pymarket.bids.demand_curves module

pymarket.bids.demand_curves.demand_curve_from_bids(bids)[source]

Creates a demand curve from a set of buying bids. It is the inverse cumulative distribution of quantity as a function of price.

Parameters:bids – Collection of all the bids in the market. The algorithm filters only the buying bids.
Returns:
  • demand_curve (np.ndarray) – Stepwise constant demand curve represented as a collection of the N rightmost points of each interval (N-1 bids). It is stored as a (N, 2) matrix where the first column is the x-coordinate and the second column is the y-coordinate. An extra point is a))dded with x coordinate at infinity and price at 0 to represent the end of the curve.
  • index (np.ndarray) – The order of the identifier of each bid in the demand curve.

Examples

A minimal example, selling bid is ignored:

>>> bm = pm.BidManager()
>>> bm.add_bid(1, 1, 0, buying=True)
0
>>> bm.add_bid(1, 1, 1, buying=False)
1
>>> dc, index = pm.demand_curve_from_bids(bm.get_df())
>>> dc
array([[ 1.,  1.],
       [inf,  0.]])
>>> index
array([0])

A larger example with reordering of bids:

>>> bm = pm.BidManager()
>>> bm.add_bid(1, 1, 0, buying=True)
0
>>> bm.add_bid(1, 1, 1, buying=False)
1
>>> bm.add_bid(3, 0.5, 2, buying=True)
2
>>> bm.add_bid(2.3, 0.1, 3, buying=True)
3
>>> dc, index = pm.demand_curve_from_bids(bm.get_df())
>>> dc
array([[1. , 1. ],
       [4. , 0.5],
       [6.3, 0.1],
       [inf, 0. ]])
>>> index
array([0, 2, 3])
pymarket.bids.demand_curves.get_value_stepwise(x, f)[source]

Returns the value of a stepwise constant function defined by the right extrems of its interval Functions are assumed to be defined in (0, inf).

Parameters:
  • x (float) – Value in which the function is to be evaluated
  • f (np.ndarray) – Stepwise function represented as a 2 column matrix. Each row is the rightmost extreme point of each constant interval. The first column contains the x coordinate and is sorted increasingly. f is assumed to be defined only in the interval :math: (0, infty)
Returns:

The image of x under f: f(x). If x is negative, then None is returned instead. If x is outside the range of the function (greater than f[-1, 0]), then the method returns None.
Return type:

float or None

Examples

>>> f = np.array([
...     [1, 1],
...     [3, 4]])
>>> [pm.get_value_stepwise(x, f)
...     for x in [-1, 0, 0.5, 1, 2, 3, 4]]
[None, 1, 1, 1, 4, 4, None]
pymarket.bids.demand_curves.intersect_stepwise(f, g, k=0.5)[source]

Finds the intersection of two stepwise constants functions where f is assumed to be bigger at 0 than g. If no intersection is found, None is returned.

Parameters:
  • f (np.ndarray) – Stepwise constant function represented as a 2 column matrix where each row is the rightmost point of the constat interval. The first column is sorted increasingly. Preconditions: f is non-increasing.
  • g (np.ndarray) – Stepwise constant function represented as a 2 column matrix where each row is the rightmost point of the constat interval. The first column is sorted increasingly. Preconditions: g is non-decreasing and f[0, 0] > g[0, 0]
  • k (float) – If the intersection is empty or an interval, a convex combination of the y-values of f and g will be returned and k will be used to determine hte final value. k=1 will be the value of g while k=0 will be the value of f.
Returns:

  • x_ast (float or None) – Axis coordinate of the intersection of both functions. If the intersection is empty, then it returns None.
  • f_ast (int or None) – Index of the rightmost extreme of the interval of f involved in the intersection. If the intersection is empty, returns None
  • g_ast (int or None) – Index of the rightmost extreme of the interval of g involved in the intersection. If the intersection is empty, returns None.
  • v (float or None) – Ordinate of the intersection if it is uniquely identified, otherwise the k-convex combination of the y values of f and g in the last point when they were both defined.

Examples

Simple intersection with diferent domains

>>> f = np.array([[1, 3], [3, 1]])
>>> g = np.array([[2,2]])
>>> pm.intersect_stepwise(f, g)
(1, 0, 0, 2)

Empty intersection, returning the middle value

>>> f = np.array([[1,3], [2, 2.5]])
>>> g = np.array([[1,1], [2, 2]])
>>> pm.intersect_stepwise(f, g)
(None, None, None, 2.25)
pymarket.bids.demand_curves.supply_curve_from_bids(bids)[source]

Creates a supply curve from a set of selling bids. It is the cumulative distribution of quantity as a function of price.

Parameters:bids (pd.DataFrame) – Collection of all the bids in the market. The algorithm filters only the selling bids.
Returns:
  • supply_curve (np.ndarray) – Stepwise constant demand curve represented as a collection of the N rightmost points of each interval (N-1 bids). It is stored as a (N, 2) matrix where the first column is the x-coordinate and the second column is the y-coordinate. An extra point is added with x coordinate at infinity and price at infinity to represent the end of the curve.
  • index (np.ndarray) – The order of the identifier of each bid in the supply curve.

Examples

A minimal example, selling bid is ignored:

>>> bm = pm.BidManager()
>>> bm.add_bid(1, 3, 0, False)
0
>>> bm.add_bid(2.1, 3, 3, True)
1
>>> sc, index = pm.supply_curve_from_bids(bm.get_df())
>>> sc
array([[ 1.,  3.],
       [inf, inf]])
>>> index
array([0])

A larger example with reordering:

>>> bm = pm.BidManager()
>>> bm.add_bid(1, 3, 0, False)
0
>>> bm.add_bid(2.1, 3, 3, True)
1
>>> bm.add_bid(0.2, 1, 3, False)
2
>>> bm.add_bid(1.7, 6, 4, False)
3
>>> sc, index = pm.supply_curve_from_bids(bm.get_df())
>>> sc
array([[0.2, 1. ],
       [1.2, 3. ],
       [2.9, 6. ],
       [inf, inf]])
>>> index
array([2, 0, 3])