differentiate

(function from pyomo.core.expr.calculus.derivatives)

pyomo.core.expr.calculus.derivatives.differentiate(expr, wrt=None, wrt_list=None, mode=Modes.reverse_numeric)[source]

Return derivative of expression.

This function returns the derivative of expr with respect to one or more variables. The type of the return value depends on the arguments wrt, wrt_list, and mode. See below for details.

Parameters:

  • expr (pyomo.core.expr.numeric_expr.NumericExpression) – The expression to differentiate

  • wrt (pyomo.core.base.var.VarData) – If specified, this function will return the derivative with respect to wrt. wrt is normally a VarData, but could also be a ParamData. wrt and wrt_list cannot both be specified.

  • wrt_list (list of pyomo.core.base.var.VarData) – If specified, this function will return the derivative with respect to each element in wrt_list. A list will be returned where the values are the derivatives with respect to the corresponding entry in wrt_list.

  • mode (pyomo.core.expr.calculus.derivatives.Modes) –

    Specifies the method to use for differentiation. Should be one of the members of the Modes enum:

    Modes.sympy:

    The pyomo expression will be converted to a sympy expression. Differentiation will then be done with sympy, and the result will be converted back to a pyomo expression. The sympy mode only does symbolic differentiation. The sympy mode requires exactly one of wrt and wrt_list to be specified.

    Modes.reverse_symbolic:

    Symbolic differentiation will be performed directly with the pyomo expression in reverse mode. If neither wrt nor wrt_list are specified, then a ComponentMap is returned where there will be a key for each node in the expression tree, and the values will be the symbolic derivatives.

    Modes.reverse_numeric:

    Numeric differentiation will be performed directly with the pyomo expression in reverse mode. If neither wrt nor wrt_list are specified, then a ComponentMap is returned where there will be a key for each node in the expression tree, and the values will be the floating point values of the derivatives at the current values of the variables.

Returns:

res – The value or expression of the derivative(s)

Return type:

float, NumericExpression, ComponentMap, or list