xs, n=None):
    """Draw a sample from xs with the same length as xs.

    xs: sequence
    n: sample size (default: len(xs))

    returns: NumPy array
    """
    if n is None:
        n = len(xs)
    return np.random.choice(xs, n, replace=True)


def SampleRows(df, nrows, replace=False):
    """Choose a sample of rows from a DataFrame.

    df: DataFrame
    nrows: number of rows
    replace: whether to sample with replacement

    returns: DataDf
    """
    indices = np.random.choice(df.index, nrows, replace=replace)
    sample = df.loc[indices]
    return sample


def ResampleRows(df):
    """Resamples rows from a DataFrame.

    df: DataFrame

    returns: DataFrame
    """
    return SampleRows(df, len(df), replace=True)


def ResampleRowsWeighted(df, column='finalwgt'):
    """Resamples a DataFrame using probabilities proportional to given column.

    df: DataFrame
    column: string column name to use as weights

    returns: DataFrame
    """
    weights = df[column]
    cdf = Cdf(dict(weights))
    indices = cdf.Sample(len(weights))
    sample = df.loc[indices]
    return sample


def PercentileRow(array, p):
    """Selects the row from a sorted array that maps to percentile p.

    p: float 0--100

    returns: NumPy array (one row)
    """
    rows, cols = array.shape
    index = int(rows * p / 100)
    return array[index,]


def PercentileRows(ys_seq, percents):
    """Given a collection of lines, selects percentiles along vertical axis.

    For example, if ys_seq contains simulation results like ys as a
    function of time, and percents contains (5, 95), the result would
    be a 90% CI for each vertical slice of the simulation results.

    ys_seq: sequence of lines (y values)
    percents: list of percentiles (0-100) to select

    returns: list of NumPy arrays, one for each pe