def do_Dawson_Fabrycky(system):
time, rv, err = system.time, system.vrad, system.error
ofac = 2.0
# Make permutations for indices of length n
def permutate(n):
A=[]
for i in range(n):
a = int(n*random.random())
if a==n: a=n-1
A.append(a)
return A
# Calculate the spectral window function and its phase angles
def specwindow(freq,time):
n = len(time)
W = [sum([cmath.exp(-2.j*pi*f*t) for t in time])/float(n) for f in freq]
amp = [sqrt(t.real*t.real + t.imag*t.imag) for t in W]
phase = [atan2(t.imag,t.real) for t in W]
return amp,phase
def fitcirc(per,K,Tc,gam,t):
phase = 2*pi*Tc/per
omega = 2. * pi / per
rv = K * cos(omega * t - phase) + gam
return rv
def fitkep(per,ecc,pomega,K,T0,gam,t):
afit = K*cos(pomega/180*pi)
bfit = -K*sin(pomega/180*pi)
cfit = K*ecc*cos(pomega/180*pi) + gam
M=(t-T0)/per*2.*pi
sE = 0.
sEtemp = 2.
while abs(sE - sEtemp) > 0.05:
sEtemp = sE
EA = ecc * sE + M
sE = sin(EA)
cE = cos(EA)
cosnu = (cE - ecc) / (1. - ecc * cE)
sinnu = sqrt(1. - ecc * ecc) * sE / (1. - ecc * cE)
rv = afit * cosnu + bfit * sinnu + cfit
return rv
plow = 0.5
n = len(err)
### GET THE REAL PERIODOGRAM
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF.periodogram_DF(array(time),array(rv),array(err),ofac,plow)
### GET THE WINDOW FUNCTION AT THOSE FREQUENCIES + plot dials
amp,phase = specwindow(freq,time)
figure(num=1,figsize=(11.69,8.27))
#### GET 3 Maximum peaks + create fake data
nf = len(freq)
temp = sorted(zip(power,freq,a_cos,b_sin,c_cte,phi))
fmax1 = (temp[nf-1])[1]
fmax2 = fmax1
i = 1
while abs(fmax2 - fmax1) < 0.01:
i += 1
fmax2 = (temp[nf-i])[1]
fmax3 = fmax2
j = i
while abs(fmax3 - fmax2) < 0.01 or abs(fmax3 - fmax1) < 0.01:
j += 1
fmax3 = (temp[nf-j])[1]
print 'Maximum frequencies at: ',fmax1,fmax2,fmax3
print 'That is periods at: ',round(1./fmax1,2),round(1./fmax2,2),round(1./fmax3,2)
a1 = (temp[nf-1])[2]
a2 = (temp[nf-i])[2]
a3 = (temp[nf-j])[2]
b1 = (temp[nf-1])[3]
b2 = (temp[nf-i])[3]
b3 = (temp[nf-j])[3]
c1 = (temp[nf-1])[4]
c2 = (temp[nf-i])[4]
c3 = (temp[nf-j])[4]
ph1 = (temp[nf-1])[5]
ph2 = (temp[nf-i])[5]
ph3 = (temp[nf-j])[5]
timemin=int(min(time))
timemax=int(max(time))
timefake=frange(timemin-10,timemax+10,0.05)
timefake = time
xdiff = max(time) - min(time)
rv_fake1 = [a1*cos(fmax1*2.*pi*i) + b1*sin(fmax1*2.*pi*i) + c1 for i in timefake]
rv_fake2 = [a2*cos(fmax2*2.*pi*i) + b2*sin(fmax2*2.*pi*i) + c2 for i in timefake]
rv_fake3 = [a3*cos(fmax3*2.*pi*i) + b3*sin(fmax3*2.*pi*i) + c3 for i in timefake]
#errfake = [0.001 for i in timefake]
errfake = err
### PLOT REAL PERIODOGRAM + DIALS
figure(num = 1)
subplot(4,1,1)
title('window function + periodogram')
semilogx(1/freq,amp,'r-', alpha=0.3)
semilogx(1/freq,power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.025*cos(ph1)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph1)],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.025*cos(ph2)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph2)],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.025*cos(ph3)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph3)],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
### PLOT FAKE PERIODOGRAMS + DIALS
#### 1st FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF.periodogram_DF(array(timefake),array(rv_fake1),array(errfake),ofac,plow)
#nf = len(freq)
#temp = sorted(zip(power,freq,a_cos,b_sin,c_cte,phi))
#fmax1 = (temp[nf-1])[1]
#fmax2 = fmax1
#i = 1
#while abs(fmax2 - fmax1) < 0.01:
# i += 1
# fmax2 = (temp[nf-i])[1]
#fmax3 = fmax2
#j = i
#while abs(fmax3 - fmax2) < 0.01 or abs(fmax3 - fmax1) < 0.01:
# j += 1
# fmax3 = (temp[nf-j])[1]
#print 'Maximum frequencies at: ',fmax1,fmax2,fmax3
#print 'That is periods at: ',round(1./fmax1,2),round(1./fmax2,2),round(1./fmax3,2)
#ph1 = (temp[nf-1])[5]
#ph2 = (temp[nf-i])[5]
#ph3 = (temp[nf-j])[5]
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,2)
semilogx([1./i for i in freq],power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
#### 2nd FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF.periodogram_DF(array(timefake),array(rv_fake2),array(errfake),ofac,plow)
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,3)
semilogx([1./i for i in freq],power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
