Function equateCoeffs

SLiCAP/SLiCAPmath.py:1217–1296

Returns the solutions of the equation transferFunction = protoTypeFunction. Both transfer and prototype should be Laplace rational functions. Their numerators should be polynomials of the Laplace variable of equal order and their denominators should be polynomials of the Laplace va

(protoType, transfer, noSolve=[], numeric=True)

    return M

def equateCoeffs(protoType, transfer, noSolve=[], numeric=True):
    """
    Returns the solutions of the equation transferFunction = protoTypeFunction.

    Both transfer and prototype should be Laplace rational functions.
    Their numerators should be polynomials of the Laplace variable of equal
    order and their denominators should be polynomials of the Laplace variable
    of equal order.

    :param protoType: Prototype rational expression of the Laplace variable
    :type protoType: sympy.Expr
    :param transfer:

    Transfer fucntion of which the parameters need to be
    solved. The numerator and the denominator of this rational
    expression should be of the same order as those of the
    prototype.

    :type transfer: sympy.Expr

    :param noSolve: List with variables (*str, sympy.core.symbol.Symbol*) that do not need
                    to be solved. These parameters will remain symbolic in the
                    solutions.

    :type noSolve: list

    :param numeric: True will convert numeric results with floats instead of rationals

    :type numeric: bool

    :return: Dictionary with key-value pairs:

             - key: name of the parameter (*sympy.core.symbol.Symbol*)
             - value: solution of this parameter: (*sympy.Expr, int, float*)

    :rtype: dict
    """
    values = {}
    pars = list(set(list(protoType.atoms(sp.Symbol)) +
                list(transfer.atoms(sp.Symbol))))
    for i in range(len(noSolve)):
        noSolve[i] = sp.Symbol(str(noSolve[i]))
    params = []
    for par in pars:
        if par != ini.laplace and par not in noSolve:
            params.append(par)
    gainP, pN, pD = coeffsTransfer(protoType)
    gainT, tN, tD = coeffsTransfer(transfer)
    if len(pN) != len(tN) or len(pD) != len(tD):
        print('Error: unequal orders of prototype and target.')
    equations = []
    for i in range(len(pN)):
        eqn = sp.Eq(pN[i], tN[i])
        if eqn != True:
            equations.append(eqn)
    for i in range(len(pD)):
        eqn = sp.Eq(pD[i], tD[i])
        if eqn != True: