"""
Copyright (c) 2010-2018 CNRS / Centre de Recherche Astrophysique de Lyon
Copyright (c) 2012-2017 Laure Piqueras <laure.piqueras@univ-lyon1.fr>
Copyright (c) 2014-2019 Simon Conseil <simon.conseil@univ-lyon1.fr>
Copyright (c) 2016 Martin Shepherd <martin.shepherd@univ-lyon1.fr>
Copyright (c) 2016-2019 Roland Bacon <roland.bacon@univ-lyon1.fr>
Copyright (c) 2018-2019 Yannick Roehlly <yannick.roehlly@univ-lyon1.fr>
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software
without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""
import numpy as np
import types
import astropy.units as u
from astropy.io import fits
from astropy.stats import gaussian_sigma_to_fwhm, gaussian_fwhm_to_sigma
from astropy.convolution import convolve, Box1DKernel
from os.path import join, abspath, dirname
from scipy import interpolate, signal
from scipy.optimize import leastsq
from . import ABmag_filters, wavelet1D
from .arithmetic import ArithmeticMixin
from .data import DataArray
from .fitting import Gauss1D
from .objs import flux2mag
__all__ = ('Spectrum', 'vactoair', 'airtovac')
[docs]def vactoair(vacwl):
"""Calculate the approximate wavelength in air for vacuum wavelengths.
Parameters
----------
vacwl : ndarray
Vacuum wavelengths.
This uses an approximate formula from the IDL astronomy library
https://idlastro.gsfc.nasa.gov/ftp/pro/astro/vactoair.pro
"""
wave2 = vacwl * vacwl
n = 1.0 + 2.735182e-4 + 131.4182 / wave2 + 2.76249e8 / (wave2 * wave2)
# Do not extrapolate to very short wavelengths.
if not isinstance(vacwl, np.ndarray):
if vacwl < 2000:
n = 1.0
else:
ignore = np.where(vacwl < 2000)
n[ignore] = 1.0
return vacwl / n
[docs]def airtovac(airwl):
"""Convert air wavelengths to vacuum wavelengths.
Parameters
----------
vacwl : ndarray
Vacuum wavelengths.
This uses the IAU standard as implemented in the IDL astronomy library
https://idlastro.gsfc.nasa.gov/ftp/pro/astro/airtovac.pro
"""
sigma2 = (1e4 / airwl)**2. # Convert to wavenumber squared
n = 1.0 + (6.4328e-5 + 2.94981e-2 / (146. - sigma2) +
2.5540e-4 / (41. - sigma2))
if not isinstance(airwl, np.ndarray):
if airwl < 2000:
n = 1.0
else:
ignore = np.where(airwl < 2000)
n[ignore] = 1.0
return airwl * n
[docs]class Spectrum(ArithmeticMixin, DataArray):
"""Spectrum objects contain 1D arrays of numbers, optionally
accompanied by corresponding variances. These numbers represent
sample fluxes along a regularly spaced grid of wavelengths.
The spectral pixel values and their variances, if any, are
available as arrays[q that can be accessed via properties of the
Spectrum object called .data and .var, respectively. These arrays
are usually masked arrays, which share a boolean masking array
that can be accessed via a property called .mask. In principle,
these arrays can also be normal numpy arrays without masks, in
which case the .mask property holds the value,
numpy.ma.nomask. However non-masked arrays are only supported by a
subset of mpdaf functions at this time, so masked arrays should be
used where possible.
When a new Spectrum object is created, the data, variance and mask
arrays can either be specified as arguments, or the name of a FITS
file can be provided to load them from.
Parameters
----------
filename : string
An optional FITS file name from which to load the spectrum.
None by default. This argument is ignored if the data
argument is not None.
ext : int or (int,int) or string or (string,string)
The optional number/name of the data extension
or the numbers/names of the data and variance extensions.
wave : `mpdaf.obj.WaveCoord`
The wavelength coordinates of the spectrum.
unit : str or `astropy.units.Unit`
The physical units of the data values. Defaults to
`astropy.units.dimensionless_unscaled`.
data : float array
An optional 1 dimensional array containing the values of each
pixel of the spectrum, stored in ascending order of wavelength
(None by default). Where given, this array should be 1
dimensional.
var : float array
An optional 1 dimensional array containing the estimated
variances of each pixel of the spectrum, stored in ascending
order of wavelength (None by default).
Attributes
----------
filename : string
The name of the originating FITS file, if any. Otherwise None.
unit : `astropy.units.Unit`
The physical units of the data values.
primary_header : `astropy.io.fits.Header`
The FITS primary header instance, if a FITS file was provided.
data_header : `astropy.io.fits.Header`
The FITS header of the DATA extension.
wave : `mpdaf.obj.WaveCoord`
The wavelength coordinates of the spectrum.
"""
# Tell the DataArray base-class that Spectrum objects require 1 dimensional
# data arrays and wavelength coordinates.
_ndim_required = 1
_has_wave = True
[docs] def subspec(self, lmin, lmax=None, unit=u.angstrom):
"""Return the flux at a given wavelength, or the sub-spectrum
of a specified wavelength range.
A single flux value is returned if the lmax argument is None
(the default), or if the wavelengths assigned to the lmin and
lmax arguments are both within the same pixel. The value that
is returned is the value of the pixel whose wavelength is
closest to the wavelength specified by the lmin argument.
Note that is a wavelength range is asked for, a view on the original
spectrum is returned and both will be modified at the same time. If
you need to modify only the sub-spectrum, you'll need to copy() it
before.
Parameters
----------
lmin : float
The minimum wavelength of a wavelength range, or the wavelength
of a single pixel if lmax is None.
lmax : float or None
The maximum wavelength of the wavelength range.
unit : `astropy.units.Unit`
The wavelength units of the lmin and lmax arguments. The
default is angstroms. If unit is None, then lmin and lmax
are interpreted as array indexes within the spectrum.
Returns
-------
out : float or `~mpdaf.obj.Spectrum`
"""
if self.wave is None:
raise ValueError('Operation forbidden without world coordinates '
'along the spectral direction')
if lmax is None:
lmax = lmin
# Are lmin and lmax array indexes?
if unit is None:
pix_min = max(0, int(lmin + 0.5))
pix_max = min(self.shape[0], int(lmax + 0.5))
# Convert wavelengths to the nearest spectrum array indexes.
else:
pix_min = max(0, self.wave.pixel(lmin, nearest=True, unit=unit))
pix_max = min(self.shape[0],
self.wave.pixel(lmax, nearest=True, unit=unit) + 1)
# If the start and end of the wavelength range select the same pixel,
# return just the value of that pixel.
if (pix_min + 1) == pix_max:
return self[pix_min]
# Otherwise return a sub-spectrum.
else:
return self[pix_min:pix_max]
[docs] def get_step(self, unit=None):
"""Return the wavelength step size.
Parameters
----------
unit : `astropy.units.Unit`
The units of the returned step-size.
Returns
-------
out : float
The width of a spectrum pixel.
"""
if self.wave is not None:
return self.wave.get_step(unit)
[docs] def get_start(self, unit=None):
"""Return the wavelength value of the first pixel of the spectrum.
Parameters
----------
unit : `astropy.units.Unit`
The units of the returned wavelength.
Returns
-------
out : float
The wavelength of the first pixel of the spectrum.
"""
if self.wave is not None:
return self.wave.get_start(unit)
[docs] def get_end(self, unit=None):
"""Return the wavelength of the last pixel of the spectrum.
Parameters
----------
unit : `astropy.units.Unit`
The units of the returned wavelength.
Returns
-------
out : float
The wavelength of the final pixel of the spectrum.
"""
if self.wave is not None:
return self.wave.get_end(unit)
[docs] def get_range(self, unit=None):
"""Return the wavelength range (Lambda_min, Lambda_max) of the spectrum.
Parameters
----------
unit : `astropy.units.Unit`
The units of the returned wavelengths.
Returns
-------
out : float array
The minimum and maximum wavelengths.
"""
if self.wave is not None:
return self.wave.get_range(unit)
[docs] def mask_region(self, lmin=None, lmax=None, inside=True, unit=u.angstrom):
"""Mask spectrum pixels inside or outside a wavelength range, [lmin,lmax].
Parameters
----------
lmin : float
The minimum wavelength of the range, or None to choose the
wavelength of the first pixel in the spectrum.
lmax : float
The maximum wavelength of the range, or None to choose the
wavelength of the last pixel in the spectrum.
unit : `astropy.units.Unit`
The wavelength units of lmin and lmax. If None, lmin and
lmax are assumed to be pixel indexes.
inside : bool
If True, pixels inside the range [lmin,lmax] are masked.
If False, pixels outside the range [lmin,lmax] are masked.
"""
if self.wave is None:
raise ValueError('Operation forbidden without world coordinates '
'along the spectral direction')
else:
if lmin is None:
pix_min = 0
else:
if unit is None:
pix_min = max(0, int(lmin + 0.5))
else:
pix_min = max(0, self.wave.pixel(lmin, nearest=True,
unit=unit))
if lmax is None:
pix_max = self.shape[0]
else:
if unit is None:
pix_max = min(self.shape[0], int(lmax + 0.5))
else:
pix_max = min(self.shape[0],
self.wave.pixel(lmax, nearest=True,
unit=unit) + 1)
if inside:
self.data[pix_min:pix_max] = np.ma.masked
else:
self.data[:pix_min] = np.ma.masked
self.data[pix_max + 1:] = np.ma.masked
def _wavelengths_to_slice(self, lmin, lmax, unit):
"""Return the slice that selects a specified wavelength range.
Parameters
----------
lmin : float
The minimum wavelength of a wavelength range, or the wavelength
of a single pixel if lmax is None.
lmax : float or None
The maximum wavelength of the wavelength range.
unit : `astropy.units.Unit`
The wavelength units of the lmin and lmax arguments. The
default is angstroms. If unit is None, then lmin and lmax
are interpreted as array indexes within the spectrum.
