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process_qsos.m
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% process_qsos: run DLA detection algorithm on specified objects
% load redshifts/DLA flags from training release
prior_catalog = ...
load(sprintf('%s/catalog', processed_directory(training_release)));
if (ischar(prior_ind))
prior_ind = eval(prior_ind);
end
prior.z_qsos = prior_catalog.z_qsos(prior_ind);
prior.dla_ind = prior_catalog.dla_inds(dla_catalog_name);
prior.dla_ind = prior.dla_ind(prior_ind);
% filter out DLAs from prior catalog corresponding to region of spectrum below
% Ly∞ QSO rest
prior.z_dlas = prior_catalog.z_dlas(dla_catalog_name);
prior.z_dlas = prior.z_dlas(prior_ind);
for i = find(prior.dla_ind)'
if (observed_wavelengths(lya_wavelength, prior.z_dlas{i}) < ...
observed_wavelengths(lyman_limit, prior.z_qsos(i)))
prior.dla_ind(i) = false;
end
end
prior = rmfield(prior, 'z_dlas');
% load QSO model from training release
variables_to_load = {'rest_wavelengths', 'mu', 'M', 'log_omega', ...
'log_c_0', 'log_tau_0', 'log_beta'};
load(sprintf('%s/learned_qso_model_%s', ...
processed_directory(training_release), ...
training_set_name), ...
variables_to_load{:});
% load DLA samples from training release
variables_to_load = {'offset_samples', 'log_nhi_samples', 'nhi_samples'};
load(sprintf('%s/dla_samples', processed_directory(training_release)), ...
variables_to_load{:});
% load redshifts from catalog to process
catalog = load(sprintf('%s/catalog', processed_directory(release)));
% load preprocessed QSOs
variables_to_load = {'all_wavelengths', 'all_flux', 'all_noise_variance', ...
'all_pixel_mask'};
load(sprintf('%s/preloaded_qsos', processed_directory(release)), ...
variables_to_load{:});
% enable processing specific QSOs via setting to_test_ind
if (ischar(test_ind))
test_ind = eval(test_ind);
end
all_wavelengths = all_wavelengths(test_ind);
all_flux = all_flux(test_ind);
all_noise_variance = all_noise_variance(test_ind);
all_pixel_mask = all_pixel_mask(test_ind);
z_qsos = catalog.z_qsos(test_ind);
num_quasars = numel(z_qsos);
% preprocess model interpolants
mu_interpolator = ...
griddedInterpolant(rest_wavelengths, mu, 'linear');
M_interpolator = ...
griddedInterpolant({rest_wavelengths, 1:k}, M, 'linear');
log_omega_interpolator = ...
griddedInterpolant(rest_wavelengths, log_omega, 'linear');
% initialize results
min_z_dlas = nan(num_quasars, 1);
max_z_dlas = nan(num_quasars, 1);
log_priors_no_dla = nan(num_quasars, 1);
log_priors_dla = nan(num_quasars, 1);
log_likelihoods_no_dla = nan(num_quasars, 1);
sample_log_likelihoods_dla = nan(num_quasars, num_dla_samples);
log_likelihoods_dla = nan(num_quasars, 1);
log_posteriors_no_dla = nan(num_quasars, 1);
log_posteriors_dla = nan(num_quasars, 1);
c_0 = exp(log_c_0);
tau_0 = exp(log_tau_0);
beta = exp(log_beta);
for quasar_ind = 1:num_quasars
tic;
z_qso = z_qsos(quasar_ind);
fprintf('processing quasar %i/%i (z_QSO = %0.4f) ...', ...
quasar_ind, num_quasars, z_qso);
this_wavelengths = all_wavelengths{quasar_ind};
this_flux = all_flux{quasar_ind};
this_noise_variance = all_noise_variance{quasar_ind};
this_pixel_mask = all_pixel_mask{quasar_ind};
% convert to QSO rest frame
this_rest_wavelengths = emitted_wavelengths(this_wavelengths, z_qso);
ind = (this_rest_wavelengths >= min_lambda) & ...
(this_rest_wavelengths <= max_lambda);
% keep complete copy of equally spaced wavelengths for absorption
% computation
this_unmasked_wavelengths = this_wavelengths(ind);
ind = ind & (~this_pixel_mask);
this_wavelengths = this_wavelengths(ind);
this_rest_wavelengths = this_rest_wavelengths(ind);
this_flux = this_flux(ind);
this_noise_variance = this_noise_variance(ind);
this_lya_zs = ...
