def do_circular_photometry(data,
positions,
radius,
effective_gain,
method,
subpixels,
r_in=None):
extents = np.zeros((len(positions), 4), dtype=int)
extents[:, 0] = positions[:, 0] - radius + 0.5
extents[:, 1] = positions[:, 0] + radius + 1.5
extents[:, 2] = positions[:, 1] - radius + 0.5
extents[:, 3] = positions[:, 1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(data, positions,
extents)
flux = np.zeros(len(positions), dtype=np.float)
# TODO: flag these objects
if np.sum(ood_filter):
flux[ood_filter] = np.nan
warnings.warn(
"The aperture at position {0} does not have any "
"overlap with the data".format(positions[ood_filter]),
AstropyUserWarning)
if np.sum(ood_filter) == len(positions):
return (flux, )
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
if method == 'center':
use_exact = 0
subpixels = 1
elif method == 'subpixel':
use_exact = 0
else:
use_exact = 1
subpixels = 1
for i in range(len(flux)):
if not np.isnan(flux[i]):
fraction = circular_overlap_grid(x_pmin[i], x_pmax[i], y_pmin[i],
y_pmax[i], x_max[i] - x_min[i],
y_max[i] - y_min[i], radius,
use_exact, subpixels)
if r_in is not None:
fraction -= circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i], r_in,
use_exact, subpixels)
flux[i] = np.sum(data[y_min[i]:y_max[i], x_min[i]:x_max[i]] *
fraction)
return (flux, )
def time_circular_big_subpixel_5():
circular_overlap_grid(-4.,
4.,
-4.,
4.,
100,
100,
3.,
use_exact=1,
subpixels=5)
def time_circular_small_exact():
circular_overlap_grid(-4.,
4.,
-4.,
4.,
10,
10,
3.,
use_exact=1,
subpixels=1)
def do_circular_photometry(data, positions, radius, effective_gain,
method, subpixels, r_in=None):
extents = np.zeros((len(positions), 4), dtype=int)
extents[:,0] = positions[:,0] - radius + 0.5
extents[:,1] = positions[:,0] + radius + 1.5
extents[:,2] = positions[:,1] - radius + 0.5
extents[:,3] = positions[:,1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(data, positions, extents)
flux = np.zeros(len(positions), dtype=np.float)
# TODO: flag these objects
if np.sum(ood_filter):
flux[ood_filter] = np.nan
warnings.warn("The aperture at position {0} does not have any "
"overlap with the data"
.format(positions[ood_filter]),
AstropyUserWarning)
if np.sum(ood_filter) == len(positions):
return (flux, )
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
if method == 'center':
use_exact = 0
subpixels = 1
elif method == 'subpixel':
use_exact = 0
else:
use_exact = 1
subpixels = 1
for i in range(len(flux)):
if not np.isnan(flux[i]):
fraction = circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
radius, use_exact, subpixels)
if r_in is not None:
fraction -= circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
r_in, use_exact, subpixels)
flux[i] = np.sum(data[y_min[i]:y_max[i],
x_min[i]:x_max[i]] * fraction)
return (flux, )
def remove_concentric(data, x_mean=512, y_mean=512, x_stddev=3, y_stddev=3, Nsig=10, dp=0.1):
"""
This function first fits a gaussian PSF to the data to find the centroid.
Then, it subtracts concentric apertures from the data rather than just
subtracting the gaussian model.