Returns
-------
out : slice
The slice needed to select pixels within the specified wavelength
range.
"""
if unit is not None and self.wave is None:
raise ValueError('Operation forbidden without world coordinates '
'along the spectral direction')
# Get the pixel index that corresponds to the minimum wavelength.
if lmin is None:
i1 = 0
else:
if unit is None:
if lmin > self.shape[0]:
raise ValueError('Minimum and maximum wavelengths '
'are outside the spectrum range')
i1 = max(0, int(lmin + 0.5))
else:
i1 = self.wave.pixel(lmin, nearest=False, unit=unit)
if i1 > self.shape[0]:
raise ValueError('Minimum and maximum wavelengths '
'are outside the spectrum range')
i1 = self.wave.pixel(lmin, nearest=True, unit=unit)
# Get the pixel index that corresponds to the maximum wavelength.
if lmax is None:
i2 = self.shape[0]
else:
if unit is None:
if lmax < 0:
raise ValueError('Minimum and maximum wavelengths '
'are outside the spectrum range')
i2 = min(self.shape[0], int(lmax + 0.5))
else:
i2 = self.wave.pixel(lmax, nearest=False, unit=unit)
if i2 < 0:
raise ValueError('Minimum and maximum wavelengths '
'are outside the spectrum range')
i2 = self.wave.pixel(lmax, nearest=True, unit=unit) + 1
return slice(i1, i2)
def _interp(self, wavelengths, spline=False):
"""return the interpolated values corresponding to the wavelength
array.
Parameters
----------
wavelengths : array of float
wavelength values
unit : `astropy.units.Unit`
Type of the wavelength coordinates
spline : bool
False: linear interpolation (use `scipy.interpolate.interp1d`),
True: spline interpolation (use `scipy.interpolate.splrep`
and `scipy.interpolate.splev`).
"""
lbda = self.wave.coord()
data = np.pad(self.data.compressed(), 1, 'edge')
w = np.concatenate(([self.get_start() - 0.5 * self.get_step()],
np.compress(~self._mask, lbda),
[self.get_end() + 0.5 * self.get_step()]))
if spline:
if self._var is not None:
_weight = 1. / np.sqrt(np.abs(self.var.filled(np.inf)))
if self.mask is np.ma.nomask:
weight = np.empty(self.shape + 2, dtype=float)
weight[1:-1] = _weight
else:
ksel = np.where(self.mask == False)
weight = np.empty(np.shape(ksel)[1] + 2)
weight[1:-1] = _weight[ksel]
weight[0] = weight[1]
weight[-1] = weight[-2]
else:
weight = None
tck = interpolate.splrep(w, data, w=weight)
return interpolate.splev(wavelengths, tck, der=0)
else:
f = interpolate.interp1d(w, data)
return f(wavelengths)
def _interp_data(self, spline=False):
"""Return data array with interpolated values for masked pixels.
Parameters
----------
spline : bool
False: linear interpolation (use `scipy.interpolate.interp1d`),
True: spline interpolation (use `scipy.interpolate.splrep`
and `scipy.interpolate.splev`).
"""
if np.count_nonzero(self._mask) in (0, self.shape[0]):
return self._data
lbda = self.wave.coord()
wnew = lbda[self._mask]
data = self._data.copy()
data[self._mask] = self._interp(wnew, spline)
return data
[docs] def interp_mask(self, spline=False):
"""Interpolate masked pixels.
Parameters
----------
spline : bool
False: linear interpolation (use `scipy.interpolate.interp1d`),
True: spline interpolation (use `scipy.interpolate.splrep`
and `scipy.interpolate.splev`).
"""
self.data = np.ma.masked_invalid(self._interp_data(spline))
[docs] def rebin(self, factor, margin='center', inplace=False):
"""Combine neighboring pixels to reduce the size of a spectrum by an
integer factor.
Each output pixel is the mean of n pixels, where n is the
specified reduction factor.
Parameters
----------
factor : int
The integer reduction factor by which the spectrum should
be shrunk.
margin : string in 'center'|'right'|'left'|'origin'
When the dimension of the input spectrum is not an integer
multiple of the reduction factor, the spectrum is
truncated to remove just enough pixels that its length is
a multiple of the reduction factor. This sub-spectrum is
then rebinned in place of the original spectrum. The
margin parameter determines which pixels of the input
spectrum are truncated, and which remain.
The options are:
'origin' or 'center':
The start of the output spectrum is coincident
with the start of the input spectrum.
'center':
The center of the output spectrum is aligned
with the center of the input spectrum, within
one pixel.
'right':
The end of the output spectrum is coincident
with the end of the input spectrum.
inplace : bool
If False, return a rebinned copy of the spectrum (the default).
If True, rebin the original spectrum in-place, and return that.
Returns
-------
out : Spectrum
"""
# Delegate the rebinning to the generic DataArray function.
return self._rebin(factor, margin, inplace)
def _decimation_filter(self, newstep, atten, unit=None):
"""This is a private function Spectrum.resample(), used to apply
a decimation filter prior to resampling.
Parameters
----------
step : float
The new pixel size along the wavelength axis of the spectrum.
atten : float
The minimum attenuation (dB), of the antialiasing
decimation filter at the Nyquist folding frequency of the
new pixel size. Larger attenuations suppress aliasing
better at the expense of worsened resolution. A good value
to choose is 40dB, which produces a response that is very
similar to a blackman filter applied within the Fourier
plane, but with less ringing in the image plane.
unit : `astropy.units.Unit`
The wavelength units of the step argument. A value of None
is equivalent to specifying self.wave.unit.
"""
# Convert the attenuation from dB to a linear scale factor.
gcut = 10.0**(-atten / 20.0)
# Calculate the Nyquist folding frequency of the new pixel size.
nyquist_folding_freq = 0.5 / newstep
# Calculate the standard deviation of a Gaussian whose Fourier
# transform drops from unity at the center to gcut at the Nyquist
# folding frequency.
sigma = (0.5 / np.pi / nyquist_folding_freq *
np.sqrt(-2.0 * np.log(gcut)))
# Convert the standard deviation from wavelength units to input pixels.
sigma /= self.get_step(unit=unit)
# Choose dimensions for the gaussian filtering kernel. Choose an
# extent from -4*sigma to +4*sigma. This truncates the gaussian
# where it drops to about 3e-4 of its peak. The following
# calculation ensures that the dimensions of the array are odd, so
# that the gaussian will be symmetrically sampled either side of a
# central pixel. This prevents spectral shifts.
gshape = int(np.ceil(4.0 * sigma)) * 2 + 1
# fftconvolve requires that the kernel be no larger than the array
# that it is convolving, so reduce the size of the kernel array if
# needed. Be careful to choose an odd sized array.
n = self.shape[0]
if gshape > n:
gshape = n if n % 2 != 0 else (n - 1)
# Sample the gaussian filter symmetrically around the central pixel.
gx = np.arange(gshape, dtype=float) - gshape // 2
gy = np.exp(-0.5 * (gx / sigma)**2)
# Area-normalize the gaussian profile.
gy /= gy.sum()
# Filter the spectrum with the gaussian filter.
self.fftconvolve(gy, inplace=True)
[docs] def resample(self, step, start=None, shape=None, unit=u.angstrom,
inplace=False, atten=40.0, cutoff=0.25):
"""Resample a spectrum to have a different wavelength interval.
Parameters
----------
step : float
The new pixel size along the wavelength axis of the spectrum.
start : float
The wavelength at the center of the first pixel of the resampled
spectrum. If None (the default) the center of the first pixel
has the same wavelength before and after resampling.
unit : `astropy.units.Unit`
The wavelength units of the step and start arguments.
The default is u.angstrom.
shape : int
The dimension of the array of the new spectrum (ie. the number
of spectral pixels). If this is not specified, the shape is
selected to encompass the wavelength range from the chosen
start wavelength to the ending wavelength of the input spectrum.
inplace : bool
If False, return a resampled copy of the spectrum (the default).
If True, resample the original spectrum in-place, and return that.
atten : float
The minimum attenuation (dB), of the antialiasing
decimation filter at the Nyquist folding frequency of the
new pixel size. Larger attenuations suppress aliasing
better at the expense of worsened resolution. The default
attenuation is 40.0 dB. To disable antialiasing, specify
atten=0.0.
cutoff : float
Mask each output pixel of which at least this fraction of the
pixel was interpolated from masked input pixels.
