table.py

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import csv
import re
import math
from ost import stutil
import itertools
import operator
import pickle
import weakref
from ost import LogError, LogWarning, LogInfo, LogVerbose

def MakeTitle(col_name):
  return col_name.replace('_', ' ')

def IsStringLike(value):
  if isinstance(value, TableCol) or isinstance(value, BinaryColExpr):
    return False
  try:
    value+''
    return True
  except:
    return False

def IsNullString(value):
  value=value.strip().upper()
  return value in ('', 'NULL', 'NONE', 'NA')

def IsScalar(value):
  if IsStringLike(value):
    return True
  try:
    if isinstance(value, TableCol) or isinstance(value, BinaryColExpr):
      return False
    iter(value)
    return False
  except:
    return True

def GuessColumnType(iterator):
  empty=True
  possibilities=set(['bool', 'int', 'float'])
  for ele in iterator:
    str_ele=str(ele).upper()
    if IsNullString(str_ele):
      continue
    empty=False
    if 'int' in possibilities:
      try:
        int(str_ele)
      except ValueError:
        possibilities.remove('int')

    if 'float' in possibilities:
      try:
        float(str_ele)
      except ValueError:
        possibilities.remove('float')
    if 'bool' in possibilities:
      if str_ele not in set(['YES', 'NO', 'TRUE', 'FALSE']):
        possibilities.remove('bool')

    if len(possibilities)==0:
      return 'string'
  if len(possibilities)==2:
    return 'int'
  if empty:
    return 'string'
  # return the last element available
  return possibilities.pop()

class BinaryColExpr:
  def __init__(self, op, lhs, rhs):
    self.op=op
    self.lhs=lhs
    self.rhs=rhs
    if IsScalar(lhs):
      self.lhs=itertools.cyle([self.lhs])
    if IsScalar(rhs):
      self.rhs=itertools.cycle([self.rhs])
  def __iter__(self):
    for l, r in zip(self.lhs, self.rhs):
      if l!=None and r!=None:
        yield self.op(l, r)
      else:
        yield None
  def __add__(self, rhs):
    return BinaryColExpr(operator.add, self, rhs)

  def __sub__(self, rhs):
    return BinaryColExpr(operator.sub, self, rhs)

  def __mul__(self, rhs):
    return BinaryColExpr(operator.mul, self, rhs)

  def __div__(self, rhs):
    return BinaryColExpr(operator.div, self, rhs)

class TableCol:
  def __init__(self, table, col):
    self._table=table
    if type(col)==str:
      self.col_index=self._table.GetColIndex(col)
    else:
      self.col_index=col

  def __iter__(self):
    for row in self._table.rows:
      yield row[self.col_index]

  def __len__(self):
    return len(self._table.rows)

  def __getitem__(self, index):
    return self._table.rows[index][self.col_index]

  def __setitem__(self, index, value):
    self._table.rows[index][self.col_index]=value
  
  def __add__(self, rhs):
    return BinaryColExpr(operator.add, self, rhs)

  def __sub__(self, rhs):
    return BinaryColExpr(operator.sub, self, rhs)

  def __mul__(self, rhs):
    return BinaryColExpr(operator.mul, self, rhs)

  def __div__(self, rhs):
    return BinaryColExpr(operator.div, self, rhs)

class TableRow:
  """
  Essentially a named tuple, but allows column names that are not valid 
  python variable names.
  """
  def __init__(self, row_data, tab):
    self.__dict__['tab'] = weakref.proxy(tab)
    self.__dict__['row_data'] = row_data

  def __getitem__(self, col_name):
    if type(col_name)==int:
      return self.row_data[col_name]
    return self.row_data[self.tab.GetColIndex(col_name)]

  def __str__(self):
    s = []
    for k, v in zip(self.__dict__['tab'].col_names, self.__dict__['row_data']):
      s.append('%s=%s' % (k, str(v)))
    return ', '.join(s)
      
      
  def __len__(self):
    return len(self.row_data)

  def __setitem__(self, col_name, val):
    if type(col_name)==int:
      self.row_data[col_name] = val
    else:
      self.row_data[self.tab.GetColIndex(col_name)] = val

  def __getattr__(self, col_name):
    if 'col_names' not in self.tab.__dict__ or col_name not in self.tab.col_names:
      raise AttributeError(col_name)
    return self.row_data[self.tab.GetColIndex(col_name)]

  def __setattr__(self, col_name, val):
    if 'col_names' not in self.tab.__dict__ or col_name not in self.tab.col_names:
      raise AttributeError(col_name)
    self.row_data[self.tab.GetColIndex(col_name)] = val

class Table(object):
  """
  
  The table class provides convenient access to data in tabular form. An empty 
  table can be easily constructed as follows
  
  .. code-block:: python
  
    tab = Table()
    
  If you want to add columns directly when creating the table, column names
  and *column types* can be specified as follows
  
  .. code-block:: python
  
    tab = Table(['nameX','nameY','nameZ'], 'sfb')
    
  this will create three columns called nameX, nameY and nameZ of type string,
  float and bool, respectively. There will be no data in the table and thus,
  the table will not contain any rows.
  
  The following *column types* are supported:
  
  ======= ========
  name     abbrev
  ======= ========
  string     s
  float      f
  int        i
  bool       b
  ======= ========
  
  If you want to add data to the table in addition, use the following:
  
  .. code-block:: python
  
    tab=Table(['nameX','nameY','nameZ'],
              'sfb',
              nameX = ['a','b','c'],
              nameY = [0.1, 1.2, 3.414],
              nameZ = [True, False, False])
              
  if values for one column is left out, they will be filled with NA, but if
  values are specified, all values must be specified (i.e. same number of
  values per column)
    
  """

  SUPPORTED_TYPES=('int', 'float', 'bool', 'string',)
  
  
  def __init__(self, col_names=[], col_types=None, **kwargs):

    self.col_names=list(col_names)
    self.comment=''
    self.name=''
    
    self.col_types = self._ParseColTypes(col_types)
    self.rows=[]    
    if len(kwargs)>=0:
      if not col_names:
        self.col_names=[v for v in list(kwargs.keys())]
      if not self.col_types:
        self.col_types=['string' for u in range(len(self.col_names))]
      if len(kwargs)>0:
        self._AddRowsFromDict(kwargs)

  def __getattr__(self, col_name):
    # pickling doesn't call the standard __init__ defined above and thus
    # col_names might not be defined. This leads to infinite recursions.
    # Protect against it by checking that col_names is contained in 
    # __dict__
    if 'col_names' not in self.__dict__ or col_name not in self.col_names:
      raise AttributeError(col_name)
    return TableCol(self, col_name)

  @staticmethod
  def _ParseColTypes(types, exp_num=None):
    if types==None:
      return None
    
    short2long = {'s' : 'string', 'i': 'int', 'b' : 'bool', 'f' : 'float'}
    allowed_short = list(short2long.keys())
    allowed_long = list(short2long.values())
    
    type_list = []
    
    # string type
    if IsScalar(types):
      if type(types)==str:
        types = types.lower()
        
        # single value
        if types in allowed_long:
          type_list.append(types)
        elif types in allowed_short:
          type_list.append(short2long[types])
        
        # comma separated list of long or short types
        elif types.find(',')!=-1:
          for t in types.split(','):
            if t in allowed_long:
              type_list.append(t)
            elif t in allowed_short:
              type_list.append(short2long[t])
            else:
              raise ValueError('Unknown type %s in types %s'%(t,types))
        
        # string of short types
        else:
          for t in types:
            if t in allowed_short:
              type_list.append(short2long[t])
            else:
              raise ValueError('Unknown type %s in types %s'%(t,types))
      
      # non-string type
      else:
        raise ValueError('Col type %s must be string or list'%types)
    
    # list type
    else:
      for t in types:
        # must be string type
        if type(t)==str:
          t = t.lower()
          if t in allowed_long:
            type_list.append(t)
          elif t in allowed_short:
            type_list.append(short2long[t])
          else:
            raise ValueError('Unknown type %s in types %s'%(t,types))
        
        # non-string type
        else:
          raise ValueError('Col type %s must be string or list'%types)
    
    if exp_num:
      if len(type_list)!=exp_num:
        raise ValueError('Parsed number of col types (%i) differs from ' + \
                         'expected (%i) in types %s'%(len(type_list),exp_num,types))
      
    return type_list

  def SetName(self, name):
    '''
    Set name of the table

    :param name: name
    :type name: :class:`str`
    '''
    self.name = name
    
  def GetName(self):
    '''
    Get name of table
    '''
    return self.name

  def RenameCol(self, old_name, new_name):
    """
    Rename column *old_name* to *new_name*.

    :param old_name: Name of the old column
    :param new_name: Name of the new column
    :raises: :exc:`ValueError` when *old_name* is not a valid column
    """
    if old_name==new_name:
      return
    self.AddCol(new_name, self.col_types[self.GetColIndex(old_name)],
                self[old_name])
    self.RemoveCol(old_name)
  def _Coerce(self, value, ty):
    '''
    Try to convert values (e.g. from :class:`str` type) to the specified type

    :param value: the value
    :type value: any type

    :param ty: name of type to convert it to (i.e. *int*, *float*, *string*,
               *bool*)
    :type ty: :class:`str`
    '''
    if value=='NA' or value==None:
      return None
    if ty=='int':
      return int(value)
    if ty=='float':
      return float(value)
    if ty=='string':
      return str(value)
    if ty=='bool':
      if isinstance(value, str) or isinstance(value, str):
        if value.upper() in ('FALSE', 'NO',):
          return False
        return True
      return bool(value)
    raise ValueError('Unknown type %s' % ty)

  def GetColIndex(self, col):
    '''
    Returns the column index for the column with the given name.

    :raises: ValueError if no column with the name is found.
    '''
    if col not in self.col_names:
      raise ValueError('Table has no column named "%s"' % col)
    return self.col_names.index(col)
  
  def GetColNames(self):
    '''
    Returns a list containing all column names.
    '''
    return self.col_names
  
  def SearchColNames(self, regex):
    '''
    Returns a list of column names matching the regex.

    :param regex: regex pattern
    :type regex: :class:`str`

    :returns: :class:`list` of column names (:class:`str`)
    '''
    matching_names = []
    for name in self.col_names:
      matches = re.search(regex, name)
      if matches:
        matching_names.append(name)
    return matching_names

  def HasCol(self, col):
    '''
    Checks if the column with a given name is present in the table.
    '''
    return col in self.col_names
  
  def __getitem__(self, k):
    if type(k)==int:
      return TableCol(self, self.col_names[k])
    else:
      return TableCol(self, k)

  def __setitem__(self, k, value):
    col_index=k
    if type(k)!=int:
      col_index=self.GetColIndex(k)
    if IsScalar(value):
      value=itertools.cycle([value])
    for r, v in zip(self.rows, value):
      r[col_index]=v

  def ToString(self, float_format='%.3f', int_format='%d', rows=None):
    '''
    Convert the table into a string representation.

    The output format can be modified for int and float type columns by
    specifying a formatting string for the parameters *float_format* and
    *int_format*.

    The option *rows* specify the range of rows to be printed. The parameter
    must be a type that supports indexing (e.g. a :class:`list`) containing the 
    start and end row *index*, e.g. [start_row_idx, end_row_idx].

