The Simfit package
Simfit is a completetly free, open-source package, distributed as 32-bit or 64-bit binaries.
The source code can be
downloaded from https://simfit.org.uk so that programmers can edit the drivers for
their own needs or compile individual subroutines.
Summary
Simfit is a computer package for simulation, statistical analysis,
curve fitting
and graph plotting, using models from a compiled library or from ASCII
text files supplied by the user. It can be used for teaching the
principles of curve fitting, simulation and statistical analysis to
students, but it will
be found most useful by those interested in serious data analysis and
creating professional, publication quality, scientific graphs.
Simfit is a collection of
forty separate programs, each dedicated to a particular area of
data analysis, but the package is run seamlessly from a program
manager (w_simfit.exe in 32-bit versions or x64_simfit.exe in
64-bit versions) that has facilities for browsing and
printing files. Data can be formatted by dedicated editors
that can check for positive values, values in increasing order,
sensible weighting factors, etc.
or you can copy tables to the clipboard from any Windows application,
then paste them into any Simfit program. Macros are provided to create
correctly formatted data files from data held in Microsoft Office
Excel format.
In order to introduce first-time users to Simfit functionality,
each time a procedure is selected a default data set is installed
to demonstrate the data format required and the sort of results anticipated.
Further, at any stage while using Simfit, the file-open dialogue has a
button labeled [Demo] which lists typical data files for browsing
or analysis. There is also a button labeled [Keyboard] for users who want to
type in small data samples from the console and a button labeled [Paste] to input
rectangular data matrices from the clipboard.
Many advisory messages are displayed to help when using
a procedure for the first time, but there is a speedup option to toggle
these on or off as required.
After each analysis the results are written to archives for retrospective
use.
There is a comprehensive reference manual (w_manual.pdf) compete with
hyperlinks and an index as well as individual tutorials explaining
each Simfit procedure. These are also distributed as a collected set
(w_examples.pdf) with the Simfit package.
Simfit menu,
Simfit home page
Statistics
All the usual descriptive statistics (bar charts, histograms, best-fit
distributions on sample cdfs, dendrograms, box and whisker or cluster
plots), multivariate statistics (distance matrices and dendrograms,
principal components and scree plots), time series (ACF, PACF, ARIMA)
and frequently used tests (mostly with exact p values not
the normal approximations), such as:
- chi-square (O/E vectors, m by n contingency tables and
wssq/ndof)
- McNemar test on n by n frequency tables
- Cochran Q test
- Fisher exact (2 by 2 contingency table) with all p values
- Fisher exact Poisson distribution test
- t (both equal and unequal variances, paired and unpaired)
- variance ratio
- F for model validation
- Bartlett and Levene tests for homogeneity of variance
- 1,2,3-way Anova (with automatic variance stabilizing
transformations and nonparametric equivalents)
- Tukey post-ANOVA Q test
- Factorial ANOVA with marginal plots
- Repeated measures ANOVA with Helmert
matrix of orthonormal contrasts, Mauchly
sphericity test and Greenhouse-Geisser/Huyn-Feldt epsilon
corrections
- MANOVA with Wilks lambda, Roy's largest root,
Lawley-Hotelling trace, and Pillai trace for equality of
mean vectors, Box's test for equality of covariance
matrices, and profile analysis for repeated measurements.
- Canonical variates and correlations for group comparisons
- Mahalanobis distance estimation for allocation to groups
using estimative or predictive Bayesian methods
- Cochran-Mantel-Haenszel 2x2xk contingency table Meta
Analysis test
- Binomial test
- Sign test
- various Hotelling T-squared tests
- Goodness of fit and non parametric tests:
- runs (all, conditional, up and down)
- signs
- Wilcoxon-Mann-Whitney U
- Wilcoxon paired-samples signed-ranks
- Kolmogorov-Smirnov 1 and 2 sample
- Kruskal-Wallis
- Friedman
- Median, Mood and David tests and Kendall coefficient of concordance
- Mallows Cp, Akaike AIC, Schwarz SC, Durbin-Watson
- tables and plots of residuals, weighted residuals,
deviance residuals, Anscombe residuals, leverages and
studentized residuals as appropriate
- half normal and normal residuals plots
- Multilinear regression by
- L1 norm
- L2 norm (weighted least squares)
- L∞ norm
- Robust regression (M-estimates)
- Also logistic, binary logistic, log-linear, orthogonal,
reduced major axis, with interactive
selection and transformation of variables in all cases.
