def mpfitpeaks(x, y, N, error=None):
pars = [1, np.min(y), 0]
parinfo = [ {"value": N, "fixed": 1, "name": "Number of Peaks",
"limited": [0, 0], "limits": [0, 0]},
{"value": 1.6, "fixed": 0, "name": "Sigma",
"limited": [0, 0], "limits": [0, 0]},
{"value": pars[1], "fixed": 0, "name": "Offset",
"limited": [0, 0], "limits": [0, 0]},
{"value": pars[2], "fixed": 0, "name": "Slope",
"limited": [0, 0], "limits": [0, 0]}]
for i in range(N):
v = {"value": np.max(y)/2., "fixed": 0, "name": "Peak Value(%i)" % i,
"limited": [1, 0], "limits": [0, 0]}
pars.append(np.max(y))
parinfo.append(v)
v = {"value": x[np.argmax(y)], "fixed": 0, "name": "Centroid(%i)" % i}
pars.append(x[np.argmax(y)])
parinfo.append(v)
fa = {"x": x, "y": y}
if error is not None: fa["error"] = error
return mpfit.mpfit(multi_gaussian_residuals, parinfo=parinfo, functkw=fa,
quiet=1)
def do_fit_wavelengths(pixels, lambdas, alphaguess,
sinbetaguess, gammaguess, deltaguess, band, pixel_y, error=None):
''' THIS HSOULD BE REMOVED'''
bmap = {"Y": 6, "J": 5, "H": 4, "K": 3}
order = bmap[band]
parinfo = [
{'fixed': 1, 'value': order, 'parname': 'order',
'limited': [0,0], 'limits': [0,0]},
{'fixed': 1, 'value': pixel_y, 'parname': 'Y',
'limited': [0,0], 'limits': [0,0]},
{'fixed': 0, 'value': alphaguess, 'parname': 'alpha', 'step': 1e-5,
'limited': [0,0], 'limits': [0,0]},
{'fixed': 0, 'value': sinbetaguess, 'parname': 'sinbeta',
'step': 1e-5, 'limited': [0,0], 'limits': [30,50]},
{'fixed': 0, 'value': gammaguess, 'parname': 'gamma','step': 1e-15,
'limited': [1,1], 'limits': [0,20e-13]},
{'fixed': 0, 'value': deltaguess, 'parname': 'delta', 'step': 1e-1,
'limited': [1,1], 'limits': [0,2048]},
]
fa = {"x": pixels, "y": lambdas}
if error is not None:
fa["error"] = error
lsf = mpfit.mpfit(wavelength_residuals, parinfo=parinfo, functkw=fa,
quiet=1, maxiter=20)
return lsf
def do_fit_wavelengths(pixels, lambdas, alphaguess,
sinbetaguess, gammaguess, deltaguess, band, pixel_y, error=None):
''' THIS HSOULD BE REMOVED'''
bmap = {"Y": 6, "J": 5, "H": 4, "K": 3}
order = bmap[band]
parinfo = [
{'fixed': 1, 'value': order, 'parname': 'order',
'limited': [0,0], 'limits': [0,0]},
{'fixed': 1, 'value': pixel_y, 'parname': 'Y',
'limited': [0,0], 'limits': [0,0]},
{'fixed': 0, 'value': alphaguess, 'parname': 'alpha', 'step': 1e-5,
'limited': [0,0], 'limits': [0,0]},
{'fixed': 0, 'value': sinbetaguess, 'parname': 'sinbeta',
'step': 1e-5, 'limited': [0,0], 'limits': [30,50]},
{'fixed': 0, 'value': gammaguess, 'parname': 'gamma','step': 1e-15,
'limited': [1,1], 'limits': [0,20e-13]},
{'fixed': 0, 'value': deltaguess, 'parname': 'delta', 'step': 1e-1,
'limited': [1,1], 'limits': [0,2048]},
]
fa = {"x": pixels, "y": lambdas}
if error is not None:
fa["error"] = error
lsf = mpfit.mpfit(wavelength_residuals, parinfo=parinfo, functkw=fa,
quiet=1, maxiter=20)
return lsf
def mpfitpeaks(x, y, N, error=None):
pars = [1, np.min(y), 0]
parinfo = [ {"value": N, "fixed": 1, "name": "Number of Peaks",
"limited": [0, 0], "limits": [0, 0]},
{"value": 1.6, "fixed": 0, "name": "Sigma",
