* Added module: wpylib.math.fitting.stochastic.

NOTE: Only imported verbatimly from Cr2_analysis_cbs.py CVS rev 1.143.

math/fitting/stochastic.py

@@ -0,0 +1,403 @@
+#
+# wpylib.math.fitting.stochastic module
+# Created: 20150528
+# Wirawan Purwanto
+#
+# Dependencies:
+# - numpy
+# - scipy
+# - matplotlib (for visualization routines)
+#
+
+"""
+wpylib.math.fitting.stochastic module
+
+Tools for stochastic curve fitting.
+"""
+
+from wpylib.math.fitting import fit_func_base
+
+
+class StochasticFitting(object):
+  """Standard stochastic fit procedure.
+
+  """
+  debug = 0
+  dbg_guess_params = True
+  def_opt_report_final_params = 3
+  def __init__(self):
+    self.use_nlf_guess = 1
+    self.use_dy_weights = True
+
+  def init_func(self, func):
+    self.func = func
+
+  def init_samples(self, x, y, dy):
+    """
+    Initializes the sample data against which we will perform
+    the stochastic fitting.
+    This function takes N measurement samples:
+    - the (multidimensional) domain points, x
+    - the measured target points, y
+    - the uncertainty of the target points, dy
+
+    """
+    x = fit_func_base.domain_array(x)
+    if not (len(x[0]) == len(y) == len(dy)):
+      raise TypeError, "Length of x, y, dy arrays are not identical."
+
+    # fix (or, actually, provide an accomodation for) a common "mistake"
+    # for 1-D domain: make it standard by adding the "first" dimension
+    if len(x.shape) == 1:
+      x = x.reshape((1, x.shape[0]))
+
+    self.samples_x = x
+    self.samples_y = numpy.array(y)
+    self.samples_dy = numpy.array(dy)
+    self.samples_wt = (self.samples_dy)**(-2)
+
+  def init_rng(self, seed=None, rng_class=numpy.random.RandomState):
+    """Initializes a standard random number generator for use in
+    the fitting routine."""
+    if seed == None:
+      seed = numpy.random.randint(numpy.iinfo(int).max)
+      print "Using random seed: ", seed
+    self.rng_seed = seed
+    self.rng = rng_class(seed)
+
+  def num_fit_params(self):
+    """An ad-hoc way to determine the number of fitting parameters.
+
+    FIXME: There is still not an a priori way to find the number of
+    fit parameters in the fit_func_base class or its derivatives.
+
+    There are a few after-the-fact ways to determine this:
+
+    1) Once the "deterministic" nonlinear fit is done, you can find the
+       number of parameters by
+
+         len(self.log_nlf_params)
+
+    2) Once the stochastic fit is done, you can also find the number
+       of fit parameters by
+  
+         len(self.log_mc_params[0])
+    """
+    try:
+      return len(self.log_nlf_params)
+    except:
+      pass
+    try:
+      return len(self.log_mc_params[0])
+    except:
+      pass
+    raise RuntimeError, "Cannot determine the number of fit parameters."
+
+  def nlfit1(self):
+    """Performs the non-stochastic, standard nonlinear fit."""
+    from numpy.linalg import norm
+
+    if self.use_dy_weights:
+      dy = self.samples_dy
+    else:
+      dy = None
+    rslt = self.func.fit(self.samples_x, self.samples_y, dy=dy)
+    self.log_nlf_params = rslt
+    self.nlf_f = self.func(self.log_nlf_params, self.samples_x)
+
+    last_fit = self.func.last_fit
+    mval_resid = self.nlf_f - self.samples_y
+    self.nlf_ussr = norm(mval_resid)**2
+    self.nlf_wssr = norm(mval_resid / self.samples_dy)**2
+    self.nlf_funcalls = last_fit['funcalls']
+    self.nlf_rec = last_fit
+
+  def mcfit_step1_toss_dice_(self):
+    """Generates a single Monte Carlo dataset for the mcfit_step1_
+    procedure."""