    :param float_format: formatting string for float columns
    :type float_format: :class:`str`

    :param int_format: formatting string for int columns
    :type int_format: :class:`str`

    :param rows: iterable containing start and end row *index*
    :type rows: iterable containing :class:`ints <int>`
    '''
    widths=[len(cn) for cn in self.col_names]
    sel_rows=self.rows
    if rows:
      sel_rows=self.rows[rows[0]:rows[1]]
    for row in sel_rows:
      for i, (ty, col) in enumerate(zip(self.col_types, row)):
        if col==None:
          widths[i]=max(widths[i], len('NA'))
        elif ty=='float':
          widths[i]=max(widths[i], len(float_format % col))
        elif ty=='int':
          widths[i]=max(widths[i], len(int_format % col))
        else:
          widths[i]=max(widths[i], len(str(col)))
    s=''
    if self.comment:
      s+=''.join(['# %s\n' % l for l in self.comment.split('\n')])
    total_width=sum(widths)+2*len(widths)
    for width, col_name in zip(widths, self.col_names):
      s+=col_name.center(width+2)
    s+='\n%s\n' % ('-'*total_width)
    for row in sel_rows:
      for width, ty, col in zip(widths, self.col_types, row):
        cs=''
        if col==None:
          cs='NA'.center(width+2)
        elif ty=='float':
          cs=(float_format % col).rjust(width+2)
        elif ty=='int':
          cs=(int_format % col).rjust(width+2)
        else:
          cs=' '+str(col).ljust(width+1)
        s+=cs
      s+='\n'
    return s

  def __str__(self):
    return self.ToString()
  
  def Stats(self, col):
     idx  = self.GetColIndex(col)
     text ='''
Statistics for column %(col)s

  Number of Rows         : %(num)d
  Number of Rows Not None: %(num_non_null)d 
  Mean                   : %(mean)f
  Median                 : %(median)f
  Standard Deviation     : %(stddev)f
  Min                    : %(min)f
  Max                    : %(max)f
'''
     data = {
       'col' : col,
       'num' : len(self.rows),
       'num_non_null' : self.Count(col),
       'median' : self.Median(col),
       'mean' : self.Mean(col),
       'stddev' : self.StdDev(col),
       'min' : self.Min(col),
       'max' : self.Max(col),
     }
     return text % data

  def _AddRowsFromDict(self, d, overwrite=None):
    '''
    Add one or more rows from a :class:`dictionary <dict>`.
    
    If *overwrite* is not None and set to an existing column name, the specified 
    column in the table is searched for the first occurrence of a value matching
    the value of the column with the same name in the dictionary. If a matching
    value is found, the row is overwritten with the dictionary. If no matching
    row is found, a new row is appended to the table.

    :param d: dictionary containing the data
    :type d: :class:`dict`

    :param overwrite: column name to overwrite existing row if value in
                      column *overwrite* matches
    :type overwrite: :class:`str`

    :raises: :class:`ValueError` if multiple rows are added but the number of
             data items is different for different columns.
    '''
    # get column indices
    idxs = [self.GetColIndex(k) for k in list(d.keys())]
    
    # convert scalar values to list
    old_len = None
    for k,v in d.items():
      if IsScalar(v):
        v = [v]
        d[k] = v
      if not old_len:
        old_len = len(v)
      elif old_len!=len(v):
        raise ValueError("Cannot add rows: length of data must be equal " + \
                         "for all columns in %s"%str(d))
    
    # convert column based dict to row based dict and create row and add data
    for i,data in enumerate(zip(*list(d.values()))):
      new_row = [None for a in range(len(self.col_names))]
      for idx,v in zip(idxs,data):
        new_row[idx] = self._Coerce(v, self.col_types[idx])
        
      # partially overwrite existing row with new data
      if overwrite:
        overwrite_idx = self.GetColIndex(overwrite)
        added = False
        for i,r in enumerate(self.rows):
          if r[overwrite_idx]==new_row[overwrite_idx]:
            for j,e in enumerate(self.rows[i]):
              if new_row[j]==None:
                new_row[j] = e
            self.rows[i] = new_row
            added = True
            break
          
      # if not overwrite or overwrite did not find appropriate row
      if not overwrite or not added:
        self.rows.append(new_row)
      
  def PairedTTest(self, col_a, col_b):
    """
    Two-sided test for the null-hypothesis that two related samples 
    have the same average (expected values).
    
    :param col_a: First column
    :type col_a:  :class:`str`
    :param col_b: Second column
    :type col_b:  :class:`str`

    :returns: P-value between 0 and 1 that the two columns have the 
       same average. The smaller the value, the less related the two
       columns are.
    """
    from scipy.stats import ttest_rel
    xs = []
    ys = []
    for x, y in self.Zip(col_a, col_b):
      if x!=None and y!=None:
        xs.append(x)
        ys.append(y)
    result = ttest_rel(xs, ys)
    return result[1]

  def AddRow(self, data, overwrite=None):
    """
    Add a row to the table.
    
    *data* may either be a dictionary or a list-like object:

     - If *data* is a dictionary, the keys in the dictionary must match the
       column names. Columns not found in the dict will be initialized to None.
       If the dict contains list-like objects, multiple rows will be added, if
       the number of items in all list-like objects is the same, otherwise a
       :class:`ValueError` is raised.

     - If *data* is a list-like object, the row is initialized from the values
       in *data*. The number of items in *data* must match the number of
       columns in the table. A :class:`ValuerError` is raised otherwise. The
       values are added in the order specified in the list, thus, the order of
       the data must match the columns.
          
    If *overwrite* is not None and set to an existing column name, the specified 
    column in the table is searched for the first occurrence of a value matching
    the value of the column with the same name in the dictionary. If a matching
    value is found, the row is overwritten with the dictionary. If no matching
    row is found, a new row is appended to the table.

    :param data: data to add
    :type data: :class:`dict` or *list-like* object

    :param overwrite: column name to overwrite existing row if value in
                      column *overwrite* matches
    :type overwrite: :class:`str`

    :raises: :class:`ValueError` if *list-like* object is used and number of
             items does *not* match number of columns in table.

    :raises: :class:`ValueError` if *dict* is used and multiple rows are added
             but the number of data items is different for different columns.

    **Example:** add multiple data rows to a subset of columns using a dictionary

    .. code-block:: python

      # create table with three float columns
      tab = Table(['x','y','z'], 'fff')

      # add rows from dict
      data = {'x': [1.2, 1.6], 'z': [1.6, 5.3]}
      tab.AddRow(data)
      print tab

      '''
      will produce the table

      ====  ====  ====
      x     y     z
      ====  ====  ====
      1.20  NA    1.60
      1.60  NA    5.30
      ====  ====  ====
      '''

      # overwrite the row with x=1.2 and add row with x=1.9
      data = {'x': [1.2, 1.9], 'z': [7.9, 3.5]}
      tab.AddRow(data, overwrite='x')
      print tab

      '''
      will produce the table

      ====  ====  ====
      x     y     z
      ====  ====  ====
      1.20  NA    7.90
      1.60  NA    5.30
      1.90  NA    3.50
      ====  ====  ====
      '''
    """
    if type(data)==dict:
      self._AddRowsFromDict(data, overwrite)
    else:
      if len(data)!=len(self.col_names):
        msg='data array must have %d elements, not %d'
        raise ValueError(msg % (len(self.col_names), len(data)))
      new_row = [self._Coerce(v, t) for v, t in zip(data, self.col_types)]
      
      # fully overwrite existing row with new data
      if overwrite:
        overwrite_idx = self.GetColIndex(overwrite)
        added = False
        for i,r in enumerate(self.rows):
          if r[overwrite_idx]==new_row[overwrite_idx]:
            self.rows[i] = new_row
            added = True
            break
      
      # if not overwrite or overwrite did not find appropriate row
      if not overwrite or not added:
        self.rows.append(new_row)

  def RemoveCol(self, col):
    """
    Remove column with the given name from the table.

    :param col: name of column to remove
    :type col: :class:`str`
    """
    idx = self.GetColIndex(col)
    del self.col_names[idx]
    del self.col_types[idx]
    for row in self.rows:
      del row[idx]

  def AddCol(self, col_name, col_type, data=None):
    """
    Add a column to the right of the table.
    
    :param col_name: name of new column
    :type col_name: :class:`str`

    :param col_type: type of new column (long versions: *int*, *float*, *bool*,
                     *string* or short versions: *i*, *f*, *b*, *s*)
    :type col_type: :class:`str`

    :param data: data to add to new column
    :type data: scalar or iterable

    **Example:**

    .. code-block:: python
    
      tab = Table(['x'], 'f', x=range(5))
      tab.AddCol('even', 'bool', itertools.cycle([True, False]))
      print tab
    
      '''
      will produce the table

      ====  ====
      x     even
      ====  ====
        0   True
        1   False
        2   True
        3   False
        4   True
      ====  ====
      '''

    If data is a constant instead of an iterable object, it's value
    will be written into each row:

    .. code-block:: python

      tab = Table(['x'], 'f', x=range(5))
      tab.AddCol('num', 'i', 1)
      print tab

      '''
      will produce the table

      ====  ====
      x     num
      ====  ====
        0   1
        1   1
        2   1
        3   1
        4   1
      ====  ====
      '''
    
    As a special case, if there are no previous rows, and data is not 
    None, rows are added for every item in data.
    """

    if col_name in self.col_names:
      raise ValueError('Column with name %s already exists'%col_name)

    col_type = self._ParseColTypes(col_type, exp_num=1)[0]
    self.col_names.append(col_name)
    self.col_types.append(col_type)

    if len(self.rows)>0:
      if IsScalar(data):
        for row in self.rows:
          row.append(data)
      else:
        if hasattr(data, '__len__') and len(data)!=len(self.rows):
          self.col_names.pop()
          self.col_types.pop()
          raise ValueError('Length of data (%i) must correspond to number of '%len(data) +\
                           'existing rows (%i)'%len(self.rows))
        for row, d in zip(self.rows, data):
          row.append(d)

    elif data!=None and len(self.col_names)==1:
      if IsScalar(data):
        self.AddRow({col_name : data})
      else:
        for v in data:
          self.AddRow({col_name : v})

  def Filter(self, *args, **kwargs):
    """
    Returns a filtered table only containing rows matching all the predicates 
    in kwargs and args For example,
    
    .. code-block:: python
    
      tab.Filter(town='Basel')
    
    will return all the rows where the value of the column "town" is equal to 
    "Basel". Several predicates may be combined, i.e.
    
    .. code-block:: python
    
      tab.Filter(town='Basel', male=True)
      
    will return the rows with "town" equal to "Basel" and "male" equal to true.
    args are unary callables returning true if the row should be included in the
    result and false if not.
    """
    filt_tab=Table(list(self.col_names), list(self.col_types))
    for row in self.rows:
      matches=True
      for func in args:
        if not func(row):
          matches=False
          break
      for key, val in kwargs.items():
        if row[self.GetColIndex(key)]!=val:
          matches=False
          break
      if matches:
        filt_tab.AddRow(row)
    return filt_tab


  def Select(self, query):

    """
    Returns a new table object containing all rows matching a logical query
    expression.
    
    *query* is a string containing the logical expression, that will be
    evaluated for every row.

    Operands have to be the name of a column or an expression that can be
    parsed to float, int, bool or string.
    Valid operators are: and, or, !=, !, <=, >=, ==, =, <, >, +, -, \\*, /
    
    .. code-block:: python
    
      subtab = tab.Select('col_a>0.5 and (col_b=5 or col_c=5)')

    The selection query should be self explaining. Allowed parenthesis are:
    (), [], {}, whereas parenthesis mismatches get recognized. Expressions like
    '3<=col_a>=col_b' throw an error, due to problems in figuring out the
    evaluation order.

