Multi-variate Piecewise Functions
Summary
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Models a multi-variate piecewise linear function. |
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A multi-variate piecewise linear function |
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Base class for transformed multi-variate piecewise linear functions |
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Discrete CC multi-variate piecewise representation |
Member Documentation
- pyomo.core.kernel.piecewise_library.transforms_nd.piecewise_nd(tri, values, input=None, output=None, bound='eq', repn='cc')[source]
Models a multi-variate piecewise linear function.
This function takes a D-dimensional triangulation and a list of function values associated with the points of the triangulation and transforms this input data into a block of variables and constraints that enforce a piecewise linear relationship between an D-dimensional vector of input variable and a single output variable. In the general case, this transformation requires the use of discrete decision variables.
- Parameters:
tri (scipy.spatial.Delaunay) –
A triangulation over the discretized variable domain. Can be generated using a list of variables using the utility function
util.generate_delaunay()
. Required attributes:points: An (npoints, D) shaped array listing the D-dimensional coordinates of the discretization points.
simplices: An (nsimplices, D+1) shaped array of integers specifying the D+1 indices of the points vector that define each simplex of the triangulation.
values (numpy.array) – An (npoints,) shaped array of the values of the piecewise function at each of coordinates in the triangulation points array.
input – A D-length list of variables or expressions bound as the inputs of the piecewise function.
output – The variable constrained to be the output of the piecewise linear function.
bound (str) –
The type of bound to impose on the output expression. Can be one of:
’lb’: y <= f(x)
’eq’: y = f(x)
’ub’: y >= f(x)
repn (str) –
The type of piecewise representation to use. Can be one of:
’cc’: convex combination
- Returns:
- a block
containing any new variables, constraints, and other components used by the piecewise representation
- Return type:
- class pyomo.core.kernel.piecewise_library.transforms_nd.PiecewiseLinearFunctionND(tri, values, validate=True, **kwds)[source]
Bases:
object
A multi-variate piecewise linear function
Multi-varite piecewise linear functions are defined by a triangulation over a finite domain and a list of function values associated with the points of the triangulation. The function value between points in the triangulation is implied through linear interpolation.
- Parameters:
tri (scipy.spatial.Delaunay) –
A triangulation over the discretized variable domain. Can be generated using a list of variables using the utility function
util.generate_delaunay()
. Required attributes:points: An (npoints, D) shaped array listing the D-dimensional coordinates of the discretization points.
simplices: An (nsimplices, D+1) shaped array of integers specifying the D+1 indices of the points vector that define each simplex of the triangulation.
values (numpy.array) – An (npoints,) shaped array of the values of the piecewise function at each of coordinates in the triangulation points array.
- __call__(x)[source]
Evaluates the piecewise linear function using interpolation. This method supports vectorized function calls as the interpolation process can be expensive for high dimensional data.
For the case when a single point is provided, the argument x should be a (D,) shaped numpy array or list, where D is the dimension of points in the triangulation.
For the vectorized case, the argument x should be a (n,D)-shaped numpy array.
- property triangulation
The triangulation over the domain of this function
- property values
The set of values used to defined this function
- class pyomo.core.kernel.piecewise_library.transforms_nd.TransformedPiecewiseLinearFunctionND(f, input=None, output=None, bound='eq')[source]
Bases:
block
Base class for transformed multi-variate piecewise linear functions
A transformed multi-variate piecewise linear functions is a block of variables and constraints that enforce a piecewise linear relationship between an vector input variables and a single output variable.
- Parameters:
f (
PiecewiseLinearFunctionND
) – The multi-variate piecewise linear function to transform.input – The variable constrained to be the input of the piecewise linear function.
output – The variable constrained to be the output of the piecewise linear function.
bound (str) –
The type of bound to impose on the output expression. Can be one of:
’lb’: y <= f(x)
’eq’: y = f(x)
’ub’: y >= f(x)
- __call__(x)[source]
Evaluates the piecewise linear function using interpolation. This method supports vectorized function calls as the interpolation process can be expensive for high dimensional data.
For the case when a single point is provided, the argument x should be a (D,) shaped numpy array or list, where D is the dimension of points in the triangulation.
For the vectorized case, the argument x should be a (n,D)-shaped numpy array.
- property bound
The bound type assigned to the piecewise relationship (‘lb’,’ub’,’eq’).
- property input
The tuple of expressions that store the inputs to the piecewise function. The returned objects can be updated by assigning to their
expr
attribute.
- property output
The expression that stores the output of the piecewise function. The returned object can be updated by assigning to its
expr
attribute.
- property triangulation
The triangulation over the domain of this function
- property values
The set of values used to defined this function
- class pyomo.core.kernel.piecewise_library.transforms_nd.piecewise_nd_cc(*args, **kwds)[source]
Bases:
TransformedPiecewiseLinearFunctionND
Discrete CC multi-variate piecewise representation
Expresses a multi-variate piecewise linear function using the CC formulation.