = cpu_count()
+        if num_proc > 1 and not have_joblib:
+            logging.warning(f'Missing joblib in the conda environment, running FitMap serially')
+            num_proc = 1
+        if num_proc > cpu_count():
+            logging.warning(f'The requested number of processors ({num_proc}) exceeds the maximum '+
+                    f'number of processors, num_proc reduced to ({cpu_count()})')
+            num_proc = cpu_count()
+        if 'try_no_bounds' in kwargs:
+            self._try_no_bounds = kwargs.pop('try_no_bounds')
+            if not isinstance(self._try_no_bounds, bool):
+                illegal_value(self._try_no_bounds, 'try_no_bounds', 'FitMap.fit', raise_error=True)
+        if 'redchi_cutoff' in kwargs:
+            self._redchi_cutoff = kwargs.pop('redchi_cutoff')
+            if not is_num(self._redchi_cutoff, gt=0):
+                illegal_value(self._redchi_cutoff, 'redchi_cutoff', 'FitMap.fit', raise_error=True)
+        if 'print_report' in kwargs:
+            self._print_report = kwargs.pop('print_report')
+            if not isinstance(self._print_report, bool):
+                illegal_value(self._print_report, 'print_report', 'FitMap.fit', raise_error=True)
+        if 'plot' in kwargs:
+            self._plot = kwargs.pop('plot')
+            if not isinstance(self._plot, bool):
+                illegal_value(self._plot, 'plot', 'FitMap.fit', raise_error=True)
+        if 'skip_init' in kwargs:
+            self._skip_init = kwargs.pop('skip_init')
+            if not isinstance(self._skip_init, bool):
+                illegal_value(self._skip_init, 'skip_init', 'FitMap.fit', raise_error=True)
+
+        # Apply mask if supplied:
+        if 'mask' in kwargs:
+            self._mask = kwargs.pop('mask')
+        if self._mask is not None:
+            self._mask = np.asarray(self._mask).astype(bool)
+            if self._x.size != self._mask.size:
+                raise ValueError(f'Inconsistent x and mask dimensions ({self._x.size} vs '+
+                        f'{self._mask.size})')
+
+        # Add constant offset for a normalized single component model
+        if self._result is None and self._norm is not None and self._norm[0]:
+            self.add_model('constant', prefix='tmp_normalization_offset_', parameters={'name': 'c',
+                    'value': -self._norm[0], 'vary': False, 'norm': True})
+                    #'value': -self._norm[0]/self._norm[1], 'vary': False, 'norm': False})
+
+        # Adjust existing parameters for refit:
+        if 'parameters' in kwargs:
+#            print('\nIn FitMap before adjusting existing parameters for refit:')
+#            self._parameters.pretty_print()
+#            if self._result is None:
+#                raise ValueError('Invalid parameter parameters ({parameters})')
+#            if self._best_values is None:
+#                raise ValueError('Valid self._best_values required for refitting in FitMap.fit')
+            parameters = kwargs.pop('parameters')
+#            print(f'\nparameters:\n{parameters}')
+            if isinstance(parameters, dict):
+                parameters = (parameters, )
+            elif not is_dict_series(parameters):
+                illegal_value(parameters, 'parameters', 'Fit.fit', raise_error=True)
+            for par in parameters:
+                name = par['name']
+                if name not in self._parameters:
+                    raise ValueError(f'Unable to match {name} parameter {par} to an existing one')
+                if self._parameters[name].expr is not None:
+                    raise ValueError(f'Unable to modify {name} parameter {par} (currently an '+
+                            'expression)')
+                value =  par.get('value')
+                vary =  par.get('vary')
+                if par.get('expr') is not None:
+                    raise KeyError(f'Illegal "expr" key in {name} parameter {par}')
+                self._parameters[name].set(value=value, vary=vary, min=par.get('min'),
+                        max=par.get('max'))
+                # Overwrite existing best values for fixed parameters when a value is specified
+#                print(f'best values befored resetting:\n{self._best_values}')
+                if isinstance(value, (int, float)) and vary is False:
+                    for i, nname in enumerate(self._best_parameters):
+                        if nname == name:
+                            self._best_values[i] = value
+#                print(f'best values after resetting (value={value}, vary={vary}):\n{self._best_values}')
+#RV            print('\nIn FitMap after adjusting existing parameters for refit:')
+#RV            self._parameters.pretty_print()
+
+        # Check for uninitialized parameters
+        for name, par in self._parameters.items():
+            if par.expr is None:
+                value = par.value
+                if value is None or np.isinf(value) or np.isnan(value):
+                    value = 1.0
+                    if self._norm is None or name not in self._parameter_norms:
+                        self._parameters[name].set(value=value)
+                    elif self._parameter_norms[name]:
+                        self._parameters[name].set(value=value*self._norm[1])
+
+        # Create the best parameter list, consisting of all varying parameters plus the expression
+        #   parameters in order to collect their errors
+        if self._result is None:
+            # Initial fit
+            assert(self._best_parameters is None)
+            self._best_parameters = [name for name, par in self._parameters.items()
+                    if par.vary or par.expr is not None]
+            num_new_parameters = 0
+        else:
+            # Refit
+            assert(len(self._best_parameters))
+            self._new_parameters = [name for name, par in self._parameters.items()
+                if name != 'tmp_normalization_offset_c' and name not in self._best_parameters and
+                    (par.vary or par.expr is not None)]
+            num_new_parameters = len(self._new_parameters)
+        num_best_parameters = len(self._best_parameters)
+
+        # Flatten and normalize the best values of the previous fit, remove the remaining results
+        #   of the previous fit
+        if self._result is not None:
+#            print('\nBefore flatten and normalize:')
+#            print(f'self._best_values:\n{self._best_values}')
+            self._out_of_bounds = None
+            self._max_nfev = None
+            self._redchi = None
+            self._success = None
+            self._best_fit = None
+            self._best_errors = None
+            assert(self._best_values is not None)
+            assert(self._best_values.shape[0] == num_best_parameters)
+            assert(self._best_values.shape[1:] == self._map_shape)
+            if self._transpose is not None:
+                self._best_values = np.transpose(self._best_values,
+                        [0]+[i+1 for i in self._transpose])
+            self._best_values = [np.reshape(self._best_values[i], self._map_dim)
+                for i in range(num_best_parameters)]
+            if self._norm is not None:
+                for i, name in enumerate(self._best_parameters):
+                    if self._parameter_norms.get(name, False):
+                        self._best_values[i] /= self._norm[1]
+#RV            print('\nAfter flatten and normalize:')
+#RV            print(f'self._best_values:\n{self._best_values}')
+
+        # Normalize the initial parameters (and best values for a refit)
+#        print('\nIn FitMap before normalize:')
+#        self._parameters.pretty_print()
+#        print(f'\nparameter_norms:\n{self._parameter_norms}\n')
+        self._normalize()
+#        print('\nIn FitMap after normalize:')
+#        self._parameters.pretty_print()
+#        print(f'\nparameter_norms:\n{self._parameter_norms}\n')
+
+        # Prevent initial values from sitting at boundaries
+        self._parameter_bounds = {name:{'min': par.min, 'max': par.max}
+                for name, par in self._parameters.items() if par.vary}
+        for name, par in self._parameters.items():
+            if par.vary:
+                par.set(value=self._reset_par_at_boundary(par, par.value))
+#        print('\nAfter checking boundaries:')
+#        self._parameters.pretty_print()
+
+        # Set parameter bounds to unbound (only use bounds when fit fails)
+        if self._try_no_bounds:
+            for name in self._parameter_bounds.keys():
+                self._parameters[name].set(min=-np.inf, max=np.inf)
+
+        # Allocate memory to store fit results
+        if self._mask is None:
+            x_size = self._x.size
+        else:
+            x_size = self._x[~self._mask].size
+        if num_proc == 1:
+            self._out_of_bounds_flat = np.zeros(self._map_dim, dtype=bool)
+            self._max_nfev_flat = np.zeros(self._map_dim, dtype=bool)
+            self._redchi_flat = np.zeros(self._map_dim, dtype=np.float64)
+            self._success_flat = np.zeros(self._map_dim, dtype=bool)
+            self._best_fit_flat = np.zeros((self._map_dim, x_size),
+                    dtype=self._ymap_norm.dtype)
+            self._best_errors_flat = [np.zeros(self._map_dim, dtype=np.float64)
+                    for _ in range(num_best_parameters+num_new_parameters)]
+            if self._result is None:
+                self._best_values_flat = [np.zeros(self._map_dim, dtype=np.float64)
+                        for _ in range(num_best_parameters)]
+            else:
+                self._best_values_flat = self._best_values
+                self._best_values_flat += [np.zeros(self._map_dim, dtype=np.float64)
+                        for _ in range(num_new_parameters)]
+        else:
+            self._memfolder = './joblib_memmap'
+            try:
+                mkdir(self._memfolder)
+            except FileExistsError:
+                pass
+            filename_memmap = path.join(self._memfolder, 'out_of_bounds_memmap')
+            self._out_of_bounds_flat = np.memmap(filename_memmap, dtype=bool,
+                    shape=(self._map_dim), mode='w+')
+            filename_memmap = path.join(self._memfolder, 'max_nfev_memmap')
+            self._max_nfev_flat = np.memmap(filename_memmap, dtype=bool,
+                    shape=(self._map_dim), mode='w+')
+            filename_memmap = path.join(self._memfolder, 'redchi_memmap')
+            self._redchi_flat = np.memmap(filename_memmap, dtype=np.float64,
+                    shape=(self._map_dim), mode='w+')
+            filename_memmap = path.join(self._memfolder, 'success_memmap')
+            self._success_flat = np.memmap(filename_memmap, dtype=bool,
+                    shape=(self._map_dim), mode='w+')
+            filename_memmap = path.join(self._memfolder, 'best_fit_memmap')
+            self._best_fit_flat = np.memmap(filename_memmap, dtype=self._ymap_norm.dtype,
+                    shape=(self._map_dim, x_size), mode='w+')
+            self._best_errors_flat = []
+            for i in range(num_best_parameters+num_new_parameters):
+                filename_memmap = path.join(self._memfolder, f'best_errors_memmap_{i}')
+                self._best_errors_flat.append(np.memmap(filename_memmap, dtype=np.float64,
+                        shape=self._map_dim, mode='w+'))
+            self._best_values_flat = []
+            for i in range(num_best_parameters):
+                filename_memmap = path.join(self._memfolder, f'best_values_memmap_{i}')
+                self._best_values_flat.append(np.memmap(filename_memmap, dtype=np.float64,
+                        shape=self._map_dim, mode='w+'))
+                if self._result is not None:
+                    self._best_values_flat[i][:] = self._best_values[i][:]
+            for i in range(num_new_parameters):
+                filename_memmap = path.join(self._memfolder,
+                        f'best_values_memmap_{i+num_best_parameters}')
+                self._best_values_flat.append(np.memmap(filename_memmap, dtype=np.float64,
+                        shape=self._map_dim, mode='w+'))
+
+        # Update the best parameter list
+        if num_new_parameters:
+            self._best_parameters += self._new_parameters
+
+        # Perform the first fit to get model component info and initial parameters
+        current_best_values = {}
+#        print(f'0 before:\n{current_best_values}')
+#        t1 = time()
+        self._result = self._fit(0, current_best_values, return_result=True, **kwargs)
+#        t2 = time()
+#        print(f'0 after:\n{current_best_values}')
+#        print('\nAfter the first fit:')
+#        self._parameters.pretty_print()
+#        print(self._result.fit_report(show_correl=False))
+
+        # Remove all irrelevant content from self._result
+        for attr in ('_abort', 'aborted', 'aic', 'best_fit', 'best_values', 'bic', 'calc_covar',
+                'call_kws', 'chisqr', 'ci_out', 'col_deriv', 'covar', 'data', 'errorbars',
+                'flatchain', 'ier', 'init_vals', 'init_fit', 'iter_cb', 'jacfcn', 'kws',
+                'last_internal_values', 'lmdif_message', 'message', 'method', 'nan_policy',
+                'ndata', 'nfev', 'nfree', 'params', 'redchi', 'reduce_fcn', 'residual', 'result',
+                'scale_covar', 'show_candidates', 'calc_covar', 'success', 'userargs', 'userfcn',
+                'userkws', 'values', 'var_names', 'weights', 'user_options'):
+            try:
+                delattr(self._result, attr)
+            except AttributeError:
+#                logging.warning(f'Unknown attribute {attr} in fit.FtMap._cleanup_result')
+                pass
+
+#        t3 = time()
+        if num_proc == 1:
+            # Perform the remaining fits serially
+            for n in range(1, self._map_dim):
+#                print(f'{n} before:\n{current_best_values}')
+                self._fit(n, current_best_values, **kwargs)
+#                print(f'{n} after:\n{current_best_values}')
+        else:
+            # Perform the remaining fits in parallel
+            num_fit = self._map_dim-1
+#            print(f'num_fit = {num_fit}')
+            if num_proc > num_fit:
+                logging.warning(f'The requested number of processors ({num_proc}) exceeds the '+
+                        f'number of fits, num_proc reduced to ({num_fit})')
+                num_proc = num_fit
+                num_fit_per_proc = 1
+            else:
+                num_fit_per_proc = round((num_fit)/num_proc)
+                if num_proc*num_fit_per_proc < num_fit:
+                    num_fit_per_proc +=1
+#            print(f'num_fit_per_proc = {num_fit_per_proc}')
+            num_fit_batch = min(num_fit_per_proc, 40)
+#            print(f'num_fit_batch = {num_fit_batch}')
+            with Parallel(n_jobs=num_proc) as parallel:
+                parallel(delayed(self._fit_parallel)(current_best_values, num_fit_batch,
+                        n_start, **kwargs) for n_start in range(1, self._map_dim, num_fit_batch))
+#        t4 = time()
+
+        # Renormalize the initial parameters for external use
+        if self._norm is not None and self._normalized:
+            init_values = {}
+            for name, value in self._result.init_values.items():
+                if name not in self._parameter_norms or self._parameters[name].expr is not None:
+                    init_values[name] = value
+                elif self._parameter_norms[name]:
+                    init_values[name] = value*self._norm[1]
+            self._result.init_values = init_values
+            for name, par in self._result.init_params.items():
+                if par.expr is None and self._parameter_norms.get(name, False):
+                    _min = par.min
+                    _max = par.max
+                    value = par.value*self._norm[1]
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min *= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max *= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+                par.init_value = par.value
+
+        # Remap the best results
+#        t5 = time()
+        self._out_of_bounds = np.copy(np.reshape(self._out_of_bounds_flat, self._map_shape))
+        self._max_nfev = np.copy(np.reshape(self._max_nfev_flat, self._map_shape))
+        self._redchi = np.copy(np.reshape(self._redchi_flat, self._map_shape))
+        self._success = np.copy(np.reshape(self._success_flat, self._map_shape))
+        self._best_fit = np.copy(np.reshape(self._best_fit_flat,
