mintvmon {ftnonpar}R Documentation

Minimization of total variation

Description

Finds a function vector which minimizes the total variation of the function or a derivative under multiresolution constraints and monotonicity and convexity constraints.

Usage

mintvmon(y, sigma = -1, DYADIC = TRUE, thresh = -1, method = 2, MONCONST = TRUE, CONVCONST = FALSE)

Arguments

y observed values (ordered by value of independent variable).
sigma if set to a positive value the standard deviation is set to sigma and not estimated from the data
DYADIC logical, if T (default) the multiresolution constraints are only verifeid on intervals with dyadic endpoints
thresh if set to a positive value other thresholds for the multiresolution criterion than the default sqrt(2*log(n))*sigma can be used.
method Number of derivative the total variation of which is minimzed. Possible values are 0,1,2. Higher values lead to numerical inconsistencies.
MONCONST logical, if T (default) additional monotonicty constraints are gathered from minimzing the total variation of f. Makes only sense, if method is 1 or 2.
CONVCONST logical, if T (default) additional convexity constraints are gathered from minimzing the total variation of f'. Makes only sense, if method is 2.

Value

A list with components

y The approximation of the given data
derivsign Vector of 1 and -1, monotonicty constraints used if MONCONST was true
secsign Vector of 1 and -1, convexity constraints used if CONVCONST was true
jact Left endpoints of active multiresolution constraints for the final approximation
kact Right endpoints of active multiresolution constraints for the final approximation
signact Vector of 1 and -1, gives for each active multiresolution constraints, if the residuals on that interval attain upper or lower bound
pl Left endpoint of piecewise constant intervals of the derivative of f being minmized
pr Right endpoint of piecewise constant intervals of the derivative of f being minmized

Author(s)

Arne Kovac

References

Kovac, A. (2003) Minimizing Total Variation under Multiresolution Conditions

See Also

pmreg

Examples

data(djdata)
djdoppler.tv0 <- mintvmon(djdoppler,method=0)
djdoppler.tv1 <- mintvmon(djdoppler,method=1)
djdoppler.tv2 <- mintvmon(djdoppler)
par(mfrow=c(2,2))
plot(djdoppler,col="lightgrey")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv0$y,col="blue")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv1$y,col="green")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv2$y,col="red")

[Package ftnonpar version 0.1-83 Index]