- Partial Least squares (PLS)
- Survival analysis (Kaplan-Meier, ML-Weibull, Mantel-Haenszel)
or, using generalized linear models with covariates (Exponential,
Weibull, Extreme value, Cox)
- Correlation analysis (Pearson product moment, Kendal Tau,
Spearman Rank) on all possible pairs of columns in a matrix,
and canonical correlations when data columns fall naturally
into two groups. Partial correlation coefficients can be
calculated for data sets with more than two variables.
- Shapiro-Wilks normality test with the large sample correction
- Normal scores plots
- Binomial distribution, analysis of proportions, exact parameter
confidence limits, likelihood ratio, odds, odds ratios and
graphical tests such as log-odds-ratios plots with exact
confidence limits for systematic variation in binomial p values
- Trinomial distribution (and confidence contour plots)
- Parameter estimates, confidence limits and goodness of fit
for:
- uniform
- normal
- binomial
- Poisson
- exponential
- gamma
- beta
- lognormal
- Weibull distributions
- All possible pairwise comparisons between columns of data
by KS-2, MWU and unpaired t tests using the Bonferroni
principle.
- Calculates False Discovery Rates FDR(HM) given p-values from multiple testing.
Simfit menu,
Simfit home page
Curve fitting
- Sums of exponentials (and estimation of AUC)
- Sums of Michaelis-Menten functions (and estimation of half
saturation points and final asymptotes)
- Sums of High/Low affinity binding sites
- Cooperative order n saturation functions (and cooperativity
analysis)
- Positive n:n rational functions
- Growth curves (derivative plots, comparison of models and
estimation of min/max growth rates, half-times and final
sizes)
- Survival curves using several models
- Polynomials (all degrees up to 6 then statistical tests for
the best model and prediction of x with confidence limits
given y)
- Cubic splines (user-placed knots, automatic knots with variable
tension, or crosss-validation data smoothing)
- Systems of differential equations (Adams, Gear, phase portrait,
orbits) using defined starting estimates and limits or random
cycles to search for a global minimum
- Calibration curves (polynomials, splines or user selected
models)
- Area under curve (AUC by choice from several methods)
- Initial rates
- Lag times
- Horizontal and inclined asymptotes
- Numerical deconvolution of sums of exponentials,
Michaelis-Mentens, trigonometric functions and Gaussian
densities
- Fitting user supplied models
- Analyzing flow cytometry profiles
- After fitting functions of 1, 2 or 3 variables, parameters
and objective functions can be stored for F, Akaike, Schwarz
and Mallows Cp tests, and the wssq/ndof contours and 3D
surface can be viewed as functions of any two chosen parameters.
With all functions of 1 variable, calibration,
evaluation, extrapolation, area calculations, derivative
estimations and interactive error bar plots can be done.
- Multi-function mode: simultaneous fitting of several functions
of the same independent variables, linked by common model
parameters
- Generalized Linear Models (GLM) can be fitted interactively
with either normal, binomial, Poisson or Gamma errors.
Appropriate links can be either identity, power, square root,
reciprocal, log, logistic, probit or complementary log-log
with canonical links as defaults and facility to supply fixed
offsets. A simplified interface is included for logistic,
binary logistic or polynomial logistic regression, bioassy,
log-lin contingency analysis or survival analysis.
- Stratified data sets can be analyzed by Cox regression and
conditional logistic regression
- Autoregressive integrated moving average models (ARIMA) to
time series with forecasting
- Facility to store parameter estimates and covariance matrices
in order to compute Mahalanobis distances between fits of the
same model to different data sets and test for significant
differences in parameter estimates.
