Archive for the ‘programming’ Category
A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. Since this is such a common query, I thought I’d write up how to do it for a very simple problem in several systems that I’m interested in
This is the Python version. For other versions,see the list below
- Simple nonlinear least squares curve fitting in Julia
- Simple nonlinear least squares curve fitting in Maple
- Simple nonlinear least squares curve fitting in Mathematica
- Simple nonlinear least squares curve fitting in MATLAB
- Simple nonlinear least squares curve fitting in R
The problem
xdata = -2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9 ydata = 0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-1.42001
and you’d like to fit the function
using nonlinear least squares. You’re starting guesses for the parameters are p1=1 and P2=0.2
For now, we are primarily interested in the following results:
- The fit parameters
- Sum of squared residuals
Future updates of these posts will show how to get other results such as confidence intervals. Let me know what you are most interested in.
Python solution using scipy
Here, I use the curve_fit function from scipy
import numpy as np from scipy.optimize import curve_fit xdata = np.array([-2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9]) ydata = np.array([0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-1.42001]) def func(x, p1,p2): return p1*np.cos(p2*x) + p2*np.sin(p1*x) popt, pcov = curve_fit(func, xdata, ydata,p0=(1.0,0.2))
The variable popt contains the fit parameters
array([ 1.88184732, 0.70022901])
We need to do a little more work to get the sum of squared residuals
p1 = popt[0] p2 = popt[1] residuals = ydata - func(xdata,p1,p2) fres = sum(residuals**2)
which gives
0.053812696547933969
- I’ve put this in an Ipython notebook which can be downloaded here. There is also a pdf version of the notebook.
A question I get asked a lot is ‘How can I do nonlinear least squares curve fitting in X?’ where X might be MATLAB, Mathematica or a whole host of alternatives. Since this is such a common query, I thought I’d write up how to do it for a very simple problem in several systems that I’m interested in
This is the Mathematica version. For other versions,see the list below
- Simple nonlinear least squares curve fitting in Maple
- Simple nonlinear least squares curve fitting in Julia
- Simple nonlinear least squares curve fitting in MATLAB
- Simple nonlinear least squares curve fitting in Python
- Simple nonlinear least squares curve fitting in R
The problem
You have the following 10 data points
xdata = -2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9 ydata = 0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-1.42001
and you’d like to fit the function
using nonlinear least squares. You’re starting guesses for the parameters are p1=1 and P2=0.2
For now, we are primarily interested in the following results:
- The fit parameters
- Sum of squared residuals
Future updates of these posts will show how to get other results such as confidence intervals. Let me know what you are most interested in.
Mathematica Solution using FindFit
FindFit is the basic nonlinear curve fitting routine in Mathematica
xdata={-2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9};
ydata={0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-1.42001};
(*Mathematica likes to have the data in the form {{x1,y1},{x2,y2},..}*)
data = Partition[Riffle[xdata, ydata], 2];
FindFit[data, p1*Cos[p2 x] + p2*Sin[p1 x], {{p1, 1}, {p2, 0.2}}, x]
Out[4]:={p1->1.88185,p2->0.70023}
Mathematica Solution using NonlinearModelFit
You can get a lot more information about the fit using the NonLinearModelFit function
(*Set up data as before*)
xdata={-2,-1.64,-1.33,-0.7,0,0.45,1.2,1.64,2.32,2.9};
ydata={0.699369,0.700462,0.695354,1.03905,1.97389,2.41143,1.91091,0.919576,-0.730975,-1.42001};
data = Partition[Riffle[xdata, ydata], 2];
(*Create the NonLinearModel object*)
nlm = NonlinearModelFit[data, p1*Cos[p2 x] + p2*Sin[p1 x], {{p1, 1}, {p2, 0.2}}, x];
The NonLinearModel object contains many properties that may be useful to us. Here’s how to list them all