+               list(self._map_shape)+[x_size]))
+        self._best_values = np.asarray([np.reshape(par, list(self._map_shape))
+                for par in self._best_values_flat])
+        self._best_errors = np.asarray([np.reshape(par, list(self._map_shape))
+                for par in self._best_errors_flat])
+        if self._inv_transpose is not None:
+            self._out_of_bounds = np.transpose(self._out_of_bounds, self._inv_transpose)
+            self._max_nfev = np.transpose(self._max_nfev, self._inv_transpose)
+            self._redchi = np.transpose(self._redchi, self._inv_transpose)
+            self._success = np.transpose(self._success, self._inv_transpose)
+            self._best_fit = np.transpose(self._best_fit,
+                    list(self._inv_transpose)+[len(self._inv_transpose)])
+            self._best_values = np.transpose(self._best_values,
+                    [0]+[i+1 for i in self._inv_transpose])
+            self._best_errors = np.transpose(self._best_errors,
+                    [0]+[i+1 for i in self._inv_transpose])
+        del self._out_of_bounds_flat
+        del self._max_nfev_flat
+        del self._redchi_flat
+        del self._success_flat
+        del self._best_fit_flat
+        del self._best_values_flat
+        del self._best_errors_flat
+#        t6 = time()
+
+        # Restore parameter bounds and renormalize the parameters
+        for name, par in self._parameter_bounds.items():
+            self._parameters[name].set(min=par['min'], max=par['max'])
+        self._normalized = False
+        if self._norm is not None:
+            for name, norm in self._parameter_norms.items():
+                par = self._parameters[name]
+                if par.expr is None and norm:
+                    value = par.value*self._norm[1]
+                    _min = par.min
+                    _max = par.max
+                    if not np.isinf(_min) and abs(_min) != float_min:
+                        _min *= self._norm[1]
+                    if not np.isinf(_max) and abs(_max) != float_min:
+                        _max *= self._norm[1]
+                    par.set(value=value, min=_min, max=_max)
+#        t7 = time()
+#        print(f'total run time in fit: {t7-t0:.2f} seconds')
+#        print(f'run time first fit: {t2-t1:.2f} seconds')
+#        print(f'run time remaining fits: {t4-t3:.2f} seconds')
+#        print(f'run time remapping results: {t6-t5:.2f} seconds')
+
+#        print('\n\nAt end fit:')
+#        self._parameters.pretty_print()
+#        print(f'self._best_values:\n{self._best_values}\n\n')
+
+        # Free the shared memory
+        self.freemem()
+
+    def _fit_parallel(self, current_best_values, num, n_start, **kwargs):
+        num = min(num, self._map_dim-n_start)
+        for n in range(num):
+#            print(f'{n_start+n} before:\n{current_best_values}')
+            self._fit(n_start+n, current_best_values, **kwargs)
+#            print(f'{n_start+n} after:\n{current_best_values}')
+
+    def _fit(self, n, current_best_values, return_result=False, **kwargs):
+#RV        print(f'\n\nstart FitMap._fit {n}\n')
+#RV        print(f'current_best_values = {current_best_values}')
+#RV        print(f'self._best_parameters = {self._best_parameters}')
+#RV        print(f'self._new_parameters = {self._new_parameters}\n\n')
+#        self._parameters.pretty_print()
+        # Set parameters to current best values, but prevent them from sitting at boundaries
+        if self._new_parameters is None:
+            # Initial fit
+            for name, value in current_best_values.items():
+                par = self._parameters[name]
+                par.set(value=self._reset_par_at_boundary(par, value))
+        else:
+            # Refit
+            for i, name in enumerate(self._best_parameters):
+                par = self._parameters[name]
+                if name in self._new_parameters:
+                    if name in current_best_values:
+                        par.set(value=self._reset_par_at_boundary(par, current_best_values[name]))
+                elif par.expr is None:
+                    par.set(value=self._best_values[i][n])
+#RV        print(f'\nbefore fit {n}')
+#RV        self._parameters.pretty_print()
+        if self._mask is None:
+            result = self._model.fit(self._ymap_norm[n], self._parameters, x=self._x, **kwargs)
+        else:
+            result = self._model.fit(self._ymap_norm[n][~self._mask], self._parameters,
+                    x=self._x[~self._mask], **kwargs)
+#        print(f'\nafter fit {n}')
+#        self._parameters.pretty_print()
+#        print(result.fit_report(show_correl=False))
+        out_of_bounds = False
+        for name, par in self._parameter_bounds.items():
+            value = result.params[name].value
+            if not np.isinf(par['min']) and value < par['min']:
+                out_of_bounds = True
+                break
+            if not np.isinf(par['max']) and value > par['max']:
+                out_of_bounds = True
+                break
+        self._out_of_bounds_flat[n] = out_of_bounds
+        if self._try_no_bounds and out_of_bounds:
+            # Rerun fit with parameter bounds in place
+            for name, par in self._parameter_bounds.items():
+                self._parameters[name].set(min=par['min'], max=par['max'])
+            # Set parameters to current best values, but prevent them from sitting at boundaries
+            if self._new_parameters is None:
+                # Initial fit
+                for name, value in current_best_values.items():
+                    par = self._parameters[name]
+                    par.set(value=self._reset_par_at_boundary(par, value))
+            else:
+                # Refit
+                for i, name in enumerate(self._best_parameters):
+                    par = self._parameters[name]
+                    if name in self._new_parameters:
+                        if name in current_best_values:
+                            par.set(value=self._reset_par_at_boundary(par,
+                                    current_best_values[name]))
+                    elif par.expr is None:
+                        par.set(value=self._best_values[i][n])
+#            print('\nbefore fit')
+#            self._parameters.pretty_print()
+#            print(result.fit_report(show_correl=False))
+            if self._mask is None:
+                result = self._model.fit(self._ymap_norm[n], self._parameters, x=self._x, **kwargs)
+            else:
+                result = self._model.fit(self._ymap_norm[n][~self._mask], self._parameters,
+                    x=self._x[~self._mask], **kwargs)
+#            print(f'\nafter fit {n}')
+#            self._parameters.pretty_print()
+#            print(result.fit_report(show_correl=False))
+            out_of_bounds = False
+            for name, par in self._parameter_bounds.items():
+                value = result.params[name].value
+                if not np.isinf(par['min']) and value < par['min']:
+                    out_of_bounds = True
+                    break
+                if not np.isinf(par['max']) and value > par['max']:
+                    out_of_bounds = True
+                    break
+#            print(f'{n} redchi < redchi_cutoff = {result.redchi < self._redchi_cutoff} success = {result.success} out_of_bounds = {out_of_bounds}')
+            # Reset parameters back to unbound
+            for name in self._parameter_bounds.keys():
+                self._parameters[name].set(min=-np.inf, max=np.inf)
+        assert(not out_of_bounds)
+        if result.redchi >= self._redchi_cutoff:
+            result.success = False
+        if result.nfev == result.max_nfev:
+#            print(f'Maximum number of function evaluations reached for n = {n}')
+#            logging.warning(f'Maximum number of function evaluations reached for n = {n}')
+            if result.redchi < self._redchi_cutoff:
+                result.success = True
+            self._max_nfev_flat[n] = True
+        if result.success:
+            assert(all(True for par in current_best_values if par in result.params.values()))
+            for par in result.params.values():
+                if par.vary:
+                    current_best_values[par.name] = par.value
+        else:
+            logging.warning(f'Fit for n = {n} failed: {result.lmdif_message}')
+        # Renormalize the data and results
+        self._renormalize(n, result)
+        if self._print_report:
+            print(result.fit_report(show_correl=False))
+        if self._plot:
+            dims = np.unravel_index(n, self._map_shape)
+            if self._inv_transpose is not None:
+                dims= tuple(dims[self._inv_transpose[i]] for i in range(len(dims)))
+            super().plot(result=result, y=np.asarray(self._ymap[dims]), plot_comp_legends=True,
+                skip_init=self._skip_init, title=str(dims))
+#RV        print(f'\n\nend FitMap._fit {n}\n')
+#RV        print(f'current_best_values = {current_best_values}')
+#        self._parameters.pretty_print()
+#        print(result.fit_report(show_correl=False))
+#RV        print(f'\nself._best_values_flat:\n{self._best_values_flat}\n\n')
+        if return_result:
+            return(result)
+
+    def _renormalize(self, n, result):
+        self._redchi_flat[n] = np.float64(result.redchi)
+        self._success_flat[n] = result.success
+        if self._norm is None or not self._normalized:
+            self._best_fit_flat[n] = result.best_fit
+            for i, name in enumerate(self._best_parameters):
+                self._best_values_flat[i][n] = np.float64(result.params[name].value)
+                self._best_errors_flat[i][n] = np.float64(result.params[name].stderr)
+        else:
+            pars = set(self._parameter_norms) & set(self._best_parameters)
+            for name, par in result.params.items():
+                if name in pars and self._parameter_norms[name]:
+                    if par.stderr is not None:
+                        par.stderr *= self._norm[1]
+                    if par.expr is None:
+                        par.value *= self._norm[1]
+                        if self._print_report:
+                            if par.init_value is not None:
+                                par.init_value *= self._norm[1]
+                            if not np.isinf(par.min) and abs(par.min) != float_min:
+                                par.min *= self._norm[1]
+                            if not np.isinf(par.max) and abs(par.max) != float_min:
+                                par.max *= self._norm[1]
+            self._best_fit_flat[n] = result.best_fit*self._norm[1]+self._norm[0]
+            for i, name in enumerate(self._best_parameters):
+                self._best_values_flat[i][n] = np.float64(result.params[name].value)
+                self._best_errors_flat[i][n] = np.float64(result.params[name].stderr)
+            if self._plot:
+                if not self._skip_init:
+                    result.init_fit = result.init_fit*self._norm[1]+self._norm[0]
+                result.best_fit = np.copy(self._best_fit_flat[n])

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/general.py	Mon Mar 20 18:30:26 2023 +0000
@@ -0,0 +1,1965 @@
+#!/usr/bin/env python3
+
+#FIX write a function that returns a list of peak indices for a given plot
+#FIX use raise_error concept on more functions to optionally raise an error
+
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Dec  6 15:36:22 2021
+
+@author: rv43
+"""
+
+import logging
+logger=logging.getLogger(__name__)
+
+import os
+import sys
+import re
+try:
+    from yaml import safe_load, safe_dump
+except:
+    pass
+try:
+    import h5py
+except:
+    pass
+import numpy as np
+try:
+    import matplotlib.pyplot as plt
+    import matplotlib.lines as mlines
+    from matplotlib import transforms
+    from matplotlib.widgets import Button
+except:
+    pass
+
+from ast import literal_eval
+try:
+    from asteval import Interpreter, get_ast_names
+except:
+    pass
+from copy import deepcopy
+try:
+    from sympy import diff, simplify
+except:
+    pass
+from time import time
+
+
+def depth_list(L): return(isinstance(L, list) and max(map(depth_list, L))+1)
+def depth_tuple(T): return(isinstance(T, tuple) and max(map(depth_tuple, T))+1)
+def unwrap_tuple(T):
+    if depth_tuple(T) > 1 and len(T) == 1:
+        T = unwrap_tuple(*T)
+    return(T)
+
+def illegal_value(value, name, location=None, raise_error=False, log=True):
+    if not isinstance(location, str):
+        location = ''
+    else:
+        location = f'in {location} '
+    if isinstance(name, str):
+        error_msg = f'Illegal value for {name} {location}({value}, {type(value)})'
+    else:
+        error_msg = f'Illegal value {location}({value}, {type(value)})'
+    if log:
+        logger.error(error_msg)
+    if raise_error:
+        raise ValueError(error_msg)
+
+def illegal_combination(value1, name1, value2, name2, location=None, raise_error=False,
+        log=True):
+    if not isinstance(location, str):
+        location = ''
+    else:
+        location = f'in {location} '
+    if isinstance(name1, str):
+        error_msg = f'Illegal combination for {name1} and {name2} {location}'+ \
+                f'({value1}, {type(value1)} and {value2}, {type(value2)})'
+    else:
+        error_msg = f'Illegal combination {location}'+ \
+                f'({value1}, {type(value1)} and {value2}, {type(value2)})'
+    if log:
+        logger.error(error_msg)
+    if raise_error:
+        raise ValueError(error_msg)
+
+def test_ge_gt_le_lt(ge, gt, le, lt, func, location=None, raise_error=False, log=True):
+    """Check individual and mutual validity of ge, gt, le, lt qualifiers
+       func: is_int or is_num to test for int or numbers
+       Return: True upon success or False when mutually exlusive
+    """
+    if ge is None and gt is None and le is None and lt is None:
+        return(True)
+    if ge is not None:
+        if not func(ge):
+            illegal_value(ge, 'ge', location, raise_error, log) 
+            return(False)
+        if gt is not None:
+            illegal_combination(ge, 'ge', gt, 'gt', location, raise_error, log) 
+            return(False)
+    elif gt is not None and not func(gt):
+        illegal_value(gt, 'gt', location, raise_error, log) 
+        return(False)
+    if le is not None:
+        if not func(le):
+            illegal_value(le, 'le', location, raise_error, log) 
+            return(False)
+        if lt is not None:
+            illegal_combination(le, 'le', lt, 'lt', location, raise_error, log) 
+            return(False)
+    elif lt is not None and not func(lt):
+        illegal_value(lt, 'lt', location, raise_error, log) 
+        return(False)
+    if ge is not None:
+        if le is not None and ge > le:
+            illegal_combination(ge, 'ge', le, 'le', location, raise_error, log) 
+            return(False)
+        elif lt is not None and ge >= lt:
+            illegal_combination(ge, 'ge', lt, 'lt', location, raise_error, log) 
+            return(False)
+    elif gt is not None:
+        if le is not None and gt >= le:
+            illegal_combination(gt, 'gt', le, 'le', location, raise_error, log) 
+            return(False)
+        elif lt is not None and gt >= lt:
+            illegal_combination(gt, 'gt', lt, 'lt', location, raise_error, log) 
+            return(False)
+    return(True)
+
+def range_string_ge_gt_le_lt(ge=None, gt=None, le=None, lt=None):
+    """Return a range string representation matching the ge, gt, le, lt qualifiers
+       Does not validate the inputs, do that as needed before calling
+    """
+    range_string = ''
+    if ge is not None:
+        if le is None and lt is None:
+            range_string += f'>= {ge}'
+        else:
+            range_string += f'[{ge}, '
+    elif gt is not None:
+        if le is None and lt is None:
+            range_string += f'> {gt}'
+        else:
+            range_string += f'({gt}, '
+    if le is not None:
+        if ge is None and gt is None:
+            range_string += f'<= {le}'
+        else:
+            range_string += f'{le}]'
+    elif lt is not None:
+        if ge is None and gt is None:
+            range_string += f'< {lt}'
+        else:
+            range_string += f'{lt})'
+    return(range_string)
+
+def is_int(v, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is an integer in range ge <= v <= le or gt < v < lt or some combination.
