0x1998 - MANAGER

Düzenlenen Dosya: arrayprint.py

"""Array printing function

$Id: arrayprint.py,v 1.9 2005/09/13 13:58:44 teoliphant Exp $

"""
from __future__ import division, absolute_import, print_function

__all__ = ["array2string", "set_printoptions", "get_printoptions"]
__docformat__ = 'restructuredtext'

#
# Written by Konrad Hinsen <hinsenk@ere.umontreal.ca>
# last revision: 1996-3-13
# modified by Jim Hugunin 1997-3-3 for repr's and str's (and other details)
# and by Perry Greenfield 2000-4-1 for numarray
# and by Travis Oliphant  2005-8-22 for numpy

import sys
import functools
if sys.version_info[0] >= 3:
    try:
        from _thread import get_ident
    except ImportError:
        from _dummy_thread import get_ident
else:
    try:
        from thread import get_ident
    except ImportError:
        from dummy_thread import get_ident

from . import numerictypes as _nt
from .umath import maximum, minimum, absolute, not_equal, isnan, isinf
from .multiarray import (array, format_longfloat, datetime_as_string,
                         datetime_data, dtype)
from .fromnumeric import ravel
from .numeric import asarray

if sys.version_info[0] >= 3:
    _MAXINT = sys.maxsize
    _MININT = -sys.maxsize - 1
else:
    _MAXINT = sys.maxint
    _MININT = -sys.maxint - 1

def product(x, y):
    return x*y

_summaryEdgeItems = 3     # repr N leading and trailing items of each dimension
_summaryThreshold = 1000  # total items > triggers array summarization

_float_output_precision = 8
_float_output_suppress_small = False
_line_width = 75
_nan_str = 'nan'
_inf_str = 'inf'
_formatter = None  # formatting function for array elements

def set_printoptions(precision=None, threshold=None, edgeitems=None,
                     linewidth=None, suppress=None,
                     nanstr=None, infstr=None,
                     formatter=None):
    """
    Set printing options.

These options determine the way floating point numbers, arrays and
    other NumPy objects are displayed.

Parameters
    ----------
    precision : int, optional
        Number of digits of precision for floating point output (default 8).
    threshold : int, optional
        Total number of array elements which trigger summarization
        rather than full repr (default 1000).
    edgeitems : int, optional
        Number of array items in summary at beginning and end of
        each dimension (default 3).
    linewidth : int, optional
        The number of characters per line for the purpose of inserting
        line breaks (default 75).
    suppress : bool, optional
        Whether or not suppress printing of small floating point values
        using scientific notation (default False).
    nanstr : str, optional
        String representation of floating point not-a-number (default nan).
    infstr : str, optional
        String representation of floating point infinity (default inf).
    formatter : dict of callables, optional
        If not None, the keys should indicate the type(s) that the respective
        formatting function applies to.  Callables should return a string.
        Types that are not specified (by their corresponding keys) are handled
        by the default formatters.  Individual types for which a formatter
        can be set are::

- 'bool'
            - 'int'
            - 'timedelta' : a `numpy.timedelta64`
            - 'datetime' : a `numpy.datetime64`
            - 'float'
            - 'longfloat' : 128-bit floats
            - 'complexfloat'
            - 'longcomplexfloat' : composed of two 128-bit floats
            - 'numpystr' : types `numpy.string_` and `numpy.unicode_`
            - 'object' : `np.object_` arrays
            - 'str' : all other strings

Other keys that can be used to set a group of types at once are::

- 'all' : sets all types
            - 'int_kind' : sets 'int'
            - 'float_kind' : sets 'float' and 'longfloat'
            - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'
            - 'str_kind' : sets 'str' and 'numpystr'

See Also
    --------
    get_printoptions, set_string_function, array2string

Notes
    -----
    `formatter` is always reset with a call to `set_printoptions`.

Examples
    --------
    Floating point precision can be set:

>>> np.set_printoptions(precision=4)
    >>> print(np.array([1.123456789]))
    [ 1.1235]

Long arrays can be summarised:

>>> np.set_printoptions(threshold=5)
    >>> print(np.arange(10))
    [0 1 2 ..., 7 8 9]

Small results can be suppressed:

>>> eps = np.finfo(float).eps
    >>> x = np.arange(4.)
    >>> x**2 - (x + eps)**2
    array([ -4.9304e-32,  -4.4409e-16,   0.0000e+00,   0.0000e+00])
    >>> np.set_printoptions(suppress=True)
    >>> x**2 - (x + eps)**2
    array([-0., -0.,  0.,  0.])

