Documentation

order type

enumeration of O types

>>> olist
[N3,N2,N32,NLogN,N1,N12,LogN,N0]

Calculate the expected performance measure

>>> promote (order N2 1) 10
100.0

Calculate the expected performance measure per n

>>> promote (order N2 1) 10
100.0

functions to compute performance measure

>>> fmap ($ 0) promote_
[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]

>>> fmap ($ 1) promote_
[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0]

Ordering makes sense around N=10

>>> fmap ($ 10) promote_
[1000.0,100.0,31.622776601683793,23.02585092994046,10.0,3.1622776601683795,2.302585092994046,1.0]

Having NP may cause big num problems

>>> fmap ($ 1000) promote_
[1.0e9,1000000.0,31622.776601683792,6907.755278982137,1000.0,31.622776601683793,6.907755278982137,1.0]

Calculate an Order from a given O, an n, and a total performance measurement

A measurement of 1e6 for n=1000 with an order of N2 is:

>>> demote N2 1000 1000000
Order {factors = [0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0]}

promote (demote N2 n m) n m == m

Calculate an Order from a measure, and an O

>>> demote1 N2 1000
Order {factors = [0.0,1000.0,0.0,0.0,0.0,0.0,0.0,0.0]}

demote1 N2 m == demote o 1 m

The factor for each O given an n, and a measurement.

>>> spectrum 100 10000
Order {factors = [1.0e-2,1.0,10.0,21.71472409516259,100.0,1000.0,2171.4724095162587,10000.0]}

a set of factors for each order, which represents a full Order specification.

find the dominant order, and it's factor

>>> bigO o
(N2,1.0)

compute the runtime component of an Order, defined as the difference between the dominant order and the total for a single run.

>>> runtime o
100.0

A set of factors consisting of the dominant order, the dominant order factor and a constant factor

compute the BigOrder

>>> fromOrder o
BigOrder {bigOrder = N2, bigFactor = 1.0}

convert a BigOrder to an Order.

toOrder . fromOrder is not a round trip iso.

>>> toOrder (fromOrder o)
Order {factors = [0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0]}

create an Order

>>> order N2 1
Order {factors = [0,1,0,0,0,0,0,0]}

The errors for a list of n's and measurements, based on the spectrum of the last measurement.

minimum error order for a list of measurements

>>> bestO ns ms
N1

fit the best order for the last measurement and return it, and the error terms for the measurements

>>> estO ns ms
(Order {factors = [0.0,0.0,0.0,0.0,102.90746947660953,0.0,0.0,0.0]},[2702.0925305233905,2446.9253052339045,-301.7469476609531,-10317.469476609534,0.0])

fit orders from the last measurement to the first, using the residuals at each step.

>>> estOs ns ms
[Order {factors = [0.0,0.0,0.0,0.0,102.90746947660953,0.0,0.0,0.0]},Order {factors = [0.0,0.0,-0.32626703235351473,0.0,0.0,0.0,0.0,0.0]},Order {factors = [0.0,0.0,0.0,0.0,0.0,0.0,0.0,24.520084692561625]},Order {factors = [0.0,0.0,0.0,0.0,0.0,0.0,0.0,2432.722690017952]},Order {factors = [0.0,0.0,0.0,0.0,0.0,0.0,0.0,245.1760228452299]}]