+       Return: True if yes or False is no
+    """
+    return(_is_int_or_num(v, 'int', ge, gt, le, lt, raise_error, log))
+
+def is_num(v, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is a number in range ge <= v <= le or gt < v < lt or some combination.
+       Return: True if yes or False is no
+    """
+    return(_is_int_or_num(v, 'num', ge, gt, le, lt, raise_error, log))
+
+def _is_int_or_num(v, type_str, ge=None, gt=None, le=None, lt=None, raise_error=False,
+        log=True):
+    if type_str == 'int':
+        if not isinstance(v, int):
+            illegal_value(v, 'v', '_is_int_or_num', raise_error, log) 
+            return(False)
+        if not test_ge_gt_le_lt(ge, gt, le, lt, is_int, '_is_int_or_num', raise_error, log):
+            return(False)
+    elif type_str == 'num':
+        if not isinstance(v, (int, float)):
+            illegal_value(v, 'v', '_is_int_or_num', raise_error, log) 
+            return(False)
+        if not test_ge_gt_le_lt(ge, gt, le, lt, is_num, '_is_int_or_num', raise_error, log):
+            return(False)
+    else:
+        illegal_value(type_str, 'type_str', '_is_int_or_num', raise_error, log) 
+        return(False)
+    if ge is None and gt is None and le is None and lt is None:
+        return(True)
+    error = False
+    if ge is not None and v < ge:
+        error = True
+        error_msg = f'Value {v} out of range: {v} !>= {ge}'
+    if not error and gt is not None and v <= gt:
+        error = True
+        error_msg = f'Value {v} out of range: {v} !> {gt}'
+    if not error and le is not None and v > le:
+        error = True
+        error_msg = f'Value {v} out of range: {v} !<= {le}'
+    if not error and lt is not None and v >= lt:
+        error = True
+        error_msg = f'Value {v} out of range: {v} !< {lt}'
+    if error:
+        if log:
+            logger.error(error_msg)
+        if raise_error:
+            raise ValueError(error_msg)
+        return(False)
+    return(True)
+
+def is_int_pair(v, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is an integer pair, each in range ge <= v[i] <= le or gt < v[i] < lt or
+           ge[i] <= v[i] <= le[i] or gt[i] < v[i] < lt[i] or some combination.
+       Return: True if yes or False is no
+    """
+    return(_is_int_or_num_pair(v, 'int', ge, gt, le, lt, raise_error, log))
+
+def is_num_pair(v, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is a number pair, each in range ge <= v[i] <= le or gt < v[i] < lt or
+           ge[i] <= v[i] <= le[i] or gt[i] < v[i] < lt[i] or some combination.
+       Return: True if yes or False is no
+    """
+    return(_is_int_or_num_pair(v, 'num', ge, gt, le, lt, raise_error, log))
+
+def _is_int_or_num_pair(v, type_str, ge=None, gt=None, le=None, lt=None, raise_error=False,
+        log=True):
+    if type_str == 'int':
+        if not (isinstance(v, (tuple, list)) and len(v) == 2 and isinstance(v[0], int) and
+                isinstance(v[1], int)):
+            illegal_value(v, 'v', '_is_int_or_num_pair', raise_error, log) 
+            return(False)
+        func = is_int
+    elif type_str == 'num':
+        if not (isinstance(v, (tuple, list)) and len(v) == 2 and isinstance(v[0], (int, float)) and
+                isinstance(v[1], (int, float))):
+            illegal_value(v, 'v', '_is_int_or_num_pair', raise_error, log) 
+            return(False)
+        func = is_num
+    else:
+        illegal_value(type_str, 'type_str', '_is_int_or_num_pair', raise_error, log)
+        return(False)
+    if ge is None and gt is None and le is None and lt is None:
+        return(True)
+    if ge is None or func(ge, log=True):
+        ge = 2*[ge]
+    elif not _is_int_or_num_pair(ge, type_str, raise_error=raise_error, log=log):
+        return(False)
+    if gt is None or func(gt, log=True):
+        gt = 2*[gt]
+    elif not _is_int_or_num_pair(gt, type_str, raise_error=raise_error, log=log):
+        return(False)
+    if le is None or func(le, log=True):
+        le = 2*[le]
+    elif not _is_int_or_num_pair(le, type_str, raise_error=raise_error, log=log):
+        return(False)
+    if lt is None or func(lt, log=True):
+        lt = 2*[lt]
+    elif not _is_int_or_num_pair(lt, type_str, raise_error=raise_error, log=log):
+        return(False)
+    if (not func(v[0], ge[0], gt[0], le[0], lt[0], raise_error, log) or
+            not func(v[1], ge[1], gt[1], le[1], lt[1], raise_error, log)):
+        return(False)
+    return(True)
+
+def is_int_series(l, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is a tuple or list of integers, each in range ge <= l[i] <= le or
+       gt < l[i] < lt or some combination.
+    """
+    if not test_ge_gt_le_lt(ge, gt, le, lt, is_int, 'is_int_series', raise_error, log):
+        return(False)
+    if not isinstance(l, (tuple, list)):
+        illegal_value(l, 'l', 'is_int_series', raise_error, log)
+        return(False)
+    if any(True if not is_int(v, ge, gt, le, lt, raise_error, log) else False for v in l):
+        return(False)
+    return(True)
+
+def is_num_series(l, ge=None, gt=None, le=None, lt=None, raise_error=False, log=True):
+    """Value is a tuple or list of numbers, each in range ge <= l[i] <= le or
+       gt < l[i] < lt or some combination.
+    """
+    if not test_ge_gt_le_lt(ge, gt, le, lt, is_int, 'is_int_series', raise_error, log):
+        return(False)
+    if not isinstance(l, (tuple, list)):
+        illegal_value(l, 'l', 'is_num_series', raise_error, log)
+        return(False)
+    if any(True if not is_num(v, ge, gt, le, lt, raise_error, log) else False for v in l):
+        return(False)
+    return(True)
+
+def is_str_series(l, raise_error=False, log=True):
+    """Value is a tuple or list of strings.
+    """
+    if (not isinstance(l, (tuple, list)) or
+            any(True if not isinstance(s, str) else False for s in l)):
+        illegal_value(l, 'l', 'is_str_series', raise_error, log)
+        return(False)
+    return(True)
+
+def is_dict_series(l, raise_error=False, log=True):
+    """Value is a tuple or list of dictionaries.
+    """
+    if (not isinstance(l, (tuple, list)) or
+            any(True if not isinstance(d, dict) else False for d in l)):
+        illegal_value(l, 'l', 'is_dict_series', raise_error, log)
+        return(False)
+    return(True)
+
+def is_dict_nums(l, raise_error=False, log=True):
+    """Value is a dictionary with single number values
+    """
+    if (not isinstance(l, dict) or
+            any(True if not is_num(v, log=False) else False for v in l.values())):
+        illegal_value(l, 'l', 'is_dict_nums', raise_error, log)
+        return(False)
+    return(True)
+
+def is_dict_strings(l, raise_error=False, log=True):
+    """Value is a dictionary with single string values
+    """
+    if (not isinstance(l, dict) or
+            any(True if not isinstance(v, str) else False for v in l.values())):
+        illegal_value(l, 'l', 'is_dict_strings', raise_error, log)
+        return(False)
+    return(True)
+
+def is_index(v, ge=0, lt=None, raise_error=False, log=True):
+    """Value is an array index in range ge <= v < lt.
+       NOTE lt IS NOT included!
+    """
+    if isinstance(lt, int):
+        if lt <= ge:
+            illegal_combination(ge, 'ge', lt, 'lt', 'is_index', raise_error, log) 
+            return(False)
+    return(is_int(v, ge=ge, lt=lt, raise_error=raise_error, log=log))
+
+def is_index_range(v, ge=0, le=None, lt=None, raise_error=False, log=True):
+    """Value is an array index range in range ge <= v[0] <= v[1] <= le or ge <= v[0] <= v[1] < lt.
+       NOTE le IS included!
