lmcholsolve: lmcholsolve

In yfyang86/optimise2: optim corrections.

Description

This function solves

H β = y

, where H>=0;

Usage

lmcholsolve(x, y)

Arguments

x	Must be a numeric matrix: integer matrix are NOT allowed.
y	Response variable

Details

Considering:

H β = y

, in each iteration newton's scalor is

β_{LSE}

. The fatest algorithm is 'sweeping method'/Cholesky Decomposition. The mian reason is that: H >= 0. If we tend not to check the condition, then

H= LL^T

, where L is low tri-angle matrix. Hence we derive

[H,y]^T[H,y]=≤ft( \begin{array}{ll} L & 0\\ l^T & d \end{array} \right) \times ≤ft( \begin{array}{ll} L^T & l\\ 0 & d \end{array} \right)

and

L l= H^Ty , L^T β = l, d^2=\|y-hat(y)\|_{\ell_2}^2

The performance cound be found in inst/doc.

Value

beta	The estimations.
Convergences	Number of non-zero diag-elements.

Note

tol=1e-9 in Cholesky decomposition.

Author(s)

Yifan Yang

References

Lange, Kenneth. Numerical analysis for statisticians. chap 7. Springer, 2010.

Examples

x <- matrix(runif(100), 10)
y = rnorm(10) * 2
x <- t(x) %*% x
lmcholsolve(x, y)
solve(x, y)

yfyang86/optimise2 documentation built on May 4, 2019, 2:32 p.m.