    There are two special expressions:

    .. code-block:: python

      #selects rows, where 1.0<=col_a<=1.5
      subtab = tab.Select('col_a=1.0:1.5')

      #selects rows, where col_a=1 or col_a=2 or col_a=3
      subtab = tab.Select('col_a=1,2,3')

    Only consistent types can be compared. If col_a is of type string and col_b
    is of type int, following expression would throw an error: 'col_a<col_b'
    """

    try:
      from .table_selector import TableSelector
    except:
      raise ImportError("Tried to import from the file table_selector.py, but could not find it!")

    selector=TableSelector(self.col_types, self.col_names, query)

    selected_tab=Table(list(self.col_names), list(self.col_types))

    for row in self.rows:
      if selector.EvaluateRow(row):
        selected_tab.AddRow(row)

    return selected_tab


  @staticmethod
  def _LoadOST(stream_or_filename):
    fieldname_pattern=re.compile(r'(?P<name>[^[]+)(\[(?P<type>\w+)\])?')
    values_pattern=re.compile("([^\" ]+|\"[^\"]*\")+")
    file_opened=False
    if not hasattr(stream_or_filename, 'read'):
      stream=open(stream_or_filename, 'r')
      file_opened=True
    else:
      stream=stream_or_filename
    header=False
    num_lines=0
    for line in stream:
      line=line.strip()
      if line.startswith('#'):
        continue
      if len(line)==0:
        continue
      num_lines+=1
      if not header:
        fieldnames=[]
        fieldtypes=[]
        for col in line.split():
          match=fieldname_pattern.match(col)
          if match:
            if match.group('type'):
              fieldtypes.append(match.group('type'))
            else:
              fieldtypes.append('string')
            fieldnames.append(match.group('name'))
        try:
          tab=Table(fieldnames, fieldtypes)
        except Exception as e:
          # potentially fails if we read in crap... clean up and pass on error
          if file_opened:
            stream.close()
          raise e
        header=True
        continue
      tab.AddRow([x.strip('"') for x in values_pattern.findall(line)])
    if file_opened:
      stream.close()
    if num_lines==0:
      raise IOError("Cannot read table from empty stream")
    return tab

  def _GuessColumnTypes(self):
    for col_idx in range(len(self.col_names)):
      self.col_types[col_idx]=GuessColumnType(self[self.col_names[col_idx]])
    for row in self.rows:
      for idx in range(len(row)):
        row[idx]=self._Coerce(row[idx], self.col_types[idx])
        
  @staticmethod
  def _LoadCSV(stream_or_filename, sep):
    file_opened=False
    if not hasattr(stream_or_filename, 'read'):
      stream=open(stream_or_filename, 'r')
      file_opened=True
    else:
      stream=stream_or_filename
    reader=csv.reader(stream, delimiter=sep)
    first=True
    for row in reader:
      if first:
        header=row
        types='s'*len(row)
        tab=Table(header, types)
        first=False
      else:
        tab.AddRow(row)
    if file_opened:
      stream.close()
    if first:
      raise IOError('trying to load table from empty CSV stream/file')

    tab._GuessColumnTypes()
    return tab

  @staticmethod
  def _LoadPickle(stream_or_filename):
    file_opened=False
    if not hasattr(stream_or_filename, 'read'):
      stream=open(stream_or_filename, 'rb')
      file_opened=True
    else:
      stream=stream_or_filename
    tab = pickle.load(stream)
    if file_opened:
      stream.close()
    return tab

  @staticmethod
  def _GuessFormat(filename):
    try:
      filename = filename.name
    except AttributeError as e:
      pass
    if filename.endswith('.csv'):
      return 'csv'
    elif filename.endswith('.pickle'):
      return 'pickle'
    else:
      return 'ost'
    
    
  @staticmethod
  def Load(stream_or_filename, format='auto', sep=','):
    """
    Load table from stream or file with given name.

    By default, the file format is set to *auto*, which tries to guess the file
    format from the file extension. The following file extensions are
    recognized:
    
    ============    ======================
    extension       recognized format
    ============    ======================
    .csv            comma separated values
    .pickle         pickled byte stream
    <all others>    ost-specific format
    ============    ======================
    
    Thus, *format* must be specified for reading file with different filename
    extensions.

    The following file formats are understood:

    - ost

      This is an ost-specific, but still human readable file format. The file
      (stream) must start with header line of the form

        col_name1[type1] <col_name2[type2]>...

      The types given in brackets must be one of the data types the
      :class:`Table` class understands. Each following line in the file then must
      contains exactly the same number of data items as listed in the header. The
      data items are automatically converted to the column format. Lines starting
      with a '#' and empty lines are ignored.

    - pickle

      Deserializes the table from a pickled byte stream.

    - csv

      Reads the table from comma separated values stream. Since there is no
      explicit type information in the csv file, the column types are guessed,
      using the following simple rules:

      * if all values are either NA/NULL/NONE the type is set to string.
      * if all non-null values are convertible to float/int the type is set to
        float/int.
      * if all non-null values are true/false/yes/no, the value is set to bool.
      * for all other cases, the column type is set to string.

    :returns: A new :class:`Table` instance
    """
    format=format.lower()
    if format=='auto':
      format = Table._GuessFormat(stream_or_filename)
      
    if format=='ost':
      return Table._LoadOST(stream_or_filename)
    if format=='csv':
      return Table._LoadCSV(stream_or_filename, sep=sep)
    if format=='pickle':
      return Table._LoadPickle(stream_or_filename)
    raise ValueError('unknown format ""' % format)

  def Sort(self, by, order='+'):
    """
    Performs an in-place sort of the table, based on column *by*.

    :param by: column name by which to sort
    :type by: :class:`str`

    :param order: ascending (``-``) or descending (``+``) order
    :type order: :class:`str` (i.e. *+*, *-*)
    """
    sign=-1
    if order=='-':
      sign=1
    key_index=self.GetColIndex(by)
    def _key_cmp(lhs, rhs):
      a = lhs[key_index]
      b = rhs[key_index]
      # mimic behaviour of the cmp function from Python2 that happily
      # compared None values
      if a is None or b is None:
        if a is None and b is not None:
          return -1 * sign
        if b is None and a is not None:
          return 1 * sign
        return 0
      return sign*((a > b) - (a < b))

    import functools
    self.rows=sorted(self.rows, key=functools.cmp_to_key(_key_cmp))
    
  def GetUnique(self, col, ignore_nan=True):
    """
    Extract a list of all unique values from one column.

    :param col: column name
    :type col: :class:`str`

    :param ignore_nan: ignore all *None* values
    :type ignore_nan: :class:`bool`
    """
    idx = self.GetColIndex(col)
    seen = {}
    result = []
    for row in self.rows:
      item = row[idx]
      if item!=None or ignore_nan==False:
        if item in seen: continue
        seen[item] = 1
        result.append(item)
    return result
    
  def Zip(self, *args):
    """
    Allows to conveniently iterate over a selection of columns, e.g.
    
    .. code-block:: python
    
      tab = Table.Load('...')
      for col1, col2 in tab.Zip('col1', 'col2'):
        print col1, col2
    
    is a shortcut for
    
    .. code-block:: python
    
      tab = Table.Load('...')
      for col1, col2 in zip(tab['col1'], tab['col2']):
        print col1, col2
    """
    return list(zip(*[self[arg] for arg in args]))

  def Plot(self, x, y=None, z=None, style='.', x_title=None, y_title=None,
           z_title=None, x_range=None, y_range=None, z_range=None,
           color=None, plot_if=None, legend=None,
           num_z_levels=10, z_contour=True, z_interpol='nn', diag_line=False,
           labels=None, max_num_labels=None, title=None, clear=True, save=False,
           **kwargs):
    """
    Function to plot values from your table in 1, 2 or 3 dimensions using
    `Matplotlib <http://matplotlib.sourceforge.net>`__

    :param x: column name for first dimension
    :type x: :class:`str`

    :param y: column name for second dimension
    :type y: :class:`str`

    :param z: column name for third dimension
    :type z: :class:`str`

    :param style: symbol style (e.g. *.*, *-*, *x*, *o*, *+*, *\\**). For a
                  complete list check (`matplotlib docu <http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.plot>`__).
    :type style: :class:`str`

    :param x_title: title for first dimension, if not specified it is
                    automatically derived from column name
    :type x_title: :class:`str`

    :param y_title: title for second dimension, if not specified it is
                    automatically derived from column name
    :type y_title: :class:`str`

    :param z_title: title for third dimension, if not specified it is
                    automatically derived from column name
    :type z_title: :class:`str`

    :param x_range: start and end value for first dimension (e.g. [start_x, end_x])
    :type x_range: :class:`list` of length two

    :param y_range: start and end value for second dimension (e.g. [start_y, end_y])
    :type y_range: :class:`list` of length two

    :param z_range: start and end value for third dimension (e.g. [start_z, end_z])
    :type z_range: :class:`list` of length two

    :param color: color for data (e.g. *b*, *g*, *r*). For a complete list check
                  (`matplotlib docu <http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.plot>`__).
    :type color: :class:`str`

    :param plot_if: callable which returnes *True* if row should be plotted. Is
                    invoked like ``plot_if(self, row)``
    :type plot_if: callable

    :param legend: legend label for data series
    :type legend: :class:`str`

    :param num_z_levels: number of levels for third dimension
    :type num_z_levels: :class:`int`

    :param diag_line: draw diagonal line
    :type diag_line: :class:`bool`

    :param labels: column name containing labels to put on x-axis for one
                   dimensional plot
    :type labels: :class:`str`

    :param max_num_labels: limit maximum number of labels
    :type max_num_labels: :class:`int`

    :param title: plot title, if not specified it is automatically derived from
                  plotted column names
    :type title: :class:`str`

    :param clear: clear old data from plot
    :type clear: :class:`bool`

    :param save: filename for saving plot
    :type save: :class:`str`

    :param z_contour: draw contour lines
    :type z_contour: :class:`bool`

    :param z_interpol: interpolation method for 3-dimensional plot (one of 'nn',
                       'linear')
    :type z_interpol: :class:`str`

    :param \\*\\*kwargs: additional arguments passed to matplotlib
    
    :returns: the ``matplotlib.pyplot`` module 

    **Examples:** simple plotting functions

    .. code-block:: python

      tab = Table(['a','b','c','d'],'iffi', a=range(5,0,-1),
                                            b=[x/2.0 for x in range(1,6)],
                                            c=[math.cos(x) for x in range(0,5)],
                                            d=range(3,8))