(this_wavelengths - lya_wavelength) / ...
lya_wavelength;
% DLA existence prior
less_ind = (prior.z_qsos < (z_qso + prior_z_qso_increase));
this_num_dlas = nnz(prior.dla_ind(less_ind));
this_num_quasars = nnz(less_ind);
this_p_dla = this_num_dlas / this_num_quasars;
log_priors_dla(quasar_ind) = ...
log( this_num_dlas) - log(this_num_quasars);
log_priors_no_dla(quasar_ind) = ...
log(this_num_quasars - this_num_dlas) - log(this_num_quasars);
fprintf_debug('\n');
fprintf_debug(' ... p( DLA | z_QSO) : %0.3f\n', this_p_dla);
fprintf_debug(' ... p(no DLA | z_QSO) : %0.3f\n', 1 - this_p_dla);
% interpolate model onto given wavelengths
this_mu = mu_interpolator( this_rest_wavelengths);
this_M = M_interpolator({this_rest_wavelengths, 1:k});
this_log_omega = log_omega_interpolator(this_rest_wavelengths);
this_omega2 = exp(2 * this_log_omega);
this_scaling_factor = 1 - exp(-tau_0 .* (1 + this_lya_zs).^beta) + c_0;
this_omega2 = this_omega2 .* this_scaling_factor.^2;
% baseline: probability of no DLA model
log_likelihoods_no_dla(quasar_ind) = ...
log_mvnpdf_low_rank(this_flux, this_mu, this_M, ...
this_omega2 + this_noise_variance);
log_posteriors_no_dla(quasar_ind) = ...
log_priors_no_dla(quasar_ind) + log_likelihoods_no_dla(quasar_ind);
fprintf_debug(' ... log p(D | z_QSO, no DLA) : %0.2f\n', ...
log_likelihoods_no_dla(quasar_ind));
min_z_dlas(quasar_ind) = min_z_dla(this_wavelengths, z_qso);
max_z_dlas(quasar_ind) = max_z_dla(this_wavelengths, z_qso);
sample_z_dlas = ...
min_z_dlas(quasar_ind) + ...
(max_z_dlas(quasar_ind) - min_z_dlas(quasar_ind)) * offset_samples;
% ensure enough pixels are on either side for convolving with
% instrument profile
padded_wavelengths = ...
[logspace(log10(min(this_unmasked_wavelengths)) - width * pixel_spacing, ...
log10(min(this_unmasked_wavelengths)) - pixel_spacing, ...
width)'; ...
this_unmasked_wavelengths; ...
logspace(log10(max(this_unmasked_wavelengths)) + pixel_spacing, ...
log10(max(this_unmasked_wavelengths)) + width * pixel_spacing, ...
width)' ...
];
% to retain only unmasked pixels from computed absorption profile
ind = (~this_pixel_mask(ind));
% compute probabilities under DLA model for each of the sampled
% (normalized offset, log(N HI)) pairs
parfor i = 1:num_dla_samples
% absorption corresponding to this sample
absorption = voigt(padded_wavelengths, sample_z_dlas(i), ...
nhi_samples(i), num_lines);
absorption = absorption(ind);
dla_mu = this_mu .* absorption;
dla_M = this_M .* absorption;
dla_omega2 = this_omega2 .* absorption.^2;
sample_log_likelihoods_dla(quasar_ind, i) = ...
log_mvnpdf_low_rank(this_flux, dla_mu, dla_M, ...
dla_omega2 + this_noise_variance);
end
% compute sample probabilities and log likelihood of DLA model in
% numerically safe manner
max_log_likelihood = max(sample_log_likelihoods_dla(quasar_ind, :));
sample_probabilities = ...
exp(sample_log_likelihoods_dla(quasar_ind, :) - ...
max_log_likelihood);
log_likelihoods_dla(quasar_ind) = ...
max_log_likelihood + log(mean(sample_probabilities));
log_posteriors_dla(quasar_ind) = ...
log_priors_dla(quasar_ind) + log_likelihoods_dla(quasar_ind);
fprintf_debug(' ... log p(D | z_QSO, DLA) : %0.2f\n', ...
log_likelihoods_dla(quasar_ind));
fprintf_debug(' ... log p(DLA | D, z_QSO) : %0.2f\n', ...
log_posteriors_dla(quasar_ind));
fprintf(' took %0.3fs.\n', toc);
end
% compute model posteriors in numerically safe manner
max_log_posteriors = ...
max([log_posteriors_no_dla, log_posteriors_dla], [], 2);
model_posteriors = ...
exp([log_posteriors_no_dla, log_posteriors_dla] - max_log_posteriors);
model_posteriors = model_posteriors ./ sum(model_posteriors, 2);
p_no_dlas = model_posteriors(:, 1);
p_dlas = 1 - p_no_dlas;
% save results
variables_to_save = {'training_release', 'training_set_name', ...
'dla_catalog_name', 'prior_ind', 'release', ...
'test_set_name', 'test_ind', 'prior_z_qso_increase', ...
'max_z_cut', 'num_lines', 'min_z_dlas', 'max_z_dlas', ...
'log_priors_no_dla', 'log_priors_dla', ...
'log_likelihoods_no_dla', 'sample_log_likelihoods_dla', ...
'log_likelihoods_dla', 'log_posteriors_no_dla', ...
'log_posteriors_dla', 'model_posteriors', 'p_no_dlas', ...
'p_dlas'};
filename = sprintf('%s/processed_qsos_%s', ...
processed_directory(release), ...
test_set_name);
save(filename, variables_to_save{:}, '-v7.3');