+    """
+    if not is_int_pair(v, raise_error=raise_error, log=log):
+        return(False)
+    if not test_ge_gt_le_lt(ge, None, le, lt, is_int, 'is_index_range', raise_error, log):
+        return(False)
+    if not ge <= v[0] <= v[1] or (le is not None and v[1] > le) or (lt is not None and v[1] >= lt):
+        if le is not None:
+            error_msg = f'Value {v} out of range: !({ge} <= {v[0]} <= {v[1]} <= {le})'
+        else:
+            error_msg = f'Value {v} out of range: !({ge} <= {v[0]} <= {v[1]} < {lt})'
+        if log:
+            logger.error(error_msg)
+        if raise_error:
+            raise ValueError(error_msg)
+        return(False)
+    return(True)
+
+def index_nearest(a, value):
+    a = np.asarray(a)
+    if a.ndim > 1:
+        raise ValueError(f'Invalid array dimension for parameter a ({a.ndim}, {a})')
+    # Round up for .5
+    value *= 1.0+sys.float_info.epsilon
+    return((int)(np.argmin(np.abs(a-value))))
+
+def index_nearest_low(a, value):
+    a = np.asarray(a)
+    if a.ndim > 1:
+        raise ValueError(f'Invalid array dimension for parameter a ({a.ndim}, {a})')
+    index = int(np.argmin(np.abs(a-value)))
+    if value < a[index] and index > 0:
+        index -= 1
+    return(index)
+
+def index_nearest_upp(a, value):
+    a = np.asarray(a)
+    if a.ndim > 1:
+        raise ValueError(f'Invalid array dimension for parameter a ({a.ndim}, {a})')
+    index = int(np.argmin(np.abs(a-value)))
+    if value > a[index] and index < a.size-1:
+        index += 1
+    return(index)
+
+def round_to_n(x, n=1):
+    if x == 0.0:
+        return(0)
+    else:
+        return(type(x)(round(x, n-1-int(np.floor(np.log10(abs(x)))))))
+
+def round_up_to_n(x, n=1):
+    xr = round_to_n(x, n)
+    if abs(x/xr) > 1.0:
+        xr += np.sign(x)*10**(np.floor(np.log10(abs(x)))+1-n)
+    return(type(x)(xr))
+
+def trunc_to_n(x, n=1):
+    xr = round_to_n(x, n)
+    if abs(xr/x) > 1.0:
+        xr -= np.sign(x)*10**(np.floor(np.log10(abs(x)))+1-n)
+    return(type(x)(xr))
+
+def almost_equal(a, b, sig_figs):
+    if is_num(a) and is_num(b):
+        return(abs(round_to_n(a-b, sig_figs)) < pow(10, -sig_figs+1))
+    else:
+        raise ValueError(f'Invalid value for a or b in almost_equal (a: {a}, {type(a)}, '+
+                f'b: {b}, {type(b)})')
+        return(False)
+
+def string_to_list(s, split_on_dash=True, remove_duplicates=True, sort=True):
+    """Return a list of numbers by splitting/expanding a string on any combination of
+       commas, whitespaces, or dashes (when split_on_dash=True)
+       e.g: '1, 3, 5-8, 12 ' -> [1, 3, 5, 6, 7, 8, 12]
+    """
+    if not isinstance(s, str):
+        illegal_value(s, location='string_to_list') 
+        return(None)
+    if not len(s):
+        return([])
+    try:
+        ll = [x for x in re.split('\s+,\s+|\s+,|,\s+|\s+|,', s.strip())]
+    except (ValueError, TypeError, SyntaxError, MemoryError, RecursionError):
+        return(None)
+    if split_on_dash:
+        try:
+            l = []
+            for l1 in ll:
+                l2 = [literal_eval(x) for x in re.split('\s+-\s+|\s+-|-\s+|\s+|-', l1)]
+                if len(l2) == 1:
+                    l += l2
+                elif len(l2) == 2 and l2[1] > l2[0]:
+                    l += [i for i in range(l2[0], l2[1]+1)]
+                else:
+                    raise ValueError
+        except (ValueError, TypeError, SyntaxError, MemoryError, RecursionError):
+            return(None)
+    else:
+        l = [literal_eval(x) for x in ll]
+    if remove_duplicates:
+        l = list(dict.fromkeys(l))
+    if sort:
+        l = sorted(l)
+    return(l)
+
+def get_trailing_int(string):
+    indexRegex = re.compile(r'\d+$')
+    mo = indexRegex.search(string)
+    if mo is None:
+        return(None)
+    else:
+        return(int(mo.group()))
+
+def input_int(s=None, ge=None, gt=None, le=None, lt=None, default=None, inset=None,
+        raise_error=False, log=True):
+    return(_input_int_or_num('int', s, ge, gt, le, lt, default, inset, raise_error, log))
+
+def input_num(s=None, ge=None, gt=None, le=None, lt=None, default=None, raise_error=False,
+        log=True):
+    return(_input_int_or_num('num', s, ge, gt, le, lt, default, None, raise_error,log))
+
+def _input_int_or_num(type_str, s=None, ge=None, gt=None, le=None, lt=None, default=None,
+        inset=None, raise_error=False, log=True):
+    if type_str == 'int':
+        if not test_ge_gt_le_lt(ge, gt, le, lt, is_int, '_input_int_or_num', raise_error, log):
+            return(None)
+    elif type_str == 'num':
+        if not test_ge_gt_le_lt(ge, gt, le, lt, is_num, '_input_int_or_num', raise_error, log):
+            return(None)
+    else:
+        illegal_value(type_str, 'type_str', '_input_int_or_num', raise_error, log)
+        return(None)
+    if default is not None:
+        if not _is_int_or_num(default, type_str, raise_error=raise_error, log=log):
+            return(None)
+        if ge is not None and default < ge:
+            illegal_combination(ge, 'ge', default, 'default', '_input_int_or_num', raise_error,
+                log)
+            return(None)
+        if gt is not None and default <= gt:
+            illegal_combination(gt, 'gt', default, 'default', '_input_int_or_num', raise_error,
+                log)
+            return(None)
+        if le is not None and default > le:
+            illegal_combination(le, 'le', default, 'default', '_input_int_or_num', raise_error,
+                log)
+            return(None)
+        if lt is not None and default >= lt:
+            illegal_combination(lt, 'lt', default, 'default', '_input_int_or_num', raise_error,
+                log)
+            return(None)
+        default_string = f' [{default}]'
+    else:
+        default_string = ''
+    if inset is not None:
+        if (not isinstance(inset, (tuple, list)) or any(True if not isinstance(i, int) else
+                False for i in inset)):
+            illegal_value(inset, 'inset', '_input_int_or_num', raise_error, log) 
+            return(None)
+    v_range = f'{range_string_ge_gt_le_lt(ge, gt, le, lt)}'
+    if len(v_range):
+        v_range = f' {v_range}'
+    if s is None:
+        if type_str == 'int':
+            print(f'Enter an integer{v_range}{default_string}: ')
+        else:
+            print(f'Enter a number{v_range}{default_string}: ')
+    else:
+        print(f'{s}{v_range}{default_string}: ')
+    try:
+        i = input()
+        if isinstance(i, str) and not len(i):
+            v = default
+            print(f'{v}')
+        else:
+            v = literal_eval(i)
+        if inset and v not in inset:
+           raise ValueError(f'{v} not part of the set {inset}')
+    except (ValueError, TypeError, SyntaxError, MemoryError, RecursionError):
+        v = None
+    except:
+        if log:
+            logger.error('Unexpected error')
+        if raise_error:
+            raise ValueError('Unexpected error')
+    if not _is_int_or_num(v, type_str, ge, gt, le, lt):
+        v = _input_int_or_num(type_str, s, ge, gt, le, lt, default, inset, raise_error, log)
+    return(v)
+
+def input_int_list(s=None, ge=None, le=None, split_on_dash=True, remove_duplicates=True,
+        sort=True, raise_error=False, log=True):
+    """Prompt the user to input a list of interger and split the entered string on any combination
+       of commas, whitespaces, or dashes (when split_on_dash is True)
+       e.g: '1 3,5-8 , 12 ' -> [1, 3, 5, 6, 7, 8, 12]
+       remove_duplicates: removes duplicates if True (may also change the order)
+       sort: sort in ascending order if True
+       return None upon an illegal input
+    """
+    return(_input_int_or_num_list('int', s, ge, le, split_on_dash, remove_duplicates, sort,
+        raise_error, log))
+
+def input_num_list(s=None, ge=None, le=None, remove_duplicates=True, sort=True, raise_error=False,
+        log=True):
+    """Prompt the user to input a list of numbers and split the entered string on any combination
+       of commas or whitespaces
+       e.g: '1.0, 3, 5.8, 12 ' -> [1.0, 3.0, 5.8, 12.0]
+       remove_duplicates: removes duplicates if True (may also change the order)
+       sort: sort in ascending order if True
+       return None upon an illegal input
+    """
+    return(_input_int_or_num_list('num', s, ge, le, False, remove_duplicates, sort, raise_error,
+        log))
+
+def _input_int_or_num_list(type_str, s=None, ge=None, le=None, split_on_dash=True,
+        remove_duplicates=True, sort=True, raise_error=False, log=True):
+    #FIX do we want a limit on max dimension?
+    if type_str == 'int':
+        if not test_ge_gt_le_lt(ge, None, le, None, is_int, 'input_int_or_num_list', raise_error,
+                log):
+            return(None)
+    elif type_str == 'num':
+        if not test_ge_gt_le_lt(ge, None, le, None, is_num, 'input_int_or_num_list', raise_error,
+                log):
+            return(None)
+    else:
+        illegal_value(type_str, 'type_str', '_input_int_or_num_list')
+        return(None)
+    v_range = f'{range_string_ge_gt_le_lt(ge=ge, le=le)}'
+    if len(v_range):
+        v_range = f' (each value in {v_range})'
+    if s is None:
+        print(f'Enter a series of integers{v_range}: ')
+    else:
+        print(f'{s}{v_range}: ')
+    try:
+        l = string_to_list(input(), split_on_dash, remove_duplicates, sort)
+    except (ValueError, TypeError, SyntaxError, MemoryError, RecursionError):
+        l = None
+    except:
+        print('Unexpected error')
+        raise
+    if (not isinstance(l, list) or
+            any(True if not _is_int_or_num(v, type_str, ge=ge, le=le) else False for v in l)):
+        if split_on_dash:
+            print('Invalid input: enter a valid set of dash/comma/whitespace separated integers '+
+                    'e.g. 1 3,5-8 , 12')
+        else:
+            print('Invalid input: enter a valid set of comma/whitespace separated integers '+
+                    'e.g. 1 3,5 8 , 12')
+        l = _input_int_or_num_list(type_str, s, ge, le, split_on_dash, remove_duplicates, sort,
+            raise_error, log)
+    return(l)
+
+def input_yesno(s=None, default=None):
+    if default is not None:
+        if not isinstance(default, str):
+            illegal_value(default, 'default', 'input_yesno') 
+            return(None)
+        if default.lower() in 'yes':
+            default = 'y'
+        elif default.lower() in 'no':
+            default = 'n'
+        else:
+            illegal_value(default, 'default', 'input_yesno') 
+            return(None)
+        default_string = f' [{default}]'
+    else:
+        default_string = ''
+    if s is None:
+        print(f'Enter yes or no{default_string}: ')
+    else:
+        print(f'{s}{default_string}: ')
+    i = input()
+    if isinstance(i, str) and not len(i):
+        i = default
+        print(f'{i}')
+    if i is not None and i.lower() in 'yes':
+        v = True
+    elif i is not None and i.lower() in 'no':
+        v = False
+    else:
+        print('Invalid input, enter yes or no')
+        v = input_yesno(s, default)
+    return(v)
+
+def input_menu(items, default=None, header=None):
+    if not isinstance(items, (tuple, list)) or any(True if not isinstance(i, str) else False
+            for i in items):
+        illegal_value(items, 'items', 'input_menu') 
+        return(None)
+    if default is not None:
+        if not (isinstance(default, str) and default in items):
+            logger.error(f'Invalid value for default ({default}), must be in {items}') 
+            return(None)
+        default_string = f' [{items.index(default)+1}]'
+    else:
+        default_string = ''
+    if header is None:
+        print(f'Choose one of the following items (1, {len(items)}){default_string}:')
+    else:
+        print(f'{header} (1, {len(items)}){default_string}:')
+    for i, choice in enumerate(items):
+        print(f'  {i+1}: {choice}')
+    try:
+        choice  = input()
+        if isinstance(choice, str) and not len(choice):
+            choice = items.index(default)
+            print(f'{choice+1}')
+        else:
+            choice = literal_eval(choice)
+            if isinstance(choice, int) and 1 <= choice <= len(items):
+                choice -= 1
+            else:
+                raise ValueError
+    except (ValueError, TypeError, SyntaxError, MemoryError, RecursionError):
+        choice = None
+    except:
+        print('Unexpected error')
+        raise
+    if choice is None:
+        print(f'Invalid choice, enter a number between 1 and {len(items)}')
+        choice = input_menu(items, default)
+    return(choice)
+
+def assert_no_duplicates_in_list_of_dicts(l: list, raise_error=False) -> list:
+    if not isinstance(l, list):
+        illegal_value(l, 'l', 'assert_no_duplicates_in_list_of_dicts', raise_error)
+        return(None)
+    if any(True if not isinstance(d, dict) else False for d in l):
+        illegal_value(l, 'l', 'assert_no_duplicates_in_list_of_dicts', raise_error)
+        return(None)
+    if len(l) != len([dict(t) for t in {tuple(sorted(d.items())) for d in l}]):
+        if raise_error:
+            raise ValueError(f'Duplicate items found in {l}')
+        else:
+            logger.error(f'Duplicate items found in {l}')
+        return(None)
+    else:
+        return(l)
+
+def assert_no_duplicate_key_in_list_of_dicts(l: list, key: str, raise_error=False) -> list:
+    if not isinstance(key, str):
+        illegal_value(key, 'key', 'assert_no_duplicate_key_in_list_of_dicts', raise_error)
+        return(None)
+    if not isinstance(l, list):
+        illegal_value(l, 'l', 'assert_no_duplicate_key_in_list_of_dicts', raise_error)
+        return(None)
+    if any(True if not isinstance(d, dict) else False for d in l):
+        illegal_value(l, 'l', 'assert_no_duplicates_in_list_of_dicts', raise_error)
+        return(None)
+    keys = [d.get(key, None) for d in l]
+    if None in keys or len(set(keys)) != len(l):
+        if raise_error:
+            raise ValueError(f'Duplicate or missing key ({key}) found in {l}')
+        else:
+            logger.error(f'Duplicate or missing key ({key}) found in {l}')
+        return(None)
+    else:
+        return(l)
+
+def assert_no_duplicate_attr_in_list_of_objs(l: list, attr: str, raise_error=False) -> list:
+    if not isinstance(attr, str):
+        illegal_value(attr, 'attr', 'assert_no_duplicate_attr_in_list_of_objs', raise_error)
+        return(None)
+    if not isinstance(l, list):
+        illegal_value(l, 'l', 'assert_no_duplicate_key_in_list_of_objs', raise_error)
+        return(None)
