Package ivs :: Package sigproc :: Module funclib

Module funclib

Database with model functions.

To be used with the ivs.sigproc.fit.minimizer function or with the evaluate function in this module.

>>> p = plt.figure()
>>> x = np.linspace(-10,10,1000)
>>> p = plt.plot(x,evaluate('gauss',x,[5,1.,2.,0.5]),label='gauss')
>>> p = plt.plot(x,evaluate('voigt',x,[20.,1.,1.5,3.,0.5]),label='voigt')
>>> p = plt.plot(x,evaluate('lorentz',x,[5,1.,2.,0.5]),label='lorentz')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib01.png]

>>> p = plt.figure()
>>> x = np.linspace(0,10,1000)[1:]
>>> p = plt.plot(x,evaluate('power_law',x,[2.,3.,1.5,0,0.5]),label='power_law')
>>> p = plt.plot(x,evaluate('power_law',x,[2.,3.,1.5,0,0.5])+evaluate('gauss',x,[1.,5.,0.5,0,0]),label='power_law + gauss')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib02.png]

>>> p = plt.figure()
>>> x = np.linspace(0,10,1000)
>>> p = plt.plot(x,evaluate('sine',x,[1.,2.,0,0]),label='sine')
>>> p = plt.plot(x,evaluate('sine_linfreqshift',x,[1.,0.5,0,0,.5]),label='sine_linfreqshift')
>>> p = plt.plot(x,evaluate('sine_expfreqshift',x,[1.,0.5,0,0,1.2]),label='sine_expfreqshift')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib03.png]

>>> p = plt.figure()
>>> p = plt.plot(x,evaluate('sine',x,[1.,2.,0,0]),label='sine')
>>> p = plt.plot(x,evaluate('sine_orbit',x,[1.,2.,0,0,0.1,10.,0.1]),label='sine_orbit')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib03a.png]

>>> p = plt.figure()
>>> x_single = np.linspace(0,10,1000)
>>> x_double = np.vstack([x_single,x_single])
>>> p = plt.plot(x_single,evaluate('kepler_orbit',x_single,[2.5,0.,0.5,0,3,1.]),label='kepler_orbit (single)')
>>> y_double = evaluate('kepler_orbit',x_double,[2.5,0.,0.5,0,3,2.,-4,2.],type='double')
>>> p = plt.plot(x_double[0],y_double[0],label='kepler_orbit (double 1)')
>>> p = plt.plot(x_double[1],y_double[1],label='kepler_orbit (double 2)')
>>> p = plt.plot(x,evaluate('box_transit',x,[2.,0.4,0.1,0.3,0.5]),label='box_transit')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib04.png]

>>> p = plt.figure()
>>> x = np.linspace(-1,1,1000)
>>> gammas = [-0.25,0.1,0.25,0.5,1,2,4]
>>> y = np.array([evaluate('soft_parabola',x,[1.,0,1.,gamma]) for gamma in gammas])
divide by zero encountered in power
>>> for iy,gamma in zip(y,gammas): p = plt.plot(x,iy,label="soft_parabola $\gamma$={:.2f}".format(gamma))
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib05.png]

>>> p = plt.figure()
>>> x = np.logspace(-1,2,1000)
>>> blbo = evaluate('blackbody',x,[10000.,1.],wave_units='micron',flux_units='W/m3')
>>> raje = evaluate('rayleigh_jeans',x,[10000.,1.],wave_units='micron',flux_units='W/m3')
>>> wien = evaluate('wien',x,[10000.,1.],wave_units='micron',flux_units='W/m3')
>>> p = plt.subplot(221)
>>> p = plt.title(r'$\lambda$ vs $F_\lambda$')
>>> p = plt.loglog(x,blbo,label='Black Body')
>>> p = plt.loglog(x,raje,label='Rayleigh-Jeans')
>>> p = plt.loglog(x,wien,label='Wien')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