"limited": [0, 0], "limits": [0, 0]},
{"value": pars[1], "fixed": 0, "name": "Offset",
"limited": [0, 0], "limits": [0, 0]},
{"value": pars[2], "fixed": 0, "name": "Slope",
"limited": [0, 0], "limits": [0, 0]}]
for i in range(N):
v = {"value": np.max(y)/2., "fixed": 0, "name": "Peak Value(%i)" % i,
"limited": [1, 0], "limits": [0, 0]}
pars.append(np.max(y))
parinfo.append(v)
v = {"value": x[np.argmax(y)], "fixed": 0, "name": "Centroid(%i)" % i}
pars.append(x[np.argmax(y)])
parinfo.append(v)
fa = {"x": x, "y": y}
if error is not None: fa["error"] = error
return mpfit.mpfit(multi_gaussian_residuals, parinfo=parinfo, functkw=fa,
quiet=1)
def mpfit_do(residual_fun, # function returned from mpfit_residuals() above
x, # input x
y, # input y = f(x)
parinfo, # initial parameter guess
error=None,
maxiter=20):
#TODO : Document parinfo part
fa = {"x": x, "y": y}
if error is not None:
fa["error"] = error
lsf = mpfit.mpfit(residual_fun, parinfo=parinfo, functkw=fa,
quiet=1, maxiter=maxiter)
return lsf
def mpfit_do(residual_fun, # function returned from mpfit_residuals() above
x, # input x
y, # input y = f(x)
parinfo, # initial parameter guess
error=None,
maxiter=20):
#TODO : Document parinfo part
fa = {"x": x, "y": y}
if error is not None:
fa["error"] = error
lsf = mpfit.mpfit(residual_fun, parinfo=parinfo, functkw=fa,
quiet=1, maxiter=maxiter)
return lsf
def mpfitpeak(x, y, error=None):
parinfo = [{"value": np.max(y), "fixed": 0, "name": "Peak Value",
'step': 10},
{"value": x[np.argmax(y)], "fixed": 0, "name": "Centroid",
'step': .1},
{"value": 1.1, "fixed": 0, "name": "Sigma",
'step': .1},
{"value": np.min(y), "fixed": 0, "name": "Offset",
'step': 10},
{"value": 0, "fixed": 0, "name": "Slope",
'step': 1e-5}]
fa = {"x": x, "y": y}
if error is not None: fa["error"] = error
return mpfit.mpfit(gaussian_residuals, parinfo=parinfo, functkw=fa, quiet=1)
def mpfitpeak(x, y, error=None):
parinfo = [{"value": np.max(y), "fixed": 0, "name": "Peak Value",
'step': 10},
{"value": x[np.argmax(y)], "fixed": 0, "name": "Centroid",
'step': .1},
{"value": 1.1, "fixed": 0, "name": "Sigma",
'step': .1},
{"value": np.min(y), "fixed": 0, "name": "Offset",
'step': 10},
{"value": 0, "fixed": 0, "name": "Slope",
'step': 1e-5}]
fa = {"x": x, "y": y}
if error is not None: fa["error"] = error
return mpfit.mpfit(gaussian_residuals, parinfo=parinfo, functkw=fa, quiet=1)
def run_fit(m, m_err, X, M, M_err, c, c_err):
p0 = [25.0, -0.05]
##########
# MPFIT
##########
print '\n\n'
print '##########'
print '# MPFIT'
print '##########'
from pytools.nmpfit import mpfit
import copy
nparams = len(p0)
infoTemplate = {'parname':'', 'value':0, 'step':0.0, 'fixed':0,
'limits':[0., 0.], 'limited':[0, 0]}
parinfo = []
for ii in range(nparams):
parinfo.append(copy.deepcopy(infoTemplate))
# Zeropoint
parinfo[0]['parname'] = 'Zeropoint'
parinfo[0]['value'] = p0[0]
parinfo[0]['limited'] = [1, 1]
parinfo[0]['limits'] = [20.0, 30.0]
# Airmass Coefficient
parinfo[1]['parname'] = 'Airmass Coefficient'
parinfo[1]['value'] = p0[1]
