def residual(pars, x, sigma=None, data=None):
yg = gauss(x, pars["amp_g"].value, pars["cen_g"].value, pars["wid_g"].value)
yl = loren(x, pars["amp_l"].value, pars["cen_l"].value, pars["wid_l"].value)
frac = pars["frac"].value
slope = pars["line_slope"].value
offset = pars["line_off"].value
model = (1 - frac) * yg + frac * yl + offset + x * slope
if data is None:
return model
if sigma is None:
return model - data
return (model - data) / sigma
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value, pars['cen_g'].value,
pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value, pars['cen_l'].value,
pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
def residual(pars, x, sigma=None, data=None):
yg = gauss(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
def residual(pars, x, data=None):
# print 'RESID ', pars['amp_g'].value, pars['amp_g'].init_value
yg = gauss(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
frac = pars['frac'].value
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = (1-frac) * yg + frac * yl + offset + x * slope
if data is None:
return model
return (model - data)
def test_constraints2():
"""add a user-defined function to symbol table"""
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value, pars['cen_g'].value,
pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value, pars['cen_l'].value,
pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
pfit = [
Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)
]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
def width_func(wpar):
""" """
return 2 * wpar
myfit.asteval.symtable['wfun'] = width_func
myfit.params.add(name='wid_l', expr='wfun(wid_g)')
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
pfit = myfit.params
fit = residual(myfit.params, x)
assert (pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert (pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert (pfit['wid_l'].value == 2 * pfit['wid_g'].value)
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gauss(x, 21, 8.1, 1.2) +
loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if HASPYLAB:
pylab.plot(x, data, 'r+')
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
def test_constraints():
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print( myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
pfit= myfit.params
fit = residual(myfit.params, x)
assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
def test_constraints(with_plot=True):
with_plot = with_plot and HASPYLAB
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print( myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params, min_correl=0.3)
fit = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert(myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert(myfit.params['amp_l'].value == myfit.params['amp_tot'].value - myfit.params['amp_g'].value)
assert(myfit.params['wid_l'].value == 2 * myfit.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
myfit.leastsq()
report_fit(myfit.params, min_correl=0.4)
fit2 = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert(myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert(myfit.params['amp_l'].value == myfit.params['amp_tot'].value - myfit.params['amp_g'].value)
assert(myfit.params['wid_l'].value == 1.25 * myfit.params['wid_g'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gauss(x, 21, 8.1, 1.2) + loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
if HASPYLAB:
pylab.plot(x, data, 'r+')
pfit = [
Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gauss(x, 21, 8.1, 1.2) +
loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if HASPYLAB:
pylab.plot(x, data, 'r+')
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
xmax = 20.0
x = linspace(xmin, xmax, n)
noise = random.normal(scale=0.2, size=n)
p_true = Parameters()
frac = 0.37
p_true.add('amp_g', value=21.0)
p_true.add('cen_g', value=8.1)
p_true.add('wid_g', value=1.6)
p_true.add('cen_l', value=13.1)
p_true.add('frac', value=frac)
p_true.add('line_off', value=-1.023)
p_true.add('line_slope', value=0.62)
data = ((1-frac)*gauss(x, p_true['amp_g'].value, p_true['cen_g'].value, p_true['wid_g'].value) +
frac*loren(x, 0.5*p_true['amp_g'].value, p_true['cen_l'].value, 2.5*p_true['wid_g'].value) +
x*p_true['line_slope'].value + p_true['line_off'].value ) + noise
if HASPYLAB:
pylab.plot(x, data, 'r+')
p_fit = Parameters()
max_x = x[where(data == max(data))][0]
print 'MAX X = ', max_x
p_fit.add('amp_g', value=15.0)
p_fit.add('cen_g', value=max_x)
p_fit.add('wid_g', value=2.0)
p_fit.add('frac', value=0.50)
p_fit.add('amp_l', expr='0.5*amp_g')
p_fit.add('cen_l', value=12.5)
p_fit.add('wid_l', expr='2.5*wid_g')
def test_constraints(with_plot=True):
with_plot = with_plot and HASPYLAB
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value, pars['cen_g'].value,
pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value, pars['cen_l'].value,
pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = [
Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='wid_l', expr='2*wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)
]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params, min_correl=0.3)
fit = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert (myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert (myfit.params['amp_l'].value == myfit.params['amp_tot'].value -
myfit.params['amp_g'].value)
assert (myfit.params['wid_l'].value == 2 * myfit.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
myfit.leastsq()
report_fit(myfit.params, min_correl=0.4)
fit2 = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert (myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert (myfit.params['amp_l'].value == myfit.params['amp_tot'].value -
myfit.params['amp_g'].value)
assert (myfit.params['wid_l'].value == 1.25 * myfit.params['wid_g'].value)