>>> blbo = evaluate('blackbody',x,[10000.,1.],wave_units='micron',flux_units='Jy')
>>> raje = evaluate('rayleigh_jeans',x,[10000.,1.],wave_units='micron',flux_units='Jy')
>>> wien = evaluate('wien',x,[10000.,1.],wave_units='micron',flux_units='Jy')
>>> p = plt.subplot(223)
>>> p = plt.title(r"$\lambda$ vs $F_\nu$")
>>> p = plt.loglog(x,blbo,label='Black Body')
>>> p = plt.loglog(x,raje,label='Rayleigh-Jeans')
>>> p = plt.loglog(x,wien,label='Wien')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

>>> x = np.logspace(0.47,3.47,1000)
>>> blbo = evaluate('blackbody',x,[10000.,1.],wave_units='THz',flux_units='Jy')
>>> raje = evaluate('rayleigh_jeans',x,[10000.,1.],wave_units='THz',flux_units='Jy')
>>> wien = evaluate('wien',x,[10000.,1.],wave_units='THz',flux_units='Jy')
>>> p = plt.subplot(224)
>>> p = plt.title(r"$\nu$ vs $F_\nu$")
>>> p = plt.loglog(x,blbo,label='Black Body')
>>> p = plt.loglog(x,raje,label='Rayleigh-Jeans')
>>> p = plt.loglog(x,wien,label='Wien')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

>>> blbo = evaluate('blackbody',x,[10000.,1.],wave_units='THz',flux_units='W/m3')
>>> raje = evaluate('rayleigh_jeans',x,[10000.,1.],wave_units='THz',flux_units='W/m3')
>>> wien = evaluate('wien',x,[10000.,1.],wave_units='THz',flux_units='W/m3')
>>> p = plt.subplot(222)
>>> p = plt.title(r"$\nu$ vs $F_\lambda$")
>>> p = plt.loglog(x,blbo,label='Black Body')
>>> p = plt.loglog(x,raje,label='Rayleigh-Jeans')
>>> p = plt.loglog(x,wien,label='Wien')
>>> leg = plt.legend(loc='best')
>>> leg.get_frame().set_alpha(0.5)

]include figure]]ivs_sigproc_fit_funclib06.png]

Functions

[hide private]

evaluate(funcname, domain, parameters, **kwargs)
Evaluate a function on specified interval with specified parameters.

source code

Function Library

blackbody(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)
Blackbody (T, scale).

source code

rayleigh_jeans(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)
Rayleigh-Jeans tail (T, scale).

source code

wien(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)
Wien approximation (T, scale).

source code

kepler_orbit(type='single')
Kepler orbits ((p,t0,e,omega,K,v0) or (p,t0,e,omega,K1,v01,K2,v02))

source code

box_transit(t0=0.)
Box transit model (cont,freq,ingress,egress,depth)

source code

polynomial(d=1)
Polynomial (a1,a0).

source code

soft_parabola()
Soft parabola (ta,vlsr,vinf,gamma).

source code

gauss(use_jacobian=True)
Gaussian (a,mu,sigma,c)

source code

sine()
Sine (ampl,freq,phase,const)

source code

sine_linfreqshift(t0=0.)
Sine with linear frequency shift (ampl,freq,phase,const,D).

source code

sine_expfreqshift(t0=0.)
Sine with exponential frequency shift (ampl,freq,phase,const,K).

source code

sine_orbit(t0=0., nmax=10)
Sine with a sinusoidal frequency shift (ampl,freq,phase,const,forb,asini,omega,(,ecc))

source code

power_law()
Power law (A,B,C,f0,const)

source code

lorentz()
Lorentz profile (ampl,mu,gamma,const)

source code

voigt()
Voigt profile (ampl,mu,sigma,gamma,const)

source code

Combination functions

multi_sine(n=10)
Multiple sines.

source code

multi_blackbody(n=3, **kwargs)
Multiple black bodies.

source code

Internal Helper functions

_complex_error_function(x)
Complex error function

source code

Variables

[hide private]

logger = logging.getLogger("SP.FUNCLIB")

Function Details

[hide private]

blackbody(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)

source code

Blackbody (T, scale).

Parameters:

wave_units (string) - wavelength units
flux_units (string) - flux units
disc_integrated (bool) - sets units equal to SED models

rayleigh_jeans(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)

source code

Rayleigh-Jeans tail (T, scale).

