def pairwise_reproducibility(df, plot=False):
    """
    Calculate the reproducibility of LA-ICPMS based on unique pairs of repeat analyses.
    
    Pairwise differences are fit with a half-Cauchy distribution, and the median and 
    95% confidence limits are returned for each analyte.
    
    Parameters
    ----------
    df : pandas.DataFrame
        A dataset
    
    plot : bool
        Whether or not to plot the resulting error distributions.
    
    Returns
    -------
    pdiffs : pandas.DataFrame
        Unique pairwise differences for all analytes.
    rep_dists : dict of scipy.stats.halfcauchy
        Half-Cauchy distribution objects fitted to the
        differences.
    rep_stats : dict of tuples
        The 50% and 95% quantiles of the half-cauchy
        distribution.
    (fig, axs) : matplotlib objects
        The figure. If not made, returnes (None, None) placeholder
    
    """
    
    ans = df.columns.values
    pdifs = []
    
    # calculate differences between unique pairs
    for ind, d in df.groupby(level=0):
        d.index = d.index.droplevel(0)

        difs = []
        for i, r in d.iterrows():
            t = d.loc[i+1:, :]
            difs.append(t[ans] - r[ans])

        pdifs.append(pd.concat(difs))
    pdifs = pd.concat(pdifs).abs()

    # calculate stats
    rep_stats = {}
    rep_dists = {}
    errfn = stats.halfcauchy
    
    for a in ans:
        d = pdifs.loc[:, a].dropna().values
        hdist = errfn.fit(d, floc=0)
        rep_dists[a] = errfn(*hdist)
        rep_stats[a] = rep_dists[a].ppf((0.5, 0.95))
    
    # make plot
    if not plot:
        return pdifs, rep_dists, rep_stats, (None, None)
    
    fig, axs = plt.subplots(1, len(ans), figsize=[len(ans) * 2, 2])
    for a, ax in zip(ans, axs):
        d = pdifs.loc[:, a].dropna().values
        hist, edges, _ = ax.hist(d, 30)
        ax.plot(edges, rep_dists[a].pdf(edges) * (sum(hist) * np.mean(np.diff(edges))))
        ax.set_title(a, loc='left')

    return pdifs, rep_dists, rep_stats, (fig, axs)
def pairwise_reproducibility(df, plot=False):
    """
    Calculate the reproducibility of LA-ICPMS based on unique pairs of repeat analyses.
    
    Pairwise differences are fit with a half-Cauchy distribution, and the median and 
    95% confidence limits are returned for each analyte.
    
    Parameters
    ----------
    df : pandas.DataFrame
        A dataset
    
    plot : bool
        Whether or not to plot the resulting error distributions.
    
    Returns
    -------
    pdiffs : pandas.DataFrame
        Unique pairwise differences for all analytes.
    rep_dists : dict of scipy.stats.halfcauchy
        Half-Cauchy distribution objects fitted to the
        differences.
    rep_stats : dict of tuples
        The 50% and 95% quantiles of the half-cauchy
        distribution.
    (fig, axs) : matplotlib objects
        The figure. If not made, returnes (None, None) placeholder
    
    """
    
    ans = df.columns.values
    pdifs = []
    
    # calculate differences between unique pairs
    for ind, d in df.groupby(level=0):
        d.index = d.index.droplevel(0)

        difs = []
        for i, r in d.iterrows():
            t = d.loc[i+1:, :]
            difs.append(t[ans] - r[ans])

        pdifs.append(pd.concat(difs))
    pdifs = pd.concat(pdifs).abs()

    # calculate stats
    rep_stats = {}
    rep_dists = {}
    errfn = stats.halfcauchy
    
    for a in ans:
        d = pdifs.loc[:, a].dropna().values
        hdist = errfn.fit(d, floc=0)
        rep_dists[a] = errfn(*hdist)
        rep_stats[a] = rep_dists[a].ppf((0.5, 0.95))
    
    # make plot
    if not plot:
        return pdifs, rep_dists, rep_stats, (None, None)
    
    fig, axs = plt.subplots(1, len(ans), figsize=[len(ans) * 2, 2])
    for a, ax in zip(ans, axs):
        d = pdifs.loc[:, a].dropna().values
        hist, edges, _ = ax.hist(d, 30)
        ax.plot(edges, rep_dists[a].pdf(edges) * (sum(hist) * np.mean(np.diff(edges))))
        ax.set_title(a, loc='left')

    return pdifs, rep_dists, rep_stats, (fig, axs)
def pairwise_reproducibility ( df , plot = False ) : ans = df . columns . values pdifs = [ ] # calculate differences between unique pairs for ind , d in df . groupby ( level = 0 ) : d . index = d . index . droplevel ( 0 ) difs = [ ] for i , r in d . iterrows ( ) : t = d . loc [ i + 1 : , : ] difs . append ( t [ ans ] - r [ ans ] ) pdifs . append ( pd . concat ( difs ) ) pdifs = pd . concat ( pdifs ) . abs ( ) # calculate stats rep_stats = { } rep_dists = { } errfn = stats . halfcauchy for a in ans : d = pdifs . loc [ : , a ] . dropna ( ) . values hdist = errfn . fit ( d , floc = 0 ) rep_dists [ a ] = errfn ( * hdist ) rep_stats [ a ] = rep_dists [ a ] . ppf ( ( 0.5 , 0.95 ) ) # make plot if not plot : return pdifs , rep_dists , rep_stats , ( None , None ) fig , axs = plt . subplots ( 1 , len ( ans ) , figsize = [ len ( ans ) * 2 , 2 ] ) for a , ax in zip ( ans , axs ) : d = pdifs . loc [ : , a ] . dropna ( ) . values hist , edges , _ = ax . hist ( d , 30 ) ax . plot ( edges , rep_dists [ a ] . pdf ( edges ) * ( sum ( hist ) * np . mean ( np . diff ( edges ) ) ) ) ax . set_title ( a , loc = 'left' ) return pdifs , rep_dists , rep_stats , ( fig , axs )
Calculate the reproducibility of LA-ICPMS based on unique pairs of repeat analyses.
    
    Pairwise differences are fit with a half-Cauchy distribution, and the median and 
    95% confidence limits are returned for each analyte.
    
    Parameters
    ----------
    df : pandas.DataFrame
        A dataset
    
    plot : bool
        Whether or not to plot the resulting error distributions.
    
    Returns
    -------
    pdiffs : pandas.DataFrame
        Unique pairwise differences for all analytes.
    rep_dists : dict of scipy.stats.halfcauchy
        Half-Cauchy distribution objects fitted to the
        differences.
    rep_stats : dict of tuples
        The 50% and 95% quantiles of the half-cauchy
        distribution.
    (fig, axs) : matplotlib objects
        The figure. If not made, returnes (None, None) placeholder
Calculate the reproducibility of LA - ICPMS based on unique pairs of repeat analyses . Pairwise differences are fit with a half - Cauchy distribution and the median and 95% confidence limits are returned for each analyte . Parameters ---------- df : pandas . DataFrame A dataset plot : bool Whether or not to plot the resulting error distributions . Returns ------- pdiffs : pandas . DataFrame Unique pairwise differences for all analytes . rep_dists : dict of scipy . stats . halfcauchy Half - Cauchy distribution objects fitted to the differences . rep_stats : dict of tuples The 50% and 95% quantiles of the half - cauchy distribution . ( fig axs ) : matplotlib objects The figure . If not made returnes ( None None ) placeholder