parinfo[1]['step'] = 0.001
parinfo[1]['limited'] = [1, 1]
parinfo[1]['limits'] = [-1, 1]
# Color Term
if nparams > 2:
parinfo[2]['parname'] = 'Color Term'
parinfo[2]['value'] = p0[2]
parinfo[2]['limited'] = [1, 1]
parinfo[2]['limits'] = [-0.1, 0.1]
parinfo[2]['step'] = 0.001
# Color-Airmass Term
if nparams > 3:
parinfo[3]['parname'] = 'Airmass/Color Term'
parinfo[3]['value'] = p0[3]
parinfo[3]['limited'] = [1, 1]
parinfo[3]['limits'] = [-0.1, 0.1]
args = {'m': m, 'merr': m_err, 'X': X, 'M': M, 'Merr': M_err,
'C': c, 'Cerr': c_err}
output = mpfit(mpfit_func_fit, p0, functkw=args, parinfo=parinfo,
xtol=1e-15, gtol=1e-16, ftol=1e-16)
print 'Fit Status:'
print ' %d %s' % (output.status, output.errmsg)
print
print "Fitted parameters at minimum:"
for ii in range(len(output.params)):
print "%2d %-20s %12f +/- %10f" % \
(ii, parinfo[ii]['parname'], output.params[ii], output.perror[ii])
print
p = output.params
p_err = output.perror
# ##########
# # SCIPY.OPTIMIZE.LEASTSQ
# ##########
# print '\n\n'
# print '##########'
# print '# SCIPY.OPTIMIZE.LEASTSQ'
# print '##########'
# weights = 1.0 / np.sqrt(m_err**2 + M_err**2)
# output = optimize.leastsq(func_fit, p0, full_output=1,
# args=(m, m_err, X,
# M, M_err, c, c_err))#,
# # diag=weights)
# p = output[0]
# cov = output[1]
# info = output[2]
# mesg = output[3]
# success = output[4]
# chisq = np.sum(info["fvec"]*info["fvec"])
# dof = len(m) - len(p)
# print 'Converged with chi squared ', chisq
# print 'degrees of freedom, dof ', dof
# print 'RMS of residuals (i.e. sqrt(chisq/dof))', math.sqrt(chisq/dof)
# print 'Reduced chisq (i.e. variance of residuals)', chisq/dof
# print ''
# # Uncertainties in parameters
# # uncertainties are calculated as per gnuplot, "fixing" the result
# # for non unit values of the reduced chisq.
# # values at min match gnuplot
# print "Fitted parameters at minimum, with 68% C.I.:"
# for i, pmin in enumerate(p):
# print "%2d %12f +/- %10f" % \
# (i, pmin, math.sqrt(cov[i,i]**2))
# print
# print "Correlation matrix"
# # correlation matrix close to gnuplot
# print " ",
# for i in range(len(p)): print "p[%d] " % (i),
# print
# for i in range(len(p)):
# print " p[%d] " % i,
# for j in range(i+1):
# print "%10f" % (cov[i,j]/math.sqrt(cov[i,i]*cov[j,j]),),
# print
# print 'Results: ', success, mesg
# print ' Zeropoint = %7.3f' % p[0]
# print ' Airmass Coefficient = %9.5f' % p[1]
# # print ' Color Term = %9.5f' % p[2]
# # print ' Airmass Color Term = %9.5f' % p[3]
# Get residuals
res, res_err = func_residuals(p, m, m_err, X, M, M_err, c, c_err)
# Get the predicted instrumental magnitude
m_pred, m_pre_err = func_calc_mag_obs_predicted(p,
M, M_err,
X, c, c_err)
return p, p_err, res, m_pred
def run_fit(m, m_err, X, M, M_err, c, c_err):
p0 = [25.0, -0.05]
##########
# MPFIT
##########
print '\n\n'
print '##########'
print '# MPFIT'
print '##########'
from pytools.nmpfit import mpfit
import copy
nparams = len(p0)
infoTemplate = {
'parname': '',
'value': 0,
'step': 0.0,
'fixed': 0,
'limits': [0., 0.],
