Call an instance of me to obtain a scalar metric that indicates the "lumpiness" of a vector Y that transitions from a lower value to a higher value.

The metric is computed using the second derivative of Y, given the accompanying X vector. The values of Y can be all positive, all negative, or transition from negative to positive. Only the derivatives matter.

The value of the metric is zero for a smooth, non-reversing transition. That is achieved when the second derivative never goes from negative to positive.

The metric is proportional (nonlinearly) to the sum of slopes of all positive-going zero crossings of the second derivative ss.

If the clipping constructor keyword is set True, the metric also includes a term c times pr, the latter being the ratio of negative 2nd-derivative peak to standard deviation of the 2nd-derivative, taken to power Nc.

With unity weight, the metric should be around one for a very lumpy vector, assuming there isn't clipping causing pr to be significant. The equation for the metric is:

   metric = weight*((a*ss/(Y[-1]-Y[0]))^b + c*pr

where ss is the sum of slopes and Y[-1]-Y[0] is the total transition that Y makes over the interval, and pr = abs((min(ddY)-mp)/mp))^Nc and mp is the maximum positive peak of ddY, if any.

The metric is scaled down by the square of the number of lumps as that number starts to exceed fifteen or so. The idea is that a vector with tons of very tiny lumps isn't really lumpy at all, just slightly quantized.

Parameters clipping Set True to check clipping with by including the pr term.

Class Variable	Ns	The number of samples +/- k for the linear regression that calculates the slopes in `slope`.
Class Variable	Nc	The exponent for calculation of pr.
Method	__init__	Undocumented
Method	find_zero_crossings_NP	Returns a list of indices of the supplied vector Y where the value is negative and the next value is positive.
Method	zero_crossingerator	Yields 2-tuples, each with (1) an index of the supplied vector Y at a zero crossing and (2) a bool that is `True` if the zero crossing was negative-going.
Method	find_next_peak	Returns a 2-tuple with (1) the sample distance to the right of index k and (2) the height of the next peak after k.
Method	find_prev_peak	Returns a 2-tuple with (1) the sample distance to the left of index k and (2) the height of the previous peak before k.
Method	slope	No summary
Method	clipping	No summary
Static Method	dydx	Undocumented
Method	__call__	Call my instance with an X vector and a corresponding vector Y of ascending values.

Ns =

The number of samples +/- k for the linear regression that calculates the slopes in slope.

Nc =

The exponent for calculation of pr.

def __init__(self, clipping=False):

Undocumented

def find_zero_crossings_NP(self, Y):

Returns a list of indices of the supplied vector Y where the value is negative and the next value is positive.

Negative values within 10^-15 of zero are not considered negative.

def zero_crossingerator(self, Y):

Yields 2-tuples, each with (1) an index of the supplied vector Y at a zero crossing and (2) a bool that is True if the zero crossing was negative-going.

def find_next_peak(self, Y, k, negative=False):

Returns a 2-tuple with (1) the sample distance to the right of index k and (2) the height of the next peak after k.

def find_prev_peak(self, Y, k, positive=False):

Returns a 2-tuple with (1) the sample distance to the left of index k and (2) the height of the previous peak before k.

def slope(self, X, Y, k, invert=False):

Returns the slope of Y vs X for the zero crossing at index k. Calculated from the difference between the adjacent negative and positive peaks divided by the distance between them.

def clipping(self, ddY):

Given the second derivative of the values ddY, returns the ratio, taken to exponent Nc, of the absolute value of the negative peak minus the standard deviation, divided by the standard deviation. If the absolute value of the negative peak is less than or equal to the standard deviation, the result is zero.

This is an indicator of an abrupt downward curvature, i.e., clipping.

@staticmethod
def dydx(X, Y):

Undocumented

def __call__(self, X, Y):

Call my instance with an X vector and a corresponding vector Y of ascending values.

Returns a 2-tuple with (1) the lumpiness metric and (2) a 2-D Numpy array of X, Y coordinates where the second derivative of Y had a zero crossing.

API Documentation for pingspice, generated by pydoctor at 2021-09-18 08:41:11.

pingspice.analysis.fixture.LumpinessCalculator(object) class documentation

`pingspice.analysis.fixture.LumpinessCalculator(object)` class documentation