* Imported more recent function fitting facility from Cr2 project.

math/fitting/funcs_pec.py

@@ -0,0 +1,141 @@
+#
+# wpylib.math.fitting.funcs_pec module
+# Created: 20150521
+# Wirawan Purwanto
+#
+# Imported 20150521 from Cr2_analysis_cbs.py
+# (dated 20141017, CVS rev 1.143).
+#
+
+"""
+wpylib.math.fitting.funcs_pec module
+A library of simple f(x) functions for PEC fitting
+
+For use with OO-style x-y curve fitting interface.
+"""
+
+import numpy
+
+
+class harm_fit_func(fit_func_base):
+  """Harmonic function object.
+  For use with fit_func function on a PEC.
+
+  Functional form:
+
+      E0 + 0.5 * k * (x - re)**2
+
+  Coefficients:
+  * C[0] = energy minimum
+  * C[1] = spring constant
+  * C[2] = equilibrium distance
+  """
+  dim = 1  # a function with 1-D domain
+  param_names = ('E0', 'k', 'r0')
+  def __call__(self, C, x):
+    xdisp = (x[0] - C[2])
+    y = C[0] + 0.5 * C[1] * xdisp**2
+    self.func_call_hook(C, x, y)
+    return y
+  def Guess_xy(self, x, y):
+    fit_rslt = fit_harm(x[0], y)
+    self.guess_params = tuple(fit_rslt[0])
+    return self.guess_params
+
+
+class harmcube_fit_func(fit_func_base):
+  """Harmonic + cubic term function object.
+  For use with fit_func function on a PEC.
+
+  Functional form:
+
+      E0 + 0.5 * k * (x - re)**2 + cub * (x - re)**3;
+
+  Coefficients:
+  * C[0] = energy minimum
+  * C[1] = spring constant
+  * C[2] = equilibrium distance
+  * C[3] = nonlinear (cubic) constant
+  """
+  dim = 1  # a function with 1-D domain
+  param_names = ('E0', 'k', 'r0', 'c3')
+  def __call__(self, C, x):
+    xdisp = (x[0] - C[2])
+    y = C[0] + 0.5 * C[1] * xdisp**2 + C[3] * xdisp**3
+    self.func_call_hook(C, x, y)
+    return y
+  def Guess_xy(self, x, y):
+    fit_rslt = fit_harm(x[0], y)
+    self.guess_params = tuple(fit_rslt[0]) + (0,)
+    return self.guess_params
+  def Guess_xy_old(self, x, y):
+    imin = numpy.argmin(y)
+    return (y[imin], 2, x[0][imin], 0.00001)
+
+
+class morse2_fit_func(fit_func_base):
+  """Morse2 function object.
+  For use with fit_func function.
+
+  Functional form:
+
+      E0 + 0.5 * k / a**2 * (1 - exp(-a * (x - re)))**2
+
+  Coefficients:
+  * C[0] = energy minimum
+  * C[1] = spring constant
+  * C[2] = equilibrium distance
+  * C[3] = nonlinear constant
+  """
+  dim = 1  # a function with 1-D domain
+  param_names = ('E0', 'k', 'r0', 'a')
+  def __call__(self, C, x):
+    from numpy import exp
+    E0, k, r0, a = self.get_params(C, *(self.param_names))
+    y = E0 + 0.5 * k / a**2 * (1 - exp(-a * (x[0] - r0)))**2
+    self.func_call_hook(C, x, y)
+    return y
+  def Guess_xy(self, x, y):
+    imin = numpy.argmin(y)
+    harm_params = fit_harm(x[0], y)
+    if self.debug >= 10:
+      print "Initial guess by fit_harm gives: ", harm_params
+    self.guess_params = (y[imin], harm_params[0][1], x[0][imin], 0.01 * harm_params[0][1])
+    return self.guess_params
+  def Guess_xy_old(self, x, y):
+    imin = numpy.argmin(y)
+    return (y[imin], 2, x[0][imin], 0.01)
+
+
+class ext3Bmorse2_fit_func(fit_func_base):
+  """ext3Bmorse2 function object.
+  For use with fit_func function.
+
+  Functional form:
+
+      E0 + 0.5 * k / a**2 * (1 - exp(-a * (x - re)))**2
+         + C3 * (1 - exp(-a * (x - re)))**3
+
+  Coefficients:
+  * C[0] = energy minimum
+  * C[1] = spring constant
+  * C[2] = equilibrium distance
+  * C[3] = nonlinear constant
+  * C[4] = coefficient of cubic term
+  """
+  dim = 1  # a function with 1-D domain
+  def __call__(self, C, x):
+    from numpy import exp
+    E = 1 - exp(-C[3] * (x[0] - C[2]))
+    y = C[0] + 0.5 * C[1] / C[3]**2 * E**2 + C[4] * E**3
+    self.func_call_hook(C, x, y)
+    return y
+  def Guess_xy(self, x, y):
+    imin = numpy.argmin(y)
+    harm_params = fit_harm(x[0], y)
+    if self.debug >= 10:
+      print "Initial guess by fit_harm gives: ", harm_params
+    self.guess_params = (y[imin], harm_params[0][1], x[0][imin], 0.01 * harm_params[0][1], 0)
+    return self.guess_params
+
+