A custom formatter can be used to display array elements as desired:

>>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})
    >>> x = np.arange(3)
    >>> x
    array([int: 0, int: -1, int: -2])
    >>> np.set_printoptions()  # formatter gets reset
    >>> x
    array([0, 1, 2])

To put back the default options, you can use:

>>> np.set_printoptions(edgeitems=3,infstr='inf',
    ... linewidth=75, nanstr='nan', precision=8,
    ... suppress=False, threshold=1000, formatter=None)
    """

global _summaryThreshold, _summaryEdgeItems, _float_output_precision
    global _line_width, _float_output_suppress_small, _nan_str, _inf_str
    global _formatter

if linewidth is not None:
        _line_width = linewidth
    if threshold is not None:
        _summaryThreshold = threshold
    if edgeitems is not None:
        _summaryEdgeItems = edgeitems
    if precision is not None:
        _float_output_precision = precision
    if suppress is not None:
        _float_output_suppress_small = not not suppress
    if nanstr is not None:
        _nan_str = nanstr
    if infstr is not None:
        _inf_str = infstr
    _formatter = formatter

def get_printoptions():
    """
    Return the current print options.

Returns
    -------
    print_opts : dict
        Dictionary of current print options with keys

- precision : int
          - threshold : int
          - edgeitems : int
          - linewidth : int
          - suppress : bool
          - nanstr : str
          - infstr : str
          - formatter : dict of callables

For a full description of these options, see `set_printoptions`.

See Also
    --------
    set_printoptions, set_string_function

"""
    d = dict(precision=_float_output_precision,
             threshold=_summaryThreshold,
             edgeitems=_summaryEdgeItems,
             linewidth=_line_width,
             suppress=_float_output_suppress_small,
             nanstr=_nan_str,
             infstr=_inf_str,
             formatter=_formatter)
    return d

def _leading_trailing(a):
    from . import numeric as _nc
    if a.ndim == 1:
        if len(a) > 2*_summaryEdgeItems:
            b = _nc.concatenate((a[:_summaryEdgeItems],
                                     a[-_summaryEdgeItems:]))
        else:
            b = a
    else:
        if len(a) > 2*_summaryEdgeItems:
            l = [_leading_trailing(a[i]) for i in range(
                min(len(a), _summaryEdgeItems))]
            l.extend([_leading_trailing(a[-i]) for i in range(
                min(len(a), _summaryEdgeItems), 0, -1)])
        else:
            l = [_leading_trailing(a[i]) for i in range(0, len(a))]
        b = _nc.concatenate(tuple(l))
    return b

def _boolFormatter(x):
    if x:
        return ' True'
    else:
        return 'False'

def _object_format(o):
    """ Object arrays containing lists should be printed unambiguously """
    if type(o) is list:
        fmt = 'list({!r})'
    else:
        fmt = '{!r}'
    return fmt.format(o)

def repr_format(x):
    return repr(x)

def _get_formatdict(data, precision, suppress_small, formatter):
    # wrapped in lambdas to avoid taking a code path with the wrong type of data
    formatdict = {'bool': lambda: _boolFormatter,
                  'int': lambda: IntegerFormat(data),
                  'float': lambda: FloatFormat(data, precision, suppress_small),
                  'longfloat': lambda: LongFloatFormat(precision),
                  'complexfloat': lambda: ComplexFormat(data, precision,
                                                 suppress_small),
                  'longcomplexfloat': lambda: LongComplexFormat(precision),
                  'datetime': lambda: DatetimeFormat(data),
                  'timedelta': lambda: TimedeltaFormat(data),
                  'object': lambda: _object_format,
                  'numpystr': lambda: repr_format,
                  'str': lambda: str}