+    self.dice_dy = self.rng.normal(size=len(self.samples_dy))
+    self.dice_y = self.samples_y + self.samples_dy * self.dice_dy
+
+  def mcfit_step1_(self):
+    """Performs a single Monte Carlo data fit."""
+    # Var name conventions:
+    # - dice_* = values related to one "dice toss" of the sample
+    # - mval_* = values related to the mean value of the samples
+    #            (i.e. samples_y)
+    # FIXME: In future this *could* be run in parallel but the state vars
+    # (such as dice_y, dice_dy, etc.) must be stored on per-thread basis.
+    from numpy.linalg import norm
+    self.mcfit_step1_toss_dice_()
+    if self.use_dy_weights:
+      dy = self.samples_dy
+    else:
+      dy = None
+    rslt = self.func.fit(self.samples_x, self.dice_y, dy=dy,
+                         Guess=self.dice_param_guess,
+                        )
+    # fit result of the stochastic data
+    self.dice_params = rslt
+    self.log_mc_params.append(rslt)
+    self.dice_f = self.func(self.dice_params, self.samples_x)
+
+    if self.dbg_guess_params:
+      self.log_guess_params.append(self.func.guess_params)
+
+    last_fit = self.func.last_fit
+    dice_resid = self.dice_f - self.dice_y
+    mval_resid = self.dice_f - self.samples_y
+    dice_ussr = norm(dice_resid)**2
+    dice_wssr = norm(dice_resid / self.samples_dy)**2
+    mval_ussr = norm(mval_resid)**2
+    mval_wssr = norm(mval_resid / self.samples_dy)**2
+    self.log_mc_stats.append((dice_ussr, dice_wssr, mval_ussr, mval_wssr))
+    self.log_mc_funcalls.append(last_fit['funcalls'])
+
+  def mcfit_step1_viz_(self, save=True):
+    """Generates a visual representation of the last MC fit step.
+    """
+    from matplotlib import pyplot
+    if not hasattr(self, "fig"):
+      self.fig = pyplot.figure()
+    self.fig.clf()
+    ax = self.fig.add_subplot(1, 1, 1)
+    title = "MC fit step %d" % self.mcfit_iter_num
+    ax.set_title(title)
+    x,y,dy = self.samples_x[0], self.samples_y, self.samples_dy
+    ax.errorbar(x=x, y=y, yerr=dy,
+                fmt="x", color="SlateGray", label="QMC",
+               )
+    samples_xmin = x.min()
+    samples_xmax = x.max()
+    samples_xrange = samples_xmax - samples_xmin
+    samples_ymin = y.min()
+    samples_ymax = y.max()
+    samples_yrange = samples_ymax - samples_ymin
+    len_plot_x = 10*len(y)
+    plot_x = numpy.linspace(start=samples_xmin - 0.03 * samples_xrange,
+                            stop=samples_xmax + 0.03 * samples_xrange,
+                            num=len_plot_x,
+                            endpoint=True)
+    ax.plot(plot_x, self.func(self.nlf_rec.xopt, [plot_x]), "-",
+            color="SlateGray", label="nlfit")
+    ax.errorbar(x=x, y=self.dice_y, yerr=dy,
+                fmt="or", label="MC toss",
+               )
+    ax.plot(plot_x, self.func(self.dice_params, [plot_x]), "-",
+            color="salmon", label="MC fit")
+
+    samples_dy_max = numpy.max(self.samples_dy)
+    ax.set_ylim((samples_ymin - samples_dy_max * 8, samples_ymax + samples_dy_max * 8))
+    if save:
+      self.fig.savefig("mcfit-%04d.png" % self.mcfit_iter_num)
+
+  def mcfit_loop_begin_(self):
+    """Performs final initialization before firing up mcfit_loop_.
+    This need to be done only before the first mcfit_loop_() call;
+    if more samples are collected later, then this routine should NOT be
+    called again or else all the accumulators would reset."""