#### 3rd FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF.periodogram_DF(array(timefake),array(rv_fake3),array(errfake),ofac,plow)
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,4)
semilogx([1./i for i in freq],power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
# savefig(name+'_DF.ps',orientation = 'Landscape')
show()
def do_Dawson_Fabrycky(system):
time, rv, err = system.time, system.vrad, system.error
ofac = 2.0
def specwindow(freq,time):
""" Calculate the spectral window function and its phase angles """
n = len(time)
W = [sum([np.exp(-2.j*pi*f*t) for t in time])/float(n) for f in freq]
amp = [np.sqrt(t.real*t.real + t.imag*t.imag) for t in W]
phase = [np.arctan2(t.imag,t.real) for t in W]
return amp,phase
plow = 0.5
n = len(err)
### GET THE REAL PERIODOGRAM
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF(time, rv, err, ofac, plow)
freq_real, power_real = freq, power
### GET THE WINDOW FUNCTION AT THOSE FREQUENCIES + plot dials
amp,phase = specwindow(freq,time)
figure(num=1,figsize=(12,8))
#### GET 3 Maximum peaks + create fake data
nf = len(freq)
temp = sorted(zip(power,freq,a_cos,b_sin,c_cte,phi))
fmax1 = (temp[nf-1])[1]
fmax2 = fmax1
i = 1
while abs(fmax2 - fmax1) < 0.01:
i += 1
fmax2 = (temp[nf-i])[1]
fmax3 = fmax2
j = i
while abs(fmax3 - fmax2) < 0.01 or abs(fmax3 - fmax1) < 0.01:
j += 1
fmax3 = (temp[nf-j])[1]
print 'Maximum frequencies at: ',fmax1,fmax2,fmax3
print 'That is periods at: ',round(1./fmax1,2),round(1./fmax2,2),round(1./fmax3,2)
a1 = (temp[nf-1])[2]
a2 = (temp[nf-i])[2]
a3 = (temp[nf-j])[2]
b1 = (temp[nf-1])[3]
b2 = (temp[nf-i])[3]
b3 = (temp[nf-j])[3]
c1 = (temp[nf-1])[4]
c2 = (temp[nf-i])[4]
c3 = (temp[nf-j])[4]
ph1 = (temp[nf-1])[5]
ph2 = (temp[nf-i])[5]
ph3 = (temp[nf-j])[5]
timemin=int(min(time))
timemax=int(max(time))
timefake=frange(timemin-10,timemax+10,0.05)
timefake = time
xdiff = max(time) - min(time)
rv_fake1 = array([a1*cos(fmax1*2.*pi*i) + b1*sin(fmax1*2.*pi*i) + c1 for i in timefake])
rv_fake2 = array([a2*cos(fmax2*2.*pi*i) + b2*sin(fmax2*2.*pi*i) + c2 for i in timefake])
rv_fake3 = array([a3*cos(fmax3*2.*pi*i) + b3*sin(fmax3*2.*pi*i) + c3 for i in timefake])
#errfake = [0.001 for i in timefake]
errfake = err
### PLOT REAL PERIODOGRAM + DIALS
figure(num = 1)
subplot(4,1,1)
title('window function + periodogram')
semilogx(1/freq,amp,'r-', alpha=0.3)
semilogx(1/freq,power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.025*cos(ph1)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph1)],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.025*cos(ph2)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph2)],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.025*cos(ph3)],[max(power)+0.1,max(power)+0.1+0.025*sin(ph3)],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
### PLOT FAKE PERIODOGRAMS + DIALS
#### 1st FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF(timefake, rv_fake1, errfake, ofac, plow)
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,2)
semilogx([1./i for i in freq],power,'k-')
fill_between(1/freq_real, power_real, 0., color='k', alpha=0.5)
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
#### 2nd FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF(timefake, rv_fake2, errfake, ofac, plow)
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,3)
semilogx([1./i for i in freq],power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
#### 3rd FAKE
freq,power,a_cos,b_sin,c_cte,phi,fNy,xdif = periodogram_DF(timefake, rv_fake3, errfake, ofac, plow)
ind1 = list(freq).index(fmax1)
ind2 = list(freq).index(fmax2)
ind3 = list(freq).index(fmax3)
subplot(4,1,4)
semilogx([1./i for i in freq],power,'k-')
semilogx(1./fmax1,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax2,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx(1./fmax3,max(power)+0.1,marker = '$\circ$',markersize=10,c='k',mew=0.3)
semilogx([1./fmax1,1./fmax1+0.045*cos(phi[ind1])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind1])],'k-',lw=1)
semilogx([1./fmax2,1./fmax2+0.045*cos(phi[ind2])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind2])],'k-',lw=1)
semilogx([1./fmax3,1./fmax3+0.045*cos(phi[ind3])],[max(power)+0.1,max(power)+0.1+0.045*sin(phi[ind3])],'k-',lw=1)
xlim(plow,xdiff*ofac)
ylim(0.0,max(power)+0.2)
# savefig(name+'_DF.ps',orientation = 'Landscape')
show()