(temporary) least squares function for combined fits with dictionaries (+ example)

pyerrors/__init__.py

@@ -457,6 +457,7 @@ from .obs import *
 from .correlators import *
 from .fits import *
 from .misc import *
+from . import combined_fits
 from . import dirac
 from . import input
 from . import linalg

pyerrors/combined_fits.py

@@ -0,0 +1,170 @@
+import iminuit
+import autograd.numpy as anp
+from autograd import jacobian
+from pyerrors.fits import Fit_result
+import numpy as np
+import pyerrors as pe
+from autograd import jacobian as auto_jacobian
+from autograd import hessian as auto_hessian
+from autograd import elementwise_grad as egrad
+from numdifftools import Jacobian as num_jacobian
+from numdifftools import Hessian as num_hessian
+import scipy.optimize
+import scipy.stats
+
+def combined_total_least_squares(x,y,funcs,silent=False,**kwargs):
+    r'''Performs a combined non-linear fit.
+    Parameters
+    ----------
+    x : ordered dict
+        dict of lists.
+    y : ordered dict
+        dict of lists of Obs.
+    funcs : ordered dict
+        dict of objects
+        fit functions have to be of the form (here a[0] is the common fit parameter)
+        ```python
+        import autograd.numpy as anp
+        funcs = {"a": func_a,
+                "b": func_b}
+                
+        def func_a(a, x):
+            return a[1] * anp.exp(-a[0] * x)
+
+        def func_b(a, x):
+            return a[2] * anp.exp(-a[0] * x)
+        ```
+        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
+        will not work.
+    silent : bool, optional
+        If true all output to the console is omitted (default False).
+    initial_guess : list
+        can provide an initial guess for the input parameters. Relevant for
+        non-linear fits with many parameters.
+    num_grad : bool
+        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
+    '''
+  
+    output = Fit_result()
+    output.fit_function = funcs
+    
+    if kwargs.get('num_grad') is True:
+        jacobian = num_jacobian
+        hessian = num_hessian
+    else:
+        jacobian = auto_jacobian
+        hessian = auto_hessian
+  
+    x_all = []
+    y_all = []
+    for key in x.keys():
+        x_all+=x[key]
+        y_all+=y[key]
+    
+    x_all = np.asarray(x_all)
+
+    # number of fit parameters
+    n_parms_ls = []
+    for key in funcs.keys():
+        for i in range(42):
+            try:
+                funcs[key](np.arange(i), x_all.T[0])
+            except TypeError:
+                continue
+            except IndexError:
+                continue
+            else:
+                break
+        else:
+            raise RuntimeError("Fit function is not valid.")
+        n_parms = i
+        n_parms_ls.append(n_parms)
+    n_parms = max(n_parms_ls)
+    if not silent:
+        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
+        
+    if 'initial_guess' in kwargs:
+        x0 = kwargs.get('initial_guess')
+        if len(x0) != n_parms:
+            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
+    else:
+        x0 = [0.1] * n_parms
+        
+    def chisqfunc(p):
+        chisq = 0.0
+        for key in funcs.keys():
+            x_array = np.asarray(x[key])
+            model = anp.array(funcs[key](p,x_array))
+            y_obs = y[key]
+            y_f = [o.value for o in y_obs]
+            dy_f = [o.dvalue for o in y_obs]
+            C_inv =  np.diag(np.diag(np.ones((len(x_array),len(x_array)))))/dy_f/dy_f
+            chisq += anp.sum((y_f - model)@ C_inv @(y_f - model))
+        return chisq
+    
+    if 'tol' in kwargs:
+        fit_result = iminuit.minimize(chisqfunc, x0,tol=kwargs.get('tol'))
+        fit_result = iminuit.minimize(chisqfunc, fit_result.x,tol=kwargs.get('tol'))
+    else:
+        fit_result = iminuit.minimize(chisqfunc, x0,tol=1e-4)
+        fit_result = iminuit.minimize(chisqfunc, fit_result.x,tol=1e-4)
+        
+    chisquare = fit_result.fun
+    
+    output.method = 'migrad'
+    output.message = fit_result.message
+
+    if x_all.shape[-1] - n_parms > 0:
+        output.chisquare = chisqfunc(fit_result.x)
+        output.dof = x_all.shape[-1] - n_parms
+        output.chisquare_by_dof = output.chisquare/output.dof
+    else:
+        output.chisquare_by_dof = float('nan')
+    
+    if not silent:
+        print(fit_result.message)
+        print('chisquare/d.o.f.:', output.chisquare_by_dof )
+        print('fit parameters',fit_result.x)
+        
+    # use ordered dicts so the data and fit parameters can be mapped correctly 
+    def chisqfunc_compact(d):
+        chisq = 0.0
+        list_tmp = []
+        c1 = 0
+        c2 = 0
+        for key in funcs.keys():
+            x_array = np.asarray(x[key])
+            c2+=len(x_array)
+            model = anp.array(funcs[key](d[:n_parms],x_array))
+            y_obs = y[key]
+            y_f = [o.value for o in y_obs]
+            dy_f = [o.dvalue for o in y_obs]
+            C_inv =  np.diag(np.diag(np.ones((len(x_array),len(x_array)))))/dy_f/dy_f
+            list_tmp.append(anp.sum((d[n_parms+c1:n_parms+c2]- model)@ C_inv @(d[n_parms+c1:n_parms+c2]- model)))
+            c1+=len(x_array)
+        chisq = anp.sum(list_tmp)
+        return chisq
+    
+    fitp = fit_result.x
+    y_f = [o.value for o in y_all] # y_f is constructed based on the ordered dictionary if the order is changed then the y values are not allocated to the the correct x and func values in the hessian
+    dy_f = [o.dvalue for o in y_all] # the same goes for dy_f
+    try:
+        hess = hessian(chisqfunc)(fitp)
+    except TypeError:
+        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+        
+    jac_jac_y = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
+
+    # Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
+    try:
+        deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms, n_parms:])
+    except np.linalg.LinAlgError:
+        raise Exception("Cannot invert hessian matrix.")
+
+    result = []
+    for i in range(n_parms):
+        result.append(pe.derived_observable(lambda x_all, **kwargs: (x_all[0] + np.finfo(np.float64).eps) / (y_all[0].value + np.finfo(np.float64).eps) * fitp[i], list(y_all), man_grad=list(deriv_y[i])))
+    
+    output.fit_parameters = result
+    
+    return output