+    self.log_guess_params = []
+    self.log_mc_params = []
+    self.log_mc_stats = []
+    self.log_mc_funcalls = []
+    if self.use_nlf_guess:
+      print "Using guess param from NLF: ",
+      self.nlfit1()
+      self.dice_param_guess = self.log_nlf_params
+      #print "- Params = ", self.log_nlf_params
+      print self.log_nlf_params
+    else:
+      self.dice_param_guess = None
+
+  def mcfit_loop_end_(self):
+    """Performs final initialization before firing up do_mc_fitting:
+    - Repackage log_mc_stats and log_mc_params as numpy array of structs
+    """
+    # Number of fit parameters:
+    num_params = len(self.log_mc_params[0])
+    #if True:
+    try:
+      pnames = self.func.param_names
+      assert len(pnames) == num_params # Otherwise it will be faulty
+      if self.func.use_lmfit_method:
+        #from lmfit import Parameter
+        ptype = float
+      else:
+        ptype = float
+      param_dtype = [ (i, ptype) for i in pnames ]
+    except:
+      param_dtype = [ ("C"+str(i), float) for i in xrange(num_params) ]
+    stats_dtype = [ (i, float) for i in ('dice_ussr', 'dice_wssr', 'mval_ussr', 'mval_wssr') ]
+
+    # Can't initialize the self.mc_params array in a single step with
+    # numpy.array construction function; we must copy the records one by one.
+    # The reason is this: each element of the log_mc_params list is already
+    # a numpy ndarray object.
+    self.mc_params = numpy.empty((len(self.log_mc_params),), dtype=param_dtype)
+    for (i,p) in enumerate(self.log_mc_params):
+      if self.func.use_lmfit_method:
+        self.mc_params[i] = tuple(p)
+      else:
+        self.mc_params[i] = p
+    self.mc_stats = numpy.array(self.log_mc_stats, dtype=stats_dtype)
+    self.fit_parameters = [ p[0] for p in param_dtype ]
+
+  def mcfit_analysis_(self):
+    """Performs analysis of the Monte Carlo fitting.
+    This version does no weighting or filtering based on some cutoff criteria.
+    """
+    flds = self.fit_parameters # == self.mc_params.dtype.names
+    rslt = {}
+    for F in flds:
+      mean = numpy.average(self.mc_params[F])
+      err = numpy.std(self.mc_params[F])
+      rslt[F] = errorbar(mean, err)
+    self.final_mc_params = rslt
+
+  def mcfit_loop1_(self, num_iter, save_fig=0):
+    """Performs the Monte-Carlo fit simulation after the
+    input parameters are set up."""
+
+    for i in xrange(num_iter):
+      self.mcfit_iter_num = i
+      if self.debug >= 2:
+        print "mcfit_loop1_: iteration %d" % i
+      self.mcfit_step1_()
+      if save_fig:
+        self.mcfit_step1_viz_(save=True)
+
+  def mcfit_report_final_params(self, format=None):
+    if format == None:
+      format = getattr(self, "opt_report_final_params", self.def_opt_report_final_params)
+    if format in (None, False, 0):
+      return # quiet!
+
+    parm = self.final_mc_params
+    if format == 3:
+      print "Final parameters          :",
+      print "  ".join([
+        "%s" % (parm[k],) for k in self.fit_parameters
+      ])
+    elif format == 2:
+      print "Final parameters:"
+      print "\n".join([
+        "  %s = %s" % (k, parm[k])
+          for k in self.fit_parameters
+      ])
+    elif format == 1:
+      print "Final parameters:"
+      print parm
+
+  def mcfit_run1(self, x=None, y=None, dy=None, data=None, func=None, rng_params=None,
+                 num_iter=100, save_fig=False):
+    """The main routine to perform stochastic fit."""
+    if data != None:
+      raise NotImplementedError
+    elif dy != None:
+      # Assume OK
+      pass
+    elif y != None and dy == None:
+      y_orig = y
+      y = errorbar_mean(y_orig)
+      dy = errorbar_err(y_orig)
+    else:
+      raise TypeError, "Invalid argument combination for the input data."
+
+    if func != None:
+      self.init_func(func)
+    if not hasattr(self, "func"):
+      raise RuntimeError, \
+        "The fit function in the fitting object is undefined."
