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import os
from numpy import arctan, array, cos, exp, log, sin
from lmfit import Parameters
thisdir, thisfile = os.path.split(__file__)
NIST_DIR = os.path.join(thisdir, '..', 'NIST_STRD')
def read_params(params):
if isinstance(params, Parameters):
return [par.value for par in params.values()]
else:
return params
def Bennet5(b, x, y=0):
b = read_params(b)
return y - b[0] * (b[1]+x)**(-1/b[2])
def BoxBOD(b, x, y=0):
b = read_params(b)
return y - b[0]*(1-exp(-b[1]*x))
def Chwirut(b, x, y=0):
b = read_params(b)
return y - exp(-b[0]*x)/(b[1]+b[2]*x)
def DanWood(b, x, y=0):
b = read_params(b)
return y - b[0]*x**b[1]
def ENSO(b, x, y=0):
b = read_params(b)
pi = 3.141592653589793238462643383279
return y - b[0] + (b[1]*cos(2*pi*x/12) + b[2]*sin(2*pi*x/12) +
b[4]*cos(2*pi*x/b[3]) + b[5]*sin(2*pi*x/b[3]) +
b[7]*cos(2*pi*x/b[6]) + b[8]*sin(2*pi*x/b[6]))
def Eckerle4(b, x, y=0):
b = read_params(b)
return y - (b[0]/b[1]) * exp(-0.5*((x-b[2])/b[1])**2)
def Gauss(b, x, y=0):
b = read_params(b)
return y - b[0]*exp(-b[1]*x) + (b[2]*exp(-(x-b[3])**2 / b[4]**2) +
b[5]*exp(-(x-b[6])**2 / b[7]**2))
def Hahn1(b, x, y=0):
b = read_params(b)
return y - ((b[0]+b[1]*x+b[2]*x**2+b[3]*x**3) /
(1+b[4]*x+b[5]*x**2+b[6]*x**3))
def Kirby(b, x, y=0):
b = read_params(b)
return y - (b[0] + b[1]*x + b[2]*x**2) / (1 + b[3]*x + b[4]*x**2)
def Lanczos(b, x, y=0):
b = read_params(b)
return y - b[0]*exp(-b[1]*x) + b[2]*exp(-b[3]*x) + b[4]*exp(-b[5]*x)
def MGH09(b, x, y=0):
b = read_params(b)
return y - b[0]*(x**2+x*b[1]) / (x**2+x*b[2]+b[3])
def MGH10(b, x, y=0):
b = read_params(b)
return y - b[0] * exp(b[1]/(x+b[2]))
def MGH17(b, x, y=0):
b = read_params(b)
return y - b[0] + b[1]*exp(-x*b[3]) + b[2]*exp(-x*b[4])
def Misra1a(b, x, y=0):
b = read_params(b)
return y - b[0]*(1-exp(-b[1]*x))
def Misra1b(b, x, y=0):
b = read_params(b)
return y - b[0] * (1-(1+b[1]*x/2)**(-2))
def Misra1c(b, x, y=0):
b = read_params(b)
return y - b[0] * (1-(1+2*b[1]*x)**(-.5))
def Misra1d(b, x, y=0):
b = read_params(b)
return y - b[0]*b[1]*x*((1+b[1]*x)**(-1))
def Nelson(b, x, y=None):
b = read_params(b)
x1 = x[:, 0]
x2 = x[:, 1]
if y is None:
return - exp(b[0] - b[1]*x1 * exp(-b[2]*x2))
return log(y) - (b[0] - b[1]*x1 * exp(-b[2]*x2))
def Rat42(b, x, y=0):
b = read_params(b)
return y - b[0] / (1+exp(b[1]-b[2]*x))
def Rat43(b, x, y=0):
b = read_params(b)
return y - b[0] / ((1+exp(b[1]-b[2]*x))**(1/b[3]))
def Roszman1(b, x, y=0):
b = read_params(b)
pi = 3.141592653589793238462643383279
return y - b[0] - b[1]*x - arctan(b[2]/(x-b[3]))/pi
def Thurber(b, x, y=0):
b = read_params(b)
return y - ((b[0] + b[1]*x + b[2]*x**2 + b[3]*x**3) /
(1 + b[4]*x + b[5]*x**2 + b[6]*x**3))
# Model name fcn, #fitting params, dim of x
Models = {'Bennett5': (Bennet5, 3, 1),
'BoxBOD': (BoxBOD, 2, 1),
'Chwirut1': (Chwirut, 3, 1),
'Chwirut2': (Chwirut, 3, 1),
'DanWood': (DanWood, 2, 1),
'ENSO': (ENSO, 9, 1),
'Eckerle4': (Eckerle4, 3, 1),
'Gauss1': (Gauss, 8, 1),
'Gauss2': (Gauss, 8, 1),
'Gauss3': (Gauss, 8, 1),
'Hahn1': (Hahn1, 7, 1),
'Kirby2': (Kirby, 5, 1),
'Lanczos1': (Lanczos, 6, 1),
'Lanczos2': (Lanczos, 6, 1),
'Lanczos3': (Lanczos, 6, 1),
'MGH09': (MGH09, 4, 1),
'MGH10': (MGH10, 3, 1),
'MGH17': (MGH17, 5, 1),
'Misra1a': (Misra1a, 2, 1),
'Misra1b': (Misra1b, 2, 1),
'Misra1c': (Misra1c, 2, 1),
'Misra1d': (Misra1d, 2, 1),
'Nelson': (Nelson, 3, 2),
'Rat42': (Rat42, 3, 1),
'Rat43': (Rat43, 4, 1),
'Roszman1': (Roszman1, 4, 1),
'Thurber': (Thurber, 7, 1)}
def ReadNistData(dataset):
"""NIST STRD data is in a simple, fixed format with
line numbers being significant!
"""
finp = open(os.path.join(NIST_DIR, "%s.dat" % dataset), 'r')
lines = [l[:-1] for l in finp.readlines()]
finp.close()
ModelLines = lines[30:39]
ParamLines = lines[40:58]
DataLines = lines[60:]
words = ModelLines[1].strip().split()
nparams = int(words[0])
start1 = [0]*nparams
start2 = [0]*nparams
certval = [0]*nparams
certerr = [0]*nparams
for i, text in enumerate(ParamLines[:nparams]):
[s1, s2, val, err] = [float(x) for x in text.split('=')[1].split()]
start1[i] = s1
start2[i] = s2
certval[i] = val
certerr[i] = err
for t in ParamLines[nparams:]:
t = t.strip()
if ':' not in t:
continue
val = float(t.split(':')[1])
if t.startswith('Residual Sum of Squares'):
sum_squares = val
elif t.startswith('Residual Standard Deviation'):
std_dev = val
elif t.startswith('Degrees of Freedom'):
nfree = int(val)
elif t.startswith('Number of Observations'):
ndata = int(val)
y, x = [], []
for d in DataLines:
vals = [float(i) for i in d.strip().split()]
y.append(vals[0])
if len(vals) > 2:
x.append(vals[1:])
else:
x.append(vals[1])
y = array(y)
x = array(x)
out = {'y': y, 'x': x, 'nparams': nparams, 'ndata': ndata,
'nfree': nfree, 'start1': start1, 'start2': start2,
'sum_squares': sum_squares, 'std_dev': std_dev,
'cert': certval, 'cert_values': certval, 'cert_stderr': certerr}
return out
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