Simfit menu,
Simfit home page
Graph plotting
- Grouping of data into histograms (with error bars if
appropriate) and cdfs
- Calculation of means and error bars with arbitrary confidence
limits from replicates can be done interactively or from data
files
- Error bars can be non-symmetrical or sloping if required
and multiple non-orthogonal error bars can be plotted
- Error bars can be added to 2D and 3D bar charts
and 3D cylinder plots
- Extrapolation of best-fit linear and nonlinear curves to
arbitrary end points
- Automatic transformation of error bars into various axes
(Hill, Lineweaver-Burk, Scatchard, log-odds, etc.)
- Immunoassay type dilution plots using logs to base 2, 3, 4,
5, 6, 7, 8, 9 as well as e and 10, and with labels as logs,
powers of the base or fractions
- Multiple axes plots
- Pie charts with arbitrary displacements, fill-styles, colours
- Bar charts with arbitrary positions, sizes, fill-styles,
colours and error-bars
- Presentation box and whisker plots, and pie or bar charts
with 3D perspective effects
- Orbits and vector field diagrams for systems of differential
equations
- Dendrograms and 3D-cluster plots for use in cluster analysis
- Scree diagrams and score or loading scatter plots for principal
components analysis (score plots can have Hotelling T^2
elliptical confidence regions)
- 3D-surfaces and 2D-projections of contours
- Curves in space and projections onto planes
- vast array of plotting characters and maths symbols
- Standard PostScript fonts, Symbol, ZapfDingbats and Isolatin1
encoding
- Professional quality PostScript files that can easily be edited
to change titles, legends, symbols, line-types and thicknesses,
etc.
- Interactive PostScript facility for arbitrarily stretching and
clipping overcrowded plots such as dendrograms without changing
aspect ratios of fonts or plotting symbols but by just changing
white-space between graphical objects
- A PostScript editor is supplied for scaling, rotating, shearing,
translating, editing, making collages and inlays from .eps files
- Transformation of .eps files into bit-map and compressed graphics
formats (e.g. bmp, pcx, tif, jpg, png, pdf)
- Plotting user defined parameteric equations such as r(theta),
x(t), y(t) in 2-space and x(t),y(t),z(t) in 3-space
- Facility to import PostScript specials automatically into
the PostScript file creation stream in order to redefine fonts,
colours, plotting symbols, add logos, etc.
- Graphical deconvolution of summation models after fitting
- 2D and 3D Biplots for multivariate data sets
Simfit menu,
Simfit home page
Calculations
- Zeros of polynomials
- Zeros of a user-defined function
- Zeros of n nonlinear functions in n variables
- Integrals of n user-defined functions in m variables
- Convolution integrals
- Bound-constrained quasi-Newton optimization
- Eigenvalues
- Determinants
- Inverses
- Singular value decomposition with right and left
singular vectors
- LU factorisation as A = PLU with matrix 1 and infinity
norms and corresponding condition numbers
- QR factorisation as in A = QR
- Cholesky factorisation as in Q = R(R^T)
- Matrix multiplication C = AB, (A^T)B, A(B^T) or (A^T)(B^T)
- Evaluation of quadratic forms (x^T)Ax or (x^T)(A^{-1})x
- Solve full-rank matrix equations Ax = b
- Solve over-determined linear systems Ax = b in the
L1,
L2 or
L∞ norms
- Solve the symmetric eigenvalue problem (A - lambda*B)x = 0
- Areas, derivatives and arc lengths of user supplied functions
- Analysis of cooperative ligand binding (zeros of binding
polynomial, Hessian, minmax Hill slope, transformed binding
constants, cooperativity indices, plotting species fractions)
- Power and sample size calculations for statistical tests used
in clinical trials, including plotting power as a function of
sample size (1 or 2 binomial proportions; 1, 2 or k normal
ANOVA samples; 1 or 2 correlation coefficients; 1 or 2
variances; chi-square test)
- Probabilities and cdf plots for the non-central t, non-central
chi-square, non-central beta or non-central F distributions
- Estimation of exact parameter confidence limits for the binomial,
normal, Poisson, etc. distributions and plotting confidence
contours for the trinomial distribution.
