Source Code for Module ComboCode.cc.ivs.sigproc.lmfit.utilfuncs

 1  """Utility mathematical functions and common lineshapes for minimizer 
 2  """ 
 3  import numpy 
 4  import scipy 
 5  from scipy.special import gamma 
 6   
 7  CUSTOM_FUNCTIONS = {} 
 8   
 9  log2 = numpy.log(2) 
10  pi = numpy.pi 
11   
12 -def gauss(x, amp, cen, wid): 
13      "gaussian function: wid = half-width at half-max" 
14      return amp * numpy.exp(-log2 * (x-cen) **2 / wid**2) 
15   
16 -def loren(x, amp, cen, wid): 
17      "lorenztian function: wid = half-width at half-max" 
18      return (amp  / (1 + ((x-cen)/wid)**2)) 
19   
20 -def gauss_area(x, amp, cen, wid): 
21      "scaled gaussian function: wid = half-width at half-max" 
22      return numpy.sqrt(log2/pi) * gauss(x, amp, cen, wid) / wid 
23   
24 -def loren_area(x, amp, cen, wid): 
25      "scaled lorenztian function: wid = half-width at half-max" 
26      return loren(x, amp, cen, wid) / (pi*wid) 
27   
28 -def pvoigt(x, amp, cen, wid, frac): 
29      """pseudo-voigt function: 
30      (1-frac)*gauss(amp, cen, wid) + frac*loren(amp, cen, wid)""" 
31      return amp * (gauss(x, (1-frac), cen, wid) + 
32                    loren(x, frac, cen, wid)) 
33   
34 -def pvoigt_area(x, amp, cen, wid, frac): 
35      """scaled pseudo-voigt function: 
36      (1-frac)*gauss_area(amp, cen, wid) + frac*loren_are(amp, cen, wid)""" 
37   
38      return amp * (gauss_area(x, (1-frac), cen, wid) + 
39                    loren_area(x, frac,     cen, wid)) 
40   
41 -def pearson7(x, amp, cen, wid, expon): 
42      """pearson peak function """ 
43      xp = 1.0 * expon 
44      return amp / (1 + ( ((x-cen)/wid)**2) * (2**(1/xp) -1) )**xp 
45   
46   
47 -def pearson7_area(x, amp, cen, wid, expon): 
48      """scaled pearson peak function """ 
49      xp = 1.0 * expon 
50      scale = gamma(xp) * sqrt((2**(1/xp) - 1)) / (gamma(xp-0.5)) 
51      return scale * pearson7(x, amp, cen, wid, xp) / (wid*sqrt(pi)) 
52   
53      return scale * pearson7(x, amp, cen, sigma, expon) / (sigma*sqrt(pi)) 
54   
55  CUSTOM_FUNCTIONS = {'gauss': gauss, 'gauss_area': gauss_area, 
56                      'loren': loren, 'loren_area': loren_area, 
57                      'pvoigt': pvoigt, 'pvoigt_area': pvoigt_area, 
58                      'pearson7': pearson7, 'pearson7_area': pearson7_area} 
59