# we need to wrap values in `formatter` in a lambda, so that the interface
    # is the same as the above values.
    def indirect(x):
        return lambda: x

if formatter is not None:
        fkeys = [k for k in formatter.keys() if formatter[k] is not None]
        if 'all' in fkeys:
            for key in formatdict.keys():
                formatdict[key] = indirect(formatter['all'])
        if 'int_kind' in fkeys:
            for key in ['int']:
                formatdict[key] = indirect(formatter['int_kind'])
        if 'float_kind' in fkeys:
            for key in ['float', 'longfloat']:
                formatdict[key] = indirect(formatter['float_kind'])
        if 'complex_kind' in fkeys:
            for key in ['complexfloat', 'longcomplexfloat']:
                formatdict[key] = indirect(formatter['complex_kind'])
        if 'str_kind' in fkeys:
            for key in ['numpystr', 'str']:
                formatdict[key] = indirect(formatter['str_kind'])
        for key in formatdict.keys():
            if key in fkeys:
                formatdict[key] = indirect(formatter[key])

return formatdict

def _get_format_function(data, precision, suppress_small, formatter):
    """
    find the right formatting function for the dtype_
    """
    dtype_ = data.dtype
    if dtype_.fields is not None:
        format_functions = []
        for field_name in dtype_.names:
            field_values = data[field_name]
            format_function = _get_format_function(
                    ravel(field_values), precision, suppress_small, formatter)
            if dtype_[field_name].shape != ():
                format_function = SubArrayFormat(format_function)
            format_functions.append(format_function)
        return StructureFormat(format_functions)

dtypeobj = dtype_.type
    formatdict = _get_formatdict(data, precision, suppress_small, formatter)
    if issubclass(dtypeobj, _nt.bool_):
        return formatdict['bool']()
    elif issubclass(dtypeobj, _nt.integer):
        if issubclass(dtypeobj, _nt.timedelta64):
            return formatdict['timedelta']()
        else:
            return formatdict['int']()
    elif issubclass(dtypeobj, _nt.floating):
        if issubclass(dtypeobj, _nt.longfloat):
            return formatdict['longfloat']()
        else:
            return formatdict['float']()
    elif issubclass(dtypeobj, _nt.complexfloating):
        if issubclass(dtypeobj, _nt.clongfloat):
            return formatdict['longcomplexfloat']()
        else:
            return formatdict['complexfloat']()
    elif issubclass(dtypeobj, (_nt.unicode_, _nt.string_)):
        return formatdict['numpystr']()
    elif issubclass(dtypeobj, _nt.datetime64):
        return formatdict['datetime']()
    elif issubclass(dtypeobj, _nt.object_):
        return formatdict['object']()
    else:
        return formatdict['numpystr']()

def _array2string(a, max_line_width, precision, suppress_small, separator=' ',
                  prefix="", formatter=None):

if a.size > _summaryThreshold:
        summary_insert = "..., "
        data = _leading_trailing(a)
    else:
        summary_insert = ""
        data = ravel(asarray(a))

# find the right formatting function for the array
    format_function = _get_format_function(data, precision,
                                           suppress_small, formatter)

# skip over "["
    next_line_prefix = " "
    # skip over array(
    next_line_prefix += " "*len(prefix)

lst = _formatArray(a, format_function, a.ndim, max_line_width,
                       next_line_prefix, separator,
                       _summaryEdgeItems, summary_insert)[:-1]
    return lst

def _recursive_guard(fillvalue='...'):
    """
    Like the python 3.2 reprlib.recursive_repr, but forwards *args and **kwargs

Decorates a function such that if it calls itself with the same first
    argument, it returns `fillvalue` instead of recursing.

Largely copied from reprlib.recursive_repr
    """

def decorating_function(f):
        repr_running = set()

@functools.wraps(f)
        def wrapper(self, *args, **kwargs):
            key = id(self), get_ident()
            if key in repr_running:
                return fillvalue
            repr_running.add(key)
            try:
                return f(self, *args, **kwargs)
            finally:
                repr_running.discard(key)

return wrapper

return decorating_function

# gracefully handle recursive calls - this comes up when object arrays contain
# themselves
@_recursive_guard()
def array2string(a, max_line_width=None, precision=None,
                 suppress_small=None, separator=' ', prefix="",
                 style=repr, formatter=None):
    """
    Return a string representation of an array.

