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

## Description

See 'dens2lqd' and 'RegulariseByAlpha' for more details. This function first (transforms the densities in 'dmatrix' to log quantile density functions, optionally followed by regularisation.

## Usage

 ```1 2 3 4 5 6 7``` ```MakeLQDsample( dmatrix, dSup, lqdSup = seq(0, 1, length.out = length(dSup)), useAlpha = FALSE, alpha = 0.01 ) ```

## Arguments

 `dmatrix` Matrix holding the density values on dSup - all rows must be strictly positive and integrate to 1 `dSup` Support (grid) for Density domain `lqdSup` Support grid for lqd domain (default = seq(0, 1, length.out = length(dSup))) `useAlpha` should regularisation be performed (default=FALSE) `alpha` Scalar to regularise the supports with (default=0.01)

## Value

list with 'LQD', a matrix of log quantile density functions, and 'lqdSup' 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

`RegulariseByAlpha,dens2lqd`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ``` x <- seq(0,1,length.out = 101) # some log quantile densities on (0, 1) y <- t(sapply(seq(0.5, 1.5, length.out = 10), function(b) -log(b^2 + 4*(1-b)*x)/2)) # Get densities y.dens = MakeDENsample(qmatrix = y, lqdSup = x, dSup = x)\$DEN matplot(x, t(y.dens), ylab = 'Density', type = 'l', lty = 1, col = 'black') # Get LQDs Back y.lqd = MakeLQDsample(y.dens, lqdSup = x, dSup = x) # These should match matplot(y.lqd\$lqdSup, t(y.lqd\$LQD), ylab = 'LQD', type = 'l', lty = 1, col = 'blue') matplot(x, t(y), ylab = 'LQD', type = 'l', lty = 1, col = 'red') ```