nlm["Properties"]
Out[10]= {"AdjustedRSquared", "AIC", "AICc", "ANOVATable", \
"ANOVATableDegreesOfFreedom", "ANOVATableEntries", "ANOVATableMeanSquares", \
"ANOVATableSumsOfSquares", "BestFit", "BestFitParameters", "BIC", \
"CorrelationMatrix", "CovarianceMatrix", "CurvatureConfidenceRegion", "Data", \
"EstimatedVariance", "FitCurvatureTable", "FitCurvatureTableEntries", \
"FitResiduals", "Function", "HatDiagonal", "MaxIntrinsicCurvature", \
"MaxParameterEffectsCurvature", "MeanPredictionBands", \
"MeanPredictionConfidenceIntervals", "MeanPredictionConfidenceIntervalTable", \
"MeanPredictionConfidenceIntervalTableEntries", "MeanPredictionErrors", \
"ParameterBias", "ParameterConfidenceIntervals", \
"ParameterConfidenceIntervalTable", \
"ParameterConfidenceIntervalTableEntries", "ParameterConfidenceRegion", \
"ParameterErrors", "ParameterPValues", "ParameterTable", \
"ParameterTableEntries", "ParameterTStatistics", "PredictedResponse", \
"Properties", "Response", "RSquared", "SingleDeletionVariances", \
"SinglePredictionBands", "SinglePredictionConfidenceIntervals", \
"SinglePredictionConfidenceIntervalTable", \
"SinglePredictionConfidenceIntervalTableEntries", "SinglePredictionErrors", \
"StandardizedResiduals", "StudentizedResiduals"}
Let’s extract the fit parameters, 95% confidence levels and residuals
{params, confidenceInt, res} =
nlm[{"BestFitParameters", "ParameterConfidenceIntervals", "FitResiduals"}]
Out[22]= {{p1 -> 1.88185,
p2 -> 0.70023}, {{1.8186, 1.9451}, {0.679124,
0.721336}}, {-0.0276906, -0.0322944, -0.0102488, 0.0566244,
0.0920392, 0.0976307, 0.114035, 0.109334, 0.0287154, -0.0700442}}
The parameters are given as replacement rules. Here, we convert them to pure numbers
{p1, p2} = {p1, p2} /. params
Out[38]= {1.88185,0.70023}
Although only a few decimal places are shown, p1 and p2 are stored in full double precision. You can see this by converting to InputForm
InputForm[{p1, p2}]
Out[43]//InputForm=
{1.8818508498053645, 0.7002298171759191}
Similarly, let’s look at the 95% confidence interval, extracted earlier, in full precision
confidenceInt // InputForm
Out[44]//InputForm=
{{1.8185969887307214, 1.9451047108800077},
{0.6791239458086734, 0.7213356885431649}}
Calculate the sum of squared residuals
resnorm = Total[res^2] Out[45]= 0.0538127
Notes
I used Mathematica 9 on Windows 7 64bit to perform these calculations
One of my favourite parts of my job at The University of Manchester is the code optimisation service that my team provides to researchers there. We take code written in languages such as MATLAB, Python, Mathematica and R and attempt (usually successfully) to make them go faster. It’s sort of a cross between training and consultancy, is a lot of fun and we can help a relatively large number of people in a short time. It also turns out to be very useful to the researchers as some of my recent testimonials demonstrate.
Other researchers,however, need something more. They already have a nice piece of code with several users and a selection of papers. They also have a bucket-load of ideas about how to turn this nice code into something amazing. They have all this good stuff and yet they find that they are struggling to get their code to the next level. What these people need is some quality time with a team of research software engineers.
Enter the Software Sustainability Institute (SSI), an organisation that I have been fortunate enough to have a fellowship with throughout 2013. These guys are software-development ninjas, have extensive experience with working with academic researchers and, right now, they have an open call for projects. It’s free to apply and, if your application is successful, all of their services will be provided for free. If you’d like an idea of the sort of projects they work on, take a look at the extensive list of past projects.
So, if you are a UK-based researcher who has a software problem, and no one else can help, maybe you can hire* the SSI team.
*for free!
Links
From the wikipedia page on Division by Zero: “The IEEE 754 standard specifies that every floating point arithmetic operation, including division by zero, has a well-defined result”.