Parameters
    ----------
    a : ndarray
        Input array.
    max_line_width : int, optional
        The maximum number of columns the string should span. Newline
        characters splits the string appropriately after array elements.
    precision : int, optional
        Floating point precision. Default is the current printing
        precision (usually 8), which can be altered using `set_printoptions`.
    suppress_small : bool, optional
        Represent very small numbers as zero. A number is "very small" if it
        is smaller than the current printing precision.
    separator : str, optional
        Inserted between elements.
    prefix : str, optional
        An array is typically printed as::

'prefix(' + array2string(a) + ')'

The length of the prefix string is used to align the
        output correctly.
    style : function, optional
        A function that accepts an ndarray and returns a string.  Used only
        when the shape of `a` is equal to ``()``, i.e. for 0-D arrays.
    formatter : dict of callables, optional
        If not None, the keys should indicate the type(s) that the respective
        formatting function applies to.  Callables should return a string.
        Types that are not specified (by their corresponding keys) are handled
        by the default formatters.  Individual types for which a formatter
        can be set are::

Other keys that can be used to set a group of types at once are::

Returns
    -------
    array_str : str
        String representation of the array.

Raises
    ------
    TypeError
        if a callable in `formatter` does not return a string.

See Also
    --------
    array_str, array_repr, set_printoptions, get_printoptions

Notes
    -----
    If a formatter is specified for a certain type, the `precision` keyword is
    ignored for that type.

This is a very flexible function; `array_repr` and `array_str` are using
    `array2string` internally so keywords with the same name should work
    identically in all three functions.

Examples
    --------
    >>> x = np.array([1e-16,1,2,3])
    >>> print(np.array2string(x, precision=2, separator=',',
    ...                       suppress_small=True))
    [ 0., 1., 2., 3.]

>>> x  = np.arange(3.)
    >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x})
    '[0.00 1.00 2.00]'

>>> x  = np.arange(3)
    >>> np.array2string(x, formatter={'int':lambda x: hex(x)})
    '[0x0L 0x1L 0x2L]'

"""

if max_line_width is None:
        max_line_width = _line_width

if precision is None:
        precision = _float_output_precision

if suppress_small is None:
        suppress_small = _float_output_suppress_small

if formatter is None:
        formatter = _formatter

if a.shape == ():
        x = a.item()
        if a.dtype.fields is not None:
            arr = array([x], dtype=a.dtype)
            format_function = _get_format_function(
                    arr, precision, suppress_small, formatter)
            lst = format_function(arr[0])
        else:
            lst = style(x)
    elif functools.reduce(product, a.shape) == 0:
        # treat as a null array if any of shape elements == 0
        lst = "[]"
    else:
        lst = _array2string(a, max_line_width, precision, suppress_small,
                            separator, prefix, formatter=formatter)
    return lst

def _extendLine(s, line, word, max_line_len, next_line_prefix):
    if len(line.rstrip()) + len(word.rstrip()) >= max_line_len:
        s += line.rstrip() + "\n"
        line = next_line_prefix
    line += word
    return s, line

def _formatArray(a, format_function, rank, max_line_len,
                 next_line_prefix, separator, edge_items, summary_insert):
    """formatArray is designed for two modes of operation:

1. Full output

2. Summarized output

"""
    if rank == 0:
        raise ValueError("rank shouldn't be zero.")

if summary_insert and 2*edge_items < len(a):
        leading_items = edge_items
        trailing_items = edge_items
        summary_insert1 = summary_insert
    else:
        leading_items = 0
        trailing_items = len(a)
        summary_insert1 = ""

if rank == 1:
        s = ""
        line = next_line_prefix
        for i in range(leading_items):
            word = format_function(a[i]) + separator
            s, line = _extendLine(s, line, word, max_line_len, next_line_prefix)

if summary_insert1:
            s, line = _extendLine(s, line, summary_insert1, max_line_len, next_line_prefix)

for i in range(trailing_items, 1, -1):
            word = format_function(a[-i]) + separator
            s, line = _extendLine(s, line, word, max_line_len, next_line_prefix)

word = format_function(a[-1])
        s, line = _extendLine(s, line, word, max_line_len, next_line_prefix)
        s += line + "]\n"
        s = '[' + s[len(next_line_prefix):]
    else:
        s = '['
        sep = separator.rstrip()
        for i in range(leading_items):
            if i > 0:
                s += next_line_prefix
            s += _formatArray(a[i], format_function, rank-1, max_line_len,
                              " " + next_line_prefix, separator, edge_items,
                              summary_insert)
            s = s.rstrip() + sep.rstrip() + '\n'*max(rank-1, 1)