Returns
-------
out : Spectrum
"""
out = self if inplace else self.copy()
# Don't allow the spectrum to be started beyond the far end of
# the spectrum, because this would result in an empty spectrum.
if start is not None and start > self.get_end(unit):
raise ValueError('The start value is past the end of the '
'spectrum range')
# Get wavelength world coordinates of the output spectrum.
newwave = self.wave.resample(step, start, unit)
# How many pixels should there be in the resampled spectrum?
# If the user didn't specify this, use newwave.shape, which
# holds the number of pixels of size 'step' needed to sample
# from 'start' to the end of the current wavelength range.
if shape is not None:
newwave.shape = shape
# Get the existing wavelength step size in the new units.
oldstep = self.wave.get_step(unit)
# If the spectrum is being resampled to a larger pixel size,
# then a decimation filter should be applied before
# resampling, to ensure that the new pixel size doesn't
# undersample rapidly changing features in the spectrum.
if step > oldstep and atten > 0.0:
out._decimation_filter(step, atten, unit=unit)
# Get the data, mask (and variance) arrays, and replace bad pixels with
# zeros.
if out._mask is not None: # Is out.data a masked array?
data = out.data.filled(0.0)
if out._var is not None:
var = out.var.filled(0.0)
else:
var = None
mask = out._mask
else: # Is out.data just a numpy array?
mask = ~np.isfinite(out._data)
data = out._data.copy()
data[mask] = 0.0
if out.var is not None:
var = out.var.copy()
var[mask] = 0.0
else:
var = None
# Get the coordinates of the pixels of the input and output spectra.
xi = self.wave.coord()
xo = newwave.coord()
# Get a resampled versions of the data array, optionally the variance
# array, and a floating point version of the mask array. Note that the
# choice of linear interpolation is required to preserve flux.
data = interpolate.griddata(xi, data, xo, method="linear",
fill_value=np.nan)
if var is not None:
var = interpolate.griddata(xi, var, xo, method="linear",
fill_value=np.nan)
mask = interpolate.griddata(xi, mask.astype(float), xo,
method="linear", fill_value=1.0)
# Create a new boolean mask in which all pixels that had an integrated
# contribution of more than 'cutoff' originally masked pixels are
# masked. Note that setting the cutoff to the "obvious" value of zero
# results in lots of pixels being masked that are far away from any
# masked pixels, due to precision errors in the griddata()
# function. Limit the minimum value of the cutoff to avoid this.
mask = np.greater(mask, max(cutoff, 1.0e-6))
# If masked arrays were not in use in the original spectrum, fill
# bad pixels with NaNs.
if out._mask is None:
data[mask] = np.nan
if var is not None:
var[mask] = np.nan
mask = None
# Install the resampled arrays.
out._data = data
out._var = var
out._mask = mask
# Install the new wavelength world coordinates.
out.wave = newwave
# When up-sampling, decimation filter the output spectrum. The
# combination of this and the linear interpolation of the preceding
# griddata() produces a much better interpolation than a cubic spline
# filter can. In particular, a spline interpolation does not conserve
# flux, whereas linear interpolation plus decimation filtering does.
if step < oldstep and atten > 0.0:
out._decimation_filter(step, atten, unit=unit)
return out
[docs] def mean(self, lmin=None, lmax=None, weight=True, unit=u.angstrom):
"""Compute the mean flux over a specified wavelength range.
Parameters
----------
lmin : float
The minimum wavelength of the range, or None to choose the
wavelength of the first pixel in the spectrum.
lmax : float
The maximum wavelength of the range, or None to choose the
wavelength of the last pixel in the spectrum.
unit : `astropy.units.Unit`
The wavelength units of lmin and lmax. If None, lmin and
lmax are assumed to be pixel indexes.
weight : bool
If weight is True, compute the weighted mean, inversely
weighting each pixel by its variance.
Returns
-------
out : (float, float)
The mean flux and its error.
"""
# Don't attempt to perform a weighted mean if there are no variances.
if self._var is None:
weight = False
# Get the slice that selects the specified wavelength range.
try:
lambda_slice = self._wavelengths_to_slice(lmin, lmax, unit)
except ValueError:
return (0.0, np.inf)
# Obtain the mean flux of the sub-spectrum.
if weight:
weights = 1.0 / self.var[lambda_slice].filled(np.inf)
flux, wsum = np.ma.average(self.data[lambda_slice],
weights=weights, returned=True)
if self.var is not None:
err_flux = np.sqrt(
np.ma.sum(self.var[lambda_slice] * weights**2) / wsum**2)
else:
err_flux = np.inf
else:
flux, wsum = np.ma.average(self.data[lambda_slice], returned=True)
if self.var is not None:
err_flux = np.sqrt(np.ma.sum(self.var[lambda_slice])) / wsum**2
else:
err_flux = np.inf
return (flux, err_flux)
[docs] def sum(self, lmin=None, lmax=None, weight=True, unit=u.angstrom):
"""Obtain the sum of the fluxes within a specified wavelength range.
Parameters
----------
lmin : float
The minimum wavelength of the range, or None to choose the
wavelength of the first pixel in the spectrum.
lmax : float
The maximum wavelength of the range, or None to choose the
wavelength of the last pixel in the spectrum.
unit : `astropy.units.Unit`
The wavelength units of lmin and lmax. If None, lmin and
lmax are assumed to be pixel indexes.
weight : bool
If weight is True, compute the weighted sum, inversely
weighting each pixel by its variance.
Returns
-------
out : float, float
The total flux and its error.
"""
# Get the slice that selects the specified wavelength range.
try:
lambda_slice = self._wavelengths_to_slice(lmin, lmax, unit)
except ValueError:
return (0.0, np.inf)
# Perform a weighted sum?
if weight and self._var is not None:
weights = 1.0 / self.var[lambda_slice].filled(np.inf)
# How many unmasked pixels will be averaged?
nsum = np.ma.count(self.data[lambda_slice])
fmean, wsum = np.ma.average(self.data[lambda_slice],
weights=weights, returned=True)
# The weighted average multiplied by the number of unmasked pixels.
flux = fmean * nsum
if self.var is not None:
err_flux = np.sqrt(
np.ma.sum(self.var[lambda_slice] * weights**2) /
wsum**2 * nsum**2)
else:
err_flux = np.inf
else:
flux = self.data[lambda_slice].sum()
if self.var is not None:
err_flux = np.sqrt(np.ma.sum(self.var[lambda_slice]))
else:
err_flux = np.inf
return (flux, err_flux)
[docs] def integrate(self, lmin=None, lmax=None, unit=u.angstrom):
"""Integrate the flux over a specified wavelength range.
The units of the integrated flux depend on the flux units of
the spectrum and the wavelength units, as follows:
If the flux units of the spectrum, self.unit, are something
like Q per angstrom, Q per nm, or Q per um, then the
integrated flux will have the units of Q. For example, if the
fluxes have units of 1e-20 erg/cm2/Angstrom/s, then the units
of the integration will be 1e-20 erg/cm2/s.
Alternatively, if unit is not None, then the unit of the
returned number will be the product of the units in self.unit
and unit. For example, if the flux units are counts/s, and
unit=u.angstrom, then the integrated flux will have units
counts*Angstrom/s.
Finally, if unit is None, then the units of the returned
number will be the product of self.unit and the units of the
wavelength axis of the spectrum (ie. self.wave.unit).
The result of the integration is returned as an astropy
Quantity, which holds the integrated value and its physical
units. The units of the returned number can be determined
from the .unit attribute of the return value. Alternatively
the returned value can be converted to another unit, using the
to() method of astropy quantities.
Parameters
----------
lmin : float
The minimum wavelength of the range to be integrated,
or None (the default), to select the minimum wavelength
of the first pixel of the spectrum. If this is below the
minimum wavelength of the spectrum, the integration
behaves as though the flux in the first pixel extended
down to that wavelength.
If the unit argument is None, lmin is a pixel index, and
the wavelength of the center of this pixel is used as the
lower wavelength of the integration.
lmax : float
The maximum wavelength of the range to be integrated,
or None (the default), to select the maximum wavelength
of the last pixel of the spectrum. If this is above the
maximum wavelength of the spectrum, the integration
behaves as though the flux in the last pixel extended
up to that wavelength.
If the unit argument is None, lmax is a pixel index, and
the wavelength of the center of this pixel is used as the
upper wavelength of the integration.
unit : `astropy.units.Unit`
The wavelength units of lmin and lmax, or None to indicate
that lmin and lmax are pixel indexes.
Returns
-------
out : `astropy.units.Quantity`, `astropy.units.Quantity`
The result of the integration and its error, expressed as
a floating point number with accompanying units. The integrated
value and its physical units can be extracted using the .value and
.unit attributes of the returned quantity. The value can also be
converted to different units, using the .to() method of the
returned objected.
"""
# Get the index of the first pixel within the wavelength range,
# and the minimum wavelength of the integration.
if lmin is None:
i1 = 0
lmin = self.wave.coord(-0.5, unit=unit)
else:
if unit is None:
l1 = lmin
lmin = self.wave.coord(max(-0.5, l1))
else:
l1 = self.wave.pixel(lmin, False, unit)
i1 = max(0, int(l1))
# Get the index of the last pixel within the wavelength range, plus
# 1, and the maximum wavelength of the integration.
if lmax is None:
i2 = self.shape[0]
lmax = self.wave.coord(i2 - 0.5, unit=unit)
else:
if unit is None:
l2 = lmax
lmax = self.wave.coord(min(self.shape[0] - 0.5, l2))
else:
l2 = self.wave.pixel(lmax, False, unit)
i2 = min(self.shape[0], int(l2) + 1)
# Get the lower wavelength of each pixel, including one extra
# pixel at the end of the range.
d = self.wave.coord(-0.5 + np.arange(i1, i2 + 1), unit=unit)
# Change the wavelengths of the first and last pixels to
# truncate or extend those pixels to the starting and ending
# wavelengths of the spectrum.
d[0] = lmin
d[-1] = lmax
if unit is None:
unit = self.wave.unit
# Get the data of the subspectrum covered by the integration.
data = self.data[i1:i2]
# If the spectrum has been calibrated, the flux units will be
# per angstrom, per nm, per um etc. If these wavelength units
# don't match the units of the wavelength axis of the
# integration, then although the results will be correct, they
# will have inconvenient units. In such cases attempt to
# convert the units of the wavelength axis to match the flux
# units.
if unit in self.unit.bases: # The wavelength units already agree.
out_unit = self.unit * unit
else:
try:
# Attempt to determine the wavelength units of the flux density
wunit = (set(self.unit.bases) &
set([u.pm, u.angstrom, u.nm, u.um])).pop()
# Scale the wavelength axis to have the same wavelength units.
d *= unit.to(wunit)
# Get the final units of the integration.
out_unit = self.unit * wunit
# If the wavelength units of the flux weren't recognized,
# simply return the units unchanged.
except Exception:
out_unit = self.unit * unit
# Integrate the spectrum by multiplying the value of each pixel
# by the difference in wavelength from the start of that pixel to
# the start of the next pixel.
flux = (data * np.diff(d)).sum() * out_unit
if self.var is None:
err_flux = np.inf
else:
err_flux = np.sqrt((self.var[i1:i2] * np.diff(d)**2).sum())
return (flux, err_flux * out_unit)
[docs] def poly_fit(self, deg, weight=True, maxiter=0,
nsig=(-3.0, 3.0), verbose=False):
"""Perform polynomial fit on normalized spectrum and returns polynomial
coefficients.