MATLAB supports this fully:
>> 1/0 ans = Inf >> 1/(-0) ans = -Inf >> 0/0 ans = NaN
Julia is almost there, but doesn’t handled the signed 0 correctly (This is using Version 0.2.0-prerelease+3768 on Windows)
julia> 1/0 Inf julia> 1/(-0) Inf julia> 0/0 NaN
Python throws an exception. (Python 2.7.5 using IPython shell)
In [4]: 1.0/0.0 --------------------------------------------------------------------------- ZeroDivisionError Traceback (most recent call last) in () ----> 1 1.0/0.0 ZeroDivisionError: float division by zero In [5]: 1.0/(-0.0) --------------------------------------------------------------------------- ZeroDivisionError Traceback (most recent call last) in () ----> 1 1.0/(-0.0) ZeroDivisionError: float division by zero In [6]: 0.0/0.0 --------------------------------------------------------------------------- ZeroDivisionError Traceback (most recent call last) in () ----> 1 0.0/0.0 ZeroDivisionError: float division by zero
Update:
Julia does do things correctly, provided I make it clear that I am working with floating point numbers:
julia> 1.0/0.0 Inf julia> 1.0/(-0.0) -Inf julia> 0.0/0.0 NaN
I support scientific applications at The University of Manchester (see my LinkedIn profile if you’re interested in the details) and part of my job involves working on code written by researchers in a variety of languages. When I say ‘variety’ I really mean it – MATLAB, Mathematica, Python, C, Fortran, Julia, Maple, Visual Basic and PowerShell are some languages I’ve worked with this month for instance.
Having to juggle the semantics of so many languages in my head sometimes leads to momentary confusion when working on someone’s program. For example, I’ve been doing a lot of Python work recently but this morning I was hacking away on someone’s MATLAB code. Buried deep within the program, it would have been very sensible to be able to do the equivalent of this:
a=rand(3,3)
a =
0.8147 0.9134 0.2785
0.9058 0.6324 0.5469
0.1270 0.0975 0.9575
>> [x,y,z]=a(:,1)
Indexing cannot yield multiple results.
That is, I want to be able to take the first column of the matrix a and broadcast it out to the variables x,y and z. The code I’m working on uses MUCH bigger matrices and this kind of assignment is occasionally useful since the variable names x,y,z have slightly more meaning than a(1,3), a(2,3), a(3,3).
The only concise way I’ve been able to do something like this using native MATLAB commands is to first convert to a cell. In MATLAB 2013a for instance:
>> temp=num2cell(a(:,1));
>> [x y z] = temp{:}
x =
0.8147
y =
0.9058
z =
0.1270
This works but I think it looks ugly and introduces conversion overheads. The problem I had for a short time is that I subconsciously expected multiple assignment to ‘Just Work’ in MATLAB since the concept makes sense in several other languages I use regularly.
from pylab import rand a=rand(3,3) [a,b,c]=a[:,0]
a = RandomReal[1, {3, 3}]
{x,y,z}=a[[All,1]]
a=rand(3,3); (x,y,z)=a[:,1]
I’ll admit that I don’t often need this construct in MATLAB but it would definitely be occasionally useful. I wonder what other opinions there are out there? Do you think multiple assignment is useful (in any language)?
While on the train to work this morning, I wondered which English words have the most anagrams that are also valid English words. So, I knocked up few lines of Mathematica code and came up with 4 sets of 7:
{{"ates", "east", "eats", "etas", "sate", "seat", "teas"},
{"pares", "parse", "pears", "rapes", "reaps", "spare", "spear"},
{"capers", "crapes", "pacers", "parsec", "recaps", "scrape", "spacer"},
{"carets", "caster", "caters", "crates", "reacts", "recast", "traces"}}
So, according to my program (and Mathematica’s dictionary), the best you can do is 7. I’m not going to post the code until later because I don’t want to influence the challenge which is ‘Write a program in your language of choice that queries a dictionary to find which English words have the most anagrams that are also valid English words.’
While working on someone’s MATLAB code today there came a point when it was necessary to generate a vector of powers. For example, [a a^2 a^3….a^10000] where a=0.999
a=0.9999; y=a.^(1:10000);
This isn’t the only way one could form such a vector and I was curious whether or not an alternative method might be faster. On my current machine we have:
>> tic;y=a.^(1:10000);toc Elapsed time is 0.001526 seconds. >> tic;y=a.^(1:10000);toc Elapsed time is 0.001529 seconds. >> tic;y=a.^(1:10000);toc Elapsed time is 0.001716 seconds.
Let’s look at the last result in the vector y
>> y(end) ans = 0.367861046432970
So, 0.0015-ish seconds to beat.
