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gaiaspec.spectrum_correction

Empirical flux correction of Gaia XP spectra.

gaiaspec.spectrum_correction

Empirical flux correction of Gaia XP spectra against CALSPEC references.

Gaia XP spectra carry a smooth flux-calibration residual. This module correlates a target spectrum against a bundled table of Gaia spectra with known CALSPEC counterparts, picks the best-matching reference and returns the multiplicative wavelength-dependent correction that maps the Gaia flux onto the CALSPEC flux.

load_gaia_corrections 

load_gaia_corrections()

Load the bundled Gaia flux-correction table.

Returns:

Type Description

pandas.DataFrame: The data/gaia_flux_correction.parquet table, with

per-row wavelength, gaia_spectrum and corrected-flux columns.
Source code in gaiaspec/spectrum_correction.py 
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def load_gaia_corrections():
    """Load the bundled Gaia flux-correction table.

    Returns:
        pandas.DataFrame: The ``data/gaia_flux_correction.parquet`` table, with
        per-row ``wavelength``, ``gaia_spectrum`` and corrected-flux columns.
    """
    dirname = utils._getPackageDir()
    filename = os.path.join(dirname, "./data/gaia_flux_correction.parquet")
    df_gaia_correction = pd.read_parquet(filename)
    return df_gaia_correction

compute_gaia_correlation 

compute_gaia_correlation(df_gaia_correction, wavelength, flux)

Correlate one spectrum against every reference in the correction table.

Interpolates the input flux onto each reference wavelength grid (ignoring NaNs) and computes the Pearson correlation coefficient.

Parameters:

Name Type Description Default
df_gaia_correction DataFrame

Correction table (see :func:load_gaia_corrections).

 required
wavelength ndarray

Input wavelength grid.

 required
flux ndarray

Input flux.

 required

Returns:

Type Description

numpy.ndarray: Correlation coefficient with each reference row.
Source code in gaiaspec/spectrum_correction.py 
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def compute_gaia_correlation(
    df_gaia_correction,
    wavelength,
    flux,
):
    """Correlate one spectrum against every reference in the correction table.

    Interpolates the input flux onto each reference wavelength grid (ignoring
    NaNs) and computes the Pearson correlation coefficient.

    Args:
        df_gaia_correction (pandas.DataFrame): Correction table (see
            :func:`load_gaia_corrections`).
        wavelength (numpy.ndarray): Input wavelength grid.
        flux (numpy.ndarray): Input flux.

    Returns:
        numpy.ndarray: Correlation coefficient with each reference row.
    """
    correlation_with_gaia = []

    for i in range(len(df_gaia_correction)):
        mask_nan_gaia_ref = ~np.isnan(df_gaia_correction["gaia_spectrum"][i])
        mask_nan_gaia = ~np.isnan(flux)

        flux_interp = np.interp(
            df_gaia_correction["wavelength"][i][mask_nan_gaia_ref],
            wavelength[mask_nan_gaia],
            flux[mask_nan_gaia],
        )

        correlation_with_gaia.append(
            np.corrcoef(
                flux_interp,
                df_gaia_correction["gaia_spectrum"][i][mask_nan_gaia_ref],
            )[0][1]
        )

    return np.array(correlation_with_gaia)

find_best_gaia_correction 

find_best_gaia_correction(df_gaia_correction, wavelength, corr_threshold=0.8, choose_corr='m3', verbose=True)

Return the correction of the best-correlated reference above a threshold.

Sorts references by correlation and, for the best one above corr_threshold, returns the corrected_flux / gaia_spectrum ratio interpolated onto wavelength (unity where no acceptable match exists).

Parameters:

Name Type Description Default
df_gaia_correction DataFrame

Correction table with a correlation_with_gaia column.

 required
wavelength ndarray

Target wavelength grid.

 required
corr_threshold float

Minimum acceptable correlation.

 0.8
choose_corr str

Correction variant column suffix (e.g. "m3" -> gaia_corrected_flux_m3).

 'm3'
verbose bool

Print when no correction is found.

 True

Returns:

Type Description

numpy.ndarray: Multiplicative correction on wavelength (ones if none).
Source code in gaiaspec/spectrum_correction.py 
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def find_best_gaia_correction(
    df_gaia_correction,
    wavelength,
    corr_threshold=0.8,
    choose_corr="m3",
    verbose=True,
):
    """Return the correction of the best-correlated reference above a threshold.