Parameters
----------
deg : int
Polynomial degree.
weight : bool
If weight is True, the weight is computed as the inverse of
variance.
maxiter : int
Maximum allowed iterations (0)
nsig : (float,float)
The low and high rejection factor in std units (-3.0,3.0)
Returns
-------
out : ndarray, shape.
Polynomial coefficients ordered from low to high.
"""
if self.shape[0] <= deg + 1:
raise ValueError('Too few points to perform polynomial fit')
if self._var is None:
weight = False
if weight:
vec_weight = 1.0 / np.sqrt(np.abs(self.var.filled(np.inf)))
else:
vec_weight = None
if self._mask is np.ma.nomask:
d = self._data
w = self.wave.coord()
else:
mask = ~self._mask
d = self._data[mask]
w = self.wave.coord()[mask]
if weight:
vec_weight = vec_weight[mask]
# normalize w
w0 = np.min(w)
dw = np.max(w) - w0
w = (w - w0) / dw
p = np.polynomial.polynomial.polyfit(w, d, deg, w=vec_weight)
if maxiter > 0:
err = d - np.polynomial.polynomial.polyval(w, p)
sig = np.std(err)
n_p = len(d)
for it in range(maxiter):
ind = np.where((err >= nsig[0] * sig) &
(np.abs(err) <= nsig[1] * sig))
if len(ind[0]) == n_p:
break
if len(ind[0]) <= deg + 1:
raise ValueError('Too few points to perform '
'polynomial fit')
if vec_weight is not None:
vec_weight = vec_weight[ind]
p = np.polynomial.polynomial.polyfit(w[ind], d[ind],
deg, w=vec_weight)
err = d[ind] - np.polynomial.polynomial.polyval(w[ind], p)
sig = np.std(err)
n_p = len(ind[0])
if verbose:
self._logger.info('Number of iteration: %d Std: %10.4e '
'Np: %d Frac: %4.2f', it + 1, sig, n_p,
100. * n_p / self.shape[0])
return p
[docs] def poly_val(self, z):
"""Update in place the spectrum data from polynomial coefficients.
Uses `numpy.poly1d`.
Parameters
----------
z : array
The polynomial coefficients, in increasing powers:
data = z0 + z1(lbda-min(lbda))/(max(lbda)-min(lbda)) + ...
+ zn ((lbda-min(lbda))/(max(lbda)-min(lbda)))**n
"""
l = self.wave.coord()
w0 = np.min(l)
dw = np.max(l) - w0
w = (l - w0) / dw
self._data = np.polynomial.polynomial.polyval(w, z)
if self._mask is not np.ma.nomask:
self._mask = ~(np.isfinite(self._data))
self._var = None
[docs] def poly_spec(self, deg, weight=True, maxiter=0,
nsig=(-3.0, 3.0), verbose=False):
"""Return a spectrum containing a polynomial fit.
Parameters
----------
deg : int
Polynomial degree.
weight : bool
If weight is True, the weight is computed as the inverse of
variance.
maxiter : int
Maximum allowed iterations (0)
nsig : (float,float)
The low and high rejection factor in std units (-3.0,3.0)
Returns
-------
out : Spectrum
"""
z = self.poly_fit(deg, weight, maxiter, nsig, verbose)
res = self.clone()
res.poly_val(z)
return res
[docs] def abmag_band(self, lbda, dlbda):
"""Compute AB magnitude corresponding to the wavelength band.
Parameters
----------
lbda : float
Mean wavelength in Angstrom.
dlbda : float
Width of the wavelength band in Angstrom.
Returns
-------
out : float, float
Magnitude value and its error
"""
vflux, err_flux = self.mean(lmin=lbda - dlbda / 2.0,
lmax=lbda + dlbda / 2.0,
weight=None, unit=u.angstrom)
if vflux == 0:
return (99, 0)
else:
unit = u.Unit('erg.s-1.cm-2.Angstrom-1')
vflux2 = (vflux * self.unit).to(unit)
err_flux2 = (err_flux * self.unit).to(unit)
return flux2mag(vflux2.value, err_flux2.value, lbda)
[docs] def abmag_filter_name(self, name):
"""Compute AB magnitude using the filter name.
Parameters
----------
name : string
'U', 'B', 'V', 'Rc', 'Ic', 'z', 'R-Johnson',
'F606W', 'F775W', 'F814W', 'F850LP'
Returns
-------
out : float, float
Magnitude value and its error
"""
if name == 'U':
return self.abmag_band(3663., 650.)
elif name == 'B':
return self.abmag_band(4361., 890.)
elif name == 'V':
return self.abmag_band(5448., 840.)
elif name == 'Rc':
return self.abmag_band(6410., 1600.)
elif name == 'Ic':
return self.abmag_band(7980., 1500.)
elif name == 'z':
return self.abmag_band(8930., 1470.)
elif name == 'R-Johnson':
(l0, lmin, lmax, tck) = ABmag_filters.mag_RJohnson()
return self._filter(l0, lmin, lmax, tck)
else:
FILTERS = join(abspath(dirname(__file__)), 'filters',
'filter_list.fits')
filtname = 'ACS_' + name
with fits.open(FILTERS) as hdul:
if filtname not in hdul:
raise ValueError("filter '{}' not found".format(filtname))
lbda = hdul[filtname].data['lambda']
thr = hdul[filtname].data['throughput']
return self.abmag_filter(lbda, thr)
[docs] def abmag_filter(self, lbda, eff):
"""Compute AB magnitude using array filter.
Parameters
----------
lbda : float array
Wavelength values in Angstrom.
eff : float array
Efficiency values.
Returns
-------
out : float, float
Magnitude value and its error
"""
lbda = np.asarray(lbda)
eff = np.asarray(eff)
if np.shape(lbda) != np.shape(eff):
raise TypeError('lbda and eff inputs have not the same size.')
l0 = np.average(lbda, weights=eff)
lmin = lbda[0]
lmax = lbda[-1]
k = 3 if lbda.shape[0] > 3 else 1
tck = interpolate.splrep(lbda, eff, k=k)
return self._filter(l0, lmin, lmax, tck)
def _filter(self, l0, lmin, lmax, tck):
"""Compute AB magnitude.
Parameters
----------
l0 : float
Mean wavelength in Angstrom.
lmin : float
Minimum wavelength in Angstrom.
lmax : float
Maximum wavelength in Angstrom.
tck : 3-tuple
(t,c,k) contains the spline representation. t = the knot-points,
c = coefficients and k = the order of the spline.
"""
try:
lambda_slice = self._wavelengths_to_slice(lmin, lmax, u.Angstrom)
except ValueError:
raise ValueError('Spectrum outside Filter band')
if lambda_slice.start == (lambda_slice.stop - 1):
raise ValueError('Filter band smaller than spectrum step')
lb = self.wave.coord(np.arange(lambda_slice.start, lambda_slice.stop),
unit=u.Angstrom)
w = interpolate.splev(lb, tck, der=0)
vflux, wsum = np.ma.average(self.data[lambda_slice], weights=w,
returned=True)
if self.var is not None:
err_flux = np.sqrt(np.ma.sum(self.var[lambda_slice] * w**2) /
wsum**2)
else:
err_flux = np.inf
unit = u.Unit('erg.s-1.cm-2.Angstrom-1')
vflux2 = (vflux * self.unit).to(unit)
err_flux2 = (err_flux * self.unit).to(unit)
return flux2mag(vflux2.value, err_flux2.value, l0)
[docs] def wavelet_filter(self, levels=9, sigmaCutoff=5.0, epsilon=0.05,
inplace=False):
"""Perform a wavelet filtering on the spectrum in 1 dimension.
Code contributed by Markus Rexroth (EPFL, 2016), and used in
https://arxiv.org/abs/1703.09239 (with funding from ERC Advanced
Grant LIDA, Swiss National Science Foundation, ERC Starting Grant
336736-CALENDS).
Parameters
----------
levels : int
Highest scale level.
sigmaCutoff : float
Cleaning threshold.
By default 5 for a 5 sigma cleaning in wavelet space.
epsilon : float in ]0,1[
Residual criterion used to perform the cleaning
inplace : bool
If False, return a filtered copy of the spectrum (the default).
If True, filter the original spectrum in-place, and return that.
Returns
-------
out : Spectrum
"""
res = self if inplace else self.copy()
deNoisedSignal = wavelet1D.cleanSignal(self._data, np.sqrt(self._var),
levels, sigmaCutoff=sigmaCutoff,
epsilon=epsilon)
res._data = deNoisedSignal
res._var = None
return res
[docs] def truncate(self, lmin=None, lmax=None, unit=u.angstrom):
"""Truncate the wavelength range of a spectrum in-place.
Parameters
----------
lmin : float
The minimum wavelength of a wavelength range, or the wavelength
of a single pixel if lmax is None.
lmax : float or None
The maximum wavelength of the wavelength range.
unit : `astropy.units.Unit`
The wavelength units of the lmin and lmax arguments. The
default is angstroms. If unit is None, then lmin and lmax
are interpreted as array indexes within the spectrum.
"""
# Get the slice that selects the specified wavelength range.
lambda_slice = self._wavelengths_to_slice(lmin, lmax, unit)
if lambda_slice.start == (lambda_slice.stop - 1):
raise ValueError('Minimum and maximum wavelengths are equal')
res = self[lambda_slice]
self._data = res._data
self._var = res._var
self._mask = res._mask
self.wave = res.wave
[docs] def fwhm(self, l0, cont=0, spline=False, unit=u.angstrom):
"""Return the fwhm of a peak.