>> tic;y1=cumprod(ones(1,10000)*a);toc Elapsed time is 0.000075 seconds. >> tic;y1=cumprod(ones(1,10000)*a);toc Elapsed time is 0.000075 seconds. >> tic;y1=cumprod(ones(1,10000)*a);toc Elapsed time is 0.000075 seconds.
soundly beaten! More than a factor of 20 in fact. Let’s check out that last result
>> y1(end) ans = 0.367861046432969
Only a difference in the 15th decimal place–I’m happy with that. What I’m wondering now, however, is will my faster method ever cause me grief?
This is only an academic exercise since this is not exactly a hot spot in the code!
In common with many higher educational establishments, the University I work for has site licenses for a wide variety of scientific software applications such as Labview, MATLAB, Mathematica, NAG, Maple and Mathcad— a great boon to students and researcher who study and work there. The computational education of a typical STEM undergraduate will include exposure to at least some of these systems along with traditional programming languages such as Java, C or Fortran and maybe even a little Excel when times are particularly bad!
Some argue that such exposure to multiple computational systems is a good thing while others argue that it leads to confusion and a ‘jack of all trades and master of none situation.’ Those who take the latter viewpoint tend to want to standardize on one system or other depending on personal preferences and expertise.
MATLAB, Python, Fortran and Mathematica are a few systems I’ve seen put forward over the years with the idea being that students will learn the basics of one system in their first few weeks and then the entire subject curriculum will be interwoven with these computational skills. In this way, students can use their computational skills as an aid to deeper subject understanding without getting bogged down with the technical details of several different computational systems. As you might expect, software vendors are extremely keen on this idea and will happily parachute in a few experts to help universities with curriculum development for free since this will possibly lead to their system being adopted.
Maybe we’ll end up with electrical engineers who’ve only ever seen Labview, mathematicians who’ve only ever used Maple, mechanical engineers who’ve only ever used MATLAB and economists who can only use Excel. While the computational framework(s) used to teach these subjects are less important than the teaching of the subject itself, I firmly believe that part of a well-rounded, numerate education should include exposure to several computational systems and such software mono-cultures should be avoided at all costs.
Part of the reason for writing this post is to ask what you think so comments are very welcome.
I was recently chatting to a research group who were considering moving to Python from MATLAB for some of their research software output. One team member was very worried about Python’s use of indentation to denote blocks of code and wondered if braces would ever find their way into the language? Another team member pointed out that this was extremely unlikely and invited us to attempt to import braces from the __future__ module.
>>> from __future__ import braces File "", line 1 SyntaxError: not a chance
Earlier this year I was awarded a fellowship from the software sustainability institute, an organization that works to improve all aspects of research software. During their recent collaborations workshop in Oxford, it occurred to me that I was aware of only a relatively tiny number of software projects at my own institution, The University of Manchester. I decided to change that and started contacting our researchers to see what software they had released freely to the world as part of their research activities.
Research software comes in many forms; from small but useful MATLAB, Python or R scripts with just a handful of users and one developer right through to fully-fledged applications used by large communities of researchers and supported by teams of specialist developers. I’m interested in knowing about all of it. After all, we live in a time when even a mistake in an Excel spreadsheet can change the world.
The list below is what’s been sent to me so far and is a mirror of an internal list that’s been doing the rounds at Manchester. I’ll update it as more information becomes available. If you are at Manchester and know of a project that I’ve missed, feel free to contact me.
Last updated: 26th Jan 2015
Centre for Imaging Sciences
- BoneFinder – BoneFinder is a fully automatic segmentation tool to extract bone contours from 2D radiographs. It is written in C++ and is available for Linux and Windows.
Faculty of Life Sciences
- antiSMASH – Genome annotation tool for secondary metabolite gene clusters.
- MultiMetEval – Flux-balance analysis tool for comparative and multi-objective analysis of genome-scale metabolic models.
- mzMatch/mzmatch.R/mzMatch.ISO – Comprehensive LC/MS metabolomics data processing toolbox.
- Rank Products – Statistical tool for the identification of differentially expressed entities in molecular profiles.
Health Informatics
- openCDMS – The openCDMS project is a community effort to develop a robust, commercial-grade, full-featured and open source clinical data management system for studies and trials.
