Function integrate_monomial_coeffs

SLiCAP/SLiCAPmath.py:2319–2399

Returns expr in which x in coefficients of monomials of variables are integrated over the range x_lower ... x_upper. If doit=True the integration will be performed, else integral operators will be returned. :param expr: Sympy expression :type param: sympy.expr :param vari

(expr, variables, x, x_lower, x_upper, doit=True, 
                              wf=1, method="auto", CDS=False, tau=None, 
                              points=1000, numeric=True)

    return new_coeffs

def integrate_monomial_coeffs(expr, variables, x, x_lower, x_upper, doit=True, 
                              wf=1, method="auto", CDS=False, tau=None, 
                              points=1000, numeric=True):
    """
    Returns expr in which x in coefficients of monomials of 
    variables are integrated over the range x_lower ... x_upper. If doit=True
    the integration will be performed, else integral operators will be returned.

    :param expr: Sympy expression
    :type param: sympy.expr

    :param variables: List or tuple with variables
                      (currently only two variables accepted)

    :type variables: list with sympy.Symbol objects

    :param x: integration variable
    :type x: sympy.Symbol

    :param x_lower: start value integration
    :type x_lower: sympy.Symbol, int or float

    :param x_upper: end value integration
    :type x_upper: sympy.Symbol, int or float

    :param doit: True/False; If True, the integration will be performed, 
                 else integral operators will be returned.
    :type doit: bool

    :param CDS: True if correlated double sampling is required, defaults to False
                If True parameter 'tau' must be given a nonzero finite value
                (can be symbolic). 
                If method=="log" a logarithmic frequency seep will be used from 
                the lowest frequency until the frequency of the first notch: 
                f=1/tau. Linear sweeping will be used for all other frequency 
                segments.
                The number of points per segment will be set to points.
                If type(points) == list, the method will be set to 'scipy'.
    :type CDS: Bool

    :param tau: CDS delay time
    :type tau: str, int, float, sp.Symbol
    
    :param method: Integration method, implemented methods are:
        
                   - "auto": automatic selection of integration method
                   - "symbolic": forces symbolic integration 
                   - "scipy": numeric integration using scipy.integrate.quad
                              CDS will use integration per section f=1/tau
                   - "log": numeric integration using numpy.trapezoid with a
                            logarithmic frequency sweep from f_min to f_max 
                            and the number of points (CDS: per section) set by points
                   - "lin": numeric integration using numpy.trapezoid with a
                            linear frequency sweep from fmin to fmax 
                            and the number of points (CDS: per section) set by points
                   - "list": numeric integration using numpy.trapezoid with frequency
                             points taken from points (CDS: switches method to 'scipy').