"""
data = data.copy() # Don't overwrite the data
nx, ny = data.shape
gauss, psf, centroid = fit_gaussian_psf(data, x_mean=x_mean, y_mean=y_mean,
x_stddev=x_stddev, y_stddev=y_stddev)
std = (gauss.x_stddev_0.value + gauss.y_stddev_0.value)/2.0
x0, y0 = centroid
radii = np.arange(dp, Nsig*std, dp)[::-1]
# Get extents using the photutils function
pos = np.atleast_2d(centroid)
extents = np.zeros((len(pos), 4), dtype=int)
extents[:, 0] = pos[:, 0] - max(radii) + 0.5
extents[:, 1] = pos[:, 0] + max(radii) + 1.5
extents[:, 2] = pos[:, 1] - max(radii) + 0.5
extents[:, 3] = pos[:, 1] + max(radii) + 1.5
_, extent, phot_extent = get_phot_extents(data, pos, extents)
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
args = [x_pmin[0], x_pmax[0], y_pmin[0], y_pmax[0], x_max[0]-x_min[0], y_max[0]-y_min[0]]
# Fit apertures
psf = np.zeros(data.shape)
for radius in radii:
Rin = radius - dp
Rout = radius
if Rin > dp/10.0:
ap = CircularAnnulus(centroid, r_in=Rin, r_out=Rout)
else:
ap = CircularAperture(centroid, r=Rout)
phot = aperture_photometry(data, ap)
avg_flux = phot['aperture_sum'].item()/ap.area()
outer = circular_overlap_grid(*args, r=Rout, use_exact=1, subpixels=5)
if Rout-dp > dp/10.0:
inner = circular_overlap_grid(*args, r=Rin, use_exact=1, subpixels=5)
else:
inner = 0.0
annulus_overlap = outer - inner
psf[y_min[0]:y_max[0], x_min[0]:x_max[0]] += annulus_overlap * avg_flux
return data - psf, psf, np.array(centroid)
def to_mask(self, x_size, y_size):
"""
This function ...
:param x_size:
:param y_size:
:return:
"""
rel_center = self.center
x_min = -rel_center.x
x_max = x_size - rel_center.x
y_min = -rel_center.y
y_max = y_size - rel_center.y
fraction = circular_overlap_grid(x_min,
x_max,
y_min,
y_max,
x_size,
y_size,
self.radius,
use_exact=0,
subpixels=1)
#from ..tools import plotting
#plotting.plot_mask(fraction)
# Return a new mask
return Mask(fraction)
def circular_mask(self, radius, xoff=0.0, yoff=0.0, use_exact=1, subsampling=1, transparency=1.0):
"""
Define a circular mask within the grid of a specified radius and offset by xoff/yoff.
Use photutils.geometry to create masks that calculate the fraction of a pixel subtended
by the circular mask. use_exact=1 performs the exact geometric calculation while
use_exact=0 will sub-sample the pixels by the specfied subsampling parameter
to estimate the subtended area.
Parameters
----------
radius: float
Radius of the circular mask
xoff: float
X position of the center of the mask
yoff: float
Y position of the center of the mask
use_exact: int (default: 1)
If 1, then use exact geometrical calculation to weight pixels partially covered by mask.
This parameter is passed directly on to photutils.geometry.circular_overlap_grid()
subsampling: int (default: 1)
If use_exact=0, then subsample pixels by this factor to calculate area of each pixel subtended
by the mask. The default value of 1 will force no partial pixels to be included in the mask.
This parameter is passed directly on to photutils.geometry.circular_overlap_grid()
transparency: float (default: 1.0)
Transparency of the mask
Returns
-------
mask: 2D np.ndarray
2D mask image
"""
if transparency < 0.0 or transparency > 1.0:
msg = "Mask transparency, %f, must be in the range of 0.0 (fully opaque) to 1.0 (fully clear)." % transparency
raise EngineInputError(value=msg)
t = self.as_dict()
# we need to use flipud because we use an origin in the UL corner of an image
# while photutils uses the LL corner.
mask = np.flipud(
circular_overlap_grid(
t['x_min'] - xoff,
t['x_max'] - xoff,
t['y_min'] - yoff,
t['y_max'] - yoff,
t['x_size'],
t['y_size'],
radius,
use_exact,
subsampling
)
)
mask *= transparency
return mask
def get_circular_overlap(*args, **kwargs):
global grid_cache
key = list(args)
for arg in ['r', 'use_exact', 'subpixels']:
key.append(kwargs[arg])
key = tuple(key)
try:
retval = grid_cache[key]
except KeyError:
retval = circular_overlap_grid(*args, **kwargs)
#grid_cache[key] = retval
return retval
def circular_photometry_weights(data, positions, radius):
"""
Return an array of weights corresponding to a circular aperture.
Parameters
----------
data : Not used in computation. Just for shape info
positions : (x,y) position of flux center recal x = column, y = rows
"""
extents = np.zeros((len(positions), 4), dtype=int)
extents[:, 0] = positions[:, 0] - radius + 0.5
extents[:, 1] = positions[:, 0] + radius + 1.5
extents[:, 2] = positions[:, 1] - radius + 0.5
extents[:, 3] = positions[:, 1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(data, positions,
extents)
weights = np.zeros(data.shape)
# TODO: flag these objects
if np.sum(ood_filter):
flux[ood_filter] = np.nan
warnings.warn(
"The aperture at position {0} does not have any "
"overlap with the data".format(positions[ood_filter]),
AstropyUserWarning)
if np.sum(ood_filter) == len(positions):
return (flux, )
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
use_exact = 1
subpixels = 1
fraction = circular_overlap_grid(x_pmin, x_pmax, y_pmin, y_pmax,
x_max - x_min, y_max - y_min, radius,
use_exact, subpixels)
yslice = slice(y_min[0], y_max[0])
xslice = slice(x_min[0], x_max[0])
weights[yslice, xslice] = fraction
return weights
def circular_photometry_weights(data, positions, radius):
"""
Return an array of weights corresponding to a circular aperture.
Parameters
----------
data : Not used in computation. Just for shape info
positions : (x,y) position of flux center recal x = column, y = rows
"""
extents = np.zeros((len(positions), 4), dtype=int)
extents[:,0] = positions[:,0] - radius + 0.5
extents[:,1] = positions[:,0] + radius + 1.5
extents[:,2] = positions[:,1] - radius + 0.5
extents[:,3] = positions[:,1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(data, positions, extents)
weights = np.zeros(data.shape)
# TODO: flag these objects
if np.sum(ood_filter):
flux[ood_filter] = np.nan
warnings.warn("The aperture at position {0} does not have any "
"overlap with the data"
.format(positions[ood_filter]),
AstropyUserWarning)
if np.sum(ood_filter) == len(positions):
return (flux, )
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
use_exact = 1
subpixels = 1
fraction = circular_overlap_grid(
x_pmin, x_pmax, y_pmin, y_pmax, x_max - x_min, y_max - y_min, radius,
use_exact, subpixels)
yslice = slice(y_min[0],y_max[0])
xslice = slice(x_min[0],x_max[0])
weights[yslice,xslice] = fraction
return weights
def to_mask(self, x_size, y_size):
"""
This function ...
:param x_size:
:param y_size:
:return:
"""
rel_center = self.center
x_min = - rel_center.x
x_max = x_size - rel_center.x
y_min = - rel_center.y
y_max = y_size - rel_center.y
fraction = circular_overlap_grid(x_min, x_max, y_min, y_max, x_size, y_size, self.radius, use_exact=0, subpixels=1)
# Return a new mask
return Mask(fraction)
def calc_masked_aperture(ap, image, method='mmm', mask=None):
positions = ap.positions
extents = np.zeros((len(positions), 4), dtype=int)
if isinstance(ap, EllipticalAnnulus):
radius = ap.a_out
elif isinstance(ap, CircularAnnulus):
radius = ap.r_out
elif isinstance(ap, CircularAperture):
radius = ap.r
elif isinstance(ap, EllipticalAperture):
radius = ap.a
extents[:, 0] = positions[:, 0] - radius + 0.5
extents[:, 1] = positions[:, 0] + radius + 1.5
extents[:, 2] = positions[:, 1] - radius + 0.5
extents[:, 3] = positions[:, 1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(image, positions,
extents)
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
bkg = np.zeros(len(positions))
area = np.zeros(len(positions))
for i in range(len(bkg)):
if isinstance(ap, EllipticalAnnulus):
fraction = elliptical_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.a_out, ap.b_out, ap.theta, 0,
1)
b_in = ap.a_in * ap.b_out / ap.a_out
fraction -= elliptical_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.a_in, b_in, ap.theta,
0, 1)
elif isinstance(ap, CircularAnnulus):
fraction = circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.r_out, 0, 1)
fraction -= circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.r_in, 0, 1)
elif isinstance(ap, CircularAperture):
fraction = circular_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.r, 0, 1)
elif isinstance(ap, EllipticalAperture):
fraction = elliptical_overlap_grid(x_pmin[i], x_pmax[i],
y_pmin[i], y_pmax[i],
x_max[i] - x_min[i],
