alan miller's fortran software.htm

The module LSQ is for unconstrained linear least-squares fitting. It is based upon Applied Statisti

  href="http://users.bigpond.net.au/amiller/NSWC/dspslv.f90">dspslv.f90</A> 
  Solution of sparse systems of linear equations using Gaussian elimination. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/dsvdc.f90">dsvdc.f90</A> 
  Calculates the singular-value decomposition (SVD) of a real matrix. There is 
  also a test program: -- 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/t_svd.f90">t_svd.f90</A> 

  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/fft.f90">fft.f90</A> 
  Fast Fourier Transform (FFT) for any length of series which has no prime 
  factor greater than 23. Also the inverse and multivariate FFT. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/hbrd.f90">hbrd.f90</A> 
  Solve sets of non-linear equations using Powell's Hybrid algorithm. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/specfunc.zip">specfunc.zip</A> 
  A zip file containing all of the special functions from the NSWC library. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/polyarea.f90">polyarea.f90</A> 
  Calculates the area of a polygon. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/p_intcpt.f90">p_intcpt.f90</A> 
  Finds the crossing points of a finite line and a polygon. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/bnd_solv.f90">bnd_solv.f90</A> 
  Solve banded linear equations using compact storage of the banded matrix. 
  There is a complex version of this -- <A 
  href="http://users.bigpond.net.au/amiller/NSWC/cbnd_slv.f90">cbnd_slv.f90</A> 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/big_solv.f90">big_solv.f90</A> 
  Solves a large set of n general linear equations using out-of-core methods, 
  requiring storage for about n^2/4 values. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/qagi.f90">qagi.f90</A> 
  Adaptive one-dimensional integration over infinite or semi-infinite ranges 
  (adapted from QUADPACK). 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/qxgs.f90">qxgs.f90</A> 
  Adaptive one-dimensional integration over finite ranges (adapted from TOMS 
  algorithm 691). 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/inc_gam.f90">inc_gam.f90</A> 
  The incomplete gamma function and its inverse. Test program: <A 
  href="http://users.bigpond.net.au/amiller/NSWC/t_incgam.f90">t_incgam.f90</A> 
  based on TOMS algorithm 654. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/constant.f90">constant.f90</A> 
  This is a module of constants used by some of the functions in the NSWC 
  collection of routines. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/qsortd.f90">qsortd.f90</A> A 
  subroutine which implements a quicksort algorithm without changing the input 
  array. It returns an integer array containing the order. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/smplx.f90">smplx.f90</A> 
  Linear programming using the simplex algorithm. This is a translation of the 
  Fortran 66 program from the NSWC (Naval Surface Warfare Center) library 
  written by Alfred Morris. There is also a simple test program <A 
  href="http://users.bigpond.net.au/amiller/NSWC/t_smplx.f90">t_smplx.f90</A>. 
  Needs the module <A 
  href="http://users.bigpond.net.au/amiller/NSWC/constant.f90">constant.f90</A> 
  which defines the precision and returns certain machine constants. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/dmexp.f90">dmexp.f90</A> 
  Calculates the exponential of a matrix. 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/fprob.f90">fprob.f90</A> 
  Cumulative F distribution. Requires <A 
  href="http://users.bigpond.net.au/amiller/NSWC/bratio.f90">bratio.f90</A> for 
  the incomplete gamma function, and <A 
  href="http://users.bigpond.net.au/amiller/NSWC/constant.f90">constant.f90</A>. 
  N.B. bratio.f90 contains code for a number of special functions including the 
  error function, the logarithm of the gamma function, the logarithm of the beta 
  function, and the digamma function. bratio was translated from the NSWC 
  library. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/dceigv.f90">dceigv.f90</A> 
  Calculate the eigenvalues and vectors of a general complex matrix. Another 
  routine from the NSWC library. Needs <A 
  href="http://users.bigpond.net.au/amiller/NSWC/constant.f90">constant.f90</A>. 
  Based upon EISPACK routines. There is a test program: <A 
  href="http://users.bigpond.net.au/amiller/NSWC/t_dceigv.f90">t_dceigv.f90</A> 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/locpt.f90">locpt.f90</A> 
  Is a point inside a polygon? 
  <LI><A href="http://users.bigpond.net.au/amiller/NSWC/qtcrt.f90">qtcrt.f90</A> 
  Solve quadratic, cubic and quartic equations. Includes a short driver program, 
  and hence includes the interfaces needed for your program. Adapted from the 
  NSWC library. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/toeplitz.f90">toeplitz.f90</A> 
  Solution of Toeplitz systems of linear equations. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/NSWC/zeroin.f90">zeroin.f90</A> 
  Finds a zero of a user-supplied function in a specified range (a, b). </LI></UL>
<HR>