- Robust calculation of location parameter with confidence
limits for one sample (median, trimmed and winsorized means,
Hodges-Lehmann estimate, etc.).
- Time series smoothing by moving averages, running medians,
Hanning or the 4253H-twice smoother
- Time series, sample autocorrelation functions and partial
autocorrelation functions and plots for chosen numbers of
lags and associated test statistics
- Auto- and cross-correlation matrices for two time series
- Distance matrices for use in cluster analysis with extensive
choice of pre-conditioning transformations and alternative link
functions, e.g. Canberra dissimilarity and Bray-Curtis similarity.
- Neaest neighbours from a distance matrix
- Classical-metric and non-metric scaling of distance matrices
- Principal components with eigenvalues, scree diagrams, loadings
and scores from multivariate data sets
- Procrustes analysis to estimate the similarity between two matrices
- Varimax or Quartimax rotation of a loading matrix
- Canonical variates with eigenvalues, scree diagrams, loadings
and scores from multivariate data sets. Group means can be
plotted with confidence regions to assign comparison data to
existing groups.
- K-means cluster analysis with plots
- Shannon, Brilloin, Pielou, and Simpson diversity indices.
- Kernel density estimation
- Smooth interpolation by cubic Bessel, piecewise monotonic, McConalogue, Butland
Simfit menu,
Simfit home page
Special functions
These can all be called by 1-line commands as described in the documentation for
user-defined models. Some of them have equivalent NAG library versions as indicated below.
Command NAG Description
arctanh(x) S11AAF Inverse hyperbolic tangent
arcsinh(x) S11AAF Inverse hyperbolic sine
arccosh(x) S11AAF Inverse hyperbolic cosine
ai(x) S17AGF Airy function Ai(x)
dai(x) S17AJF Derivative of Ai(x)
bi(x) S17AHF Airy function Bi(x)
dbi(x) S17AKF Derivative of Bi(x)
besj0(x) S17AEF Bessel function J0
besj1(x) S17AFF Bessel function J1
besy0(x) S17ACF Bessel function Y0
besy1(x) S17ADF Bessel function Y1
besi0(x) S18ADF Bessel function I0
besi1(x) S18AFF Bessel function I1
besk0(x) S18ACF Bessel function K0
besk1(x) S18ADF Bessel function K1
phi(x) S15ABF Normal cdf
phic(x) S15ACF Normal cdf complement
erf(x) S15AEF Error function
erfc(x) S15ADF Error function complement
dawson(x) S15AFF Dawson integral
ci(x) S13ACF Cosine integral Ci(x)
si(x) S13ADF Sine integral Si(x)
e1(x) S13AAF Exponential integral E1(x)
ei(x) ...... Exponential integral Ei(x)
rc(x,y) S21BAF Elliptic integral RC
rf(x,y,z) S21BBF Elliptic integral RF
rd(x,y,z) S21BCF Elliptic integral RD
rj(x,y,z,r) S21BDF Elliptic integral RJ
sn(x,m) S21CAF Jacobi elliptic function SN
cn(x,m) S21CAF Jacobi elliptic function CN
dn(x,m) S21CAF Jacobi elliptic function DN
ln(1+x) S01BAF ln(1 + x) for x near zero
mchoosen(m,n) ...... Binomial coefficient
gamma(x) S13AAF Gamma function
lngamma(x) S14ABF log Gamma function
psi(x) S14ADF Digamma function, (d/dx)log(Gamma(x))
dpsi(x) S14ADF Trigamma function, (d^2/dx^2)log(Gamma(x))
igamma(x,a) S14BAF Incomplete Gamma function
igammac(x,a) S14BAF Complement of Incomplete Gamma function
fresnelc(x) S20ADF Fresnel C function
fresnels(x) S20ACF Fresnel S function
bei(x) S19ABF Kelvin bei function
ber(x) S19AAF Kelvin ber function
kei(x) S19ADF Kelvin kei function
ker(x) S19ACF Kelvin ker function
cdft(x,m) G01EBF cdf for t distribution
cdfc(x,m) G01ECF cdf for chi-square distribution
cdff(x,m,n) G01EDF cdf for F distribution (m = num, n = denom)
cdfb(x,a,b) G01EEF cdf for beta distribution
cdfg(x,a,b) G01EFF cdf for gamma distribution
invn(x) G01FAF inverse normal
invt(x,m) G01FBF inverse t
invc(x,m) G01FCF inverse chi-square
invb(x,a,b) G01FEF inverse beta
invg(x,a,b) G01FFF inverse gamma
spence(x) ...... Spence integral: 0 to x of -(1/y)log|(1-y)|
clausen(x) ...... Clausen integral: 0 to x of -log(2*sin(t/2))