IT Services
- idiffh – Research software can produce huge text files (e.g. logs). The GNU diff program needs to read the files into memory and therefore has an upper bound on file size. idiffh might only use a simple heuristic but is only bounded by the maximum file size (and free file store).
- nearest_correlation – Python versions of nearest correlation matrix algorithms
- ParaFEM – A portable library for parallel finite element analysis. Contributions from MACE, SEAES, School of Materials.
- Shadow – This is an Apple Mac OS X shell level application that can monitor Dropbox shared folders for file deletions and restore them.
- The Reality Grid Steering Library – A software library for steering and monitoring numerical simulations, APIs available for Fortran/C++/Java and steering clients available for installation on laptops and mobile devices. Developed in collaboration with the School of computer science.
Manchester Institute of Biotechnology
- Copasi – COPASI is a software application for simulation and analysis of biochemical networks and their dynamics.
- Condor Copasi – Condor-COPASI is a web-based interface for integrating COPASI with the Condor High Throughput Computing (HTC) environment.
School of Chemical Engineering & Analytical Science
- SurfaceSpectra Identity– is free software that allows you to view and export isotope patterns.
School of Chemistry
- DOSY Toolbox – A free, open source programme for processing PFG NMR diffusion data (a.k.a. DOSY data).
- Clinical NERC – Clinical NERC is a simple customizable state-of-the-art named entity recognition, and classification software for clinical concepts or entities.
- EasyChair – EasyChair is a free conference management system.
- GPC – The University of Manchester GPC library is a flexible and highly robust polygon set operations library for use with C, C#, Delphi, Java, Perl, Python, Haskell, Lua, VB.Net (and other) applications.
- HiPLAR – High Performance Linear Algebra in R. A collaboration between Manchester and Imperial.
- iProver – 7 times word champion in theorem proving.
- INSEE – Interconnection Networks Simulation and Evaluation Environment
- KUPKB (The Kidney & Urinary Pathway Knowledge Base) – The KUPKB is a collection of omics datasets that have been extracted from scientific publications and other related renal databases. The iKUP browser provides a single point of entry for you to query and browse these datasets.
- ManTIME – ManTIME is an open-source machine learning pipeline for the extraction of temporal expressions from general domain texts.
- MethodBox – MethodBox provides a simple, easy to use environment for browsing and sharing surveys, methods and data.
- myExperiment – myExperiment makes it easy to find, use and share scientific workflows and other Research Objects, and to build communities.
- Open PHACTS Discovery Platform – Freely available, this platform integrates pharmacological data from a variety of information resources and provides tools and services to question this integrated data to support pharmacological research.
- OWL API – A Java API and reference implementation for creating, manipulating and serialising OWL Ontologies. The latest version of the API is focused towards OWL 2. The OWL API is open source and is available under either the LGPL or Apache Licenses.
- OWL Tools – a collection of tools for working with OWL ontologies
- OWL Webapps – a collection of web apps for working with OWL ontologies
- RightField – Semantic annotation by stealth. RightField is tool for adding ontology term selection to Excel spreadsheets to create templates which are then reused by Scientists to collect and annotate their data without any need to understand, or even be aware of, RightField or the ontologies used. Later the annotations can be collected as RDF
- SEEK – SEEK is a web-based platform, with associated tools, for finding, sharing and exchanging Data, Models and Processes in Systems Biology.
- ServiceCatalographer – ServiceCatalographer is an open-source Web-based platform for describing, annotating, searching and monitoring REST and SOAP Web services.
- Simple Spreadsheet Extractor – A simple ruby gem that provides a facility to read an XLS or XLSX Excel spreadsheet document and produce an XML representation of its content.
- Taverna – Taverna is an open source and domain-independent Workflow Management System – a suite of tools used to design and execute scientific workflows and aid in silico experimentation.
- TERN – TERN is a temporal expressions identification and normalisation software; designed for clinical data.
- Utopia Documents – Utopia Documents brings a fresh new perspective to reading the scientific literature, combining the convenience and reliability of the PDF with the flexibility and power of the web.
School of Earth, Atmospheric and Environmental Sciences
- ManUniCast – iPad/iPhone app. Weather and Air-Quality Forecasts for the UK and Europe
School of Electrical and Electronic Engineering
- Automatic classification of eye fixations – Identify fixations and saccades from point-of-gaze data without parametric assumptions or expert judgement. MATLAB code.
