# MakeDENsample: Convenience function for converting log quantile densities to... In fdadensity: Functional Data Analysis for Density Functions by Transformation to a Hilbert Space

## Description

See 'lqd2dens' and 'DeregulariseByAlpha' for more details. This function transforms the log quantile densities in 'qmatrix' to density functions, optionally followed by deregularisation.

## Usage

 ```1 2 3 4 5 6 7``` ```MakeDENsample( qmatrix, lqdSup = seq(0, 1, length.out = ncol(qmatrix)), dSup = seq(0, 1, length.out = ncol(qmatrix)), useAlpha = FALSE, alpha = 0 ) ```

## Arguments

 `qmatrix` Matrix holding the log quantile density values on [0,1] `lqdSup` Support grid for input log quantile densities (default = seq(0, 1, length.out = ncol(qmatrix))) `dSup` Support grid for output densities (default = seq(0, 1, length.out = ncol(qmatrix))) `useAlpha` Logical indicator to deregularise the densities (default = FALSE) `alpha` Scalar to deregularise the density - where possible, this will be the minimum value for the deregularised densities (default=0)

## Value

list with the 'DEN' transformed data, and 'dSup' that matches the input argument.

## References

Functional Data Analysis for Density Functions by Transformation to a Hilbert space, Alexander Petersen and Hans-Georg Mueller, 2016

`DeregulariseByAlpha,lqd2dens`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ``` x <- seq(0,1,length.out = 101) # linear densities on (0, 1) y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) b + 2*(1 - b)*x)) # Get LQDs y.lqd = MakeLQDsample(dmatrix = y, dSup = x) matplot(y.lqd\$lqdSup, t(y.lqd\$LQD), ylab = 'LQD', type = 'l', lty = 1, col = 'black') # Get Densities Back y.dens = MakeDENsample(y.lqd\$LQD, lqdSup = x, dSup = x) # should equate to y above # These should look the same matplot(y.dens\$dSup, t(y.dens\$DEN), ylab = 'Density', type = 'l', lty = 1, col = 'blue') matplot(x, t(y), ylab = 'Original Density', type = 'l', lty = 1, col = 'red') ```