Parameters
----------
l0 : float
Wavelength value corresponding to the peak position.
unit : `astropy.units.Unit`
Type of the wavelength coordinates. If None, inputs are in pixels.
cont : int
The continuum [default 0].
spline : bool
Linear/spline interpolation to interpolate masked values.
Returns
-------
out : float
"""
if unit is None:
k0 = int(l0 + 0.5)
step = 1
else:
k0 = self.wave.pixel(l0, nearest=True, unit=unit)
step = self.wave.get_step(unit=unit)
d = self._interp_data(spline) - cont
f2 = d[k0] / 2
try:
k2 = np.argwhere(d[k0:-1] < f2)[0][0] + k0
i2 = np.interp(f2, d[k2:k2 - 2:-1], [k2, k2 - 1])
k1 = k0 - np.argwhere(d[k0:-1] < f2)[0][0]
i1 = np.interp(f2, d[k1:k1 + 2], [k1, k1 + 1])
fwhm = (i2 - i1) * step
return fwhm
except Exception:
try:
k2 = np.argwhere(d[k0:-1] > f2)[0][0] + k0
i2 = np.interp(f2, d[k2:k2 - 2:-1], [k2, k2 - 1])
k1 = k0 - np.argwhere(d[k0:-1] > f2)[0][0]
i1 = np.interp(f2, d[k1:k1 + 2], [k1, k1 + 1])
fwhm = (i2 - i1) * step
return fwhm
except Exception:
raise ValueError('Error in fwhm estimation')
[docs] def gauss_fit(self, lmin, lmax, lpeak=None, flux=None, fwhm=None,
cont=None, peak=False, spline=False, weight=True,
plot=False, plot_factor=10, unit=u.angstrom,
fix_lpeak=False):
"""Perform a Gaussian fit.
Uses `scipy.optimize.leastsq` to minimize the sum of squares.
Parameters
----------
lmin : float or (float,float)
Minimum wavelength value or wavelength range
used to initialize the gaussian left value (in angstrom)
lmax : float or (float,float)
Maximum wavelength or wavelength range
used to initialize the gaussian right value (in angstrom)
lpeak : float
Input gaussian center (in angstrom), if None it is estimated
with the wavelength corresponding to the maximum value
in [max(lmin), min(lmax)]
unit : `astropy.units.Unit`
Type of the wavelength coordinates. If None, inputs are in pixels.
flux : float
Integrated gaussian flux or gaussian peak value if peak is True.
fwhm : float
Input gaussian fwhm (in angstrom), if None it is estimated.
peak : bool
If true, flux contains the gaussian peak value .
cont : float
Continuum value, if None it is estimated by the line through points
(max(lmin),mean(data[lmin])) and (min(lmax),mean(data[lmax])).
spline : bool
Linear/spline interpolation to interpolate masked values.
weight : bool
If weight is True, the weight is computed as the inverse of
variance.
plot : bool
If True, the Gaussian is plotted.
plot_factor : double
oversampling factor for the overplotted fit
Returns
-------
out : `mpdaf.obj.Gauss1D`
"""
# truncate the spectrum and compute right and left gaussian values
if np.isscalar(lmin):
fmin = None
else:
lmin = np.array(lmin, dtype=float)
fmin = self.mean(lmin[0], lmin[1], unit=unit)[0]
lmin = (lmin[0] + lmin[1]) / 2.
if np.isscalar(lmax):
fmax = None
else:
lmax = np.array(lmax, dtype=float)
fmax = self.mean(lmax[0], lmax[1], unit=unit)[0]
lmax = (lmax[0] + lmax[1]) / 2.
spec = self.subspec(lmin, lmax, unit=unit)
data = spec._interp_data(spline)
if unit is None:
l = np.arange(self.shape, dtype=float)
else:
l = spec.wave.coord(unit=unit)
lmin = l[0]
lmax = l[-1]
if fmin is None:
fmin = data[0]
if fmax is None:
fmax = data[-1]
# initial gaussian peak position
if lpeak is None:
lpeak = l[data.argmax()]
# continuum value
if cont is None:
cont0 = ((fmax - fmin) * lpeak + lmax *
fmin - lmin * fmax) / (lmax - lmin)
else:
cont0 = cont
# initial sigma value
if fwhm is None:
try:
fwhm = spec.fwhm(lpeak, cont0, spline, unit=unit)
except Exception:
lpeak2 = l[data.argmin()]
fwhm = spec.fwhm(lpeak2, cont0, spline, unit=unit)
sigma = fwhm * gaussian_fwhm_to_sigma
# initial gaussian integrated flux
if flux is None:
if unit is None:
pixel = int(lpeak + 0.5)
else:
pixel = spec.wave.pixel(lpeak, nearest=True, unit=unit)
peak = data[pixel] - cont0
flux = peak * np.sqrt(2 * np.pi * (sigma ** 2))
elif peak is True:
peak = flux - cont0
flux = peak * np.sqrt(2 * np.pi * (sigma ** 2))
else:
pass
# 1d gaussian function: p = (ampl, sigma, center)
if fix_lpeak:
if cont is None:
gaussfit = lambda p, x: \
((fmax - fmin) * x + lmax * fmin - lmin * fmax) \
/ (lmax - lmin) + np.abs(p[0]) \
* (1 / np.sqrt(2 * np.pi * (p[1] ** 2))) \
* np.exp(-(x - lpeak) ** 2 / (2 * p[1] ** 2))
else:
gaussfit = lambda p, x: \
cont + p[0] * (1 / np.sqrt(2 * np.pi * (p[1] ** 2))) \
* np.exp(-(x - lpeak) ** 2 / (2 * p[1] ** 2))
else:
if cont is None:
gaussfit = lambda p, x: \
((fmax - fmin) * x + lmax * fmin - lmin * fmax) \
/ (lmax - lmin) + p[0] \
* (1 / np.sqrt(2 * np.pi * (p[1] ** 2))) \
* np.exp(-(x - p[2]) ** 2 / (2 * p[1] ** 2))
else:
gaussfit = lambda p, x: \
cont + p[0] * (1 / np.sqrt(2 * np.pi * (p[1] ** 2))) \
* np.exp(-(x - p[2]) ** 2 / (2 * p[1] ** 2))
if spec.var is not None and weight:
wght = 1.0 / np.sqrt(np.abs(spec.var))
np.ma.fix_invalid(wght, copy=False, fill_value=0)
else:
wght = np.ones(spec.shape)
# inital guesses for Gaussian Fit
v0 = [flux, sigma]
if not fix_lpeak:
v0.append(lpeak)
# Minimize the sum of squares
e_gauss_fit = lambda p, x, y, w: w * (gaussfit(p, x) - y)
v, covar, info, mesg, success = leastsq(e_gauss_fit, v0[:],
args=(l, data, wght),
maxfev=100000, full_output=1)
# calculate the errors from the estimated covariance matrix
chisq = sum(info["fvec"] * info["fvec"])
dof = len(info["fvec"]) - len(v)
if covar is not None:
err = np.array([np.sqrt(np.abs(covar[i, i])) *
np.sqrt(np.abs(chisq / dof))
for i in range(len(v))])
else:
err = [np.nan] * len(v)
if plot:
import matplotlib.pyplot as plt
xxx = np.arange(l[0], l[-1], (l[1] - l[0]) / plot_factor)
ccc = gaussfit(v, xxx)
plt.plot(xxx, ccc, 'r--')
# return a Gauss1D object
v = list(v)
err = list(err)
if not fix_lpeak:
lpeak = v.pop()
err_lpeak = err.pop()
else:
err_lpeak = 0
flux, sigma = v[0], np.abs(v[1])
fwhm = sigma * gaussian_sigma_to_fwhm
peak = flux / np.sqrt(2 * np.pi * (sigma ** 2))
err_flux, err_sigma = err
err_fwhm = err_sigma * gaussian_sigma_to_fwhm
err_peak = np.abs(1. / np.sqrt(2 * np.pi) *
(err_flux * sigma - flux * err_sigma) /
sigma / sigma)
return Gauss1D(lpeak, peak, flux, fwhm, cont0, err_lpeak,
err_peak, err_flux, err_fwhm, chisq, dof)
[docs] def add_gaussian(self, lpeak, flux, fwhm, cont=0, peak=False,
unit=u.angstrom):
"""Add a gaussian on spectrum in place.
Parameters
----------
lpeak : float
Gaussian center.
flux : float
Integrated gaussian flux or gaussian peak value if peak is True.
fwhm : float
Gaussian fwhm.
cont : float
Continuum value.
peak : bool
If true, flux contains the gaussian peak value
unit : `astropy.units.Unit`
Type of the wavelength coordinates. If None, inputs are in pixels.
"""
gauss = lambda p, x: cont \
+ p[0] * (1 / np.sqrt(2 * np.pi * (p[2] ** 2))) \
* np.exp(-(x - p[1]) ** 2 / (2 * p[2] ** 2))
sigma = fwhm * gaussian_fwhm_to_sigma
if peak is True:
flux = flux * np.sqrt(2 * np.pi * (sigma ** 2))
lmin = lpeak - 5 * sigma
lmax = lpeak + 5 * sigma
if unit is None:
imin = int(lmin + 0.5)
imax = int(lmax + 0.5)
else:
imin = self.wave.pixel(lmin, nearest=True, unit=unit)
imax = self.wave.pixel(lmax, nearest=True, unit=unit)
if imin == imax:
if imin == 0 or imin == self.shape[0]:
raise ValueError('Gaussian outside spectrum wavelength range')
if unit is None:
wave = np.arange(imin, imax, dtype=float)
else:
wave = self.wave.coord(unit=unit)[imin:imax]
v = [flux, lpeak, sigma]
self.data[imin:imax] += gauss(v, wave)
[docs] def gauss_dfit(self, lmin, lmax, wratio, lpeak_1=None,
flux_1=None, fratio=1., fwhm=None, cont=None,
peak=False, spline=False, weight=True,
plot=False, plot_factor=10, unit=u.angstrom):
"""Truncate the spectrum and fit it as a sum of two gaussian functions.