struveh(x,m) ...... Struve H function order m (m = 0, 1)
struvel(x,m) ...... Struve L function order m (m = 0, 1)
kummerm(x,a,b)...... Confluent hypergeometric function M(a,b,x)
kummeru(x,a,b)...... U(a,b,x), b = 1 + n, the logarithmic solution
lpol(x,m,n) ...... Legendre polynomial of the 1st kind, P_n^m(x),
-1 =< x =< 1, 0 =< m =< n
abram(x,m) ...... Abramovitz function order m (m = 0, 1, 2), x > 0,
integral: 0 to infinity of t^m exp( - t^2 - x/t)
debye(x,m) ...... Debye function of order m (m = 1, 2, 3, 4)
(m/x^m)[integral: 0 to x of t^m/(exp(t) - 1)]
fermi(x,a) ...... Fermi-Dirac integral (1/Gamma(1 + a))[integral:
0 to infinity t^a/(1 + exp(t - x))]
heaviside(x,a)...... Heaviside unit function h(x - a)
delta(i,j) ...... Kronecker delta function
impulse(x,a,b)...... Unit impulse function (small b for Dirac delta)
spike(x,a,b) ...... Unit triangular spike function
gauss(x,a,b) ...... Gauss pdf
sqwave(x,a) ...... Square wave amplitude 1, period 2a
rtwave(x,a) ...... Rectified triangular wave amplitude 1, period 2a
mdwave(x,a) ...... Morse dot wave amplitude 1, period 2a
stwave(x,a) ...... Sawtooth wave amplitude 1, period a
rswave(x,a) ...... Rectified sine wave amplitude 1, period pi/a
shwave(x,a) ...... Sine half-wave amplitude 1, period 2*pi/a
uiwave(x,a,b) ...... Unit impulse wave area 1, period a, width b
Simfit menu,
Simfit home page
NAG library routines
Early versions of Simfit used the NAG library routines for numerical
procedures, and this can still be done if a valid license is available. Otherwise
Simfit has a built-in library to use public domain versions of these routines.
Some of these replacement routines have additional functionality
and, where routines have been removed from the NAG library,
additional code has been included so that newer NAG routines will be called when
the NAG library is being used instead of the Simfit library.
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c02agf
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g04adf,
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s18acf,
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s19aaf,
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x01aaf,
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Simfit menu,
Simfit home page
Simulation
- Generating exact data from a library of models or from
user-defined models
- User defined models can be multiple equations in several
variables or sets of nonlinear differential equations, and
can have conditional logical branching (equivalent to
if...elseif...else) for models that swap at critical values
of subsidiary functions or independent variables
- Logical operators like IF, IFNOT, AND, OR, NOT, XOR, etc. can
be used to control model execution
- Special functions that can be used within models include
- Airy functions Ai(x), Bi(x) and derivatives
- Hyperbolic and inverse hyperbolic functions cosh(x),
sinh(x), tanh(x), arccosh(x), arcsinh(x), arctanh(x)
- Bessel functions J0, J1, Y0, Y1, I0, I1, K0, K1
- Normal integral phi(x), error function erf(x) and
complements phic(x) and erfc(x), Dawson's integral
- Exponential, sine and cosine integrals, E1(x), Ei(x),
Si(x), Ci(x)
- Fresnel, Spence, Debye, Fermi-Dirac, Abramovitz,
Clausen integrals
- Kelvin bei(x), ber(x), kei(x) and ker(x) functions
- Elliptic integrals RC, RF, RD, RJ and Jacobi functions
sn(u,m), cn(u,m) and dn(u,m)
- Binomial coefficients, gamma function, incomplete gamma
function, log(gamma(x)), digamma (psi(x)), and trigamma
functions
- Struve confluent hypergeometric functions
- Legendre polynomials of degree n and order m, spherical
harmonics
- Cumulative distribution functions for the normal, t, F,
chi-square, beta and gamma distributions
- Inverse functions for the normal, t, F, chi-square, beta
and gamma distributions
- Impulse functions: Heaviside, Kronecker delta, Dirac delta,