      # one dimensional plot of column 'd' vs. index
      plt = tab.Plot('d')
      plt.show()

      # two dimensional plot of 'a' vs. 'c'
      plt = tab.Plot('a', y='c', style='o-')
      plt.show()

      # three dimensional plot of 'a' vs. 'c' with values 'b'
      plt = tab.Plot('a', y='c', z='b')
      # manually save plot to file
      plt.savefig("plot.png")
    """
    try:
      import matplotlib.pyplot as plt
      import matplotlib.mlab as mlab
      import numpy as np
      idx1 = self.GetColIndex(x)
      xs = []
      ys = []
      zs = []

      if clear:
        plt.figure(figsize=[8, 6])
      
      if x_title!=None:
        nice_x=x_title
      else:
        nice_x=MakeTitle(x)
      
      if y_title!=None:
        nice_y=y_title
      else:
        if y:
          nice_y=MakeTitle(y)
        else:
          nice_y=None
      
      if z_title!=None:
        nice_z = z_title
      else:
        if z:
          nice_z = MakeTitle(z)
        else:
          nice_z = None

      if x_range and (IsScalar(x_range) or len(x_range)!=2):
        raise ValueError('parameter x_range must contain exactly two elements')
      if y_range and (IsScalar(y_range) or len(y_range)!=2):
        raise ValueError('parameter y_range must contain exactly two elements')
      if z_range and (IsScalar(z_range) or len(z_range)!=2):
        raise ValueError('parameter z_range must contain exactly two elements')

      if color:
        kwargs['color']=color
      if legend:
        kwargs['label']=legend
      if y and z:
        idx3 = self.GetColIndex(z)
        idx2 = self.GetColIndex(y)
        for row in self.rows:
          if row[idx1]!=None and row[idx2]!=None and row[idx3]!=None:
            if plot_if and not plot_if(self, row):
              continue
            xs.append(row[idx1])
            ys.append(row[idx2])
            zs.append(row[idx3])
        levels = []
        if z_range:
          z_spacing = (z_range[1] - z_range[0]) / num_z_levels
          l = z_range[0]
        else:
          l = self.Min(z)
          z_spacing = (self.Max(z) - l) / num_z_levels
        
        for i in range(0,num_z_levels+1):
          levels.append(l)
          l += z_spacing
  
        xi = np.linspace(min(xs),max(xs),len(xs)*10)
        yi = np.linspace(min(ys),max(ys),len(ys)*10)
        zi = mlab.griddata(xs, ys, zs, xi, yi, interp=z_interpol)
  
        if z_contour:
          plt.contour(xi,yi,zi,levels,linewidths=0.5,colors='k')

        plt.contourf(xi,yi,zi,levels,cmap=plt.cm.jet)
        plt.colorbar(ticks=levels)
            
      elif y:
        idx2=self.GetColIndex(y)
        for row in self.rows:
          if row[idx1]!=None and row[idx2]!=None:
            if plot_if and not plot_if(self, row):
              continue
            xs.append(row[idx1])
            ys.append(row[idx2])
        plt.plot(xs, ys, style, **kwargs)
        
      else:
        label_vals=[]
        
        if labels:
          label_idx=self.GetColIndex(labels)
        for row in self.rows:
          if row[idx1]!=None:
            if plot_if and not plot_if(self, row):
              continue
            xs.append(row[idx1])
            if labels:
              label_vals.append(row[label_idx])
        plt.plot(xs, style, **kwargs)
        if labels:
          interval = 1
          if max_num_labels:
            if len(label_vals)>max_num_labels:
              interval = int(math.ceil(float(len(label_vals))/max_num_labels))
              label_vals = label_vals[::interval]
          plt.xticks(np.arange(0, len(xs), interval), label_vals, rotation=45,
                     size='x-small')
      
      if title==None:
        if nice_z:
          title = '%s of %s vs. %s' % (nice_z, nice_x, nice_y)
        elif nice_y:
          title = '%s vs. %s' % (nice_x, nice_y)
        else:
          title = nice_x
  
      plt.title(title, size='x-large', fontweight='bold',
                verticalalignment='bottom')
      
      if legend:
        plt.legend(loc=0)
      
      if x and y:
        plt.xlabel(nice_x, size='x-large')
        if x_range:
          plt.xlim(x_range[0], x_range[1])
        if y_range:
          plt.ylim(y_range[0], y_range[1])
        if diag_line:
          plt.plot(x_range, y_range, '-', color='black')
        
        plt.ylabel(nice_y, size='x-large')
      else:
        if y_range:
          plt.ylim(y_range[0], y_range[1])
        if x_title:
          plt.xlabel(x_title, size='x-large')
        plt.ylabel(nice_y, size='x-large')
      if save:
        plt.savefig(save)
      return plt
    except ImportError:
      LogError("Function needs numpy and matplotlib, but I could not import it.")
      raise
    
  def PlotHistogram(self, col, x_range=None, num_bins=10, normed=False,
                    histtype='stepfilled', align='mid', x_title=None,
                    y_title=None, title=None, clear=True, save=False,
                    color=None, y_range=None):
    """
    Create a histogram of the data in col for the range *x_range*, split into
    *num_bins* bins and plot it using Matplotlib.

    :param col: column name with data
    :type col: :class:`str`

    :param x_range: start and end value for first dimension (e.g. [start_x, end_x])
    :type x_range: :class:`list` of length two

    :param y_range: start and end value for second dimension (e.g. [start_y, end_y])
    :type y_range: :class:`list` of length two

    :param num_bins: number of bins in range
    :type num_bins: :class:`int`

    :param color: Color to be used for the histogram. If not set, color will be 
        determined by matplotlib
    :type color: :class:`str`

    :param normed: normalize histogram
    :type normed: :class:`bool`

    :param histtype: type of histogram (i.e. *bar*, *barstacked*, *step*,
                     *stepfilled*). See (`matplotlib docu <http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.hist>`__).
    :type histtype: :class:`str`

    :param align: style of histogram (*left*, *mid*, *right*). See
                  (`matplotlib docu <http://matplotlib.sourceforge.net/api/pyplot_api.html#matplotlib.pyplot.hist>`__).
    :type align: :class:`str`

    :param x_title: title for first dimension, if not specified it is
                    automatically derived from column name
    :type x_title: :class:`str`

    :param y_title: title for second dimension, if not specified it is
                    automatically derived from column name
    :type y_title: :class:`str`

    :param title: plot title, if not specified it is automatically derived from
                  plotted column names
    :type title: :class:`str`

    :param clear: clear old data from plot
    :type clear: :class:`bool`

    :param save: filename for saving plot
    :type save: :class:`str`

    **Examples:** simple plotting functions

    .. code-block:: python

      tab = Table(['a'],'f', a=[math.cos(x*0.01) for x in range(100)])

      # one dimensional plot of column 'd' vs. index
      plt = tab.PlotHistogram('a')
      plt.show()

    """
    try:
      import matplotlib.pyplot as plt
      import numpy as np
      
      if len(self.rows)==0:
        return None
      kwargs={}
      if color:
        kwargs['color']=color
      idx = self.GetColIndex(col)
      data = []
      for r in self.rows:
        if r[idx]!=None:
          data.append(r[idx])
        
      if clear:
        plt.clf()
        
      n, bins, patches = plt.hist(data, bins=num_bins, range=x_range,
                                  normed=normed, histtype=histtype, align=align,
                                  **kwargs)
      
      if x_title!=None:
        nice_x=x_title
      else:
        nice_x=MakeTitle(col)
      plt.xlabel(nice_x, size='x-large')
      if y_range:
        plt.ylim(y_range) 
      if y_title!=None:
        nice_y=y_title
      else:
        nice_y="bin count"  
      plt.ylabel(nice_y, size='x-large')
      
      if title!=None:
        nice_title=title
      else:
        nice_title="Histogram of %s"%nice_x
      plt.title(nice_title, size='x-large', fontweight='bold')
      
      if save:
        plt.savefig(save)
      return plt
    except ImportError:
      LogError("Function needs numpy and matplotlib, but I could not import it.")
      raise
 
  def _Max(self, col):
    if len(self.rows)==0:
      return None, None
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type=='int' or col_type=='float':
      max_val = -float('inf')
    elif col_type=='bool':
      max_val = False
    elif col_type=='string':
      max_val = chr(0)
    max_idx = None
    for i in range(0, len(self.rows)):
      val = self.rows[i][idx]
      if val and val > max_val:
        max_val = self.rows[i][idx]
        max_idx = i
    return max_val, max_idx

  def PlotBar(self, cols=None, rows=None, xlabels=None, set_xlabels=True, xlabels_rotation='horizontal', y_title=None, title=None, 
              colors=None, width=0.8, bottom=0, legend=False, legend_names=None, show=False, save=False):

    """
    Create a barplot of the data in cols. Every column will be represented
    at one position. If there are several rows, each column will be grouped 
    together.

    :param cols: List of column names. Every column will be represented as a 
                 single bar. If cols is None, every column of the table gets 
                 plotted.
    :type cols: :class:`list`

    :param rows: List of row indices. Values from given rows will be plotted 
                 in parallel at one column position. If set to None, all rows 
                 of the table will be plotted. Note, that the maximum number 
                 of rows is 7.
    :type rows: :class:`list`

    :param xlabels: Label for every col on x-axis. If set to None, the column 
                    names are used. The xlabel plotting can be supressed by 
                    the parameter set_xlabel.
    :type xlabels: :class:`list`

    :param set_xlabels: Controls whether xlabels are plotted or not.
    :type set_xlabels: :class:`bool`

    :param x_labels_rotation: Can either be 'horizontal', 'vertical' or an 
                              integer, that describes the rotation in degrees.

    :param y_title: Y-axis description
    :type y_title: :class:`str`

    :title: Title of the plot. No title appears if set to None
    :type title: :class:`str`

    :param colors: Colors of the different bars in each group. Must be a list 
                   of valid colors in matplotlib. Length of color and rows must 
                   be consistent.
    :type colors: :class:`list`

    :param width: The available space for the groups on the x-axis is divided 
                  by the exact number of groups. The parameters width is the 
                  fraction of what is actually used. If it would be 1.0 the 
                  bars of the different groups would touch each other.
                  Value must be between [0;1]
    :type width: :class:`float`

    :param bottom: Bottom
    :type bottom: :class:`float`

    :param legend: Legend for color explanation, the corresponding row 
                   respectively. If set to True, legend_names must be provided.
    :type legend: :class:`bool`

    :param legend_names: List of names, that describe the differently colored 
                         bars. Length must be consistent with number of rows.

    :param show: If set to True, the plot is directly displayed.

    :param save: If set, a png image with name save in the current working 
                 directory will be saved.
    :type save: :class:`str`

    """
    try:
      import numpy as np
      import matplotlib.pyplot as plt
    except:
      raise ImportError('PlotBar relies on numpy and matplotlib, but I could' \
                        'not import it!')
      
    standard_colors=['b','g','y','c','m','r','k']
    data=[]

    if cols==None:
      cols=self.col_names

    if width<=0 or width>1:
      raise ValueError('Width must be in [0;1]')

    if rows==None:
      if len(self.rows)>7:
        raise ValueError('Table contains too many rows to represent them at one '\
                         'bar position in parallel. You can Select a Subtable or '\
                         'specify the parameter rows with a list of row indices '\
                         '(max 7)')
      else:
        rows=list(range(len(self.rows)))
    else:
      if not isinstance(rows,list):
        rows=[rows]
      if len(rows)>7:
        raise ValueError('Too many rows to represent (max 7). Please note, that '\
                         'data from multiple rows from one column gets '\
                         'represented at one position in parallel.')

    for r_idx in rows:
      row=self.rows[r_idx] 
      temp=list()
      for c in cols:
        try:
          c_idx=self.GetColIndex(c)
        except:
          raise ValueError('Cannot find column with name '+str(c))
        temp.append(row[c_idx])
      data.append(temp)  

    if colors==None:
      colors=standard_colors[:len(rows)]

    if len(rows)!=len(colors):
      raise ValueError("Number of rows and number of colors must be consistent!")