if summary_insert1:
            s += next_line_prefix + summary_insert1 + "\n"

for i in range(trailing_items, 1, -1):
            if leading_items or i != trailing_items:
                s += next_line_prefix
            s += _formatArray(a[-i], format_function, rank-1, max_line_len,
                              " " + next_line_prefix, separator, edge_items,
                              summary_insert)
            s = s.rstrip() + sep.rstrip() + '\n'*max(rank-1, 1)
        if leading_items or trailing_items > 1:
            s += next_line_prefix
        s += _formatArray(a[-1], format_function, rank-1, max_line_len,
                          " " + next_line_prefix, separator, edge_items,
                          summary_insert).rstrip()+']\n'
    return s

class FloatFormat(object):
    def __init__(self, data, precision, suppress_small, sign=False):
        self.precision = precision
        self.suppress_small = suppress_small
        self.sign = sign
        self.exp_format = False
        self.large_exponent = False
        self.max_str_len = 0
        try:
            self.fillFormat(data)
        except (TypeError, NotImplementedError):
            # if reduce(data) fails, this instance will not be called, just
            # instantiated in formatdict.
            pass

def fillFormat(self, data):
        from . import numeric as _nc

with _nc.errstate(all='ignore'):
            special = isnan(data) | isinf(data)
            valid = not_equal(data, 0) & ~special
            non_zero = absolute(data.compress(valid))
            if len(non_zero) == 0:
                max_val = 0.
                min_val = 0.
            else:
                max_val = maximum.reduce(non_zero)
                min_val = minimum.reduce(non_zero)
                if max_val >= 1.e8:
                    self.exp_format = True
                if not self.suppress_small and (min_val < 0.0001
                                           or max_val/min_val > 1000.):
                    self.exp_format = True

if self.exp_format:
            self.large_exponent = 0 < min_val < 1e-99 or max_val >= 1e100
            self.max_str_len = 8 + self.precision
            if self.large_exponent:
                self.max_str_len += 1
            if self.sign:
                format = '%+'
            else:
                format = '%'
            format = format + '%d.%de' % (self.max_str_len, self.precision)
        else:
            format = '%%.%df' % (self.precision,)
            if len(non_zero):
                precision = max([_digits(x, self.precision, format)
                                 for x in non_zero])
            else:
                precision = 0
            precision = min(self.precision, precision)
            self.max_str_len = len(str(int(max_val))) + precision + 2
            if _nc.any(special):
                self.max_str_len = max(self.max_str_len,
                                       len(_nan_str),
                                       len(_inf_str)+1)
            if self.sign:
                format = '%#+'
            else:
                format = '%#'
            format = format + '%d.%df' % (self.max_str_len, precision)

self.special_fmt = '%%%ds' % (self.max_str_len,)
        self.format = format

def __call__(self, x, strip_zeros=True):
        from . import numeric as _nc

with _nc.errstate(invalid='ignore'):
            if isnan(x):
                if self.sign:
                    return self.special_fmt % ('+' + _nan_str,)
                else:
                    return self.special_fmt % (_nan_str,)
            elif isinf(x):
                if x > 0:
                    if self.sign:
                        return self.special_fmt % ('+' + _inf_str,)
                    else:
                        return self.special_fmt % (_inf_str,)
                else:
                    return self.special_fmt % ('-' + _inf_str,)

s = self.format % x
        if self.large_exponent:
            # 3-digit exponent
            expsign = s[-3]
            if expsign == '+' or expsign == '-':
                s = s[1:-2] + '0' + s[-2:]
        elif self.exp_format:
            # 2-digit exponent
            if s[-3] == '0':
                s = ' ' + s[:-3] + s[-2:]
        elif strip_zeros:
            z = s.rstrip('0')
            s = z + ' '*(len(s)-len(z))
        return s

def _digits(x, precision, format):
    if precision > 0:
        s = format % x
        z = s.rstrip('0')
        return precision - len(s) + len(z)
    else:
        return 0