<H2>
<CENTER>Miscellaneous code</A></CENTER></H2>
<P><FONT size=2>
<HR>

<UL>
  <LI><A href="http://users.bigpond.net.au/amiller/qsort.f90">qsort.f90</A> A 
  version of the quicksort algorithm adapted from Walt Brainerd's code. 
  <LI><A href="http://users.bigpond.net.au/amiller/cobyla.f90">cobyla.f90</A> 
  Mike Powell's routine for minimization of non-linear functions with smooth 
  non-linear constraints, using local linear approximations to the constraints. 
  <LI><A href="http://users.bigpond.net.au/amiller/tron.zip">tron.zip</A> 
  Newton's method for large bound-constrained optimization problems by Chih-Jen 
  Lin &amp; Jorge More', a MINPACK-2 project. Use PKUNZIP or WINZIP to unpack 
  the file. 
  <LI><A href="http://users.bigpond.net.au/amiller/lm.zip">lm.zip</A> 
  Levenberg-Marquardt algorithm for non-linear least squares (unconstrained). 
  This is a translation of the MINPACK routines, LMDER &amp; LMDIF. Use LMDER 
  for functions which can be differentiated, and LMDIF when it is necessary to 
  use differences. The ZIPped file includes the MINPACK test programs, and a 
  simple example fitting a 4-parameter logistic. 
  <LI><A href="http://users.bigpond.net.au/amiller/conmin.zip">conmin.zip</A> 
  The classic CONMIN package for constrained minimization updated to Fortran 90. 
  Test examples and the manual are included in the ZIP file. N.B. CONMIN is 
  included as just one of the algorithms in TOMS algorithm 734 which can be 
  downloaded from netlib (http://www.netlib.org). 
  <LI><A href="http://users.bigpond.net.au/amiller/minim.f90">minim.f90</A> The 
  Nelder-Mead simplex algorithm for unconstrained minimization. It does NOT 
  require or use derivatives. N.B. This is NOT for linear programming! <A 
  href="http://users.bigpond.net.au/amiller/t_minim.f90">t_minim.f90</A> is a 
  very simple test program for minim.f90 which may help users. This is now 
  ELF90-compatible. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/primefac.f90">primefac.f90</A> A 
  program to find prime factors. 
  <LI><A href="http://users.bigpond.net.au/amiller/uobyqa.f90">uobyqa.f90</A> 
  Mike Powell's package for unconstrained minimization when derivatives are not 
  available. There is a test/driver program:<BR><A 
  href="http://users.bigpond.net.au/amiller/t_uobyqa.f90">t_uobyqa.f90</A> and a 
  file of results from the test program:<BR><A 
  href="http://users.bigpond.net.au/amiller/test.out">test.out</A> The 
  documentation, which is in gzipped postscript, can be downloaded from the 
  Optimization Decision Tree at: <A 
  href="http://plato.lasu.edu/topics/problems/nlounres.html" A <>
  <LI><A href="http://users.bigpond.net.au/amiller/tn.zip">tn.zip</A> Stephen 
  Nash's truncated-Newton code for the minimization of continuous functions. It 
  can use differences instead of derivatives, and bounds may be imposed on the 
  parameters. 
  <LI><A href="http://users.bigpond.net.au/amiller/xdlegf.f90">xdlegf.f90</A> 
  Legendre functions and polynomials, from the CMLIB library. 
  <LI><A href="http://users.bigpond.net.au/amiller/datesub.f90">datesub.f90</A> 
  Some date manipulation routines collected together by H.D. Knoble. 
  <LI><A href="http://users.bigpond.net.au/amiller/global.f90">global.f90</A> At 
  Arnold Neumaier's web site, this is recommended as the most successful of the 
  global optimization packages. There is a sample program <A 
  href="http://users.bigpond.net.au/amiller/fit.f90">fit.f90</A> and the 
  original documentation <A 
  href="http://users.bigpond.net.au/amiller/global.txt">global.txt</A> for the 
  f77 version. I have included <A 