+    attrs = [getattr(obj, attr, None) for obj in l]
+    if None in attrs or len(set(attrs)) != len(l):
+        if raise_error:
+            raise ValueError(f'Duplicate or missing attr ({attr}) found in {l}')
+        else:
+            logger.error(f'Duplicate or missing attr ({attr}) found in {l}')
+        return(None)
+    else:
+        return(l)
+
+def file_exists_and_readable(path):
+    if not os.path.isfile(path):
+        raise ValueError(f'{path} is not a valid file')
+    elif not os.access(path, os.R_OK):
+        raise ValueError(f'{path} is not accessible for reading')
+    else:
+        return(path)
+
+def create_mask(x, bounds=None, exclude_bounds=False, current_mask=None):
+    # bounds is a pair of number in the same units a x
+    if not isinstance(x, (tuple, list, np.ndarray)) or not len(x):
+        logger.warning(f'Invalid input array ({x}, {type(x)})')
+        return(None)
+    if bounds is not None and not is_num_pair(bounds):
+        logger.warning(f'Invalid bounds parameter ({bounds} {type(bounds)}, input ignored')
+        bounds = None
+    if bounds is not None:
+        if exclude_bounds:
+            mask = np.logical_or(x < min(bounds), x > max(bounds))
+        else:
+            mask = np.logical_and(x > min(bounds), x < max(bounds))
+    else:
+        mask = np.ones(len(x), dtype=bool)
+    if current_mask is not None:
+        if not isinstance(current_mask, (tuple, list, np.ndarray)) or len(current_mask) != len(x):
+            logger.warning(f'Invalid current_mask ({current_mask}, {type(current_mask)}), '+
+                    'input ignored')
+        else:
+            mask = np.logical_or(mask, current_mask)
+    if not True in mask:
+        logger.warning('Entire data array is masked')
+    return(mask)
+
+def eval_expr(name, expr, expr_variables, user_variables=None, max_depth=10, raise_error=False,
+        log=True, **kwargs):
+    """Evaluate an expression of expressions
+    """
+    if not isinstance(name, str):
+        illegal_value(name, 'name', 'eval_expr', raise_error, log)
+        return(None)
+    if not isinstance(expr, str):
+        illegal_value(expr, 'expr', 'eval_expr', raise_error, log)
+        return(None)
+    if not is_dict_strings(expr_variables, log=False):
+        illegal_value(expr_variables, 'expr_variables', 'eval_expr', raise_error, log)
+        return(None)
+    if user_variables is not None and not is_dict_nums(user_variables, log=False):
+        illegal_value(user_variables, 'user_variables', 'eval_expr', raise_error, log)
+        return(None)
+    if not is_int(max_depth, gt=1, log=False):
+        illegal_value(max_depth, 'max_depth', 'eval_expr', raise_error, log)
+        return(None)
+    if not isinstance(raise_error, bool):
+        illegal_value(raise_error, 'raise_error', 'eval_expr', raise_error, log)
+        return(None)
+    if not isinstance(log, bool):
+        illegal_value(log, 'log', 'eval_expr', raise_error, log)
+        return(None)
+#    print(f'\nEvaluate the full expression for {expr}')
+    if 'chain' in kwargs:
+        chain = kwargs.pop('chain')
+        if not is_str_series(chain):
+            illegal_value(chain, 'chain', 'eval_expr', raise_error, log)
+            return(None)
+    else:
+        chain = []
+    if len(chain) > max_depth:
+        error_msg = 'Exceeded maximum depth ({max_depth}) in eval_expr'
+        if log:
+            logger.error(error_msg)
+        if raise_error:
+            raise ValueError(error_msg)
+        return(None)
+    if name not in chain:
+        chain.append(name)
+#    print(f'start: chain = {chain}')
+    if 'ast' in kwargs:
+        ast = kwargs.pop('ast')
+    else:
+        ast = Interpreter()
+    if user_variables is not None:
+        ast.symtable.update(user_variables)
+    chain_vars = [var for var in get_ast_names(ast.parse(expr))
+            if var in expr_variables and var not in ast.symtable]
+#    print(f'chain_vars: {chain_vars}')
+    save_chain = chain.copy()
+    for var in chain_vars:
+#        print(f'\n\tname = {name}, var = {var}:\n\t\t{expr_variables[var]}')
+#        print(f'\tchain = {chain}')
+        if var in chain:
+            error_msg = f'Circular variable {var} in eval_expr'
+            if log:
+               logger.error(error_msg)
+            if raise_error:
+               raise ValueError(error_msg)
+            return(None)
+#        print(f'\tknown symbols:\n\t\t{ast.user_defined_symbols()}\n')
+        if var in ast.user_defined_symbols():
+            val = ast.symtable[var]
+        else:
+            #val = eval_expr(var, expr_variables[var], expr_variables, user_variables=user_variables,
+            val = eval_expr(var, expr_variables[var], expr_variables, max_depth=max_depth,
+                    raise_error=raise_error, log=log, chain=chain, ast=ast)
+            if val is None:
+                return(None)
+            ast.symtable[var] = val
+#        print(f'\tval = {val}')
+#        print(f'\t{var} = {ast.symtable[var]}')
+        chain = save_chain.copy()
+#        print(f'\treset loop for {var}: chain = {chain}')
+    val = ast.eval(expr)
+#    print(f'return val for {expr} = {val}\n')
+    return(val)
+
+def full_gradient(expr, x, expr_name=None, expr_variables=None, valid_variables=None, max_depth=10,
+        raise_error=False, log=True, **kwargs):
+    """Compute the full gradient dexpr/dx
+    """
+    if not isinstance(x, str):
+        illegal_value(x, 'x', 'full_gradient', raise_error, log)
+        return(None)
+    if expr_name is not None and not isinstance(expr_name, str):
+        illegal_value(expr_name, 'expr_name', 'eval_expr', raise_error, log)
+        return(None)
+    if expr_variables is not None and not is_dict_strings(expr_variables, log=False):
+        illegal_value(expr_variables, 'expr_variables', 'full_gradient', raise_error, log)
+        return(None)
+    if valid_variables is not None and not is_str_series(valid_variables, log=False):
+        illegal_value(valid_variables, 'valid_variables', 'full_gradient', raise_error, log)
+    if not is_int(max_depth, gt=1, log=False):
+        illegal_value(max_depth, 'max_depth', 'eval_expr', raise_error, log)
+        return(None)
+    if not isinstance(raise_error, bool):
+        illegal_value(raise_error, 'raise_error', 'eval_expr', raise_error, log)
+        return(None)
+    if not isinstance(log, bool):
+        illegal_value(log, 'log', 'eval_expr', raise_error, log)
+        return(None)
+#    print(f'\nGet full gradient of {expr_name} = {expr} with respect to {x}')
+    if expr_name is not None and expr_name == x:
+        return(1.0)
+    if 'chain' in kwargs:
+        chain = kwargs.pop('chain')
+        if not is_str_series(chain):
+            illegal_value(chain, 'chain', 'eval_expr', raise_error, log)
+            return(None)
+    else:
+        chain = []
+    if len(chain) > max_depth:
+        error_msg = 'Exceeded maximum depth ({max_depth}) in eval_expr'
+        if log:
+            logger.error(error_msg)
+        if raise_error:
+            raise ValueError(error_msg)
+        return(None)
+    if expr_name is not None and expr_name not in chain:
+        chain.append(expr_name)
+#    print(f'start ({x}): chain = {chain}')
+    ast = Interpreter()
+    if expr_variables is None:
+        chain_vars = []
+    else:
+        chain_vars = [var for var in get_ast_names(ast.parse(f'{expr}'))
+                if var in expr_variables and var != x and var not in ast.symtable]
+#    print(f'chain_vars: {chain_vars}')
+    if valid_variables is not None:
+        unknown_vars = [var for var in chain_vars if var not in valid_variables]
+        if len(unknown_vars):
+            error_msg = f'Unknown variable {unknown_vars} in {expr}'
+            if log:
+               logger.error(error_msg)
+            if raise_error:
+               raise ValueError(error_msg)
+            return(None)
+    dexpr_dx = diff(expr, x)
+#    print(f'direct gradient: d({expr})/d({x}) = {dexpr_dx} ({type(dexpr_dx)})')
+    save_chain = chain.copy()
+    for var in chain_vars:
+#        print(f'\n\texpr_name = {expr_name}, var = {var}:\n\t\t{expr}')
+#        print(f'\tchain = {chain}')
+        if var in chain:
+            error_msg = f'Circular variable {var} in full_gradient'
+            if log:
+               logger.error(error_msg)
+            if raise_error:
+               raise ValueError(error_msg)
+            return(None)
+        dexpr_dvar = diff(expr, var)
+#        print(f'\td({expr})/d({var}) = {dexpr_dvar}')
+        if dexpr_dvar:
+            dvar_dx = full_gradient(expr_variables[var], x, expr_name=var,
+                    expr_variables=expr_variables, valid_variables=valid_variables,
+                    max_depth=max_depth, raise_error=raise_error, log=log, chain=chain)
+#            print(f'\t\td({var})/d({x}) = {dvar_dx}')
+            if dvar_dx:
+                dexpr_dx = f'{dexpr_dx}+({dexpr_dvar})*({dvar_dx})'
+#            print(f'\t\t2: chain = {chain}')
+        chain = save_chain.copy()
+#        print(f'\treset loop for {var}: chain = {chain}')
+#    print(f'full gradient: d({expr})/d({x}) = {dexpr_dx} ({type(dexpr_dx)})')
+#    print(f'reset end: chain = {chain}\n\n')
+    return(simplify(dexpr_dx))
+
+def bounds_from_mask(mask, return_include_bounds:bool=True):
+    bounds = []
+    for i, m in enumerate(mask):
+        if m == return_include_bounds:
+            if len(bounds) == 0 or type(bounds[-1]) == tuple:
+                bounds.append(i)
+        else:
+            if len(bounds) > 0 and isinstance(bounds[-1], int):
+                bounds[-1] = (bounds[-1], i-1)
+    if len(bounds) > 0 and isinstance(bounds[-1], int):
+        bounds[-1] = (bounds[-1], mask.size-1)
+    return(bounds)
+
+def draw_mask_1d(ydata, xdata=None, current_index_ranges=None, current_mask=None,
+        select_mask=True, num_index_ranges_max=None, title=None, legend=None, test_mode=False):
+    #FIX make color blind friendly
+    def draw_selections(ax, current_include, current_exclude, selected_index_ranges):
+        ax.clear()
+        ax.set_title(title)
+        ax.legend([legend])
+        ax.plot(xdata, ydata, 'k')
+        for (low, upp) in current_include:
+            xlow = 0.5*(xdata[max(0, low-1)]+xdata[low])
+            xupp = 0.5*(xdata[upp]+xdata[min(num_data-1, upp+1)])
+            ax.axvspan(xlow, xupp, facecolor='green', alpha=0.5)
+        for (low, upp) in current_exclude:
+            xlow = 0.5*(xdata[max(0, low-1)]+xdata[low])
+            xupp = 0.5*(xdata[upp]+xdata[min(num_data-1, upp+1)])
+            ax.axvspan(xlow, xupp, facecolor='red', alpha=0.5)
+        for (low, upp) in selected_index_ranges:
+            xlow = 0.5*(xdata[max(0, low-1)]+xdata[low])
+            xupp = 0.5*(xdata[upp]+xdata[min(num_data-1, upp+1)])
+            ax.axvspan(xlow, xupp, facecolor=selection_color, alpha=0.5)
+        ax.get_figure().canvas.draw()
+
+    def onclick(event):
+        if event.inaxes in [fig.axes[0]]:
+            selected_index_ranges.append(index_nearest_upp(xdata, event.xdata))
+
+    def onrelease(event):
+        if len(selected_index_ranges) > 0:
+            if isinstance(selected_index_ranges[-1], int):
+                if event.inaxes in [fig.axes[0]]:
+                    event.xdata = index_nearest_low(xdata, event.xdata)
+                    if selected_index_ranges[-1] <= event.xdata:
+                        selected_index_ranges[-1] = (selected_index_ranges[-1], event.xdata)
+                    else:
+                        selected_index_ranges[-1] = (event.xdata, selected_index_ranges[-1])
+                    draw_selections(event.inaxes, current_include, current_exclude, selected_index_ranges)
+                else:
+                    selected_index_ranges.pop(-1)
+
+    def confirm_selection(event):
+        plt.close()
+    
+    def clear_last_selection(event):
+        if len(selected_index_ranges):
+            selected_index_ranges.pop(-1)
+        else:
+            while len(current_include):
+                current_include.pop()
+            while len(current_exclude):
+                current_exclude.pop()
+            selected_mask.fill(False)
+        draw_selections(ax, current_include, current_exclude, selected_index_ranges)
+
+    def update_mask(mask, selected_index_ranges, unselected_index_ranges):
+        for (low, upp) in selected_index_ranges:
+            selected_mask = np.logical_and(xdata >= xdata[low], xdata <= xdata[upp])
+            mask = np.logical_or(mask, selected_mask)
+        for (low, upp) in unselected_index_ranges:
+            unselected_mask = np.logical_and(xdata >= xdata[low], xdata <= xdata[upp])
+            mask[unselected_mask] = False
+        return(mask)
+
+    def update_index_ranges(mask):
+        # Update the currently included index ranges (where mask is True)
+        current_include = []
+        for i, m in enumerate(mask):
+            if m == True:
+                if len(current_include) == 0 or type(current_include[-1]) == tuple:
+                    current_include.append(i)
+            else:
+                if len(current_include) > 0 and isinstance(current_include[-1], int):
+                    current_include[-1] = (current_include[-1], i-1)
+        if len(current_include) > 0 and isinstance(current_include[-1], int):
+            current_include[-1] = (current_include[-1], num_data-1)
+        return(current_include)
+
+    # Check inputs
+    ydata = np.asarray(ydata)
+    if ydata.ndim > 1:
+        logger.warning(f'Invalid ydata dimension ({ydata.ndim})')
+        return(None, None)
+    num_data = ydata.size
+    if xdata is None:
+        xdata = np.arange(num_data)
+    else:
+        xdata = np.asarray(xdata, dtype=np.float64)
+        if xdata.ndim > 1 or xdata.size != num_data:
+            logger.warning(f'Invalid xdata shape ({xdata.shape})')
+            return(None, None)
+        if not np.all(xdata[:-1] < xdata[1:]):
+            logger.warning('Invalid xdata: must be monotonically increasing')
+            return(None, None)
+    if current_index_ranges is not None:
+        if not isinstance(current_index_ranges, (tuple, list)):
+            logger.warning('Invalid current_index_ranges parameter ({current_index_ranges}, '+
+                    f'{type(current_index_ranges)})')
+            return(None, None)
+    if not isinstance(select_mask, bool):
+        logger.warning('Invalid select_mask parameter ({select_mask}, {type(select_mask)})')
+        return(None, None)
+    if num_index_ranges_max is not None:
