Function normalizeRational

SLiCAP/SLiCAPmath.py:296–330

Normalizes a rational expression to: .. math:: F(s) = gain\\,s^{\\ell} \\frac{1+b_1s + ... + b_ms^m}{1+a_1s + ... + a_ns^n} :param Rational: Rational function of the variable. :type Rational: sympy.Expr :param var: Variable of the rational function :type var: sy

(rational, var=ini.laplace, method='lowest')

    return (gain, numCoeffs, denCoeffs)

def normalizeRational(rational, var=ini.laplace, method='lowest'):
    """
    Normalizes a rational expression to:

    .. math::

        F(s) = gain\\,s^{\\ell}  \\frac{1+b_1s + ... + b_ms^m}{1+a_1s + ... + a_ns^n}

    :param Rational: Rational function of the variable.
    :type Rational: sympy.Expr

    :param var: Variable of the rational function
    :type var: sympy.Symbol

    :param method: Normalization method:

                   - "highest": the coefficients of the highest order of
                     <variable> of the denominator will be noramalized to unity.
                   - "lowest": the coefficients of the lowest order of
                     <variable> of the denominator will be noramalized to unity.

    :type method: str

    :return:  Normalized rational function of the variable.
    :rtype: sympy.Expr
    """
    gain, numCoeffs, denCoeffs = coeffsTransfer(
        rational, var=var, method=method)
    if len(numCoeffs) and len(denCoeffs):
        numCoeffs = list(reversed(numCoeffs))
        denCoeffs = list(reversed(denCoeffs))
        num = sp.Poly(numCoeffs, var).as_expr()
        den = sp.Poly(denCoeffs, var).as_expr()
        rational = gain*num/den
    return rational

def _cancelPZ(poles, zeros):
    """