y_max[i] - y_min[i],
ap.a, ap.b, ap.theta, 0,
1)
pixel_data = image[y_min[i]:y_max[i], x_min[i]:x_max[i]] * fraction
if mask is not None:
pixel_data[mask[y_min[i]:y_max[i], x_min[i]:x_max[i]]] = 0.0
good_pixels = pixel_data[pixel_data != 0.0].flatten()
if method == 'mmm':
skymod, skysigma, skew = mmm(good_pixels)
bkg[i] = skymod
elif method == 'sum':
bkg[i] = np.sum(good_pixels)
elif method == 'max':
bkg[i] = np.nanmax(good_pixels)
area[i] = len(good_pixels)
return bkg, area
def fpf_calculator(image,filetype,planet_position,radius,method='exact',subpix=20,plot=False,
no_planet_nghbr=True,name='fpf_test',save='False',save_dir='None', j=None):
####### PARAMETERS:
## image : fits OR 2d-array : (PynPointed) image where to perform the SNR & FPF calculation (as an array or a single fits file)
# n.b.: during the whole analysis the image is assumed to be centered on the central star.
## filetype : string : format of the image. Possibilities are: 'fits' or 'array'
## planet_position : array of two values : rough position of the target in (integer) pixels, as an array: [x,y] (n.b.: if the
# 'method' is 'exact' this position will be assumed to be the best position)
## radius : float : desired radius for the apertures (in pixels)
## method : string : how to search for the best position given the rough one. Possibilities are:
# 'exact' : the given planet_position is assumed to be the best one
# 'search' : the best position is found performing a search for the local maximum pixel value
# around the given planet_position in a square of side = (2 * r) * 2, rounded up
# (nb: the best position is found as integer pixels)
# 'fit' : the best position is found fitting a 2D gaussian on the given planet_position. The best
# position found in this way allows for floating pixels values.
## subpix : integer : how much refined the subpixel grid for the creation of the aperture should be. Each pixel is resampled in
# subpix*subpix other pixels. (Quick test showed that after a value of 10-15, the final results are
# quite stable, so the default is 20).
## plot : boolean : whether to plot or not the final image together with the created apertures, the SNR and the FPF value
## no_planet_nghbr : boolean : whether to consider or not the two background apertures near the signal aperture.
## name : string : desired name with which save the final result (if save==True).
## save : boolean : whether or not save the results. If true, two images will be saved as fits files: the initial image
# with the apertures, and the initial image plus the gaussian fit.
## save_dir : string : path to a folder where to save (if save==True) the images as fits files
##### OUTPUT:
## the function returns:
# fpf : float : value of the False Probability Fraction evaluated from the t_test value
# t_test : float : value of the t_test
# snr : float : value of the snr
# planet_pos : array of two values : best planet position (evaluated with the desired method) in pixels
# bckg_aps_cntr : multidimensional array : it contains (in pixel values) all the centers of ALL the apertures created
# for the analysis (including the signal aperture and the two apertures nearby). n.b.: the last is the
# center position of the signal aperture, i.e.: the best position (found with the desired method)
# fpf_bckgs : array : it contains the FPF values evaluated for all the background apertures with respect to each other.
# n.b.: the signal aperture is ALWAYS excluded, while the background apertures nearby are excluded only if requested
## if method == 'fit', it also returns:
# popt : array : best fit parameters found for the 2D gaussian fit (amplitude, xo, yo, sigma_x, sigma_y, theta, offset)
# pcov : 2d array : the estimated covariance of popt as returned by the function scipy.optimize.curve_fit
#############################################
#Let's import the image:
if filetype=='fits':
data=fits.open(image)[0].data #NB: the fits file must consist of a single image (NO datacube)!
if filetype=='array':
data=image
#Get the image size:
size = len(data[0])
#Define the center (i.e.: the image is supposed to be centered on the central star):
center=np.array([size/2.,size/2.])
#Round up the size of the range of search for the local maximum:
ros=math.ceil(radius)#*2) #* 2.
print 'ROS ',ros
#Let's find the planet position:
if method =='exact':
planet_pos=planet_position
if method == 'search':
planet_pos=planets_finder(data,'array','local_max',planet_position=planet_position,range_of_search=ros)[0]
if method == 'fit':
planet_pos_guess=planets_finder(data,'array','local_max',planet_position=planet_position,range_of_search=ros)[0]
#Create grid for the fit:
x = range(size)
y = range(size)
x, y = np.meshgrid(x, y)
sigma = (radius*2)/(2.*np.sqrt(2.*np.log(2.)))
#create arrays of initial guess:
#See which quadrant the planet is in, and give accordingly the correct additional factor for the arctan calculation:
if planet_position[0]>= size/2. and planet_position[1]>=size/2.: #first quadrant
arctan_fac=0.
angle_factor=90.
if planet_position[0]<=size/2. and planet_position[1]>=size/2.:#second quadrant
arctan_fac=180.
angle_factor=360.+90.
if planet_position[0]<=size/2. and planet_position[1]<=size/2.:#third quadrant
arctan_fac=180.
angle_factor=270.+180.
if planet_position[0]>=size/2. and planet_position[1]<=size/2.:#fourth quadrant
arctan_fac=360.
angle_factor=180.+270.
theta=np.deg2rad(angle_factor-(np.degrees(np.arctan((planet_position[1] - size/2.)/(planet_position[0] - size/2.))) + arctan_fac))
p0=[data[planet_pos_guess[1]][planet_pos_guess[0]],planet_pos_guess[0],planet_pos_guess[1],sigma,sigma,theta,0.]
print '\n\ninitial guess : '+str(p0)
popt, pcov = opt.curve_fit(twoD_Gaussian, (x, y), data.flatten(),p0=p0)
planet_pos=np.array([popt[1],popt[2]])
data_fitted=twoD_Gaussian((x,y),*popt)
print popt
#[planet_pos_guess[0]-5:planet_pos_guess[0]+5, planet_pos_guess[1]-5:planet_pos_guess[1]+5]
#let's calculate the distance between the planet and the star (i.e.: ASSUMING IMAGE CENTERING):
d=np.sqrt((planet_pos[0] - center[0])**2 + (planet_pos[1]-center[1])**2)
#Now, starting from the position of the planet, let's create a series of background apertures:
#Let's calculate how many apertures can I put at that distance and given a certain radius of the aperture:
n_bckg_aps=np.int((2*np.pi*d)/(2.*radius)) #NB: np.int assures that the number is rounded down to avoid overlaps
#Let's save the center positions of all the background apertures:
bckg_aps_cntr=np.ones((n_bckg_aps,2))
angle_i=360./n_bckg_aps
for i_apertures in range(0,n_bckg_aps):
bckg_aps_cntr[i_apertures]=angular_coords_float(center,planet_pos,angle_i)
angle_i=angle_i+(360./(n_bckg_aps))
#Define the area (given the radius):
area= np.pi * radius**2
#Create the apertures and calculate the weighted pixel values in all of them: (the LAST one is the signal aperture)
#Define some void arrays to be filled with the flux inside each aperture (i.e.: sum of all the weighted pixels),
# the single weighted pixel values for all the apertures, the fractions for to be multiplied for all the apertures
# and the not-weighted pixel values:
# flux = np.zeros(len(bckg_aps_cntr), dtype=np.float)
fractions=[]
bckg_values=[]
bckg_apertures=[]
signal_aperture=[]
#Let's define the extention of the region of interest for each aperture
extents = np.zeros((len(bckg_aps_cntr), 4), dtype=int)
extents[:, 0] = bckg_aps_cntr[:, 0] - radius + 0.5
extents[:, 1] = bckg_aps_cntr[:, 0] + radius + 1.5
extents[:, 2] = bckg_aps_cntr[:, 1] - radius + 0.5
extents[:, 3] = bckg_aps_cntr[:, 1] + radius + 1.5
ood_filter, extent, phot_extent = get_phot_extents(data, bckg_aps_cntr,extents)
x_min, x_max, y_min, y_max = extent
x_pmin, x_pmax, y_pmin, y_pmax = phot_extent
if no_planet_nghbr==True:
print 'Ignore the two apertures near the signal aperture'
#For each aperture, let's calculate the fraction values given by the intersection between the pixel region of interest
# and a circle of radius r, then use these fractions to evaluate the final weighted pixel values for each aperture:
for index in range(len(bckg_aps_cntr)):
fraction= geometry.circular_overlap_grid(x_pmin[index], x_pmax[index],
y_pmin[index], y_pmax[index],
x_max[index] - x_min[index],
y_max[index]- y_min[index],
radius, 0, subpix)
fractions.append(fraction)
#now, let's return the weighted pixel values but erasing the values ==0. (since the subpixel sampling can result