- Bootstrap Threshold Software – Estimate a threshold and a robust SD from stimulus-response data with a normal cumulative distribution. Written in C.
- LDLTS – Laplace transform Transient Processor and Deep Level Spectroscopy. A collaboration between Manchester and the Institute of Physics Polish Academy of Sciences in Warsaw
- Model-Free Psychometric Function Software – Fit a stimulus-response curve and estimate a threshold and SD without a parametric model
- Raspbian – Raspbian is a free operating system based on Debian optimized for the Raspberry Pi hardware.
- Signal Wizard – Digital signal processing software.
School of Mathematics
- EIDORS – Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software.
- Fractional Matrix Powers – MATLAB functions to compute fractional matrix powers with Frechet derivatives and condition number estimate
- fAbcond – Python code for the condition number of a matrix exponential times a vector
- funm_quad – Quadrature-based Arnoldi restarts for matrix function computations in MATLAB
- IFISS – IFISS is a graphical package for the interactive numerical study of incompressible flow problems which can be run under Matlab or Octave.
- MARKOVFUNMV – An adaptive black-box rational Arnoldi method for the approximation of Markov functions.
- Matrix Computation Toolbox – The Matrix Computation Toolbox is a collection of MATLAB M-files containing functions for constructing test matrices, computing matrix factorizations, visualizing matrices, and carrying out direct search optimization.
- Matrix Function Toolbox – The Matrix Function Toolbox is a MATLAB toolbox connected with functions of matrices.
- Matrix Logarithm – MATLAB Files. Two functions for computing the matrix logarithm by the inverse scaling and squaring method.
- Matrix Logarithm with Frechet Derivatives and Condition Number – MATLAB files
- NLEVP A Collection of Nonlinear Eigenvalue Problems – This MATLAB Toolbox provides a collection of nonlinear eigenvalue problems.
- oomph-lib – An object-oriented, open-source finite-element library for the simulation of multiphysics problems.
- rktoolbox – A Rational Krylov Toolbox for MATLAB
- Shrinking (MATLAB) – MATLAB codes for restoring definiteness of a symmetric matrix by shrinking
- Shrinking (Python) – Python codes for restoring definiteness of a symmetric matrix by shrinking
- Simfit – Free software for simulation, curve fitting, statistics, and plotting.
- SmallOverlap – SmallOverlap is a GAP 4 package which implements new, highly efficient algorithms for computing with finitely presented semigroups and monoids whose defining presentations satisfy small overlap conditions (in the sense of J.H.Remmers)
- Symmetric eigenvalue decomposition and the SVD – MATLAB files
- testing_matrix_functions – MATLAB files for testing matrix function algorithms using identities such as exp(log(A)) = A
School of Mechanical, Aerospace and Civil Engineering (MACE)
- DualSPHysics – DualSPHysics is based on the Smoothed Particle Hydrodynamics model named SPHysics and makes use of GPUs.
- FLIGHT – FLIGHT specialises in the prediction and modelling of fixed-wing aircraft performance
- SPHYSICS – SPHysics is a platform of Smoothed Particle Hydrodynamics (SPH) codes inspired by the formulation of Monaghan (1992) developed jointly by researchers at the Johns Hopkins University (U.S.A.), the University of Vigo (Spain), the University of Manchester (U.K.) and the University of Rome La Sapienza (Italy).
- SWAB Online – Innovative and User Friendly Web Application in Running Fortran-based 1-D Shallow Water near Shore Wave Simulation Modelling
School of Physics and Astronomy
- Herwig++ – Herwig++ is a new event generator, written in C++, built on the experience gained with the well-known event generator HERWIG, which was used by the particle physics community for nearly 30 years. Herwig++ is used by the LHC experiments to predict the results of their collisions and as an essential component of their data analysis. It is developed by a consortium of four main nodes, including Manchester, and its published write-up has been cited over 500 times.
- im3shape – Im3shape measures the shapes of galaxies in astronomical survey images, taking into account that they have been distorted by a point-spread function.
- MAD8/madinput – Mathematica code and MAD8 installer for performing optics calculations for particle accelerator design.
- PolyParticleTracker – MATLAB code for particle tracking against complex optical backgrounds