    ind=np.arange(len(data[0]))
    single_bar_width=float(width)/len(data)
    
    fig=plt.figure()
    ax=fig.add_subplot(111)
    legend_data=[]

    for i in range(len(data)):
      legend_data.append(ax.bar(ind+i*single_bar_width+(1-width)/2,data[i],single_bar_width,bottom=bottom,color=colors[i])[0])
      
    if title!=None:
      ax.set_title(title, size='x-large', fontweight='bold')  
    
    if y_title!=None:
      nice_y=y_title
    else:
      nice_y="value" 
    ax.set_ylabel(nice_y)
    
    if xlabels:
      if len(data[0])!=len(xlabels):
        raise ValueError('Number of xlabels is not consistent with number of cols!')
    else:
      xlabels=cols
      
    if set_xlabels:
      ax.set_xticks(ind+0.5)
      ax.set_xticklabels(xlabels, rotation = xlabels_rotation)
    else:
      ax.set_xticks([])
      
    if legend == True:
      if legend_names==None:
        raise ValueError('You must provide legend names! e.g. names for the rows, '\
                         'that are printed in parallel.')
      if len(legend_names)!=len(data):
        raise ValueError('length of legend_names must be consistent with number '\
                         'of plotted rows!')
      ax.legend(legend_data, legend_names)   

    if save:
      plt.savefig(save)

    if show:
      plt.show()
    
    return plt
      
  def PlotHexbin(self, x, y, title=None, x_title=None, y_title=None, x_range=None, y_range=None, binning='log',
                 colormap='jet', show_scalebar=False, scalebar_label=None, clear=True, save=False, show=False):

    """
    Create a heatplot of the data in col x vs the data in col y using matplotlib

    :param x: column name with x data
    :type x: :class:`str`

    :param y: column name with y data
    :type y: :class:`str`

    :param title: title of the plot, will be generated automatically if set to None
    :type title: :class:`str`

    :param x_title: label of x-axis, will be generated automatically if set to None
    :type title: :class:`str`

    :param y_title: label of y-axis, will be generated automatically if set to None
    :type title: :class:`str`

    :param x_range: start and end value for first dimension (e.g. [start_x, end_x])
    :type x_range: :class:`list` of length two

    :param y_range: start and end value for second dimension (e.g. [start_y, end_y])
    :type y_range: :class:`list` of length two

    :param binning: type of binning. If set to None, the value of a hexbin will
                    correspond to the number of datapoints falling into it. If
                    set to 'log', the value will be the log with base 10 of the above
                    value (log(i+1)). If an integer is provided, the number of a 
                    hexbin is equal the number of datapoints falling into it divided 
                    by the integer. If a list of values is provided, these values
                    will be the lower bounds of the bins.
    
    :param colormap: colormap, that will be used. Value can be every colormap defined
                     in matplotlib or an own defined colormap. You can either pass a
                     string with the name of the matplotlib colormap or a colormap
                     object.

    :param show_scalebar: If set to True, a scalebar according to the chosen colormap is shown
    :type show_scalebar: :class:`bool`

    :param scalebar_label: Label of the scalebar
    :type scalebar_label: :class:`str`

    :param clear: clear old data from plot
    :type clear: :class:`bool`

    :param save: filename for saving plot
    :type save: :class:`str`

    :param show: directly show plot
    :type show: :class:`bool`
    
    """

    try:
      import matplotlib.pyplot as plt
      import matplotlib.cm as cm
    except:
      raise ImportError('PlotHexbin relies on matplotlib, but I could not import it')

    idx=self.GetColIndex(x)
    idy=self.GetColIndex(y)
    xdata=[]
    ydata=[]

    for r in self.rows:
      if r[idx]!=None and r[idy]!=None:
        xdata.append(r[idx])
        ydata.append(r[idy])

    if clear:
      plt.clf()
      
    if x_title!=None:
      nice_x=x_title
    else:
      nice_x=MakeTitle(x)
      
    if y_title!=None:
      nice_y=y_title
    else:
      nice_y=MakeTitle(y)

    if title==None:
      title = '%s vs. %s' % (nice_x, nice_y)
  
    if IsStringLike(colormap):
      colormap=getattr(cm, colormap)

    if x_range and (IsScalar(x_range) or len(x_range)!=2):
      raise ValueError('parameter x_range must contain exactly two elements')
    if y_range and (IsScalar(y_range) or len(y_range)!=2):
      raise ValueError('parameter y_range must contain exactly two elements')

    ext = [min(xdata),max(xdata),min(ydata),max(ydata)]

    if x_range:
      plt.xlim((x_range[0], x_range[1]))
      ext[0]=x_range[0]
      ext[1]=x_range[1]
    if y_range:
      plt.ylim(y_range[0], y_range[1])
      ext[2]=y_range[0]
      ext[3]=y_range[1]


    plt.hexbin(xdata, ydata, bins=binning, cmap=colormap, extent=ext)

    plt.title(title, size='x-large', fontweight='bold',
              verticalalignment='bottom')

    plt.xlabel(nice_x)
    plt.ylabel(nice_y)
        
    if show_scalebar:
      cb=plt.colorbar()
      if scalebar_label:
        cb.set_label(scalebar_label)

    if save:
      plt.savefig(save)

    if show:
      plt.show()

    return plt
        
  def MaxRow(self, col):
    """
    Returns the row containing the cell with the maximal value in col. If 
    several rows have the highest value, only the first one is returned.
    ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`

    :returns: row with maximal col value or None if the table is empty
    """
    val, idx = self._Max(col)
    if idx!=None:
      return self.rows[idx]
  
  def Max(self, col):
    """
    Returns the maximum value in col. If several rows have the highest value,
    only the first one is returned. ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`
    """
    val, idx = self._Max(col)
    return val
  
  def MaxIdx(self, col):
    """
    Returns the row index of the cell with the maximal value in col. If
    several rows have the highest value, only the first one is returned.
    ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`
    """
    val, idx = self._Max(col)
    return idx
  
  def _Min(self, col):
    if len(self.rows)==0:
      return None, None
    idx=self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type=='int' or col_type=='float':
      min_val=float('inf')
    elif col_type=='bool':
      min_val=True
    elif col_type=='string':
      min_val=chr(255)
    min_idx=None
    for i,row in enumerate(self.rows):
      if row[idx]!=None and row[idx]<min_val:
        min_val=row[idx]
        min_idx=i
    return min_val, min_idx

  def Min(self, col):
    """
    Returns the minimal value in col. If several rows have the lowest value,
    only the first one is returned. ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`
    """
    val, idx = self._Min(col)
    return val
  
  def MinRow(self, col):
    """
    Returns the row containing the cell with the minimal value in col. If 
    several rows have the lowest value, only the first one is returned.
    ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`

    :returns: row with minimal col value or None if the table is empty
    """
    val, idx = self._Min(col)
    if idx!=None:
      return self.rows[idx]
  
  def MinIdx(self, col):
    """
    Returns the row index of the cell with the minimal value in col. If
    several rows have the lowest value, only the first one is returned.
    ''None'' values are ignored.

    :param col: column name
    :type col: :class:`str`
    """
    val, idx = self._Min(col)
    return idx
  
  def Sum(self, col):
    """
    Returns the sum of the given column. Cells with ''None'' are ignored. Returns 
    0.0, if the column doesn't contain any elements. Col must be of numeric
    column type ('float', 'int') or boolean column type.

    :param col: column name
    :type col: :class:`str`

    :raises: :class:`TypeError` if column type is ``string``
    """
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float' and col_type!='bool':
      raise TypeError("Sum can only be used on numeric column types")
    s = 0.0
    for r in self.rows:
      if r[idx]!=None:
        s += r[idx] 
    return s 

  def Mean(self, col):
    """
    Returns the mean of the given column. Cells with ''None'' are ignored. Returns 
    None, if the column doesn't contain any elements. Col must be of numeric
    ('float', 'int') or boolean column type.

    If column type is *bool*, the function returns the ratio of
    number of 'Trues' by total number of elements.

    :param col: column name
    :type col: :class:`str`

    :raises: :class:`TypeError` if column type is ``string``
    """
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float' and col_type!='bool':
      raise TypeError("Mean can only be used on numeric or bool column types")
    
    vals=[]
    for v in self[col]:
      if v!=None:
        vals.append(v)
    try:
      return stutil.Mean(vals)
    except:
      return None
    
  def RowMean(self, mean_col_name, cols):
    """
    Adds a new column of type 'float' with a specified name (*mean_col_name*),
    containing the mean of all specified columns for each row.
    
    Cols are specified by their names and must be of numeric column
    type ('float', 'int') or boolean column type. Cells with None are ignored.
    Adds ''None'' if the row doesn't contain any values.
    
    :param mean_col_name: name of new column containing mean values
    :type mean_col_name: :class:`str`

    :param cols: name or list of names of columns to include in computation of
                 mean
    :type cols: :class:`str` or :class:`list` of strings

    :raises: :class:`TypeError` if column type of columns in *col* is ``string``
    
    == Example ==
   
    Staring with the following table:
    
    ==== ==== ====
    x     y    u           
    ==== ==== ====
     1    10  100 
     2    15  None 
     3    20  400 
    ==== ==== ====
    
    the code here adds a column with the name 'mean' to yield the table below:
    
    .. code-block::python
    
      tab.RowMean('mean', ['x', 'u'])
    
    
    ==== ==== ==== ===== 
    x     y    u   mean           
    ==== ==== ==== =====
     1    10  100  50.5 
     2    15  None 2
     3    20  400  201.5 
    ==== ==== ==== =====
      
    """
    
    if IsScalar(cols):
      cols = [cols]
    
    cols_idxs = []
    for col in cols:
      idx = self.GetColIndex(col)
      col_type = self.col_types[idx]
      if col_type!='int' and col_type!='float' and col_type!='bool':
        raise TypeError("RowMean can only be used on numeric column types")
      cols_idxs.append(idx)
      
    mean_rows = []
    for row in self.rows:
      vals = []
      for idx in cols_idxs:
        v = row[idx]
        if v!=None:
          vals.append(v)
      try:
        mean = stutil.Mean(vals)
        mean_rows.append(mean)
      except:
        mean_rows.append(None)
    
    self.AddCol(mean_col_name, 'f', mean_rows)
    
  def Percentiles(self, col, nths):
    """
    Returns the percentiles of column *col* given in *nths*.

    The percentiles are calculated as 
    
    .. code-block:: python

      values[min(len(values)-1, int(math.floor(len(values)*nth/100.0)))]

    where values are the sorted values of *col* not equal to ''None''

    :param col: column name
    :type col:  :class:`str`
    :param nths: list of percentiles to be calculated. Each percentile is a
                 number between 0 and 100.
    :type nths:  :class:`list` of numbers

    :raises: :class:`TypeError` if column type is ``string``
    :returns: List of percentiles in the same order as given in *nths*
    """
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float' and col_type!='bool':
      raise TypeError("Median can only be used on numeric column types")
    
    for nth in nths:
      if nth < 0 or nth > 100:
        raise ValueError("percentiles must be between 0 and 100")
    vals=[]
    for v in self[col]:
      if v!=None:
        vals.append(v)
    vals=sorted(vals)
    if len(vals)==0:
      return [None]*len(nths)
    percentiles=[]
    
    for nth in nths:
      # rounding behaviour between Python2 and Python3 changed....
      # p=vals[min(len(vals)-1, int(round(len(vals)*nth/100.0+0.5)-1))]
      p=vals[min(len(vals)-1, int(math.floor(len(vals)*nth/100.0)))]
      percentiles.append(p)
    return percentiles

  def Median(self, col):
    """
    Returns the median of the given column. Cells with ''None'' are ignored. Returns 
    ''None'', if the column doesn't contain any elements. Col must be of numeric
    column type ('float', 'int') or boolean column type.

