def test_spectrum_methods(spec_var, spec_novar):
"""Spectrum class: testing sum/mean/abs/sqrt methods"""
wave = WaveCoord(crpix=2.0, cdelt=3.0, crval=0.5, cunit=u.nm, shape=10)
spectrum1 = Spectrum(data=np.array([0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
wave=wave)
sum1 = spectrum1.sum()
assert_almost_equal(sum1[0], spectrum1.data.sum())
spectrum2 = spectrum1[1:-2]
sum1 = spectrum1.sum(lmin=spectrum1.wave.coord(1),
lmax=spectrum1.wave.coord(10 - 3),
unit=u.nm)
sum2 = spectrum2.sum()
assert_almost_equal(sum1, sum2)
mean1 = spectrum1.mean(lmin=spectrum1.wave.coord(1),
lmax=spectrum1.wave.coord(10 - 3),
unit=u.nm)
mean2 = spectrum2.mean()
assert_almost_equal(mean1, mean2)
spvar2 = spec_var.abs()
assert spvar2[23] == np.abs(spec_var[23])
spvar2 = spec_var.abs().sqrt()
assert spvar2[8] == np.sqrt(np.abs(spec_var[8]))
assert_almost_equal(spec_var.mean()[0], 11.526, 2)
assert_almost_equal(spec_novar.mean()[0], 11.101, 2)
spvarsum = spvar2 + 4 * spvar2 - 56 / spvar2
assert_almost_equal(spvarsum[10],
spvar2[10] + 4 * spvar2[10] - 56 / spvar2[10], 2)
assert_almost_equal(spec_var.get_step(), 0.630, 2)
assert_almost_equal(spec_var.get_start(), 4602.604, 2)
assert_almost_equal(spec_var.get_end(), 7184.289, 2)
assert_almost_equal(spec_var.get_range()[0], 4602.604, 2)
assert_almost_equal(spec_var.get_range()[1], 7184.289, 2)
def test_resample2():
"""Spectrum class: testing resampling function
with a spectrum of integers and resampling to a smaller pixel size"""
wave = WaveCoord(crpix=2.0, cdelt=3.0, crval=0.5, cunit=u.nm)
spectrum1 = Spectrum(data=np.array([0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0]),
wave=wave)
flux1 = spectrum1.sum()[0] * spectrum1.wave.get_step()
spectrum2 = spectrum1.resample(0.3)
flux2 = spectrum2.sum()[0] * spectrum2.wave.get_step()
assert_almost_equal(flux1, flux2, 2)
def test_integrate():
"""Spectrum class: testing integration"""
wave = WaveCoord(crpix=2.0, cdelt=3.0, crval=0.5, cunit=u.nm)
spectrum1 = Spectrum(data=np.array([0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
wave=wave,
unit=u.Unit('ct/Angstrom'))
# Integrate the whole spectrum, by not specifying starting or ending
# wavelengths. This should be the sum of the pixel values multiplied
# by cdelt in angstroms (because the flux units are per angstrom).
result, err = spectrum1.integrate()
expected = spectrum1.get_step(unit=u.angstrom) * spectrum1.sum()[0]
assert_almost_equal(result.value, expected)
assert result.unit == u.ct
assert np.isinf(err)
# The result should not change if we change the wavelength units of
# the wavelength limits to nanometers.
result = spectrum1.integrate(unit=u.nm)[0]
expected = spectrum1.get_step(unit=u.angstrom) * spectrum1.sum()[0]
assert_almost_equal(result.value, expected)
assert result.unit == u.ct
# new spectrum with variance
spectrum1 = Spectrum(data=np.array([0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
var=np.ones(10),
wave=wave,
unit=u.Unit('ct/Angstrom'))
# Integrate over a wavelength range 3.5 to 6.5 nm. The WCS
# conversion equation from wavelength to pixel index is,
#
# index = crpix-1 + (lambda-crval)/cdelt
# index = 1 + (lambda - 0.5) / 3.0
#
# So wavelengths 3.5 and 6.5nm, correspond to pixel indexes
# of 2.0 and 3.0. These are the centers of pixels 2 and 3.
# Thus the integration should be the value of pixel 2 times
# half of cdelt, plus the value of pixel 3 times half of cdelt.
# This comes to 2*3.0/2 + 3*3.0/2 = 7.5 ct/Angstrom*nm, which
# should be rescaled to 75 ct, since nm/Angstrom is 10.0.
result, err = spectrum1.integrate(lmin=3.5, lmax=6.5, unit=u.nm)
assert_almost_equal(result.value, 75)
assert result.unit == u.ct
datasum, var = spectrum1.sum(lmin=3.5, lmax=6.5, unit=u.nm)
assert_almost_equal(result.value, datasum * 15)
assert_almost_equal(err.value, var * 15)