+        logger.warning('num_index_ranges_max input not yet implemented in draw_mask_1d')
+    if title is None:
+        title = 'select ranges of data'
+    elif not isinstance(title, str):
+        illegal(title, 'title')
+        title = ''
+    if legend is None and not isinstance(title, str):
+        illegal(legend, 'legend')
+        legend = None
+
+    if select_mask:
+        title = f'Click and drag to {title} you wish to include'
+        selection_color = 'green'
+    else:
+        title = f'Click and drag to {title} you wish to exclude'
+        selection_color = 'red'
+
+    # Set initial selected mask and the selected/unselected index ranges as needed
+    selected_index_ranges = []
+    unselected_index_ranges = []
+    selected_mask = np.full(xdata.shape, False, dtype=bool)
+    if current_index_ranges is None:
+        if current_mask is None:
+            if not select_mask:
+                selected_index_ranges = [(0, num_data-1)]
+                selected_mask = np.full(xdata.shape, True, dtype=bool)
+        else:
+            selected_mask = np.copy(np.asarray(current_mask, dtype=bool))
+    if current_index_ranges is not None and len(current_index_ranges):
+        current_index_ranges = sorted([(low, upp) for (low, upp) in current_index_ranges])
+        for (low, upp) in current_index_ranges:
+            if low > upp or low >= num_data or upp < 0:
+                continue
+            if low < 0:
+                low = 0
+            if upp >= num_data:
+                upp = num_data-1
+            selected_index_ranges.append((low, upp))
+        selected_mask = update_mask(selected_mask, selected_index_ranges, unselected_index_ranges)
+    if current_index_ranges is not None and current_mask is not None:
+        selected_mask = np.logical_and(current_mask, selected_mask)
+    if current_mask is not None:
+        selected_index_ranges = update_index_ranges(selected_mask)
+
+    # Set up range selections for display
+    current_include = selected_index_ranges
+    current_exclude = []
+    selected_index_ranges = []
+    if not len(current_include):
+        if select_mask:
+            current_exclude = [(0, num_data-1)]
+        else:
+            current_include = [(0, num_data-1)]
+    else:
+        if current_include[0][0] > 0:
+            current_exclude.append((0, current_include[0][0]-1))
+        for i in range(1, len(current_include)):
+            current_exclude.append((current_include[i-1][1]+1, current_include[i][0]-1))
+        if current_include[-1][1] < num_data-1:
+            current_exclude.append((current_include[-1][1]+1, num_data-1))
+
+    if not test_mode:
+
+        # Set up matplotlib figure
+        plt.close('all')
+        fig, ax = plt.subplots()
+        plt.subplots_adjust(bottom=0.2)
+        draw_selections(ax, current_include, current_exclude, selected_index_ranges)
+
+        # Set up event handling for click-and-drag range selection
+        cid_click = fig.canvas.mpl_connect('button_press_event', onclick)
+        cid_release = fig.canvas.mpl_connect('button_release_event', onrelease)
+
+        # Set up confirm / clear range selection buttons
+        confirm_b = Button(plt.axes([0.75, 0.05, 0.15, 0.075]), 'Confirm')
+        clear_b = Button(plt.axes([0.59, 0.05, 0.15, 0.075]), 'Clear')
+        cid_confirm = confirm_b.on_clicked(confirm_selection)
+        cid_clear = clear_b.on_clicked(clear_last_selection)
+
+        # Show figure
+        plt.show(block=True)
+
+        # Disconnect callbacks when figure is closed
+        fig.canvas.mpl_disconnect(cid_click)
+        fig.canvas.mpl_disconnect(cid_release)
+        confirm_b.disconnect(cid_confirm)
+        clear_b.disconnect(cid_clear)
+
+    # Swap selection depending on select_mask
+    if not select_mask:
+        selected_index_ranges, unselected_index_ranges = unselected_index_ranges, \
+                selected_index_ranges
+
+    # Update the mask with the currently selected/unselected x-ranges
+    selected_mask = update_mask(selected_mask, selected_index_ranges, unselected_index_ranges)
+
+    # Update the currently included index ranges (where mask is True)
+    current_include = update_index_ranges(selected_mask)
+    
+    return(selected_mask, current_include)
+
+def select_peaks(ydata:np.ndarray, x_values:np.ndarray=None, x_mask:np.ndarray=None,
+                 peak_x_values:np.ndarray=np.array([]), peak_x_indices:np.ndarray=np.array([]),
+                 return_peak_x_values:bool=False, return_peak_x_indices:bool=False,
+                 return_peak_input_indices:bool=False, return_sorted:bool=False,
+                 title:str=None, xlabel:str=None, ylabel:str=None) -> list :
+
+    # Check arguments
+    if (len(peak_x_values) > 0 or return_peak_x_values) and not len(x_values) > 0:
+        raise RuntimeError('Cannot use peak_x_values or return_peak_x_values without x_values')
+    if not ((len(peak_x_values) > 0) ^ (len(peak_x_indices) > 0)):
+        raise RuntimeError('Use exactly one of peak_x_values or peak_x_indices')
+    return_format_iter = iter((return_peak_x_values, return_peak_x_indices, return_peak_input_indices))
+    if not (any(return_format_iter) and not any(return_format_iter)):
+        raise RuntimeError('Exactly one of return_peak_x_values, return_peak_x_indices, or '+
+                'return_peak_input_indices must be True')
+
+    EXCLUDE_PEAK_PROPERTIES = {'color': 'black', 'linestyle': '--','linewidth': 1,
+                               'marker': 10, 'markersize': 5, 'fillstyle': 'none'}
+    INCLUDE_PEAK_PROPERTIES = {'color': 'green', 'linestyle': '-', 'linewidth': 2,
+                               'marker': 10, 'markersize': 10, 'fillstyle': 'full'}
+    MASKED_PEAK_PROPERTIES = {'color': 'gray', 'linestyle': ':', 'linewidth': 1}
+
+    # Setup reference data & plot
+    x_indices = np.arange(len(ydata))
+    if x_values is None:
+        x_values = x_indices
+    if x_mask is None:
+        x_mask = np.full(x_values.shape, True, dtype=bool)
+    fig, ax = plt.subplots()
+    handles = ax.plot(x_values, ydata, label='Reference data')
+    handles.append(mlines.Line2D([], [], label='Excluded / unselected HKL', **EXCLUDE_PEAK_PROPERTIES))
+    handles.append(mlines.Line2D([], [], label='Included / selected HKL', **INCLUDE_PEAK_PROPERTIES))
+    handles.append(mlines.Line2D([], [], label='HKL in masked region (unselectable)', **MASKED_PEAK_PROPERTIES))
+    ax.legend(handles=handles, loc='upper right')
+    ax.set(title=title, xlabel=xlabel, ylabel=ylabel)
+
+
+    # Plot vertical line at each peak
+    value_to_index = lambda x_value: int(np.argmin(abs(x_values - x_value)))
+    if len(peak_x_indices) > 0:
+        peak_x_values = x_values[peak_x_indices]
+    else:
+        peak_x_indices = np.array(list(map(value_to_index, peak_x_values)))
+    peak_vlines = []
+    for loc in peak_x_values:
+        nearest_index = value_to_index(loc)
+        if nearest_index in x_indices[x_mask]:
+            peak_vline = ax.axvline(loc, **EXCLUDE_PEAK_PROPERTIES)
+            peak_vline.set_picker(5)
+        else:
+            peak_vline = ax.axvline(loc, **MASKED_PEAK_PROPERTIES)
+        peak_vlines.append(peak_vline)
+
+    # Indicate masked regions by gray-ing out the axes facecolor
+    mask_exclude_bounds = bounds_from_mask(x_mask, return_include_bounds=False)
+    for (low, upp) in mask_exclude_bounds:
+        xlow = x_values[low]
+        xupp = x_values[upp]
+        ax.axvspan(xlow, xupp, facecolor='gray', alpha=0.5)
+
+    # Setup peak picking
+    selected_peak_input_indices = []
+    def onpick(event):
+        try:
+            peak_index = peak_vlines.index(event.artist)
+        except:
+            pass
+        else:
+            peak_vline = event.artist
+            if peak_index in selected_peak_input_indices:
+                peak_vline.set(**EXCLUDE_PEAK_PROPERTIES)
+                selected_peak_input_indices.remove(peak_index)
+            else:
+                peak_vline.set(**INCLUDE_PEAK_PROPERTIES)
+                selected_peak_input_indices.append(peak_index)
+            plt.draw()
+    cid_pick_peak = fig.canvas.mpl_connect('pick_event', onpick)
+
+    # Setup "Confirm" button
+    def confirm_selection(event):
+        plt.close()
+    plt.subplots_adjust(bottom=0.2)
+    confirm_b = Button(plt.axes([0.75, 0.05, 0.15, 0.075]), 'Confirm')
+    cid_confirm = confirm_b.on_clicked(confirm_selection)
+
+    # Show figure for user interaction
+    plt.show()
+
+    # Disconnect callbacks when figure is closed
+    fig.canvas.mpl_disconnect(cid_pick_peak)
+    confirm_b.disconnect(cid_confirm)
+
+    if return_peak_input_indices:
+        selected_peaks = np.array(selected_peak_input_indices)
+    if return_peak_x_values:
+        selected_peaks = peak_x_values[selected_peak_input_indices]
+    if return_peak_x_indices:
+        selected_peaks = peak_x_indices[selected_peak_input_indices]
+
+    if return_sorted:
+        selected_peaks.sort()
+
+    return(selected_peaks)
+
+def find_image_files(path, filetype, name=None):
+    if isinstance(name, str):
+        name = f'{name.strip()} '
+    else:
+        name = ''
+    # Find available index range
+    if filetype == 'tif':
+        if not isinstance(path, str) or not os.path.isdir(path):
+            illegal_value(path, 'path', 'find_image_files')
+            return(-1, 0, [])
+        indexRegex = re.compile(r'\d+')
+        # At this point only tiffs
+        files = sorted([f for f in os.listdir(path) if os.path.isfile(os.path.join(path, f)) and
+                f.endswith('.tif') and indexRegex.search(f)])
+        num_img = len(files)
+        if num_img < 1:
+            logger.warning(f'No available {name}files')
+            return(-1, 0, [])
+        first_index = indexRegex.search(files[0]).group()
+        last_index = indexRegex.search(files[-1]).group()
+        if first_index is None or last_index is None:
+            logger.error(f'Unable to find correctly indexed {name}images')
+            return(-1, 0, [])
+        first_index = int(first_index)
+        last_index = int(last_index)
+        if num_img != last_index-first_index+1:
+            logger.error(f'Non-consecutive set of indices for {name}images')
+            return(-1, 0, [])
+        paths = [os.path.join(path, f) for f in files]
+    elif filetype == 'h5':
+        if not isinstance(path, str) or not os.path.isfile(path):
+            illegal_value(path, 'path', 'find_image_files')
+            return(-1, 0, [])
+        # At this point only h5 in alamo2 detector style
+        first_index = 0
+        with h5py.File(path, 'r') as f:
+            num_img = f['entry/instrument/detector/data'].shape[0]
+            last_index = num_img-1
+        paths = [path]
+    else:
+        illegal_value(filetype, 'filetype', 'find_image_files')
+        return(-1, 0, [])
+    logger.info(f'Number of available {name}images: {num_img}')
+    logger.info(f'Index range of available {name}images: [{first_index}, '+
+            f'{last_index}]')
+
+    return(first_index, num_img, paths)
+
+def select_image_range(first_index, offset, num_available, num_img=None, name=None,
+        num_required=None):
+    if isinstance(name, str):
+        name = f'{name.strip()} '
+    else:
+        name = ''
+    # Check existing values
+    if not is_int(num_available, gt=0):
+        logger.warning(f'No available {name}images')
+        return(0, 0, 0)
+    if num_img is not None and not is_int(num_img, ge=0):
+        illegal_value(num_img, 'num_img', 'select_image_range')
+        return(0, 0, 0)
+    if is_int(first_index, ge=0) and is_int(offset, ge=0):
+        if num_required is None:
+            if input_yesno(f'\nCurrent {name}first image index/offset = {first_index}/{offset},'+
+                    'use these values (y/n)?', 'y'):
+                if num_img is not None:
+                    if input_yesno(f'Current number of {name}images = {num_img}, '+
+                            'use this value (y/n)? ', 'y'):
+                        return(first_index, offset, num_img)
+                else:
+                    if input_yesno(f'Number of available {name}images = {num_available}, '+
+                            'use all (y/n)? ', 'y'):
+                        return(first_index, offset, num_available)
+        else:
+            if input_yesno(f'\nCurrent {name}first image offset = {offset}, '+
+                    f'use this values (y/n)?', 'y'):
+                return(first_index, offset, num_required)
+
+    # Check range against requirements
+    if num_required is None:
+        if num_available == 1:
+            return(first_index, 0, 1)
+    else:
+        if not is_int(num_required, ge=1):
+            illegal_value(num_required, 'num_required', 'select_image_range')
+            return(0, 0, 0)
+        if num_available < num_required:
+            logger.error(f'Unable to find the required {name}images ({num_available} out of '+
+                    f'{num_required})')
+            return(0, 0, 0)
+
+    # Select index range
+    print(f'\nThe number of available {name}images is {num_available}')
+    if num_required is None:
+        last_index = first_index+num_available
+        use_all = f'Use all ([{first_index}, {last_index}])'
+        pick_offset = 'Pick the first image index offset and the number of images'
+        pick_bounds = 'Pick the first and last image index'
+        choice = input_menu([use_all, pick_offset, pick_bounds], default=pick_offset)
+        if not choice:
+            offset = 0
+            num_img = num_available
+        elif choice == 1:
+            offset = input_int('Enter the first index offset', ge=0, le=last_index-first_index)
+            if first_index+offset == last_index:
+                num_img = 1
+            else:
+                num_img = input_int('Enter the number of images', ge=1, le=num_available-offset)
+        else:
+            offset = input_int('Enter the first index', ge=first_index, le=last_index)
+            num_img = 1-offset+input_int('Enter the last index', ge=offset, le=last_index)
+            offset -= first_index
+    else:
+        use_all = f'Use ([{first_index}, {first_index+num_required-1}])'
+        pick_offset = 'Pick the first index offset'
+        choice = input_menu([use_all, pick_offset], pick_offset)
+        offset = 0
+        if choice == 1:
+            offset = input_int('Enter the first index offset', ge=0, le=num_available-num_required)
+        num_img = num_required
+
+    return(first_index, offset, num_img)
+
+def load_image(f, img_x_bounds=None, img_y_bounds=None):
+    """Load a single image from file.