Parameters:

wave_units (string) - wavelength units
flux_units (string) - flux units
disc_integrated (bool) - sets units equal to SED models

wien(wave_units='AA', flux_units='erg/s/cm2/AA', disc_integrated=True)

source code

Wien approximation (T, scale).

Parameters:

wave_units (string) - wavelength units
flux_units (string) - flux units
disc_integrated (bool) - sets units equal to SED models

kepler_orbit(type='single')

source code

Kepler orbits ((p,t0,e,omega,K,v0) or (p,t0,e,omega,K1,v01,K2,v02))

A single kepler orbit parameters are: [p, t0, e, omega, k, v0]

A double kepler orbit parameters are: [p, t0, e, omega, k_1, v0_1, k_2, v0_2] Warning: This function uses 2d input and output!

box_transit(t0=0.)

source code

Box transit model (cont,freq,ingress,egress,depth)

Parameters:

t0 (float) - reference time (defaults to 0)

polynomial(d=1)

source code

Polynomial (a1,a0).

y(x) = ai*x**i + a(i-1)*x**(i-1) + ... + a1*x + a0

Parameters:

d (int) - degree of the polynomial

soft_parabola()

source code

Soft parabola (ta,vlsr,vinf,gamma).

See Olofsson 1993ApJS...87...267O.

T_A(x) = T_A(0) * [ 1 - ((x- v_lsr)/v_inf)**2 ] ** (gamma/2)

gauss(use_jacobian=True)

source code

Gaussian (a,mu,sigma,c)

f(x) = a * exp( - (x - mu)**2 / (2 * sigma**2) ) + c

sine()

source code

Sine (ampl,freq,phase,const)

f(x) = ampl * sin(2pi*freq*x + 2pi*phase) + const

sine_linfreqshift(t0=0.)

source code

Sine with linear frequency shift (ampl,freq,phase,const,D).

Similar to sine, but with extra parameter 'D', which is the linear frequency shift parameter.

Parameters:

t0 (float) - reference time (defaults to 0)

sine_expfreqshift(t0=0.)

source code

Sine with exponential frequency shift (ampl,freq,phase,const,K).

Similar to sine, but with extra parameter 'K', which is the exponential frequency shift parameter.

frequency(x) = freq / log(K) * (K**(x-t0)-1)

f(x) = ampl * sin( 2*pi * (frequency + phase))

Parameters:

t0 (float) - reference time (defaults to 0)

sine_orbit(t0=0., nmax=10)

source code

Sine with a sinusoidal frequency shift (ampl,freq,phase,const,forb,asini,omega,(,ecc))

Similar to sine, but with extra parameter 'asini' and 'forb', which are the orbital parameters. forb in cycles/day or something similar, asini in au.

For eccentric orbits, add longitude of periastron 'omega' (radians) and 'ecc' (eccentricity).

Parameters:

t0 (float) - reference time (defaults to 0)
nmax (int) - number of terms to include in series for eccentric orbit

power_law()

source code

Power law (A,B,C,f0,const)

P(f) = A / (1+ B(f-f0))**C + const

lorentz()

source code

Lorentz profile (ampl,mu,gamma,const)

P(f) = A / ( (x-mu)**2 + gamma**2) + const

voigt()

source code

Voigt profile (ampl,mu,sigma,gamma,const)

z = (x + gamma*i) / (sigma*sqrt(2)) V = A * Real[cerf(z)] / (sigma*sqrt(2*pi))

multi_sine(n=10)

source code

Multiple sines.

Parameters:

n (int) - number of sines

multi_blackbody(n=3, **kwargs)

source code

Multiple black bodies.

Parameters:

n (int) - number of blackbodies

evaluate(funcname, domain, parameters, **kwargs)

source code

Evaluate a function on specified interval with specified parameters.

Extra keywords are passed to the funcname.

Example:

>>> x = np.linspace(-5,5,1000)
>>> y = evaluate('gauss',x,[1.,0.,2.,0.])

Parameters:

funcname (str) - name of the function
domain (array) - domain to evaluate onto
parameters (array) - parameter of the function