triangular spike, Gaussian
- Periodic wave impulse functions: square, rectified triangle,
Morse dot, sawtooth, rectified sine, rectified half sine,
unit impulse
- One-line commands can be used for vector arithmetic (initialisation,
norms, dot products), for evaluating polynomials or Chebyshev
expansions, or for calling for mathematical constants
(like Euler's gamma)
- Submodels can be defined, and these can be called from a
main model for function evaluation, root finding, or adaptive
quadrature or they can be called dynamically with arbitrary
arguments
- A one line command is all that is necessary to estimate a
convolution integral for any two sub-models over any range
- Adding random error to exact data sets to simulate experimental
error
- Systems of differential equations
After simulating, selected orbits can be stored and, with
autonomous systems, vector field
phase portraits can be plotted to identify singularities.
- Generating random numbers and 1,2,3-D random walks from the:
- uniform
- normal
- chi-square
- F
- logistic
- Weibull
- Cauchy
- Poisson
- binomial distributions.
- Generating n by m normally distributed random matrices.
- Generating random permutations of lists and Latin squares.
Simfit menu,
Simfit home page
Documentation
- Help documents are available in several formats as follows:
- ASCII text files can be read by any text editor
(e.g. Notepad), or using a Simfit viewer, which
is safer as it does not allow editing.
- HTML documents can be viewed by a built in HTML
interpreter without using your own browser.
- PostScript documents (.ps) can be read using GSview or
transformed into Portable Document Format.
- Portable Document Format (.pdf) files can be read and
printed using Adobe Acrobat reader.
- Binary files that can only be read using a built in
interpreter.
- A short HTML program can be viewed from the main Simfit
program manager, w_simfit.exe.
- Each program has a dedicated self contained tutorial.
- Many of the specialized controls have individual tutorials.
- There is an extensive set of readme files (w_readme.0
gives details) which describe advanced features and
technical details.
- A document (simfit_summary.pdf) summarizes the package and contains
collages.
- A document (MS_office.pdf) describes the interface to MS Office
and, in particular, explains how to use the macros to extract
data from MS Excel spreadsheets.
- A document (PS_fonts.pdf) lists the PostScript font encodings,
for those who want to create special effects.
- A detailed reference manual (w_manual.pdf) is provided
in monochrome, colour, .ps and .pdf formats. The coloured pdf version incorporates hyperlinks
between the contents, index and page references and provides
book marks.
- A document (source.pdf) explains how to compile the source code.
- A document (speedup.pdf) explains how to speed up Simfit analysis by suppressing
advisory messages intended for first-time users.
- There is a full set of test files containing appropriate
data to test every Simfit procedure.
Simfit menu,
Simfit home page
Installation
- Copy down the file simfit_setup7_a_b.exe (or x64_simfit_setup7_a_b.exe) onto your PC, open it and accept
the default installation folder.
- Make a desk top shortcut to the driver file w_simfit.exe (or x64_simfit.exe) in the
...\Simfit\bin folder.
- To run Simfit double click on the desktop icon.
- Use the [Configure], [Check], [Apply] options to configure the package.
- Other software:
You need a PDF viewer such as sumatraPDF or Adobe Acrobat Reader,
and GSview could be useful to view *.EPS files and transorm *.EPS into *.SVG.
Simfit menu,
Simfit home page
Help
Requests for help may be answered by:
W.G.Bardsley
University of Manchester
Email: bill.bardsley@simfit.org.uk
I always repair errors and will usually help simfit users, including adding new mathematical models to the library.