'limited': [0, 0]
}
parinfo = []
for ii in range(nparams):
parinfo.append(copy.deepcopy(infoTemplate))
# Zeropoint
parinfo[0]['parname'] = 'Zeropoint'
parinfo[0]['value'] = p0[0]
parinfo[0]['limited'] = [1, 1]
parinfo[0]['limits'] = [20.0, 30.0]
# Airmass Coefficient
parinfo[1]['parname'] = 'Airmass Coefficient'
parinfo[1]['value'] = p0[1]
parinfo[1]['step'] = 0.001
parinfo[1]['limited'] = [1, 1]
parinfo[1]['limits'] = [-1, 1]
# Color Term
if nparams > 2:
parinfo[2]['parname'] = 'Color Term'
parinfo[2]['value'] = p0[2]
parinfo[2]['limited'] = [1, 1]
parinfo[2]['limits'] = [-0.1, 0.1]
parinfo[2]['step'] = 0.001
# Color-Airmass Term
if nparams > 3:
parinfo[3]['parname'] = 'Airmass/Color Term'
parinfo[3]['value'] = p0[3]
parinfo[3]['limited'] = [1, 1]
parinfo[3]['limits'] = [-0.1, 0.1]
args = {
'm': m,
'merr': m_err,
'X': X,
'M': M,
'Merr': M_err,
'C': c,
'Cerr': c_err
}
output = mpfit(mpfit_func_fit,
p0,
functkw=args,
parinfo=parinfo,
xtol=1e-15,
gtol=1e-16,
ftol=1e-16)
print 'Fit Status:'
print ' %d %s' % (output.status, output.errmsg)
print
print "Fitted parameters at minimum:"
for ii in range(len(output.params)):
print "%2d %-20s %12f +/- %10f" % \
(ii, parinfo[ii]['parname'], output.params[ii], output.perror[ii])
print
p = output.params
p_err = output.perror
# ##########
# # SCIPY.OPTIMIZE.LEASTSQ
# ##########
# print '\n\n'
# print '##########'
# print '# SCIPY.OPTIMIZE.LEASTSQ'
# print '##########'
# weights = 1.0 / np.sqrt(m_err**2 + M_err**2)
# output = optimize.leastsq(func_fit, p0, full_output=1,
# args=(m, m_err, X,
# M, M_err, c, c_err))#,
# # diag=weights)
# p = output[0]
# cov = output[1]
# info = output[2]
# mesg = output[3]
# success = output[4]
# chisq = np.sum(info["fvec"]*info["fvec"])
# dof = len(m) - len(p)
# print 'Converged with chi squared ', chisq
# print 'degrees of freedom, dof ', dof
# print 'RMS of residuals (i.e. sqrt(chisq/dof))', math.sqrt(chisq/dof)
# print 'Reduced chisq (i.e. variance of residuals)', chisq/dof
# print ''
# # Uncertainties in parameters
# # uncertainties are calculated as per gnuplot, "fixing" the result
# # for non unit values of the reduced chisq.
# # values at min match gnuplot
# print "Fitted parameters at minimum, with 68% C.I.:"
# for i, pmin in enumerate(p):
# print "%2d %12f +/- %10f" % \
# (i, pmin, math.sqrt(cov[i,i]**2))
# print
# print "Correlation matrix"
# # correlation matrix close to gnuplot
# print " ",
# for i in range(len(p)): print "p[%d] " % (i),
# print
# for i in range(len(p)):
# print " p[%d] " % i,
# for j in range(i+1):
# print "%10f" % (cov[i,j]/math.sqrt(cov[i,i]*cov[j,j]),),
# print
# print 'Results: ', success, mesg
# print ' Zeropoint = %7.3f' % p[0]
# print ' Airmass Coefficient = %9.5f' % p[1]
# # print ' Color Term = %9.5f' % p[2]
# # print ' Airmass Color Term = %9.5f' % p[3]
# Get residuals
res, res_err = func_residuals(p, m, m_err, X, M, M_err, c, c_err)
# Get the predicted instrumental magnitude
m_pred, m_pre_err = func_calc_mag_obs_predicted(p, M, M_err, X, c, c_err)
return p, p_err, res, m_pred