source: inundation/wiki/least_squares_redesign.txt @ 2022

Project Plan

By Duncan Gray

INTRODUCTION

 Software, called least squares, has been developed to implement a
penalised least-squares fit and associated interpolations. It is
currently in least_squares.py.  Steven Roberts outlined the least
squares algorithm used. The code is currently not meeting user
requirements with regards to speed and memory use.  Additional
functionality is also needed.


SCOPE

This is looking at redesigning the least_squares module, excluding
interpolate_function and pts2rectangle.  (Other modules will
be modified, based on these changes.)


LIFE-CYCLE

Use a staged delivery life-cycle (see rapid development), with the
proviso that additional functionality to supporting objects, such as
build_quadtree in quad.py can be worked on after requirements have
been determined.  Also, the current least squares may be tinkered with
to check the feasibility of concepts and general maintanance.  The
main thrust will be refactoring though. 


______________________________________________________________________
Least Squares Refactoring Software Requirements Specification

By Duncan Gray


INTRODUCTION

This document specifies the requirements of the redesign of least squares.

DEFINITIONS

  
REQUIREMENT SECTION

Introduction

Assume that all the requirements of the current least squares code will
stay the same, unless stated.  Note implementation and names used are
not regarded as requirements.  


Requirements - Fitting

When in verbose mode display how many points are in the
mesh and how many are outside its boundary. Also display the max # of
points/ triangle and the minimum number of points.  If this operation
takes a lot of time, let it be optional.

Raise an exception if no points are inside the mesh.

Fitting 5 million points to a one million triangles mesh will not cause a
memory error.

Remove least_squares commandline interface.

Points do not have to be supplied all at once.  They can be supplied
as blocks. (This will improve memory use)

Requirements - Interpolation

Return information on which points were outside the mesh (in such a
way that it can not be interpreted as real data).  If attribute
information for points outside the mesh is returned, that can only be
a float, let the user set the default value that is returned for
points outside the mesh. if the value can be set to NAN, then set it
to NAN, if no default is given.

Reduce the time spent building matrix A. (not a testable requirement)

Points do not have to be supplied all at once.  They can be supplied
as blocks. (This will improve memory use)

A target to aim for
Algorithmic complexity of build equations should be linear in number
of data points and logorithmic in the number of vertices.

Constraint
Memory consumption of least squares equations must be indepenent on
the number of datapoints. (Except for the memory used to store the points.) 
___________________________________________________________________________
Least Squares System Design Specification

By Duncan Gray - lots of good ideas by Ole


INTRODUCTION

This specifies design choices for the least squares code.

DESIGN IDEAS, to meet requirements
*To save memory;
When interpolating, don't build AtA, B and D. (This has been implemented)
When fitting, don't build A. - Work with AtA and Atz. Build Atz
directly, rather than through At*z - use code similar to AtA.


* To save memory

This is for the layer interpolation and fitting with IO: Use blocking
when interpolating/fitting a large number of points (how large?  Can the
program check the available memory and work out a good block size?
Maybe have it user specified.  Do have the option for user specified)

The code has to be refactored so fitting can handle blocked point
info.  Need a building phase and a solve phase.  


*To reduce the time spent building matrix A.

Change the expansion algorithm, when determining what triangle a point
 is in, when none of the vertices are in the cell the point is in.

Options (still thinking about this one)
*  It should look in the cell of the point and then all adjacent
cells. If it isn't there then ... expand more. 
- Building the structure to keep this info could be prohibitive.

*A feature that could work for the current implementation is to keep a
 list of triangles that have been checked, so each incorrect triangle
 isn't checked three times, if all three verts are in the cell being checked. 

Another speed up option is to write the bottlenecks in C. Do it if necessary.

* To give warnings.
Use warnings module?  Check this out.

DESIGN IDEAS, refactoring

Remove georeferencing from build_interpolation_matrix_A. Change the
point co-ords to conform to the mesh co-ords early in the code.

Currently there is one class, called Interpolation, that holds the
matrix data and methods for fitting and interpolation.  Break this
into two classes, one for fittting, the other for interpolation. Have
processes common to both classes in functions.     

Have least squares as two stand alone packages.  One that has the guts
of LS (e.g. the two new classes).  One that has the IO API's
(functions that load and write files and do the blocking).  The guts
package will be dependent of the general mesh package.  The IO API
will rely on an IO module.

HOW WILL IMPLEMENTATION OCCUR?
Code a new least squares module in a seperate directory.  Heavily cut
and paste from the old least squares. Implement memory and time tests
on the old least squares (and new LS) before doing any changes.  

For the speed up, discuss/ get go ahead from Ole before implementing
any major changes, since there is no obvious way forward.