class IntegerFormat(object):
    def __init__(self, data):
        try:
            max_str_len = max(len(str(maximum.reduce(data))),
                              len(str(minimum.reduce(data))))
            self.format = '%' + str(max_str_len) + 'd'
        except (TypeError, NotImplementedError):
            # if reduce(data) fails, this instance will not be called, just
            # instantiated in formatdict.
            pass
        except ValueError:
            # this occurs when everything is NA
            pass

def __call__(self, x):
        if _MININT < x < _MAXINT:
            return self.format % x
        else:
            return "%s" % x

class LongFloatFormat(object):
    # XXX Have to add something to determine the width to use a la FloatFormat
    # Right now, things won't line up properly
    def __init__(self, precision, sign=False):
        self.precision = precision
        self.sign = sign

def __call__(self, x):
        if isnan(x):
            if self.sign:
                return '+' + _nan_str
            else:
                return ' ' + _nan_str
        elif isinf(x):
            if x > 0:
                if self.sign:
                    return '+' + _inf_str
                else:
                    return ' ' + _inf_str
            else:
                return '-' + _inf_str
        elif x >= 0:
            if self.sign:
                return '+' + format_longfloat(x, self.precision)
            else:
                return ' ' + format_longfloat(x, self.precision)
        else:
            return format_longfloat(x, self.precision)

class LongComplexFormat(object):
    def __init__(self, precision):
        self.real_format = LongFloatFormat(precision)
        self.imag_format = LongFloatFormat(precision, sign=True)

def __call__(self, x):
        r = self.real_format(x.real)
        i = self.imag_format(x.imag)
        return r + i + 'j'

class ComplexFormat(object):
    def __init__(self, x, precision, suppress_small):
        self.real_format = FloatFormat(x.real, precision, suppress_small)
        self.imag_format = FloatFormat(x.imag, precision, suppress_small,
                                       sign=True)

def __call__(self, x):
        r = self.real_format(x.real, strip_zeros=False)
        i = self.imag_format(x.imag, strip_zeros=False)
        if not self.imag_format.exp_format:
            z = i.rstrip('0')
            i = z + 'j' + ' '*(len(i)-len(z))
        else:
            i = i + 'j'
        return r + i

class DatetimeFormat(object):
    def __init__(self, x, unit=None, timezone=None, casting='same_kind'):
        # Get the unit from the dtype
        if unit is None:
            if x.dtype.kind == 'M':
                unit = datetime_data(x.dtype)[0]
            else:
                unit = 's'

if timezone is None:
            timezone = 'naive'
        self.timezone = timezone
        self.unit = unit
        self.casting = casting

def __call__(self, x):
        return "'%s'" % datetime_as_string(x,
                                    unit=self.unit,
                                    timezone=self.timezone,
                                    casting=self.casting)

class TimedeltaFormat(object):
    def __init__(self, data):
        if data.dtype.kind == 'm':
            nat_value = array(['NaT'], dtype=data.dtype)[0]
            int_dtype = dtype(data.dtype.byteorder + 'i8')
            int_view = data.view(int_dtype)
            v = int_view[not_equal(int_view, nat_value.view(int_dtype))]
            if len(v) > 0:
                # Max str length of non-NaT elements
                max_str_len = max(len(str(maximum.reduce(v))),
                                  len(str(minimum.reduce(v))))
            else:
                max_str_len = 0
            if len(v) < len(data):
                # data contains a NaT
                max_str_len = max(max_str_len, 5)
            self.format = '%' + str(max_str_len) + 'd'
            self._nat = "'NaT'".rjust(max_str_len)

def __call__(self, x):
        # TODO: After NAT == NAT deprecation should be simplified:
        if (x + 1).view('i8') == x.view('i8'):
            return self._nat
        else:
            return self.format % x.astype('i8')

class SubArrayFormat(object):
    def __init__(self, format_function):
        self.format_function = format_function

def __call__(self, arr):
        if arr.ndim <= 1:
            return "[" + ", ".join(self.format_function(a) for a in arr) + "]"
        return "[" + ", ".join(self.__call__(a) for a in arr) + "]"

class StructureFormat(object):
    def __init__(self, format_functions):
        self.format_functions = format_functions
        self.num_fields = len(format_functions)

def __call__(self, x):
        s = "("
        for field, format_function in zip(x, self.format_functions):
            s += format_function(field) + ", "
        return (s[:-2] if 1 < self.num_fields else s[:-1]) + ")"

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