    Sorts references by correlation and, for the best one above
    ``corr_threshold``, returns the ``corrected_flux / gaia_spectrum`` ratio
    interpolated onto ``wavelength`` (unity where no acceptable match exists).

    Args:
        df_gaia_correction (pandas.DataFrame): Correction table with a
            ``correlation_with_gaia`` column.
        wavelength (numpy.ndarray): Target wavelength grid.
        corr_threshold (float, optional): Minimum acceptable correlation.
        choose_corr (str, optional): Correction variant column suffix
            (e.g. ``"m3"`` -> ``gaia_corrected_flux_m3``).
        verbose (bool, optional): Print when no correction is found.

    Returns:
        numpy.ndarray: Multiplicative correction on ``wavelength`` (ones if none).
    """
    df_gaia_correction_sorted = df_gaia_correction.sort_values(
        "correlation_with_gaia", ascending=False
    )
    for i in df_gaia_correction_sorted.index:
        if df_gaia_correction_sorted["correlation_with_gaia"][i] < corr_threshold:
            if verbose:
                print("no GAIA correction was found under the selected criteria")
            return np.ones_like(wavelength)
        if (df_gaia_correction_sorted["correlation_with_gaia"][i] is not np.nan) and (
            df_gaia_correction_sorted[f"gaia_corrected_flux_{choose_corr}"][i]
            is not None
        ):
            correction_ref = (
                df_gaia_correction_sorted[f"gaia_corrected_flux_{choose_corr}"][i]
                / df_gaia_correction_sorted["gaia_spectrum"][i]
            )
            wave = df_gaia_correction_sorted["wavelength"][i]
            correction = np.interp(wavelength, wave, correction_ref)
            correction[np.isnan(correction)] = 1.0
            return correction
        else:
            return np.ones_like(wavelength)

return_gaia_spectra_correction 

return_gaia_spectra_correction(wavelength, flux, corr_threshold=0.8, choose_corr='m3')

Compute the empirical flux correction for a single spectrum.

Convenience wrapper chaining :func:load_gaia_corrections, :func:compute_gaia_correlation and :func:find_best_gaia_correction.

Parameters:

Name Type Description Default
wavelength ndarray

Input wavelength grid.

 required
flux ndarray

Input flux.

 required
corr_threshold float

Minimum acceptable correlation.

 0.8
choose_corr str

Correction variant suffix.

 'm3'

Returns:

Type Description

numpy.ndarray: Multiplicative correction on wavelength.
Source code in gaiaspec/spectrum_correction.py 
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def return_gaia_spectra_correction(
    wavelength,
    flux,
    corr_threshold=0.8,
    choose_corr="m3",
):
    """Compute the empirical flux correction for a single spectrum.

    Convenience wrapper chaining :func:`load_gaia_corrections`,
    :func:`compute_gaia_correlation` and :func:`find_best_gaia_correction`.

    Args:
        wavelength (numpy.ndarray): Input wavelength grid.
        flux (numpy.ndarray): Input flux.
        corr_threshold (float, optional): Minimum acceptable correlation.
        choose_corr (str, optional): Correction variant suffix.

    Returns:
        numpy.ndarray: Multiplicative correction on ``wavelength``.
    """
    df_gaia_correction = load_gaia_corrections()

    df_gaia_correction["correlation_with_gaia"] = compute_gaia_correlation(
        df_gaia_correction,
        wavelength,
        flux,
    )

    correction = find_best_gaia_correction(
        df_gaia_correction,
        wavelength,
        corr_threshold=corr_threshold,
        choose_corr=choose_corr,
    )
    return correction

multi_pearsonr 

multi_pearsonr(x, y)

Pearson correlation of many row-vectors x against one vector y.

Vectorised equivalent of calling :func:scipy.stats.pearsonr for each row of x against y.

Parameters:

Name Type Description Default
x ndarray

Array of shape (n, m) (n spectra of length m).

 required
y ndarray

Reference vector of length m.

 required

Returns:

Type Description

numpy.ndarray: Length-n correlation coefficients, clipped to

[-1, 1].
Source code in gaiaspec/spectrum_correction.py 
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def multi_pearsonr(x, y):
    """Pearson correlation of many row-vectors ``x`` against one vector ``y``.

    Vectorised equivalent of calling :func:`scipy.stats.pearsonr` for each row
    of ``x`` against ``y``.

    Args:
        x (numpy.ndarray): Array of shape ``(n, m)`` (``n`` spectra of length m).
        y (numpy.ndarray): Reference vector of length ``m``.

