implement quadratic optimization splitter
Splitting abridged data into a fine grid of ages using the quadratic optimization method. Using data that is grouped with arbirtrary age bounds, the algorithm de-groups the input probabilities into single age years and smoothes the transitions in between.
This function is derrived from "MPIDR Technical Report TR 2018-00" by Anatoli I. Michalski, Pavel Grigoriev, Vasily P. Gorlishchev.
For further explainations see:
- Anatoli I. Michalski, Pavel Grigoriev, Vasily P. Gorlishchev. (2018): R programs for splitting abridged fertility data into a fine grid of ages using the quadratic optimization method. URL: https://www.demogr.mpg.de/papers/technicalreports/tr-2018-002.pdf
- Pavel Grigoriev, Vasily P. Gorlishchev, Dmitri A. Jdanov, Vladimir M. Shkolnikov (2018): New methods for estimating detailed fertility schedules from abridged data.Human Fertility Database Research Report. URL: https://www.demogr.mpg.de/papers/working/wp-2018-001.pdf