Returns the two gaussian functions as `mpdaf.obj.Gauss1D` objects.
From Johan Richard and Vera Patricio.
Parameters
----------
lmin : float or (float,float)
Minimum wavelength value or wavelength range
used to initialize the gaussian left value.
lmax : float or (float,float)
Maximum wavelength or wavelength range
used to initialize the gaussian right value.
wratio : float
Ratio between the two gaussian centers
lpeak_1 : float
Input gaussian center of the first gaussian. if None it is
estimated with the wavelength corresponding to the maximum value
in [max(lmin), min(lmax)]
flux_1 : float
Integrated gaussian flux or gaussian peak value if peak is True.
fratio : float
Ratio between the two integrated gaussian fluxes.
fwhm : float
Input gaussian fwhm, if None it is estimated.
peak : bool
If true, flux contains the gaussian peak value .
cont : float
Continuum value, if None it is estimated by the line through points
(max(lmin),mean(data[lmin])) and (min(lmax),mean(data[lmax])).
spline : bool
Linear/spline interpolation to interpolate masked values.
weight : bool
If weight is True, the weight is computed as the inverse of
variance.
plot : bool
If True, the resulted fit is plotted.
plot_factor : double
oversampling factor for the overplotted fit
unit : `astropy.units.Unit`
Type of the wavelength coordinates. If None, inputs are in pixels.
Returns
-------
out : `mpdaf.obj.Gauss1D`, `mpdaf.obj.Gauss1D`
"""
if np.isscalar(lmin):
fmin = None
else:
lmin = np.array(lmin, dtype=float)
fmin = self.mean(lmin[0], lmin[1], weight=False, unit=unit)[0]
lmin = lmin[1]
if np.isscalar(lmax):
fmax = None
else:
lmax = np.array(lmax, dtype=float)
fmax = self.mean(lmax[0], lmax[1], weight=False, unit=unit)[0]
lmax = lmax[0]
# spec = self.truncate(lmin, lmax)
spec = self.subspec(lmin, lmax, unit=unit)
data = spec._interp_data(spline)
if unit is None:
l = np.arange(self.shape, dtype=float)
else:
l = spec.wave.coord(unit=unit)
lmin = l[0]
lmax = l[-1]
if fmin is None:
fmin = data[0]
if fmax is None:
fmax = data[-1]
# initial gaussian peak position
if lpeak_1 is None:
lpeak_1 = l[data.argmax()]
# continuum value
if cont is None:
cont0 = ((fmax - fmin) * lpeak_1 + lmax *
fmin - lmin * fmax) / (lmax - lmin)
else:
cont0 = cont
# initial sigma value
if fwhm is None:
try:
fwhm = spec.fwhm(lpeak_1, cont0, spline, unit=unit)
except Exception:
lpeak_1 = l[data.argmin()]
fwhm = spec.fwhm(lpeak_1, cont0, spline, unit=unit)
sigma = fwhm * gaussian_fwhm_to_sigma
# initial gaussian integrated flux
if flux_1 is None:
if unit is None:
pixel = int(lpeak_1 + 0.5)
else:
pixel = spec.wave.pixel(lpeak_1, nearest=True, unit=unit)
peak_1 = data[pixel] - cont0
flux_1 = peak_1 * np.sqrt(2 * np.pi * (sigma ** 2))
elif peak is True:
peak_1 = flux_1 - cont0
flux_1 = peak_1 * np.sqrt(2 * np.pi * (sigma ** 2))
else:
pass
flux_2 = fratio * flux_1
# 1d gaussian function
# p[0]: flux 1, p[1]:center 1, p[2]: fwhm, p[3] = peak 2
gaussfit = lambda p, x: cont0 + \
p[0] * (1 / np.sqrt(2 * np.pi * (p[2] ** 2))) * \
np.exp(-(x - p[1]) ** 2 / (2 * p[2] ** 2)) + \
p[3] * (1 / np.sqrt(2 * np.pi * (p[2] ** 2))) * \
np.exp(-(x - (p[1] * wratio)) ** 2 / (2 * p[2] ** 2))
# 1d gaussian fit
if spec.var is not None and weight:
wght = 1.0 / np.sqrt(np.abs(spec.var))
np.ma.fix_invalid(wght, copy=False, fill_value=0)
else:
wght = np.ones(spec.shape)
e_gauss_fit = lambda p, x, y, w: w * (gaussfit(p, x) - y)
# inital guesses for Gaussian Fit
v0 = [flux_1, lpeak_1, sigma, flux_2]
# Minimize the sum of squares
v, covar, info, mesg, success = leastsq(
e_gauss_fit, v0[:], args=(l, data, wght), maxfev=100000,
full_output=1)
# calculate the errors from the estimated covariance matrix
chisq = sum(info["fvec"] * info["fvec"])
dof = len(info["fvec"]) - len(v)
if covar is not None:
err = np.array([np.sqrt(np.abs(covar[i, i])) *
np.sqrt(np.abs(chisq / dof))
for i in range(len(v))])
else:
err = None
if plot:
import matplotlib.pyplot as plt
xxx = np.arange(l[0], l[-1], (l[1] - l[0]) / plot_factor)
ccc = gaussfit(v, xxx)
plt.plot(xxx, ccc, 'r--')
# return a Gauss1D object
flux_1 = v[0]
flux_2 = v[3]
lpeak_1 = v[1]
lpeak_2 = lpeak_1 * wratio
sigma = np.abs(v[2])
fwhm = sigma * gaussian_sigma_to_fwhm
peak_1 = flux_1 / np.sqrt(2 * np.pi * (sigma ** 2))
peak_2 = flux_2 / np.sqrt(2 * np.pi * (sigma ** 2))
if err is not None:
err_flux_1 = err[0]
err_flux_2 = err[3]
err_lpeak_1 = err[1]
err_lpeak_2 = err[1] * wratio
err_sigma = err[2]
err_fwhm = err_sigma * gaussian_sigma_to_fwhm
err_peak_1 = np.abs(1. / np.sqrt(2 * np.pi) *
(err_flux_1 * sigma - flux_1 * err_sigma) /
sigma / sigma)
err_peak_2 = np.abs(1. / np.sqrt(2 * np.pi) *
(err_flux_2 * sigma - flux_2 * err_sigma) /
sigma / sigma)
else:
err_flux_1 = np.NAN
err_flux_2 = np.NAN
err_lpeak_1 = np.NAN
err_lpeak_2 = np.NAN
err_sigma = np.NAN
err_fwhm = np.NAN
err_peak_1 = np.NAN
err_peak_2 = np.NAN
return (Gauss1D(lpeak_1, peak_1, flux_1, fwhm, cont0, err_lpeak_1,
err_peak_1, err_flux_1, err_fwhm, chisq, dof),
Gauss1D(lpeak_2, peak_2, flux_2, fwhm, cont0, err_lpeak_2,
err_peak_2, err_flux_2, err_fwhm, chisq, dof))
[docs] def gauss_asymfit(self, lmin, lmax, lpeak=None, flux=None, fwhm=None,
cont=None, peak=False, spline=False, weight=True,
plot=False, plot_factor=10, ax=None, unit=u.angstrom):
"""Truncate the spectrum and fit it with an asymetric gaussian
function.
Returns the two gaussian functions (right and left) as
`mpdaf.obj.Gauss1D` objects.
From Johan Richard and Vera Patricio, modified by Jeremy Blaizot.
Parameters
----------
lmin : float or (float,float)
Minimum wavelength value or wavelength range
used to initialize the gaussian left value.
lmax : float or (float,float)
Maximum wavelength or wavelength range
used to initialize the gaussian right value.
lpeak : float
Input gaussian center. if None it is estimated with the wavelength
corresponding to the maximum value in ``[max(lmin), min(lmax)]``.
flux : float
Integrated gaussian flux or gaussian peak value if peak is True.
fwhm : float
Input gaussian fwhm, if None it is estimated.
peak : bool
If true, flux contains the gaussian peak value .
cont : float
Continuum value, if None it is estimated by the line through points
(max(lmin),mean(data[lmin])) and (min(lmax),mean(data[lmax])).
spline : bool
Linear/spline interpolation to interpolate masked values.
weight : bool
If weight is True, the weight is computed as the inverse of
variance.
unit : `astropy.units.Unit`
type of the wavelength coordinates. If None, inputs are in pixels.
plot : bool
If True, the resulted fit is plotted.
plot_factor : double
oversampling factor for the overplotted fit
Returns
-------
out : `mpdaf.obj.Gauss1D`, `mpdaf.obj.Gauss1D`
Left and right Gaussian functions.