+    """
+    if not os.path.isfile(f):
+        logger.error(f'Unable to load {f}')
+        return(None)
+    img_read = plt.imread(f)
+    if not img_x_bounds:
+        img_x_bounds = (0, img_read.shape[0])
+    else:
+        if (not isinstance(img_x_bounds, (tuple, list)) or len(img_x_bounds) != 2 or 
+                not (0 <= img_x_bounds[0] < img_x_bounds[1] <= img_read.shape[0])):
+            logger.error(f'inconsistent row dimension in {f}')
+            return(None)
+    if not img_y_bounds:
+        img_y_bounds = (0, img_read.shape[1])
+    else:
+        if (not isinstance(img_y_bounds, list) or len(img_y_bounds) != 2 or 
+                not (0 <= img_y_bounds[0] < img_y_bounds[1] <= img_read.shape[1])):
+            logger.error(f'inconsistent column dimension in {f}')
+            return(None)
+    return(img_read[img_x_bounds[0]:img_x_bounds[1],img_y_bounds[0]:img_y_bounds[1]])
+
+def load_image_stack(files, filetype, img_offset, num_img, num_img_skip=0,
+        img_x_bounds=None, img_y_bounds=None):
+    """Load a set of images and return them as a stack.
+    """
+    logger.debug(f'img_offset = {img_offset}')
+    logger.debug(f'num_img = {num_img}')
+    logger.debug(f'num_img_skip = {num_img_skip}')
+    logger.debug(f'\nfiles:\n{files}\n')
+    img_stack = np.array([])
+    if filetype == 'tif':
+        img_read_stack = []
+        i = 1
+        t0 = time()
+        for f in files[img_offset:img_offset+num_img:num_img_skip+1]:
+            if not i%20:
+                logger.info(f'    loading {i}/{num_img}: {f}')
+            else:
+                logger.debug(f'    loading {i}/{num_img}: {f}')
+            img_read = load_image(f, img_x_bounds, img_y_bounds)
+            img_read_stack.append(img_read)
+            i += num_img_skip+1
+        img_stack = np.stack([img_read for img_read in img_read_stack])
+        logger.info(f'... done in {time()-t0:.2f} seconds!')
+        logger.debug(f'img_stack shape = {np.shape(img_stack)}')
+        del img_read_stack, img_read
+    elif filetype == 'h5':
+        if not isinstance(files[0], str) and not os.path.isfile(files[0]):
+            illegal_value(files[0], 'files[0]', 'load_image_stack')
+            return(img_stack)
+        t0 = time()
+        logger.info(f'Loading {files[0]}')
+        with h5py.File(files[0], 'r') as f:
+            shape = f['entry/instrument/detector/data'].shape
+            if len(shape) != 3:
+                logger.error(f'inconsistent dimensions in {files[0]}')
+            if not img_x_bounds:
+                img_x_bounds = (0, shape[1])
+            else:
+                if (not isinstance(img_x_bounds, (tuple, list)) or len(img_x_bounds) != 2 or 
+                        not (0 <= img_x_bounds[0] < img_x_bounds[1] <= shape[1])):
+                    logger.error(f'inconsistent row dimension in {files[0]} {img_x_bounds} '+
+                            f'{shape[1]}')
+            if not img_y_bounds:
+                img_y_bounds = (0, shape[2])
+            else:
+                if (not isinstance(img_y_bounds, list) or len(img_y_bounds) != 2 or 
+                        not (0 <= img_y_bounds[0] < img_y_bounds[1] <= shape[2])):
+                    logger.error(f'inconsistent column dimension in {files[0]}')
+            img_stack = f.get('entry/instrument/detector/data')[
+                    img_offset:img_offset+num_img:num_img_skip+1,
+                    img_x_bounds[0]:img_x_bounds[1],img_y_bounds[0]:img_y_bounds[1]]
+        logger.info(f'... done in {time()-t0:.2f} seconds!')
+    else:
+        illegal_value(filetype, 'filetype', 'load_image_stack')
+    return(img_stack)
+
+def combine_tiffs_in_h5(files, num_img, h5_filename):
+    img_stack = load_image_stack(files, 'tif', 0, num_img)
+    with h5py.File(h5_filename, 'w') as f:
+        f.create_dataset('entry/instrument/detector/data', data=img_stack)
+    del img_stack
+    return([h5_filename])
+
+def clear_imshow(title=None):
+    plt.ioff()
+    if title is None:
+        title = 'quick imshow'
+    elif not isinstance(title, str):
+        illegal_value(title, 'title', 'clear_imshow')
+        return
+    plt.close(fig=title)
+
+def clear_plot(title=None):
+    plt.ioff()
+    if title is None:
+        title = 'quick plot'
+    elif not isinstance(title, str):
+        illegal_value(title, 'title', 'clear_plot')
+        return
+    plt.close(fig=title)
+
+def quick_imshow(a, title=None, path=None, name=None, save_fig=False, save_only=False,
+            clear=True, extent=None, show_grid=False, grid_color='w', grid_linewidth=1,
+            block=False, **kwargs):
+    if title is not None and not isinstance(title, str):
+        illegal_value(title, 'title', 'quick_imshow')
+        return
+    if path is not None and not isinstance(path, str):
+        illegal_value(path, 'path', 'quick_imshow')
+        return
+    if not isinstance(save_fig, bool):
+        illegal_value(save_fig, 'save_fig', 'quick_imshow')
+        return
+    if not isinstance(save_only, bool):
+        illegal_value(save_only, 'save_only', 'quick_imshow')
+        return
+    if not isinstance(clear, bool):
+        illegal_value(clear, 'clear', 'quick_imshow')
+        return
+    if not isinstance(block, bool):
+        illegal_value(block, 'block', 'quick_imshow')
+        return
+    if not title:
+        title='quick imshow'
+#    else:
+#        title = re.sub(r"\s+", '_', title)
+    if name is None:
+        ttitle = re.sub(r"\s+", '_', title)
+        if path is None:
+            path = f'{ttitle}.png'
+        else:
+            path = f'{path}/{ttitle}.png'
+    else:
+        if path is None:
+            path = name
+        else:
+            path = f'{path}/{name}'
+    if 'cmap' in kwargs and a.ndim == 3 and (a.shape[2] == 3 or a.shape[2] == 4):
+        use_cmap = True
+        if a.shape[2] == 4 and a[:,:,-1].min() != a[:,:,-1].max():
+            use_cmap = False
+        if any(True if a[i,j,0] != a[i,j,1] and a[i,j,0] != a[i,j,2] else False
+                for i in range(a.shape[0]) for j in range(a.shape[1])):
+            use_cmap = False
+        if use_cmap:
+            a = a[:,:,0]
+        else:
+            logger.warning('Image incompatible with cmap option, ignore cmap')
+            kwargs.pop('cmap')
+    if extent is None:
+        extent = (0, a.shape[1], a.shape[0], 0)
+    if clear:
+        try:
+            plt.close(fig=title)
+        except:
+            pass
+    if not save_only:
+        if block:
+            plt.ioff()
+        else:
+            plt.ion()
+    plt.figure(title)
+    plt.imshow(a, extent=extent, **kwargs)
+    if show_grid:
+        ax = plt.gca()
+        ax.grid(color=grid_color, linewidth=grid_linewidth)
+#    if title != 'quick imshow':
+#        plt.title = title
+    if save_only:
+        plt.savefig(path)
+        plt.close(fig=title)
+    else:
+        if save_fig:
+            plt.savefig(path)
+        if block:
+            plt.show(block=block)
+
+def quick_plot(*args, xerr=None, yerr=None, vlines=None, title=None, xlim=None, ylim=None,
+        xlabel=None, ylabel=None, legend=None, path=None, name=None, show_grid=False,
+        save_fig=False, save_only=False, clear=True, block=False, **kwargs):
+    if title is not None and not isinstance(title, str):
+        illegal_value(title, 'title', 'quick_plot')
+        title = None
+    if xlim is not None and not isinstance(xlim, (tuple, list)) and len(xlim) != 2:
+        illegal_value(xlim, 'xlim', 'quick_plot')
+        xlim = None
+    if ylim is not None and not isinstance(ylim, (tuple, list)) and len(ylim) != 2:
+        illegal_value(ylim, 'ylim', 'quick_plot')
+        ylim = None
+    if xlabel is not None and not isinstance(xlabel, str):
+        illegal_value(xlabel, 'xlabel', 'quick_plot')
+        xlabel = None
+    if ylabel is not None and not isinstance(ylabel, str):
+        illegal_value(ylabel, 'ylabel', 'quick_plot')
+        ylabel = None
+    if legend is not None and not isinstance(legend, (tuple, list)):
+        illegal_value(legend, 'legend', 'quick_plot')
+        legend = None
+    if path is not None and not isinstance(path, str):
+        illegal_value(path, 'path', 'quick_plot')
+        return
+    if not isinstance(show_grid, bool):
+        illegal_value(show_grid, 'show_grid', 'quick_plot')
+        return
+    if not isinstance(save_fig, bool):
+        illegal_value(save_fig, 'save_fig', 'quick_plot')
+        return
+    if not isinstance(save_only, bool):
+        illegal_value(save_only, 'save_only', 'quick_plot')
+        return
+    if not isinstance(clear, bool):
+        illegal_value(clear, 'clear', 'quick_plot')
+        return
+    if not isinstance(block, bool):
+        illegal_value(block, 'block', 'quick_plot')
+        return
+    if title is None:
+        title = 'quick plot'
+#    else:
+#        title = re.sub(r"\s+", '_', title)
+    if name is None:
+        ttitle = re.sub(r"\s+", '_', title)
+        if path is None:
+            path = f'{ttitle}.png'
+        else:
+            path = f'{path}/{ttitle}.png'
+    else:
+        if path is None:
+            path = name
+        else:
+            path = f'{path}/{name}'
+    if clear:
+        try:
+            plt.close(fig=title)
+        except:
+            pass
+    args = unwrap_tuple(args)
+    if depth_tuple(args) > 1 and (xerr is not None or yerr is not None):
+        logger.warning('Error bars ignored form multiple curves')
+    if not save_only:
+        if block:
+            plt.ioff()
+        else:
+            plt.ion()
+    plt.figure(title)
+    if depth_tuple(args) > 1:
+       for y in args:
+           plt.plot(*y, **kwargs)
+    else:
+        if xerr is None and yerr is None:
+            plt.plot(*args, **kwargs)
+        else:
+            plt.errorbar(*args, xerr=xerr, yerr=yerr, **kwargs)
+    if vlines is not None:
+        if isinstance(vlines, (int, float)):
+            vlines = [vlines]
+        for v in vlines:
+            plt.axvline(v, color='r', linestyle='--', **kwargs)
+#    if vlines is not None:
+#        for s in tuple(([x, x], list(plt.gca().get_ylim())) for x in vlines):
+#            plt.plot(*s, color='red', **kwargs)
+    if xlim is not None:
+        plt.xlim(xlim)
+    if ylim is not None:
+        plt.ylim(ylim)
+    if xlabel is not None:
+        plt.xlabel(xlabel)
+    if ylabel is not None:
+        plt.ylabel(ylabel)
+    if show_grid:
+        ax = plt.gca()
+        ax.grid(color='k')#, linewidth=1)
+    if legend is not None:
+        plt.legend(legend)
+    if save_only:
+        plt.savefig(path)
+        plt.close(fig=title)
+    else:
+        if save_fig:
+            plt.savefig(path)
+        if block:
+            plt.show(block=block)
+
+def select_array_bounds(a, x_low=None, x_upp=None, num_x_min=None, ask_bounds=False,
+        title='select array bounds'):
+    """Interactively select the lower and upper data bounds for a numpy array.