    :param col: column name
    :type col: :class:`str`

    :raises: :class:`TypeError` if column type is ``string``
    """
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float' and col_type!='bool':
      raise TypeError("Median can only be used on numeric column types")
    
    vals=[]
    for v in self[col]:
      if v!=None:
        vals.append(v)
    stutil.Median(vals)
    try:
      return stutil.Median(vals)
    except:
      return None
    
  def StdDev(self, col):
    """
    Returns the standard deviation of the given column. Cells with ''None'' are
    ignored. Returns ''None'', if the column doesn't contain any elements. Col must
    be of numeric column type ('float', 'int') or boolean column type.

    :param col: column name
    :type col: :class:`str`

    :raises: :class:`TypeError` if column type is ``string``
    """
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float' and col_type!='bool':
      raise TypeError("StdDev can only be used on numeric column types")
    
    vals=[]
    for v in self[col]:
      if v!=None:
        vals.append(v)
    try:
      return stutil.StdDev(vals)
    except:
      return None

  def Count(self, col, ignore_nan=True):
    """
    Count the number of cells in column that are not equal to ''None''.

    :param col: column name
    :type col: :class:`str`

    :param ignore_nan: ignore all *None* values
    :type ignore_nan: :class:`bool`
    """
    count=0
    idx=self.GetColIndex(col)
    for r in self.rows:
      if ignore_nan:
        if r[idx]!=None:
          count+=1
      else:
        count+=1
    return count

  def Correl(self, col1, col2):
    """
    Calculate the Pearson correlation coefficient between *col1* and *col2*, only
    taking rows into account where both of the values are not equal to *None*.
    If there are not enough data points to calculate a correlation coefficient,
    *None* is returned.

    :param col1: column name for first column
    :type col1: :class:`str`

    :param col2: column name for second column
    :type col2: :class:`str`
    """
    if IsStringLike(col1) and IsStringLike(col2):
      col1 = self.GetColIndex(col1)
      col2 = self.GetColIndex(col2)
    vals1, vals2=([],[])
    for v1, v2 in zip(self[col1], self[col2]):
      if v1!=None and v2!=None:
        vals1.append(v1)
        vals2.append(v2)
    try:
      return stutil.Correl(vals1, vals2)
    except:
      return None

  def SpearmanCorrel(self, col1, col2):
    """
    Calculate the Spearman correlation coefficient between col1 and col2, only 
    taking rows into account where both of the values are not equal to None. If 
    there are not enough data points to calculate a correlation coefficient, 
    None is returned.
    
    :warning: The function depends on the following module: *scipy.stats.mstats*

    :param col1: column name for first column
    :type col1: :class:`str`

    :param col2: column name for second column
    :type col2: :class:`str`
    """
    try:
      import scipy.stats.mstats
      
      if IsStringLike(col1) and IsStringLike(col2):
        col1 = self.GetColIndex(col1)
        col2 = self.GetColIndex(col2)
      vals1, vals2=([],[])
      for v1, v2 in zip(self[col1], self[col2]):
        if v1!=None and v2!=None:
          vals1.append(v1)
          vals2.append(v2)
      try:
        correl = scipy.stats.mstats.spearmanr(vals1, vals2)[0]
        if scipy.isnan(correl):
          return None
        return correl
      except:
        return None

    except ImportError:
      LogError("Function needs scipy.stats.mstats, but I could not import it.")
      raise
    

  def Save(self, stream_or_filename, format='ost', sep=','):
    """
    Save the table to stream or filename. The following three file formats
    are supported (for more information on file formats, see :meth:`Load`):

    =============   =======================================
    ost             ost-specific format (human readable)
    csv             comma separated values (human readable)
    pickle          pickled byte stream (binary)
    html            HTML table
    context         ConTeXt table
    =============   =======================================

    :param stream_or_filename: filename or stream for writing output
    :type stream_or_filename: :class:`str` or :class:`file`

    :param format: output format (i.e. *ost*, *csv*, *pickle*)
    :type format: :class:`str`

    :raises: :class:`ValueError` if format is unknown
    """
    format=format.lower()
    if format=='ost':
      return self._SaveOST(stream_or_filename)
    if format=='csv':
      return self._SaveCSV(stream_or_filename, sep=sep)
    if format=='pickle':
      return self._SavePickle(stream_or_filename)
    if format=='html':
      return self._SaveHTML(stream_or_filename)
    if format=='context':
      return self._SaveContext(stream_or_filename)
    raise ValueError('unknown format "%s"' % format)

  def _SavePickle(self, stream):
    file_opened=False
    if not hasattr(stream, 'write'):
      stream=open(stream, 'wb')
      file_opened=True
    pickle.dump(self, stream, pickle.HIGHEST_PROTOCOL)
    if file_opened:
      stream.close()

  def _SaveHTML(self, stream_or_filename):
    def _escape(s):
      return s.replace('&', '&amp;').replace('>', '&gt;').replace('<', '&lt;')

    file_opened = False
    if not hasattr(stream_or_filename, 'write'):
      stream = open(stream_or_filename, 'w')
      file_opened = True
    else:
      stream = stream_or_filename
    stream.write('<table>') 
    stream.write('<tr>')
    for col_name in self.col_names:
      stream.write('<th>%s</th>' % _escape(col_name)) 
    stream.write('</tr>')
    for row in self.rows:
      stream.write('<tr>')
      for i, col in enumerate(row):
        val = ''
        if col != None:
           if self.col_types[i] == 'float':
             val = '%.3f' % col
           elif self.col_types[i] == 'int':
             val = '%d' % col
           elif self.col_types[i] == 'bool':
             val = col and 'true' or 'false'
           else:
             val  = str(col)
        stream.write('<td>%s</td>' % _escape(val))
      stream.write('</tr>')
    stream.write('</table>')
    if file_opened:
      stream.close()
  def _SaveContext(self, stream_or_filename):
    file_opened = False
    if not hasattr(stream_or_filename, 'write'):
      stream = open(stream_or_filename, 'w')
      file_opened = True
    else:
      stream = stream_or_filename
    stream.write('\\starttable[') 
    for col_type in self.col_types:
      if col_type =='string':
        stream.write('l|')
      elif col_type=='int':
        stream.write('r|')
      elif col_type =='float':
        stream.write('i3r|')
      else:
        stream.write('l|')
    stream.write(']\n\\HL\n')
    for col_name in self.col_names:
      stream.write('\\NC \\bf %s' % col_name) 
    stream.write(' \\AR\\HL\n')
    for row in self.rows:
      for i, col in enumerate(row):
        val = '---'
        if col != None:
           if self.col_types[i] == 'float':
             val = '%.3f' % col
           elif self.col_types[i] == 'int':
             val = '%d' % col
           elif self.col_types[i] == 'bool':
             val = col and 'true' or 'false'
           else:
             val  = str(col)
        stream.write('\\NC %s' % val)
      stream.write(' \\AR\n')
    stream.write('\\HL\n')
    stream.write('\\stoptable')
    if file_opened:
      stream.close()

  def _SaveCSV(self, stream, sep):
    file_opened=False
    if not hasattr(stream, 'write'):
      stream=open(stream, 'w')
      file_opened=True

    writer=csv.writer(stream, delimiter=sep)
    writer.writerow(['%s' % n for n in self.col_names])
    for row in self.rows:
      row=list(row)
      for i, c in enumerate(row):
        if c==None:
          row[i]='NA'
      writer.writerow(row)
    if file_opened:
      stream.close()


  def _SaveOST(self, stream):
    file_opened=False
    if hasattr(stream, 'write'):
      writer=csv.writer(stream, delimiter=' ')
    else:
      stream=open(stream, 'w')
      writer=csv.writer(stream, delimiter=' ')
      file_opened=True
    if self.comment:
      stream.write(''.join(['# %s\n' % l for l in self.comment.split('\n')]))
    writer.writerow(['%s[%s]' % t for t in zip(self.col_names, self.col_types)])
    for row in self.rows:
      row=list(row)
      for i, c in enumerate(row):
        if c==None:
          row[i]='NA'
      writer.writerow(row)
    if file_opened:
      stream.close()

  def GetNumpyMatrixAsArray(self, *args):
    '''
    Returns a numpy array containing the selected columns from the table as 
    columns as a matrix.

    Only columns of type *int* or *float* are supported. *NA* values in the
    table will be converted to *None* values.

    Originally the function used the numpy matrix class but that is going to be
    deprecated in the future. Numpy itself suggests replacing numpy matrix by
    numpy array.

    :param \\*args: column names to include in numpy array

    :warning: The function depends on *numpy*
    '''
    try:
      import numpy as np
      
      if len(args)==0:
        raise RuntimeError("At least one column must be specified.")
      
      idxs = []
      for arg in args:
        idx = self.GetColIndex(arg)
        col_type = self.col_types[idx]
        if col_type!='int' and col_type!='float':
          raise TypeError("Numpy matrix can only be generated from numeric "+\
                          "column types")
        idxs.append(idx)

      a = np.array([list(self[i]) for i in idxs])
      return a.T
    
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise

  def GetNumpyMatrix(self, *args):
    '''
    *Caution*: Numpy is deprecating the use of the numpy matrix class.

    Returns a numpy matrix containing the selected columns from the table as 
    columns in the matrix.

    Only columns of type *int* or *float* are supported. *NA* values in the
    table will be converted to *None* values.

    :param \\*args: column names to include in numpy matrix

    :warning: The function depends on *numpy*
    '''
    LogWarning("table.GetNumpyMatrix is deprecated, please use "+
               "table.GetNumpyMatrixAsArray instead")
    try:
      import numpy as np
      m = self.GetNumpyMatrixAsArray(*args)
      return np.matrix(m)
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise

  def GaussianSmooth(self, col, std=1.0, na_value=0.0, padding='reflect', c=0.0):

    '''
    In place Gaussian smooth of a column in the table with a given standard deviation.
    All nan are set to nan_value before smoothing.

    :param col: column name
    :type col: :class:`str`

    :param std: standard deviation for gaussian kernel
    :type std: `scalar` 

    :param na_value: all na (None) values of the speciefied column are set to na_value before smoothing
    :type na_value: `scalar`

    :param padding: allows to handle padding behaviour see scipy ndimage.gaussian_filter1d documentation for more information. standard is reflect
    :type padding: :class:`str`

    :param c: constant value used for padding if padding mode is constant
    :type c: `scalar`



    :warning: The function depends on *scipy*
    ''' 

    try:
      from scipy import ndimage
      import numpy as np
    except ImportError:
      LogError("I need scipy.ndimage and numpy, but could not import it")
      raise
      
    idx = self.GetColIndex(col)
    col_type = self.col_types[idx]
    if col_type!='int' and col_type!='float':
      raise TypeError("GaussianSmooth can only be used on numeric column types")

    vals=[]
    for v in self[col]:
      if v!=None:
        vals.append(v)
      else:
        vals.append(na_value)

    
    smoothed_values_ndarray=ndimage.gaussian_filter1d(vals,std, mode=padding, cval=c)

    result=[]

    for v in smoothed_values_ndarray:
      result.append(v)

    self[col]=result


  def GetOptimalPrefactors(self, ref_col, *args, **kwargs):
    '''
    This returns the optimal prefactor values (i.e. :math:`a, b, c, ...`) for
    the following equation
    
    .. math::
      :label: op1

      a*u + b*v + c*w + ... = z
    
    where :math:`u, v, w` and :math:`z` are vectors. In matrix notation
    
    .. math::
      :label: op2

      A*p = z
    
    where :math:`A` contains the data from the table :math:`(u,v,w,...)`,
    :math:`p` are the prefactors to optimize :math:`(a,b,c,...)` and :math:`z`
    is the vector containing the result of equation :eq:`op1`.
    
