HasGP.Support.Solve
Description
HasGP Gaussian Process Library. This module contains assorted functions that support the efficient solution of sets of linear equations
Copyright (C) 2011 Sean Holden. sbh11@cl.cam.ac.uk.
Documentation
upperSolve :: DMatrix -> DVector -> DVectorSource
It's not clear whether the use of linearSolve from HMatrix will induce a performance hit when the matrix is upper or lower triangular. Pro: it's a call to something presumably from LaPack. Con: we've got some structure that should allow us to make it O(n^2) instead of O(n^3).
To do: try some timed runs to see if these are needed.
Solve an upper triangular system.
lowerSolve :: DMatrix -> DVector -> DVectorSource
Solve a lower triangular system.
Arguments
| :: DVector | nth row of M |
| -> Double | y_n |
| -> Int | n |
| -> DVector | current x vector |
| -> DVector | x vector with x_n computed. |
Used by lowerSolve.
Used by upperSolve.
Compute the value of x_n when solving a lower triangular set of equations Mx=y. It is assumed that all values x_i where i < n are already in the vector x and that the rest of the elements of x are 0.
generalSolve :: (DMatrix -> DVector -> DVector) -> DMatrix -> DMatrix -> DMatrixSource
General solver for linear equations of the relevant kind.
First parameter is either upperSolve or lowerSolve. Next two parameters are the upper/lower triangular matrix from the Cholesky decomposition, then another matrix. Returns the solution as a matrix.