# Do the same test, but specify the wavelength limits in angstroms.
# The result should be the same as before.
result = spectrum1.integrate(lmin=35.0, lmax=65.0, unit=u.angstrom)[0]
assert_almost_equal(result.value, 75)
assert result.unit == u.ct
assert_almost_equal(result.value, datasum * 15)
assert_almost_equal(err.value, var * 15)
# Do the same experiment yet again, but this time after changing
# the flux units of the spectrum to simple counts, without any per
# wavelength units. Since there are no wavelength units in the
# flux units, the result should not be rescaled from the native
# value of 7.5, and because we specified a wavelength range in
# angstroms, the resulting units should be counts * nm.
spectrum1.unit = u.ct
result = spectrum1.integrate(lmin=3.5, lmax=6.5, unit=u.nm)[0]
assert_almost_equal(result.value, 7.5)
assert result.unit == u.ct * u.nm
def test_resample():
"""Spectrum class: Test resampling"""
# Choose the dimensions of the spectrum, choosing a large number that is
# *not* a convenient power of 2.
oldshape = 4000
# Choose the wavelength pixel size and the default wavelength units.
oldstep = 1.0
oldunit = u.angstrom
# Create the wavelength axis coordinates.
wave = WaveCoord(crpix=2.0,
cdelt=oldstep,
crval=0.5,
cunit=oldunit,
shape=oldshape)
# Specify the desired increase in pixel size, and the resulting pixel size.
factor = 6.5
newstep = ((factor * oldstep) * oldunit).to(u.nm).value
# Specify the wavelength at which the peak of the resampled spectrum should
# be expected.
expected_peak_wave = 3000.0
# Create the array in which the test spectrum will be composed.
data = np.zeros(oldshape)
# Get the wavelength coordinates of each pixel in the spectrum.
w = wave.coord()
# Add the following list gaussians to the spectrum, where each
# gaussian is specified as: (amplitude, sigma_in_pixels,
# center_wavelength). Given that narrow gaussians are reduced in
# amplitude by resampling more than wide gaussians, we arrange
# that the peak gaussian before and after correctly resampling are
# different.
gaussians = [
(0.5, 12.0, 800.0),
(0.7, 5.0, 1200.0),
(0.4, 700.0, 1600.0),
(1.5, 2.6, 1980.0), # Peak before resampling
(1.2, 2.6, 2000.0),
(1.3, 15.0, expected_peak_wave), # Peak if resampled correctly
(1.0, 2.0, 3200.0)
]
for amp, sigma, center in gaussians:
sigma *= oldstep
data += amp * np.exp(-0.5 * ((center - w) / sigma)**2)
# Fill the variance array with a simple window function.
var = np.hamming(oldshape)
# Add gaussian random noise to the spectrum, but leave 3 output
# pixel widths zero at each end of the spectrum so that the PSF of
# the output grid doesn't spread flux from the edges off the edge
# of the output grid. It takes about 3 pixel widths for the gaussian
# PSF to drop to about 0.01 of its peak.
margin = np.ceil(3 * factor).astype(int)
data[margin:-margin] += np.random.normal(scale=0.1,
size=data.shape - 2 * margin)
# Install the spectral data in a Spectrum container.
oldsp = Spectrum(data=data, var=var, wave=wave)
# Mask a few pixels.
masked_slice = slice(900, 910)
oldsp.mask[masked_slice] = True
# Create a down-sampled version of the input spectrum.
newsp = oldsp.resample(newstep, unit=u.nm)
# Check that the integral flux in the resampled spectrum matches that of
# the original spectrum.
expected_flux = oldsp.sum(weight=False)[0] * oldsp.wave.get_step(
unit=oldunit)
actual_flux = newsp.sum(weight=False)[0] * newsp.wave.get_step(
unit=oldunit)
assert_allclose(actual_flux, expected_flux, 1e-2)
# Do the same test, but with fluxes weighted by the inverse of the variances.
expected_flux = oldsp.sum(weight=True)[0] * oldsp.wave.get_step(
unit=oldunit)
actual_flux = newsp.sum(weight=True)[0] * newsp.wave.get_step(unit=oldunit)
assert_allclose(actual_flux, expected_flux, 1e-2)
# Check that the peak of the resampled spectrum is at the wavelength
# where the strongest gaussian was centered in the input spectrum.
assert_allclose(np.argmax(newsp.data),
newsp.wave.pixel(expected_peak_wave, nearest=True))
# Now upsample the downsampled spectrum to the original pixel size.
# This won't recover the same spectrum, since higher spatial frequencies
# are lost when downsampling, but the total flux should be about the
# same, and the peak should be at the same wavelength as the peak in
# original spectrum within one pixel width of the downsampled spectrum.
newsp2 = newsp.resample(oldstep, unit=oldunit)
# Check that the doubly resampled spectrum has the same integrated flux
# as the original.
expected_flux = oldsp.sum(weight=False)[0] * oldsp.wave.get_step(
unit=oldunit)
actual_flux = newsp2.sum(weight=False)[0] * newsp2.wave.get_step(
unit=oldunit)
assert_allclose(actual_flux, expected_flux, 1e-2)
# Check that the peak of the up-sampled spectrum is at the wavelength
# of the peak of the down-sampled spectrum to within the pixel resolution
# of the downsampled spectrum.
assert_allclose(
newsp.wave.pixel(newsp2.wave.coord(np.argmax(newsp2.data)),
nearest=True),
newsp.wave.pixel(expected_peak_wave, nearest=True))
# Check that pixels that were masked in the input spectrum are still
# masked in the final spectrum.
np.testing.assert_equal(newsp2.mask[masked_slice],
oldsp.mask[masked_slice])