    The parameter ref_col equals to :math:`z` in both equations, and \\*args
    are columns :math:`u`, :math:`v` and :math:`w` (or :math:`A` in :eq:`op2`).
    All columns must be specified by their names.
    
    **Example:**

    .. code-block:: python
    
      tab.GetOptimalPrefactors('colC', 'colA', 'colB')
    
    The function returns a list containing the prefactors
    :math:`a, b, c, ...` in the correct order (i.e. same as columns were
    specified in \\*args).
    
    Weighting:
    If the kwarg weights="columX" is specified, the equations are weighted by
    the values in that column. Each row is multiplied by the weight in that
    row, which leads to :eq:`op3`:
    
    .. math::
      :label: op3

      \\textit{weight}*a*u + \\textit{weight}*b*v + \\textit{weight}*c*w + ...
      = \\textit{weight}*z
    
    Weights must be float or int and can have any value. A value of 0 ignores
    this equation, a value of 1 means the same as no weight. If all weights are
    the same for each row, the same result will be obtained as with no weights.
    
    **Example:**
    
    .. code-block:: python
    
      tab.GetOptimalPrefactors('colC', 'colA', 'colB', weights='colD')
    
    '''
    try:
      import numpy as np
  
      if len(args)==0:
        raise RuntimeError("At least one column must be specified.")
      
      b = self.GetNumpyMatrixAsArray(ref_col)
      a = self.GetNumpyMatrixAsArray(*args)

      if len(kwargs)!=0:
        if 'weights' in kwargs:
          w = self.GetNumpyMatrixAsArray(kwargs['weights'])
          b = np.multiply(b,w)
          a = np.multiply(a,w)
          
        else:
          raise RuntimeError("specified unrecognized kwargs, use weights as key")
      
      k = np.linalg.inv(a.T@a)@a.T@b
      return list(k.T.reshape(-1))
    
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise

  def PlotEnrichment(self, score_col, class_col, score_dir='-', 
                     class_dir='-', class_cutoff=2.0,
                     style='-', title=None, x_title=None, y_title=None,
                     clear=True, save=None):
    '''
    Plot an enrichment curve using matplotlib of column *score_col* classified
    according to *class_col*.
    
    For more information about parameters of the enrichment, see
    :meth:`ComputeEnrichment`, and for plotting see :meth:`Plot`.
    
    :warning: The function depends on *matplotlib*
    '''
    try:
      import matplotlib.pyplot as plt
    
      enrx, enry = self.ComputeEnrichment(score_col, class_col, score_dir,
                                          class_dir, class_cutoff)
      
      if not title:
        title = 'Enrichment of %s'%score_col
        
      if not x_title:
        x_title = '% database'
        
      if not y_title:
        y_title = '% positives'
        
      if clear:
        plt.clf()
        
      plt.plot(enrx, enry, style)
      
      plt.title(title, size='x-large', fontweight='bold')     
      plt.ylabel(y_title, size='x-large')
      plt.xlabel(x_title, size='x-large')
      
      if save:
        plt.savefig(save)
      
      return plt
    except ImportError:
      LogError("Function needs matplotlib, but I could not import it.")
      raise
    
  def ComputeEnrichment(self, score_col, class_col, score_dir='-', 
                        class_dir='-', class_cutoff=2.0):
    '''
    Computes the enrichment of column *score_col* classified according to
    *class_col*.
    
    For this it is necessary, that the datapoints are classified into positive
    and negative points. This can be done in two ways:
    
     - by using one 'bool' type column (*class_col*) which contains *True* for
       positives and *False* for negatives
       
     - by specifying a classification column (*class_col*), a cutoff value
       (*class_cutoff*) and the classification columns direction (*class_dir*).
       This will generate the classification on the fly

       * if ``class_dir=='-'``: values in the classification column that are less than or equal to class_cutoff will be counted as positives
       * if ``class_dir=='+'``: values in the classification column that are larger than or equal to class_cutoff will be counted as positives

    During the calculation, the table will be sorted according to *score_dir*,
    where a '-' values means smallest values first and therefore, the smaller
    the value, the better.
    
    :warning: If either the value of *class_col* or *score_col* is *None*, the
              data in this row is ignored.
    '''
    
    ALLOWED_DIR = ['+','-']
    
    score_idx = self.GetColIndex(score_col)
    score_type = self.col_types[score_idx]
    if score_type!='int' and score_type!='float':
      raise TypeError("Score column must be numeric type")
    
    class_idx = self.GetColIndex(class_col)
    class_type = self.col_types[class_idx]
    if class_type!='int' and class_type!='float' and class_type!='bool':
      raise TypeError("Classifier column must be numeric or bool type")
    
    if (score_dir not in ALLOWED_DIR) or (class_dir not in ALLOWED_DIR):
      raise ValueError("Direction must be one of %s"%str(ALLOWED_DIR))
    
    self.Sort(score_col, score_dir)
    
    x = [0]
    y = [0]
    enr = 0
    old_score_val = None
    i = 0

    for row in self.rows:
      class_val = row[class_idx]
      score_val = row[score_idx]
      if class_val==None or score_val==None:
        continue
      if class_val!=None:
        if old_score_val==None:
          old_score_val = score_val
        if score_val!=old_score_val:
          x.append(i)
          y.append(enr)
          old_score_val = score_val
        i+=1
        if class_type=='bool':
          if class_val==True:
            enr += 1
        else:
          if (class_dir=='-' and class_val<=class_cutoff) or (class_dir=='+' and class_val>=class_cutoff):
            enr += 1
    x.append(i)
    y.append(enr)

    # if no false positives or false negatives values are found return None
    if x[-1]==0 or y[-1]==0:
      return None

    x = [float(v)/x[-1] for v in x]
    y = [float(v)/y[-1] for v in y]
    return x,y
    
  def ComputeEnrichmentAUC(self, score_col, class_col, score_dir='-', 
                           class_dir='-', class_cutoff=2.0):
    '''
    Computes the area under the curve of the enrichment using the trapezoidal
    rule.
    
    For more information about parameters of the enrichment, see
    :meth:`ComputeEnrichment`.

    :warning: The function depends on *numpy*
    '''
    try:
      import numpy as np
      
      enr = self.ComputeEnrichment(score_col, class_col, score_dir,
                                          class_dir, class_cutoff)
      
      if enr==None:
        return None
      return np.trapz(enr[1], enr[0])
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise

  def ComputeROC(self, score_col, class_col, score_dir='-',
                 class_dir='-', class_cutoff=2.0):
    '''
    Computes the receiver operating characteristics (ROC) of column *score_col*
    classified according to *class_col*.

    For this it is necessary, that the datapoints are classified into positive
    and negative points. This can be done in two ways:

     - by using one 'bool' column (*class_col*) which contains True for positives
       and False for negatives
     - by using a non-bool column (*class_col*), a cutoff value (*class_cutoff*)
       and the classification columns direction (*class_dir*). This will generate
       the classification on the fly

       - if ``class_dir=='-'``: values in the classification column that are less than or equal to *class_cutoff* will be counted as positives
       - if ``class_dir=='+'``: values in the classification column that are larger than or equal to *class_cutoff* will be counted as positives

    During the calculation, the table will be sorted according to *score_dir*,
    where a '-' values means smallest values first and therefore, the smaller
    the value, the better.

    If *class_col* does not contain any positives (i.e. value is True (if column
    is of type bool) or evaluated to True (if column is of type int or float
    (depending on *class_dir* and *class_cutoff*))) the ROC is not defined and
    the function will return *None*.

    :warning: If either the value of *class_col* or *score_col* is *None*, the
              data in this row is ignored.
    '''

    ALLOWED_DIR = ['+','-']

    score_idx = self.GetColIndex(score_col)
    score_type = self.col_types[score_idx]
    if score_type!='int' and score_type!='float':
      raise TypeError("Score column must be numeric type")

    class_idx = self.GetColIndex(class_col)
    class_type = self.col_types[class_idx]
    if class_type!='int' and class_type!='float' and class_type!='bool':
      raise TypeError("Classifier column must be numeric or bool type")

    if (score_dir not in ALLOWED_DIR) or (class_dir not in ALLOWED_DIR):
      raise ValueError("Direction must be one of %s"%str(ALLOWED_DIR))

    self.Sort(score_col, score_dir)

    x = [0]
    y = [0]
    tp = 0
    fp = 0
    old_score_val = None

    for i,row in enumerate(self.rows):
      class_val = row[class_idx]
      score_val = row[score_idx]
      if class_val==None or score_val==None:
        continue
      if class_val!=None:
        if old_score_val==None:
          old_score_val = score_val
        if score_val!=old_score_val:
          x.append(fp)
          y.append(tp)
          old_score_val = score_val
        if class_type=='bool':
          if class_val==True:
            tp += 1
          else:
            fp += 1
        else:
          if (class_dir=='-' and class_val<=class_cutoff) or (class_dir=='+' and class_val>=class_cutoff):
            tp += 1
          else:
            fp += 1
    x.append(fp)
    y.append(tp)
    
    # if no false positives or false negatives values are found return None
    if x[-1]==0 or y[-1]==0:
      return None
    
    x = [float(v)/x[-1] for v in x]
    y = [float(v)/y[-1] for v in y]
    return x,y

  def ComputeROCAUC(self, score_col, class_col, score_dir='-',
                    class_dir='-', class_cutoff=2.0):
    '''
    Computes the area under the curve of the receiver operating characteristics
    using the trapezoidal rule.
    
    For more information about parameters of the ROC, see
    :meth:`ComputeROC`.

    :warning: The function depends on *numpy*
    '''
    try:
      import numpy as np

      roc = self.ComputeROC(score_col, class_col, score_dir,
                            class_dir, class_cutoff)

      if not roc:
        return None
      return np.trapz(roc[1], roc[0])
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise
    
  def ComputeLogROCAUC(self, score_col, class_col, score_dir='-',
                       class_dir='-', class_cutoff=2.0):
    '''
    Computes the area under the curve of the log receiver operating 
    characteristics (logROC) where the x-axis is semilogarithmic
    using the trapezoidal rule.
    
    The logROC is computed with a lambda of 0.001 according to 
    Rapid Context-Dependent Ligand Desolvation in Molecular Docking
    Mysinger M. and Shoichet B., Journal of Chemical Information and Modeling
    2010 50 (9), 1561-1573
    
    For more information about parameters of the ROC, see
    :meth:`ComputeROC`.

    :warning: The function depends on *numpy*
    '''
    try:
      import numpy as np

      roc = self.ComputeROC(score_col, class_col, score_dir,
                            class_dir, class_cutoff)

      if not roc:
        return None
      
      rocxt, rocyt = roc
      rocx=[]
      rocy=[]
      
      # define lambda
      l=0.001
      
      # remove all duplicate x-values
      rocxt = [x if x>0 else l for x in rocxt]
      for i in range(len(rocxt)-1):
        if rocxt[i]==rocxt[i+1]:
          continue
        rocx.append(rocxt[i])
        rocy.append(rocyt[i])
      rocx.append(1.0)
      rocy.append(1.0)
      
      # compute logauc
      value = 0
      for i in range(len(rocx)-1):
        x = rocx[i]
        if rocx[i]==rocx[i+1]:
          continue
        b = rocy[i+1]-rocx[i+1]*((rocy[i+1]-rocy[i])/(rocx[i+1]-rocx[i]))
        value += ((rocy[i+1]-rocy[i])/math.log(10))+b*(math.log10(rocx[i+1])-math.log10(rocx[i]))
      return value/math.log10(1.0/l)
      
    except ImportError:
      LogError("Function needs numpy, but I could not import it.")
      raise

  def PlotROC(self, score_col, class_col, score_dir='-',
              class_dir='-', class_cutoff=2.0,
              style='-', title=None, x_title=None, y_title=None,
              clear=True, save=None):
    '''
    Plot an ROC curve using matplotlib.
    