+    self.init_samples(x=x,
+                      y=y,
+                      dy=dy,
+                    )
+    if rng_params != None:
+      self.init_rng(**rng_params)
+    elif not hasattr(self, "rng"):
+      self.init_rng()
+
+    self.mcfit_loop_begin_()
+    self.mcfit_loop1_(num_iter=num_iter, save_fig=save_fig)
+    self.mcfit_loop_end_()
+    self.mcfit_analysis_()
+    self.mcfit_report_final_params()
+    return self.final_mc_params
+
+  # The two routines below gives convenient way to evaluate the
+  # fitted curve at arbitrary x values (good so long as they are not
+  # far out from the range given by self.samples_x)
+
+  def mcfit_eval_raw(self, x=None, yscale=1.0):
+    """Evaluates the curve (y) values for a given set of x value(s).
+    This routine generates the raw values based on the stochastically
+    sampled parameter values."""
+    if x == None:
+      x = self.samples_x
+    else:
+      x = fit_func_base.domain_array(x)
+
+    xlen = len(x[0])
+    mc_curve_y = numpy.empty((len(self.mc_params), xlen))
+    # The following loop could have been written as a batch operation,
+    # but it requires some nontrivial change in the convention of how
+    # fit_func_base.__call__() is written.
+    # Double broadcasting and other dimensional retrofitting/reduction
+    # ('dot product'?) may be required.
+    # Example: in harm_fit_func class, the statement
+    #     xdisp = (x[0] - C[2])
+    # will have to be changed becasuse the length of x[0]
+    # (which is the number of data points in the "x" argument)
+    # and the length of C[2]
+    # (which is the number of MC iterations)
+    # will not match--and these numbers must NOT be subtracted elementwise!
+    for (i,ppp) in enumerate(self.mc_params):
+      mc_curve_y[i] = self.func(ppp, x)
+
+    return mc_curve_y
+
+  def mcfit_eval(self, x=None, yscale=1.0, ddof=1, outfmt=0):
+    """Evaluates the curve (y) values for a given set of x value(s).
+    This routine generates the finalized values (with errorbar estimate)
+    based on the stochastically sampled parameter values."""
+
+    # WARNING: CONVENTION CHANGES FROM ORIGINAL make_curve_errorbar() ROUTINE!
+    # The default delta degree of freedom (ddof) should be 1 because we need
+    # to take one out for the average itself.
+    # If you need to reproduce old result, can revert to ddof=0.
+    if x == None:
+      x = self.samples_x
+    else:
+      x = fit_func_base.domain_array(x)
+    mc_curve_y = self.mcfit_eval_raw(x=x)
+
+    xlen = len(x[0])
+    final_mc_curve = numpy.empty((xlen,), dtype=[('val',float),('err',float)])
+    final_mc_curve['val'] = numpy.average(mc_curve_y, axis=0)
+    final_mc_curve['err'] = numpy.std(mc_curve_y, axis=0, ddof=ddof)
+    if yscale != 1.0:
+      final_mc_curve['val'] *= yscale
+      final_mc_curve['err'] *= yscale
+    if outfmt == 0:
+      pass # already in that format
+    elif outfmt == 1:
+      # Formatted as an array of "errorbar" objects
+      final_mc_curve = numpy.array([errorbar(y,dy) for (y,dy) in final_mc_curve], dtype=errorbar)
+    else:
+      raise ValueError, "Unsupported outfmt value=%s." % (outfmt)
+    return final_mc_curve
+
+  def mcfit_dump_param_samples(self, out):
+    """Dump the generated parameter samples for diagnostic purposes.
+    """
+    O = text_output(out)
+    pnames = self.mc_params.dtype.names
+    snames = self.mc_stats.dtype.names
+    O.write("# %s ; %s ; nfev\n" % (" ".join(pnames), " ".join(snames)))
+    O.write(matrix_str(array_hstack([ self.mc_params[k] for k in pnames ] + \
+                                    [ self.mc_stats[k] for k in snames ] + \
+                                    [ self.log_mc_funcalls]),
+                       " %#17.10g")+ "\n")
+
+
+