+    """
+    if isinstance(a, (tuple, list)):
+        a = np.array(a)
+    if not isinstance(a, np.ndarray) or a.ndim != 1:
+        illegal_value(a.ndim, 'array type or dimension', 'select_array_bounds')
+        return(None)
+    len_a = len(a)
+    if num_x_min is None:
+        num_x_min = 1
+    else:
+        if num_x_min < 2 or num_x_min > len_a:
+            logger.warning('Invalid value for num_x_min in select_array_bounds, input ignored')
+            num_x_min = 1
+
+    # Ask to use current bounds
+    if ask_bounds and (x_low is not None or x_upp is not None):
+        if x_low is None:
+            x_low = 0
+        if not is_int(x_low, ge=0, le=len_a-num_x_min):
+            illegal_value(x_low, 'x_low', 'select_array_bounds')
+            return(None)
+        if x_upp is None:
+            x_upp = len_a
+        if not is_int(x_upp, ge=x_low+num_x_min, le=len_a):
+            illegal_value(x_upp, 'x_upp', 'select_array_bounds')
+            return(None)
+        quick_plot((range(len_a), a), vlines=(x_low,x_upp), title=title)
+        if not input_yesno(f'\nCurrent array bounds: [{x_low}, {x_upp}] '+
+                    'use these values (y/n)?', 'y'):
+            x_low = None
+            x_upp = None
+        else:
+            clear_plot(title)
+            return(x_low, x_upp)
+
+    if x_low is None:
+        x_min = 0
+        x_max = len_a
+        x_low_max = len_a-num_x_min
+        while True:
+            quick_plot(range(x_min, x_max), a[x_min:x_max], title=title)
+            zoom_flag = input_yesno('Set lower data bound (y) or zoom in (n)?', 'y')
+            if zoom_flag:
+                x_low = input_int('    Set lower data bound', ge=0, le=x_low_max)
+                break
+            else:
+                x_min = input_int('    Set lower zoom index', ge=0, le=x_low_max)
+                x_max = input_int('    Set upper zoom index', ge=x_min+1, le=x_low_max+1)
+    else:
+        if not is_int(x_low, ge=0, le=len_a-num_x_min):
+            illegal_value(x_low, 'x_low', 'select_array_bounds')
+            return(None)
+    if x_upp is None:
+        x_min = x_low+num_x_min
+        x_max = len_a
+        x_upp_min = x_min
+        while True:
+            quick_plot(range(x_min, x_max), a[x_min:x_max], title=title)
+            zoom_flag = input_yesno('Set upper data bound (y) or zoom in (n)?', 'y')
+            if zoom_flag:
+                x_upp = input_int('    Set upper data bound', ge=x_upp_min, le=len_a)
+                break
+            else:
+                x_min = input_int('    Set upper zoom index', ge=x_upp_min, le=len_a-1)
+                x_max = input_int('    Set upper zoom index', ge=x_min+1, le=len_a)
+    else:
+        if not is_int(x_upp, ge=x_low+num_x_min, le=len_a):
+            illegal_value(x_upp, 'x_upp', 'select_array_bounds')
+            return(None)
+    print(f'lower bound = {x_low} (inclusive)\nupper bound = {x_upp} (exclusive)]')
+    quick_plot((range(len_a), a), vlines=(x_low,x_upp), title=title)
+    if not input_yesno('Accept these bounds (y/n)?', 'y'):
+        x_low, x_upp = select_array_bounds(a, None, None, num_x_min, title=title)
+    clear_plot(title)
+    return(x_low, x_upp)
+
+def select_image_bounds(a, axis, low=None, upp=None, num_min=None, title='select array bounds',
+        raise_error=False):
+    """Interactively select the lower and upper data bounds for a 2D numpy array.
+    """
+    a = np.asarray(a)
+    if a.ndim != 2:
+        illegal_value(a.ndim, 'array dimension', location='select_image_bounds',
+                raise_error=raise_error)
+        return(None)
+    if axis < 0 or axis >= a.ndim:
+        illegal_value(axis, 'axis', location='select_image_bounds', raise_error=raise_error)
+        return(None)
+    low_save = low
+    upp_save = upp
+    num_min_save = num_min
+    if num_min is None:
+        num_min = 1
+    else:
+        if num_min < 2 or num_min > a.shape[axis]:
+            logger.warning('Invalid input for num_min in select_image_bounds, input ignored')
+            num_min = 1
+    if low is None:
+        min_ = 0
+        max_ = a.shape[axis]
+        low_max = a.shape[axis]-num_min
+        while True:
+            if axis:
+                quick_imshow(a[:,min_:max_], title=title, aspect='auto',
+                        extent=[min_,max_,a.shape[0],0])
+            else:
+                quick_imshow(a[min_:max_,:], title=title, aspect='auto',
+                        extent=[0,a.shape[1], max_,min_])
+            zoom_flag = input_yesno('Set lower data bound (y) or zoom in (n)?', 'y')
+            if zoom_flag:
+                low = input_int('    Set lower data bound', ge=0, le=low_max)
+                break
+            else:
+                min_ = input_int('    Set lower zoom index', ge=0, le=low_max)
+                max_ = input_int('    Set upper zoom index', ge=min_+1, le=low_max+1)
+    else:
+        if not is_int(low, ge=0, le=a.shape[axis]-num_min):
+            illegal_value(low, 'low', location='select_image_bounds', raise_error=raise_error)
+            return(None)
+    if upp is None:
+        min_ = low+num_min
+        max_ = a.shape[axis]
+        upp_min = min_
+        while True:
+            if axis:
+                quick_imshow(a[:,min_:max_], title=title, aspect='auto',
+                        extent=[min_,max_,a.shape[0],0])
+            else:
+                quick_imshow(a[min_:max_,:], title=title, aspect='auto',
+                        extent=[0,a.shape[1], max_,min_])
+            zoom_flag = input_yesno('Set upper data bound (y) or zoom in (n)?', 'y')
+            if zoom_flag:
+                upp = input_int('    Set upper data bound', ge=upp_min, le=a.shape[axis])
+                break
+            else:
+                min_ = input_int('    Set upper zoom index', ge=upp_min, le=a.shape[axis]-1)
+                max_ = input_int('    Set upper zoom index', ge=min_+1, le=a.shape[axis])
+    else:
+        if not is_int(upp, ge=low+num_min, le=a.shape[axis]):
+            illegal_value(upp, 'upp', location='select_image_bounds', raise_error=raise_error)
+            return(None)
+    bounds = (low, upp)
+    a_tmp = np.copy(a)
+    a_tmp_max = a.max()
+    if axis:
+        a_tmp[:,bounds[0]] = a_tmp_max
+        a_tmp[:,bounds[1]-1] = a_tmp_max
+    else:
+        a_tmp[bounds[0],:] = a_tmp_max
+        a_tmp[bounds[1]-1,:] = a_tmp_max
+    print(f'lower bound = {low} (inclusive)\nupper bound = {upp} (exclusive)')
+    quick_imshow(a_tmp, title=title, aspect='auto')
+    del a_tmp
+    if not input_yesno('Accept these bounds (y/n)?', 'y'):
+        bounds = select_image_bounds(a, axis, low=low_save, upp=upp_save, num_min=num_min_save,
+            title=title)
+    return(bounds)
+
+def select_one_image_bound(a, axis, bound=None, bound_name=None, title='select array bounds',
+        default='y', raise_error=False):
+    """Interactively select a data boundary for a 2D numpy array.
+    """
+    a = np.asarray(a)
+    if a.ndim != 2:
+        illegal_value(a.ndim, 'array dimension', location='select_one_image_bound',
+                raise_error=raise_error)
+        return(None)
+    if axis < 0 or axis >= a.ndim:
+        illegal_value(axis, 'axis', location='select_one_image_bound', raise_error=raise_error)
+        return(None)
+    if bound_name is None:
+        bound_name = 'data bound'
+    if bound is None:
+        min_ = 0
+        max_ = a.shape[axis]
+        bound_max = a.shape[axis]-1
+        while True:
+            if axis:
+                quick_imshow(a[:,min_:max_], title=title, aspect='auto',
+                        extent=[min_,max_,a.shape[0],0])
+            else:
+                quick_imshow(a[min_:max_,:], title=title, aspect='auto',
+                        extent=[0,a.shape[1], max_,min_])
+            zoom_flag = input_yesno(f'Set {bound_name} (y) or zoom in (n)?', 'y')
+            if zoom_flag:
+                bound = input_int(f'    Set {bound_name}', ge=0, le=bound_max)
+                clear_imshow(title)
+                break
+            else:
+                min_ = input_int('    Set lower zoom index', ge=0, le=bound_max)
+                max_ = input_int('    Set upper zoom index', ge=min_+1, le=bound_max+1)
+
+    elif not is_int(bound, ge=0, le=a.shape[axis]-1):
+        illegal_value(bound, 'bound', location='select_one_image_bound', raise_error=raise_error)
+        return(None)
+    else:
+        print(f'Current {bound_name} = {bound}')
+    a_tmp = np.copy(a)
+    a_tmp_max = a.max()
+    if axis:
+        a_tmp[:,bound] = a_tmp_max
+    else:
+        a_tmp[bound,:] = a_tmp_max
+    quick_imshow(a_tmp, title=title, aspect='auto')
+    del a_tmp
+    if not input_yesno(f'Accept this {bound_name} (y/n)?', default):
+        bound = select_one_image_bound(a, axis, bound_name=bound_name, title=title)
+    clear_imshow(title)
+    return(bound)
+
+
+class Config:
+    """Base class for processing a config file or dictionary.
+    """
+    def __init__(self, config_file=None, config_dict=None):
+        self.config = {}
+        self.load_flag = False
+        self.suffix = None
+
+        # Load config file 
+        if config_file is not None and config_dict is not None:
+            logger.warning('Ignoring config_dict (both config_file and config_dict are specified)')
+        if config_file is not None:
+           self.load_file(config_file)
+        elif config_dict is not None:
+           self.load_dict(config_dict)
+
+    def load_file(self, config_file):
+        """Load a config file.
+        """
+        if self.load_flag:
+            logger.warning('Overwriting any previously loaded config file')
+        self.config = {}
+
+        # Ensure config file exists
+        if not os.path.isfile(config_file):
+            logger.error(f'Unable to load {config_file}')
+            return
+
+        # Load config file (for now for Galaxy, allow .dat extension)
+        self.suffix = os.path.splitext(config_file)[1]
+        if self.suffix == '.yml' or self.suffix == '.yaml' or self.suffix == '.dat':
+            with open(config_file, 'r') as f:
+                self.config = safe_load(f)
+        elif self.suffix == '.txt':
+            with open(config_file, 'r') as f:
+                lines = f.read().splitlines()
+            self.config = {item[0].strip():literal_eval(item[1].strip()) for item in
+                    [line.split('#')[0].split('=') for line in lines if '=' in line.split('#')[0]]}
+        else:
+            illegal_value(self.suffix, 'config file extension', 'Config.load_file')
+
+        # Make sure config file was correctly loaded
+        if isinstance(self.config, dict):
+            self.load_flag = True
+        else:
+            logger.error(f'Unable to load dictionary from config file: {config_file}')
+            self.config = {}
+
+    def load_dict(self, config_dict):
+        """Takes a dictionary and places it into self.config.
+        """
+        if self.load_flag:
+            logger.warning('Overwriting the previously loaded config file')
+
+        if isinstance(config_dict, dict):
+            self.config = config_dict
+            self.load_flag = True
+        else:
+            illegal_value(config_dict, 'dictionary config object', 'Config.load_dict')
+            self.config = {}
+
+    def save_file(self, config_file):
+        """Save the config file (as a yaml file only right now).
+        """
+        suffix = os.path.splitext(config_file)[1]
+        if suffix != '.yml' and suffix != '.yaml':
+            illegal_value(suffix, 'config file extension', 'Config.save_file')
+
+        # Check if config file exists
+        if os.path.isfile(config_file):
+            logger.info(f'Updating {config_file}')
+        else:
+            logger.info(f'Saving {config_file}')
+
+        # Save config file
+        with open(config_file, 'w') as f:
+            safe_dump(self.config, f)
+
+    def validate(self, pars_required, pars_missing=None):
+        """Returns False if any required keys are missing.
+        """
+        if not self.load_flag:
+            logger.error('Load a config file prior to calling Config.validate')
+
+        def validate_nested_pars(config, par):
+            par_levels = par.split(':')
+            first_level_par = par_levels[0]
+            try:
+                first_level_par = int(first_level_par)
+            except:
+                pass
+            try:
+                next_level_config = config[first_level_par]
+                if len(par_levels) > 1:
+                    next_level_par = ':'.join(par_levels[1:])
+                    return(validate_nested_pars(next_level_config, next_level_par))
+                else:
+                    return(True)
+            except:
+                return(False)
+
+        pars_missing = [p for p in pars_required if not validate_nested_pars(self.config, p)]
+        if len(pars_missing) > 0:
+            logger.error(f'Missing item(s) in configuration: {", ".join(pars_missing)}')
+            return(False)
+        else:
+            return(True)