    For more information about parameters of the ROC, see
    :meth:`ComputeROC`, and for plotting see :meth:`Plot`.

    :warning: The function depends on *matplotlib*
    '''

    try:
      import matplotlib.pyplot as plt

      roc = self.ComputeROC(score_col, class_col, score_dir,
                                   class_dir, class_cutoff)
      
      if not roc:
        return None

      enrx, enry = roc

      if not title:
        title = 'ROC of %s'%score_col

      if not x_title:
        x_title = 'false positive rate'

      if not y_title:
        y_title = 'true positive rate'

      if clear:
        plt.clf()

      plt.plot(enrx, enry, style)

      plt.title(title, size='x-large', fontweight='bold')
      plt.ylabel(y_title, size='x-large')
      plt.xlabel(x_title, size='x-large')

      if save:
        plt.savefig(save)

      return plt
    except ImportError:
      LogError("Function needs matplotlib, but I could not import it.")
      raise
    
  def PlotLogROC(self, score_col, class_col, score_dir='-',
                 class_dir='-', class_cutoff=2.0,
                 style='-', title=None, x_title=None, y_title=None,
                 clear=True, save=None):
    '''
    Plot an logROC curve where the x-axis is semilogarithmic using matplotlib 
    
    For more information about parameters of the ROC, see
    :meth:`ComputeROC`, and for plotting see :meth:`Plot`.

    :warning: The function depends on *matplotlib*
    '''

    try:
      import matplotlib.pyplot as plt

      roc = self.ComputeROC(score_col, class_col, score_dir,
                                   class_dir, class_cutoff)
      
      if not roc:
        return None

      rocx, rocy = roc

      if not title:
        title = 'logROC of %s'%score_col

      if not x_title:
        x_title = 'false positive rate'

      if not y_title:
        y_title = 'true positive rate'

      if clear:
        plt.clf()
     
      rocx = [x if x>0 else 0.001 for x in rocx]
      
      
      plt.plot(rocx, rocy, style)

      plt.title(title, size='x-large', fontweight='bold')
      plt.ylabel(y_title, size='x-large')
      plt.xlabel(x_title, size='x-large')
      try:
        plt.xscale('log', basex=10)
      except:
        plt.xscale('log', base=10) # breaking change in matplotlib 3.5
      plt.xlim(0.001, 1.0)

      if save:
        plt.savefig(save)

      return plt
    except ImportError:
      LogError("Function needs matplotlib, but I could not import it.")
      raise  
  
  def ComputeMCC(self, score_col, class_col, score_dir='-',
                 class_dir='-', score_cutoff=2.0, class_cutoff=2.0):
    '''
    Compute Matthews correlation coefficient (MCC) for one column (*score_col*)
    with the points classified into true positives, false positives, true
    negatives and false negatives according to a specified classification
    column (*class_col*).
    
    The datapoints in *score_col* and *class_col* are classified into
    positive and negative points. This can be done in two ways:
    
     - by using 'bool' columns which contains True for positives and False
       for negatives
       
     - by using 'float' or 'int' columns and specifying a cutoff value and the
       columns direction. This will generate the classification on the fly
       
       * if ``class_dir``/``score_dir=='-'``: values in the classification column that are less than or equal to *class_cutoff*/*score_cutoff* will be counted as positives
       * if ``class_dir``/``score_dir=='+'``: values in the classification column that are larger than or equal to *class_cutoff*/*score_cutoff* will be counted as positives
                                    
    The two possibilities can be used together, i.e. 'bool' type for one column
    and 'float'/'int' type and cutoff/direction for the other column.
    '''
    ALLOWED_DIR = ['+','-']

    score_idx = self.GetColIndex(score_col)
    score_type = self.col_types[score_idx]
    if score_type!='int' and score_type!='float' and score_type!='bool':
      raise TypeError("Score column must be numeric or bool type")

    class_idx = self.GetColIndex(class_col)
    class_type = self.col_types[class_idx]
    if class_type!='int' and class_type!='float' and class_type!='bool':
      raise TypeError("Classifier column must be numeric or bool type")

    if (score_dir not in ALLOWED_DIR) or (class_dir not in ALLOWED_DIR):
      raise ValueError("Direction must be one of %s"%str(ALLOWED_DIR))
     
    tp = 0
    fp = 0
    fn = 0
    tn = 0

    for i,row in enumerate(self.rows):
      class_val = row[class_idx]
      score_val = row[score_idx]
      if class_val!=None:
        if (class_type=='bool' and class_val==True) or (class_type!='bool' and ((class_dir=='-' and class_val<=class_cutoff) or (class_dir=='+' and class_val>=class_cutoff))):
          if (score_type=='bool' and score_val==True) or (score_type!='bool' and ((score_dir=='-' and score_val<=score_cutoff) or (score_dir=='+' and score_val>=score_cutoff))):
            tp += 1
          else:
            fn += 1
        else:
          if (score_type=='bool' and score_val==False) or (score_type!='bool' and ((score_dir=='-' and score_val>score_cutoff) or (score_dir=='+' and score_val<score_cutoff))):
            tn += 1
          else:
            fp += 1

    mcc = None
    msg = None
    if (tp+fn)==0:
      msg = 'factor (tp + fn) is zero'
    elif (tp+fp)==0:
      msg = 'factor (tp + fp) is zero'
    elif (tn+fn)==0:
      msg = 'factor (tn + fn) is zero'
    elif (tn+fp)==0:
      msg = 'factor (tn + fp) is zero'
    
    if msg:
      LogWarning("Could not compute MCC: MCC is not defined since %s"%msg)
    else:
      mcc = ((tp*tn)-(fp*fn)) / math.sqrt((tp+fn)*(tp+fp)*(tn+fn)*(tn+fp))
    return mcc
    

  def IsEmpty(self, col_name=None, ignore_nan=True):
    '''
    Checks if a table is empty.
    
    If no column name is specified, the whole table is checked for being empty,
    whereas if a column name is specified, only this column is checked.
    
    By default, all NAN (or None) values are ignored, and thus, a table
    containing only NAN values is considered as empty. By specifying the 
    option ignore_nan=False, NAN values are counted as 'normal' values.
    '''
    
    # table with no columns and no rows
    if len(self.col_names)==0:
      if col_name:
        raise ValueError('Table has no column named "%s"' % col_name)
      return True
    
    # column name specified
    if col_name:
      if self.Count(col_name, ignore_nan=ignore_nan)==0:
        return True
      else:
        return False
      
    # no column name specified -> test whole table
    else:
      for row in self.rows:
        for cell in row:
          if ignore_nan:
            if cell!=None:
              return False
          else:
            return False
    return True
    

  def Extend(self, tab, overwrite=None):
    """
    Append each row of *tab* to the current table. The data is appended based
    on the column names, thus the order of the table columns is *not* relevant,
    only the header names.
    
    If there is a column in *tab* that is not present in the current table,
    it is added to the current table and filled with *None* for all the rows
    present in the current table.
    
    If the type of any column in *tab* is not the same as in the current table
    a *TypeError* is raised.
    
    If *overwrite* is not None and set to an existing column name, the specified 
    column in the table is searched for the first occurrence of a value matching
    the value of the column with the same name in the dictionary. If a matching
    value is found, the row is overwritten with the dictionary. If no matching
    row is found, a new row is appended to the table.
    """
    # add column to current table if it doesn't exist
    for name,typ in zip(tab.col_names, tab.col_types):
      if not name in self.col_names:
        self.AddCol(name, typ)
    
    # check that column types are the same in current and new table
    for name in self.col_names:
      if name in tab.col_names:
        curr_type = self.col_types[self.GetColIndex(name)]
        new_type = tab.col_types[tab.GetColIndex(name)]
        if curr_type!=new_type:
          raise TypeError('cannot extend table, column %s in new '%name +\
                          'table different type (%s) than in '%new_type +\
                          'current table (%s)'%curr_type)
    
    num_rows = len(tab.rows)
    for i in range(0,num_rows):
      row = tab.rows[i]
      data = dict(list(zip(tab.col_names,row)))
      self.AddRow(data, overwrite)
    

def Merge(table1, table2, by, only_matching=False):
  """
  Returns a new table containing the data from both tables. The rows are 
  combined based on the common values in the column(s) by. The option 'by' can
  be a list of column names. When this is the case, merging is based on
  multiple columns.
  For example, the two tables below

  ==== ====
  x     y            
  ==== ====
   1    10
   2    15
   3    20
  ==== ====
  
  ==== ====
  x     u
  ==== ====
    1  100
    3  200
    4  400
  ==== ====

  when merged by column x, produce the following output:

  ===== ===== =====
  x      y     u
  ===== ===== =====
  1      10    100
  2      15    None
  3      20    200
  4      None  400
  ===== ===== =====
  

  """
  def _key(row, indices):
    return tuple([row[i] for i in indices])
  def _keep(indices, cn, ct, ni):
    ncn, nct, nni=([],[],[])
    for i in range(len(cn)):
      if i not in indices:
        ncn.append(cn[i])
        nct.append(ct[i])
        nni.append(ni[i])
    return ncn, nct, nni
  col_names=list(table2.col_names)
  col_types=list(table2.col_types)
  new_index=[i for i in range(len(col_names))]
  if isinstance(by, str):
    common2_indices=[col_names.index(by)]
  else:
    common2_indices=[col_names.index(b) for b in by]
  col_names, col_types, new_index=_keep(common2_indices, col_names, 
                                        col_types, new_index)

  for i, name in enumerate(col_names):
    try_name=name
    counter=1
    while try_name in table1.col_names:
      counter+=1
      try_name='%s_%d' % (name, counter)
    col_names[i]=try_name
  common1={}
  if isinstance(by, str):
    common1_indices=[table1.col_names.index(by)]
  else:
    common1_indices=[table1.col_names.index(b) for b in by]
  for row in table1.rows:
    key=_key(row, common1_indices)
    if key in common1:
      raise ValueError('duplicate key "%s in first table"' % (str(key)))
    common1[key]=row
  common2={}
  for row in table2.rows:
    key=_key(row, common2_indices)
    if key in common2:
      raise ValueError('duplicate key "%s" in second table' % (str(key)))
    common2[key]=row
  new_tab=Table(table1.col_names+col_names, table1.col_types+col_types)
  for k, v in common1.items():
    row=v+[None for i in range(len(table2.col_names)-len(common2_indices))]
    matched=False
    if k in common2:
      matched=True
      row2=common2[k]
      for i, index in enumerate(new_index):
        row[len(table1.col_names)+i]=row2[index]
    if only_matching and not matched:
      continue
    new_tab.AddRow(row)
  if only_matching:
    return new_tab
  for k, v in common2.items():
    if not k in common1:
      v2=[v[i] for i in new_index]
      row=[None for i in range(len(table1.col_names))]+v2
      for common1_index, common2_index in zip(common1_indices, common2_indices):
        row[common1_index]=v[common2_index]
      new_tab.AddRow(row)
  return new_tab


#  LocalWords:  numpy Numpy