"""
if np.isscalar(lmin):
fmin = None
else:
lmin = np.array(lmin, dtype=float)
fmin = self.mean(lmin[0], lmin[1], weight=False, unit=unit)[0]
lmin = lmin[1]
if np.isscalar(lmax):
fmax = None
else:
lmax = np.array(lmax, dtype=float)
fmax = self.mean(lmax[0], lmax[1], weight=False, unit=unit)[0]
lmax = lmax[0]
spec = self.subspec(lmin, lmax, unit=unit)
data = spec._interp_data(spline)
if unit is None:
l = np.arange(self.shape, dtype=float)
else:
l = spec.wave.coord(unit=unit)
lmin = l[0]
lmax = l[-1]
if fmin is None:
fmin = data[0]
if fmax is None:
fmax = data[-1]
# initial gaussian peak position
if lpeak is None:
lpeak = l[data.argmax()]
# continuum value
if cont is None:
cont0 = ((fmax - fmin) * lpeak + lmax * fmin -
lmin * fmax) / (lmax - lmin)
else:
cont0 = cont
# initial sigma value
if fwhm is None:
try:
fwhm = spec.fwhm(lpeak, cont0, spline, unit=unit)
except Exception:
lpeak = l[data.argmin()]
fwhm = spec.fwhm(lpeak, cont0, spline, unit=unit)
sigma = fwhm * gaussian_fwhm_to_sigma
# initial gaussian integrated flux
if flux is None:
if unit is None:
pixel = int(lpeak + 0.5)
else:
pixel = spec.wave.pixel(lpeak, nearest=True, unit=unit)
peak = data[pixel] - cont0
flux = peak * np.sqrt(2 * np.pi * (sigma ** 2))
elif peak is True:
peak = flux - cont0
flux = peak * np.sqrt(2 * np.pi * (sigma ** 2))
else:
pass
# Asymetric gaussian function (p[0]: flux of the right-hand side if it
# was full... ; p[1]: lambda peak; p[2]:sigma_right; p[3]: sigma_left)
asymfit = lambda p, x: np.where(
x > p[1],
cont0 + p[0] / np.sqrt(2 * np.pi) / p[2] *
np.exp(-(x - p[1]) ** 2 / (2. * p[2] ** 2)),
cont0 + p[0] * p[3] / p[2] / np.sqrt(2 * np.pi) / p[3] *
np.exp(-(x - p[1]) ** 2 / (2. * p[3] ** 2))
)
# 1d Gaussian fit
if spec.var is not None and weight:
wght = 1.0 / np.sqrt(np.abs(spec.var))
np.ma.fix_invalid(wght, copy=False, fill_value=0)
else:
wght = np.ones(spec.shape)
e_asym_fit = lambda p, x, y, w: w * (asymfit(p, x) - y)
# inital guesses for Gaussian Fit
v0 = [peak, lpeak, sigma, sigma]
# Minimize the sum of squares
v, covar, info, mesg, success = leastsq(
e_asym_fit, v0[:], args=(l, data, wght), maxfev=100000,
full_output=1)
# calculate the errors from the estimated covariance matrix
chisq = sum(info["fvec"] * info["fvec"])
dof = len(info["fvec"]) - len(v)
if covar is not None:
err = np.array([np.sqrt(np.abs(covar[i, i])) *
np.sqrt(np.abs(chisq / dof))
for i in range(len(v))])
else:
err = None
if plot:
# Same wavelength grid as input spectrum
import matplotlib.pyplot as plt
xxx = np.arange(l[0], l[-1], (l[1] - l[0]) / plot_factor)
ccc = asymfit(v, xxx)
if ax is None:
plt.plot(xxx, ccc, 'm--', label='Asymmetric')
else:
ax.plot(xxx, ccc, 'm--', label='Asymmetric')
# return a Gauss1D object
sigma_right = np.abs(v[2])
sigma_left = np.abs(v[3])
flux_right = 0.5 * v[0]
flux_left = flux_right * sigma_left / sigma_right
flux = flux_right + flux_left
fwhm_right = sigma_right * gaussian_sigma_to_fwhm
fwhm_left = sigma_left * gaussian_sigma_to_fwhm
lpeak = v[1]
peak = flux_right / np.sqrt(2 * np.pi * sigma_right ** 2)
if err is not None:
err_flux = err[0]
err_lpeak = err[1]
err_sigma_right = err[2]
err_sigma_left = err[3]
err_fwhm_right = err_sigma_right * gaussian_sigma_to_fwhm
err_fwhm_left = err_sigma_left * gaussian_sigma_to_fwhm
err_peak = np.abs(
1. / np.sqrt(2 * np.pi) *
(err_flux * sigma_right - flux * err_sigma_right) /
sigma_right / sigma_right)
else:
err_flux = np.NAN
err_lpeak = np.NAN
err_sigma_right = np.NAN
err_sigma_left = np.NAN
err_fwhm_right = np.NAN
err_fwhm_left = np.NAN
err_peak = np.NAN
return (Gauss1D(lpeak, peak, flux_left, fwhm_left, cont0, err_lpeak,
err_peak, err_flux / 2, err_fwhm_left, chisq, dof),
Gauss1D(lpeak, peak, flux_right, fwhm_right, cont0, err_lpeak,
err_peak, err_flux / 2, err_fwhm_right, chisq, dof))
[docs] def add_asym_gaussian(self, lpeak, flux, fwhm_right, fwhm_left, cont=0,
peak=False, unit=u.angstrom):
"""Add an asymetric gaussian on spectrum in place.
Parameters
----------
lpeak : float
Gaussian center.
flux : float
Integrated gaussian flux or gaussian peak value if peak is True.
fwhm_right : float
Gaussian fwhm on the right (red) side
fwhm_left : float
Gaussian fwhm on the right (red) side
cont : float
Continuum value.
peak : bool
If true, flux contains the gaussian peak value.
unit : `astropy.units.Unit`
Type of the wavelength coordinates. If None, inputs are in pixels.
"""
asym_gauss = lambda p, x: np.where(
x > p[1],
cont + p[0] / np.sqrt(2 * np.pi) / p[2] *
np.exp(-(x - p[1]) ** 2 / (2. * p[2] ** 2)),
cont + p[0] * p[3] / p[2] / np.sqrt(2 * np.pi) / p[3] *
np.exp(-(x - p[1]) ** 2 / (2. * p[3] ** 2))
)
sigma_left = fwhm_left * gaussian_fwhm_to_sigma
sigma_right = fwhm_right * gaussian_fwhm_to_sigma
# if peak is True:
# right_norm = flux * np.sqrt(2. * np.pi * sigma_right ** 2)
# else:
# right_norm = 2. * flux / (1. + sigma_left / sigma_right)
lmin = lpeak - 5 * sigma_left
lmax = lpeak + 5 * sigma_right
if unit is None:
imin = int(lmin + 0.5)
imax = int(lmax + 0.5)
else:
imin = self.wave.pixel(lmin, True, unit=unit)
imax = self.wave.pixel(lmax, True, unit=unit)
if imin == imax:
if imin == 0 or imin == self.shape[0]:
raise ValueError('Gaussian outside spectrum wavelength range')
if unit is None:
wave = np.arange(imin, imax, dtype=float)
else:
wave = self.wave.coord(unit=unit)[imin:imax]
v = [flux, lpeak, sigma_right, sigma_left]
self.data[imin:imax] = self.data[imin:imax] + asym_gauss(v, wave)
[docs] def filter(self, kernel = Box1DKernel, **parameters):
"""Perform filtering on the spectrum.
Uses `astropy.convolution` kernels and convolution.
Parameters
----------
kernel : `astropy.convolution.Kernel1D`
astropy kernel to use
(see `https://docs.astropy.org/en/stable/convolution/kernels.html#available-kernels`)
- Box1DKernel (default, parameters: width)
- Gaussan1DKernel (parameters: stddev)
parameters : keywords
parameters to pass to the kernel
Returns
-------
out : Spectrum
"""
res = self.copy()
data = res.data
data = convolve(data, kernel(**parameters))
res._data = data
res._var = None
return res
[docs] def convolve(self, other, inplace=False):
"""Convolve a Spectrum with a 1D array or another Spectrum, using
the discrete convolution equation.
This function, which uses the discrete convolution equation,
is usually slower than Image.fftconvolve(). However it can be
faster when other.data.size is small, and it always uses much
less memory, so it is sometimes the only practical choice.
Masked values in self.data and self.var are replaced with zeros before
the convolution is performed, but are masked again after the
convolution.
If self.var exists, the variances are propagated using the equation:
result.var = self.var (*) other**2
where (*) indicates convolution. This equation can be derived by
applying the usual rules of error-propagation to the discrete
convolution equation.
The speed of this function scales as O(Nd x No) where
Nd=self.data.size and No=other.data.size.
Uses `scipy.signal.convolve`.
Parameters
----------
other : Spectrum or numpy.ndarray
The 1D array with which to convolve the spectrum in self.data.
This can be an array of the same size as self, or it can be a
smaller array, such as a small gaussian profile to use to smooth
the spectrum.
When other.data contains a symmetric filtering function, such as a
gaussian profile, the center of the function should be placed at
the center of pixel:
``(other.shape - 1) // 2``
If ``other`` is an MPDAF Spectrum object, note that only its data
array is used. Masked values in this array are treated as
zero. Any variances found in other.var are ignored.
inplace : bool
If False (the default), return the results in a new Spectrum.
If True, record the result in self and return that.
Returns
-------
out : `~mpdaf.obj.Spectrum`
"""
# Delegate the task to DataArray._convolve()
return self._convolve(signal.convolve, other=other, inplace=inplace)
[docs] def fftconvolve(self, other, inplace=False):
"""Convolve a Spectrum with a 1D array or another Spectrum, using
the Fourier convolution theorem.
This function, which performs the convolution by multiplying the
Fourier transforms of the two arrays, is usually much faster than
Spectrum.convolve(), except when other.data.size is small. However it
uses much more memory, so Spectrum.convolve() is sometimes a better
choice.
Masked values in self.data and self.var are replaced with zeros before
the convolution is performed, but they are masked again after the
convolution.
If self.var exists, the variances are propagated using the equation:
result.var = self.var (*) other**2
where (*) indicates convolution. This equation can be derived by
applying the usual rules of error-propagation to the discrete
convolution equation.
The speed of this function scales as O(Nd x log(Nd)) where
Nd=self.data.size. This function temporarily allocates a pair of
arrays that have the sum of the shapes of self.shape and other.shape,
rounded up to a power of two along each axis. This can involve a lot
of memory being allocated. For this reason, when other.shape is small,
Spectrum.convolve() may be more efficient than Spectrum.fftconvolve().
Uses `scipy.signal.fftconvolve`.
Parameters
----------
other : Spectrum or numpy.ndarray
The 1D array with which to convolve the spectrum in self.data.