    Returns:
        numpy.ndarray: Length-``n`` correlation coefficients, clipped to
        ``[-1, 1]``.
    """
    xmean = x.mean(axis=1)
    ymean = y.mean()
    xm = x - xmean[:, None]
    ym = y - ymean
    normxm = np.linalg.norm(xm, axis=1)
    normym = np.linalg.norm(ym)
    return np.clip(np.dot(xm / normxm[:, None], ym / normym), -1.0, 1.0)

compute_gaia_correlation_multiple_spectra 

compute_gaia_correlation_multiple_spectra(df_gaia_correction, wavelength, fluxes)

Correlate many spectra against every reference in the correction table.

Vectorised counterpart of :func:compute_gaia_correlation for a batch of input spectra sharing one wavelength grid.

Parameters:

Name Type Description Default
df_gaia_correction DataFrame

Correction table.

 required
wavelength ndarray

Shared input wavelength grid.

 required
fluxes iterable[ndarray]

Input fluxes.

 required

Returns:

Type Description

numpy.ndarray: Correlation array of shape (n_fluxes, n_references).
Source code in gaiaspec/spectrum_correction.py 
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def compute_gaia_correlation_multiple_spectra(
    df_gaia_correction,
    wavelength,
    fluxes,
):
    """Correlate many spectra against every reference in the correction table.

    Vectorised counterpart of :func:`compute_gaia_correlation` for a batch of
    input spectra sharing one ``wavelength`` grid.

    Args:
        df_gaia_correction (pandas.DataFrame): Correction table.
        wavelength (numpy.ndarray): Shared input wavelength grid.
        fluxes (iterable[numpy.ndarray]): Input fluxes.

    Returns:
        numpy.ndarray: Correlation array of shape ``(n_fluxes, n_references)``.
    """
    df_gaia_correction_interpolated = np.zeros(
        (df_gaia_correction.shape[0], wavelength.size)
    )

    for i, index in enumerate(df_gaia_correction.index):
        wave_gaia_correction = df_gaia_correction["wavelength"][index]
        flux_gaia_correction = df_gaia_correction["gaia_spectrum"][index]

        mask_nan_gaia_correction = ~np.isnan(flux_gaia_correction)
        df_gaia_correction_interpolated[i] = np.interp(
            wavelength,
            wave_gaia_correction[mask_nan_gaia_correction],
            flux_gaia_correction[mask_nan_gaia_correction],
        )

    correlation_with_gaia = []

    for flux in fluxes:
        pearsonr_values = multi_pearsonr(df_gaia_correction_interpolated, flux)
        correlation_with_gaia.append(pearsonr_values)

    return np.array(correlation_with_gaia)

return_gaia_spectra_correction_multiple 

return_gaia_spectra_correction_multiple(wavelength, fluxes, corr_threshold=0.8, choose_corr='m3')

Compute the empirical flux correction for several spectra at once.

Parameters:

Name Type Description Default
wavelength ndarray

Shared input wavelength grid.

 required
fluxes iterable[ndarray]

Input fluxes.

 required
corr_threshold float

Minimum acceptable correlation.

 0.8
choose_corr str

Correction variant suffix.

 'm3'

Returns:

Type Description

numpy.ndarray: One multiplicative correction per input flux.
Source code in gaiaspec/spectrum_correction.py 
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def return_gaia_spectra_correction_multiple(
    wavelength,
    fluxes,
    corr_threshold=0.8,
    choose_corr="m3",
):
    """Compute the empirical flux correction for several spectra at once.

    Args:
        wavelength (numpy.ndarray): Shared input wavelength grid.
        fluxes (iterable[numpy.ndarray]): Input fluxes.
        corr_threshold (float, optional): Minimum acceptable correlation.
        choose_corr (str, optional): Correction variant suffix.

    Returns:
        numpy.ndarray: One multiplicative correction per input flux.
    """
    df_gaia_correction = load_gaia_corrections()

    correlation_with_gaia = compute_gaia_correlation_multiple_spectra(
        df_gaia_correction,
        wavelength,
        fluxes,
    )
    corrections = []
    for i, _ in enumerate(fluxes):
        df_gaia_correction["correlation_with_gaia"] = correlation_with_gaia[i]

        correction = find_best_gaia_correction(
            df_gaia_correction,
            wavelength,
            corr_threshold=corr_threshold,
            choose_corr=choose_corr,
            verbose=False,
        )
        corrections.append(correction)

    return np.array(corrections)