# in a fraction =0 and so the pixel value is weighted by 0. and so it is =0. But it is not really 0.)
#Ignore, if requested, the two apertures near the signal aperture:
if no_planet_nghbr==True:
if index != len(bckg_aps_cntr)-1 and index != len(bckg_aps_cntr)-2 and index != 0:
bckg_values += (filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
bckg_apertures.append(filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
if index==len(bckg_aps_cntr)-1:
signal_aperture += (filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
else:
if index != len(bckg_aps_cntr)-1:
bckg_values += (filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
bckg_apertures.append(filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
else:
signal_aperture += (filter(lambda a: a !=0.,np.array((data[y_min[index]:y_max[index],x_min[index]:x_max[index]] * fraction)).ravel()))
signal_aperture=np.array(signal_aperture)
bckg_values=np.array(bckg_values)
bckg_apertures=np.array(bckg_apertures)
##################################################################################
### SNR calculation (as in Meshkat et al. 2014)
snr=(np.sum(signal_aperture) - (np.mean(bckg_values)) * len(signal_aperture))/\
(np.std(bckg_values) * np.sqrt(len(signal_aperture)) )
##################################################################################
### t-test value calculation:
# Define the sample composed by the means inside the background apertures:
bckg_apertures_means=[]
bckg_apertures_fluxes=[]
for index_mean in range(len(bckg_apertures)):
bckg_apertures_means.append(np.sum(bckg_apertures[index_mean]) / area)
bckg_apertures_fluxes.append(np.sum(bckg_apertures[index_mean]))
bckg_apertures_means=np.array(bckg_apertures_means)
bckg_apertures_fluxes=np.array(bckg_apertures_fluxes)
#Calculate t-test value (according to Mawet et al. 2014):
# In this way, the value that I am assigning to each resolution element is the MEAN of the pixel values:
t_test=np.abs(((np.sum(signal_aperture)/area) - np.sum(bckg_apertures_means)/len(bckg_apertures_means))/\
(np.std(bckg_apertures_means) * np.sqrt(1. + 1./len(bckg_apertures_means))))
# #In this way, the value that I am assigning to each resolution element is the FLUX of the pixel values:
# t_test=np.abs(((np.sum(signal_aperture)) - np.sum(bckg_apertures_fluxes)/len(bckg_apertures_fluxes))/\
# (np.std(bckg_apertures_fluxes) * np.sqrt(1. + 1./len(bckg_apertures_fluxes))))
#Calculate the t-test value and fpf for all of the other background aperture (but always ignoring the signal one):
fpf_bckgs=np.zeros(len(bckg_apertures_means))
for i_t_test in range(len(bckg_apertures_means)):
bckg_apertures_means_i=np.delete(bckg_apertures_means,i_t_test)
t_test_i=np.abs((np.sum(bckg_apertures[i_t_test])/area - np.sum(bckg_apertures_means_i)/len(bckg_apertures_means_i))/\
(np.std(bckg_apertures_means_i) * np.sqrt(1. + 1./len(bckg_apertures_means_i))))
fpf_i= 1. - t.cdf(t_test_i,len(bckg_apertures_means_i)-1)
fpf_bckgs[i_t_test]=fpf_i
#Given the t-test value, calculate the false alarm probability:
# nb: define in this way, it is a ONE SIDE TEST!!
fpf= 1. - t.cdf(t_test,len(bckg_apertures_means)-1)
# print 'FPF : '+str(fpf)
##################################################################################
#Plot the image together with the apertures, if requested:
if plot ==True:
# these are matplotlib.patch.Patch properties:
props = dict(boxstyle='square', facecolor='white')
#Let's create all the circles:
#For the planet aperture:
signal_aperture=plt.Circle((planet_pos[0],planet_pos[1]),radius,color='Crimson',fill=False,linewidth=1)
fig = plt.gcf()
ax=fig.add_subplot(111)
plt.title(name,size=22)
plt.imshow(data,origin='lower',alpha=0.5)
fig.gca().add_artist(signal_aperture)
plt.hold(True)
if no_planet_nghbr==False:
for i_plot in range(n_bckg_aps-1):# the minus 1 is to exclude the planet aperture
background_aperture=plt.Circle((bckg_aps_cntr[i_plot][0],bckg_aps_cntr[i_plot][1]),radius,color='b',fill=False,linewidth=1)
fig.gca().add_artist(background_aperture)
if no_planet_nghbr==True:
for i_plot in range(n_bckg_aps):
if i_plot != 0 and i_plot != n_bckg_aps-1 and i_plot != n_bckg_aps-2:
background_aperture=plt.Circle((bckg_aps_cntr[i_plot][0],bckg_aps_cntr[i_plot][1]),radius,color='b',fill=False,linewidth=1)
fig.gca().add_artist(background_aperture)
plt.text(0.55,0.8,'FPF = '+str('%s' % float('%.2g' % fpf))+'\npos = ['+str('%s' % float('%.3g' % planet_pos[0]))+' , '+str('%s' % float('%.3g' % planet_pos[1]))+']'
,color='black',size=18,bbox=props,transform=ax.transAxes)
plt.xlim(0,size)
plt.ylim(0,size)
plt.colorbar()
if save==True:
plt.savefig(str(save_dir)+str(name)+'%s.pdf'%j,clobber=1)
plt.show()
#now, let's plot the gaussian fit:
if method=='fit':
fig, ax = plt.subplots(1, 1)
plt.title(name,size=22)
ax.hold(True)
ax.imshow(data,origin='lower',alpha=0.5)
ax.contour(x, y, data_fitted.reshape(size, size), 5, colors='k')
plt.text(0.55,0.85,'pos = ['+str('%s' % float('%.3g' % planet_pos[0]))+' , '+
str('%s' % float('%.3g' % planet_pos[1]))+']'
,color='black',size=18,bbox=props,transform=ax.transAxes)
plt.xlim(0,size)
plt.ylim(0,size)
if save==True:
plt.savefig(str(save_dir)+'fit/'+str(name)+'_FIT.pdf')
plt.show()
# if method=='fit':
# print 'Fit : '+str(popt)
#Save the result as an ASCII table:
names=['FPF','t_test','SNR','Planet_pos_x','Planet_pos_y','Method']
results=Table([[fpf],[t_test],[snr],[planet_pos[0]],[planet_pos[1]],[method]],names=names)
results_name=save_dir+str(name)+'.txt'
#Print the results:
results.pprint(max_lines=-1,max_width=-1,align='^')
#if requested, save the results
if save==True:
results.write(results_name,format='ascii.basic',delimiter='\t')
print 'The result has been saved in '+str(results_name)+'\n'
#return the final values:
if method!='fit':
return (fpf,t_test,snr,planet_pos,bckg_aps_cntr,fpf_bckgs)
if method=='fit':
return (fpf,t_test,snr,planet_pos,bckg_aps_cntr,fpf_bckgs,popt,pcov)
def time_circular_small_exact():
circular_overlap_grid(-4., 4., -4., 4., 10, 10, 3.,
use_exact=1, subpixels=1)
def time_circular_big_subpixel_5():
circular_overlap_grid(-4., 4., -4., 4., 100, 100, 3.,
use_exact=1, subpixels=5)