This can be an array of the same size as self.data, or it can be a
smaller array, such as a small gaussian to use to smooth the
spectrum.
When ``other`` contains a symmetric filtering function, such as a
gaussian profile, the center of the function should be placed at
the center of pixel:
``(other.shape - 1) // 2``
If other is an MPDAF Spectrum object, note that only its data
array is used. Masked values in this array are treated as
zero. Any variances found in other.var are ignored.
inplace : bool
If False (the default), return the results in a new Spectrum.
If True, record the result in self and return that.
Returns
-------
out : `~mpdaf.obj.Spectrum`
"""
# Delegate the task to DataArray._convolve()
return self._convolve(signal.fftconvolve, other=other, inplace=inplace)
[docs] def correlate(self, other, inplace=False):
"""Cross-correlate the spectrum with a other spectrum or an array.
Uses `scipy.signal.correlate`. self and other must have the same
size.
Parameters
----------
other : 1d-array or Spectrum
Second spectrum or 1d-array.
inplace : bool
If True, replace the input spectrum with the correlation.
Returns
-------
out : Spectrum
"""
res = self if inplace else self.copy()
try:
if isinstance(other, Spectrum):
if res.shape != other.shape:
raise IOError('Operation forbidden for spectra '
'with different sizes')
else:
data = other._data
if res.unit != other.unit:
data = (data * other.unit).to(res.unit).value
res._data = signal.correlate(res._data, data, mode='same')
if res._var is not None:
res._var = signal.correlate(res._var, data,
mode='same')
except IOError as e:
raise e
except Exception:
try:
res._data = signal.correlate(res._data, other, mode='same')
if res._var is not None:
res._var = signal.correlate(res._var, other, mode='same')
except Exception:
raise IOError('Operation forbidden')
return res
[docs] def fftconvolve_gauss(self, fwhm, nsig=5, unit=u.angstrom, inplace=False):
"""Convolve the spectrum with a Gaussian using fft.
Parameters
----------
fwhm : float
Gaussian fwhm.
nsig : int
Number of standard deviations.
unit : `astropy.units.Unit`
type of the wavelength coordinates
inplace : bool
If True, convolve the original spectrum in-place, and return that.
Returns
-------
out : Spectrum
"""
from scipy import special
res = self if inplace else self.copy()
sigma = fwhm * gaussian_fwhm_to_sigma
if unit is None:
s = sigma
else:
s = sigma / res.get_step(unit=unit)
n = nsig * int(s + 0.5)
n = int(n / 2) * 2
data = np.arange(-n, n + 1)
kernel = special.erf((1 + 2 * data) / (2 * np.sqrt(2) * s)) \
+ special.erf((1 - 2 * data) / (2 * np.sqrt(2) * s))
kernel /= kernel.sum()
res._data = signal.correlate(res._data, kernel, mode='same')
if res._var is not None:
res._var = signal.correlate(res._var, kernel, mode='same')
return res
[docs] def LSF_convolve(self, lsf, size, **kwargs):
"""Convolve spectrum with LSF.
Parameters
----------
lsf : python function
`mpdaf.MUSE.LSF` object or function f describing the LSF.
The first three parameters of the function f must be lbda
(wavelength value in A), step (in A) and size (odd integer).
f returns an np.array with shape=2*(size/2)+1 and centered in lbda
Example: from mpdaf.MUSE import LSF
size : odd int
size of LSF in pixels.
kwargs : kwargs
it can be used to set function arguments.
Returns
-------
out : `~mpdaf.obj.Spectrum`
"""
res = self.clone()
if self._data.sum() == 0:
return res
step = self.get_step(u.angstrom)
lbda = self.wave.coord(u.angstrom)
if size % 2 == 0:
raise ValueError('Size must be an odd number')
else:
k = size // 2
if isinstance(lsf, types.FunctionType):
f = lsf
else:
try:
f = getattr(lsf, 'get_LSF')
except Exception:
raise ValueError('lsf parameter is not valid')
data = np.empty(len(self._data) + 2 * k)
data[k:-k] = self._data
data[:k] = self._data[k:0:-1]
data[-k:] = self._data[-2:-k - 2:-1]
res._data = np.array([(f(lbda[i], step, size, **kwargs) *
data[i:i + size]).sum()
for i in range(self.shape[0])])
res._mask = self._mask
if self._var is None:
res._var = None
else:
res._var = np.array([(f(lbda[i], step, size, **kwargs) *
data[i:i + size]).sum()
for i in range(self.shape[0])])
return res
[docs] def fit_lines(self, redshift, **kwargs):
"""Use pyplatefit to fit the spectrum lines.
This method uses the `pyplatefit.fit_spec` function to
perform a line fitting. Refer to its documentation.
Parameters
----------
redshift : float
Expected redshift of the spectrum.
**kwargs : keyword arguments
Additional arguments passed to the `fit_spec` function.
Returns
-------
See pyplatefit documentation.
"""
try:
from pyplatefit import fit_spec
except ImportError:
raise ImportError("You need to install pyplatefit.")
return fit_spec(self, z=redshift, **kwargs)
[docs] def plot(self, max=None, title=None, noise=False, snr=False,
lmin=None, lmax=None, ax=None, stretch='linear', unit=u.angstrom,
noise_kwargs=None, **kwargs):
"""Plot the spectrum.
By default, the matplotlib drawstyle option is set to
'steps-mid'. The reason for this is that in MPDAF integer
pixel indexes correspond to the centers of their pixels, and
the floating point pixel indexes of a pixel extend from half a
pixel below the integer central position to half a pixel above
it.
Parameters
----------
max : float
If max is not None (the default), it should be a floating
point value. The plotted data will be renormalized such
that the peak in the plot has this value.
title : string
The title to give the figure (None by default).
noise : bool
If noise is True, colored extensions above and below
the plotted points indicate the square-root of the
variances of each pixel (if any).
snr : bool
If snr is True, data/sqrt(var) is plotted.
lmin : float
The minimum wavelength to be plotted, or None (the default)
to start the plot from the minimum wavelength in the spectrum.
lmax : float
The maximum wavelength to be plotted, or None (the default)
to start the plot from the maximum wavelength in the spectrum.
ax : matplotlib.Axes
The Axes instance in which the spectrum is drawn, or None
(the default), to request that an Axes object be created
internally.
unit : `astropy.units.Unit`
The wavelength units of the lmin and lmax arguments, or None
to indicate that lmin and lmax are floating point pixel
indexes.
noise_kwargs : dict
Properties for the noise plot (if ``noise=True``). Default to
``color='0.75', facecolor='0.75', alpha=0.5``.
kwargs : dict
kwargs can be used to set properties of the plot such as:
line label (for auto legends), linewidth, anitialising,
marker face color, etc.
"""
# Create an Axes instance for the plot?
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
# If a sub-set of the spectrum's wavelengths have been
# specified, get a truncated copy of the spectrum that just
# contains this range.
res = self.copy()
if lmin is not None or lmax is not None:
res.truncate(lmin, lmax, unit)
# Get the wavelengths to be plotted along the X axis,
# preferably in the units specified for lmin and lmax,
# if any. If the specified units can't be used, use
# the native wavelength units of the spectrum.
try:
x = res.wave.coord(unit=unit)
except u.UnitConversionError:
unit = res.wave.unit
x = res.wave.coord(unit=unit)
# Get the pixel values to be plotted.
data = res.data
# Disable the noise and snr options if no variances
# are available.
if res.var is None:
noise = False
snr = False
# Compute the SNR?
if snr:
data /= np.sqrt(res.var)
# Renormalize to make the peak value equal to max?
if max is not None:
data = data * max / data.max()
# Set the default plot arguments.
kwargs.setdefault('drawstyle', 'steps-mid')
kwargs.setdefault('linewidth', 1)
# Plot the data with a linear or logarithmic Y axis.
if stretch == 'linear':
ax.plot(x, data, **kwargs)
elif stretch == 'log':
ax.semilogy(x, data, **kwargs)
else:
raise ValueError("Unknow stretch '{}'".format(stretch))
# Plot extensions above and below the points to represent
# their uncertainties?
if noise:
sigma = np.sqrt(res.var)
noisekw = dict(color='0.75', facecolor='0.75', alpha=0.5)
if noise_kwargs is not None:
noisekw.update(noise_kwargs)
ax.fill_between(x, data + sigma, data - sigma, **noisekw)
# Label the plot.
if title is not None:
ax.set_title(title)
if unit is not None:
ax.set_xlabel(r'$\lambda$ (%s)' % unit)
if res.unit is not None:
ax.set_ylabel(res.unit)
if lmin is None and lmax is None:
ax.set_xlim(*self.wave.get_range(unit=unit))
# Arrange for cursor motion events to display corresponding
# coordinates and values below the plot.
def _on_move(event): # pragma: no cover
"""print xc,yc,k,lbda and data in the figure toolbar."""
if event.inaxes is not None:
xc, yc = event.xdata, event.ydata
try:
i = self.wave.pixel(xc, nearest=True, unit=unit)
x = self.wave.coord(i, unit=self._unit)
event.canvas.toolbar.set_message(
'xc= %g yc=%g k=%d lbda=%g data=%g' %
(xc, yc, i, x, self._data[i]))
except Exception:
pass
self._unit = unit
plt.connect('motion_notify_event', _on_move)
self._plot_id = len(ax.lines) - 1
[docs] def to_spectrum1d(self, unit_wave=u.angstrom):
"""Return a ``specutils.Spectrum1D`` object."""
from astropy.nddata import StdDevUncertainty
try:
from specutils import Spectrum1D
except ImportError:
self._logger.error('specutils package not found')
raise
flux = u.Quantity(self._data, unit=self.unit, copy=False)
std = StdDevUncertainty(np.sqrt(self._var), unit=self.unit, copy=False)
return Spectrum1D(flux=flux, uncertainty=std, mask=self._mask,
wcs=self.wave.wcs, copy=False)