  href="http://users.bigpond.net.au/amiller/testfunc.f90">testfunc.f90</A> which 
  will eventually contain all of Neumaier's 30 test functions. N.B. Users of 
  local optimization packages usually obtain satisfactory convergence after 10s 
  or sometimes 100s of function evaluations. Global optimization routines 
  usually require many 1000s of function evaluations. 
  <LI><A href="http://users.bigpond.net.au/toms/tensolve.zip">tensolve.zip</A> A 
  package for solving sets of non-linear equations using Robert Schnabel's 
  tensor method. This is a translation of TOMS algorithm 768. The file was 
  compressed using PKZIP. It is now compatible with version 4.0 of ELF90, but 
  misbehaves on example 2. 
  <LI><A href="http://users.bigpond.net.au/amiller/KS2.f90">KS2.f90</A> 
  Calculates 1 and 2-tail probabilities for the single-sample Kolmogorov-Smirnov 
  statistic. For 2-tail probabilities, it uses a combination of the first 
  algorithm from CACM 487, double the single-tail probability, and the 
  asymptotic distribution. See also TOMS algorithm 519. 
  <LI><A href="http://users.bigpond.net.au/amiller/nCr.f90">nCr.f90</A> 
  Calculates number of combinations of r out of n. 
  <LI><A href="http://users.bigpond.net.au/amiller/update.f90">update.f90</A> 
  Three very short subroutines to update the sample mean and sum of squares of 
  deviations about the mean (and hence update variances or std. deviations), 
  when one observation is added, dropped or replaced with another. Designed for 
  fast, repeated use with no checks. 
  <LI><A href="http://users.bigpond.net.au/amiller/mvnpack.f90">mvnpack.f90</A> 
  Alan Genz's package of 4 methods of evaluating multivariate normal integrals. 
  <LI><A href="http://users.bigpond.net.au/amiller/bivnorm.f90">bivnorm.f90</A> 
  A function for calculating bivariate normal probabilities, extracted from Alan 
  Genz's package for multivariate normal integration. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/genz2d3d.f90">genz2d3d.f90</A> This 
  is code for bivariate and trivariate normal integrals which I discovered on 
  Alan Genz's web site. I have made it compatible with ELF90. It is more recent 
  (January 2001) than bivnorm above. 
  <LI><A href="http://users.bigpond.net.au/amiller/dcuhre.f90">dcuhre.f90</A> 
  Alan Genz's program for general multivariate integration, not just of one 
  function but simultaneously for a vector of functions over the same 
  multivariate region. There is also a test program <A 
  href="http://users.bigpond.net.au/amiller/dtest1.f90">dtest1.f90</A> and a 
  text file <A 
  href="http://users.bigpond.net.au/amiller/dcuhre.txt">dcuhre.txt</A>. which 
  contains the results from the test program (run in single precision) N.B. 
  While the Fortran 77 version of this code is still at Alan Genz's web site, he 
  is referring users to the CUBPACK project at: <A 
  href="http://www.cs.kuleuven.ac.be/~nines/research/CUBPACK">CUBPACK</A> 
  <LI><A href="http://users.bigpond.net.au/amiller/tfunc.f90">tfunc.f90</A> A 
  module for calculating bivariate normal probabilities using code by Baughman 
  and Patefield. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/t_bivnor.f90">t_bivnor.f90</A> 
  Comparison of 3 functions for the bivariate normal - those of Donnelly (CACM 
  462), Genz, and Baughman/Patefield. 
  <LI><A href="http://users.bigpond.net.au/amiller/hash.f90">hash.f90</A> and <A 
  href="http://users.bigpond.net.au/amiller/hashord.f90">hashord.f90</A> Hashing 
  routines by Richard Brent and Donald Knuth, taken from Herman Noble's web site 
  (http://ftp.cac.psu.edu/pub/ger/fortran/). 
  <LI><A href="http://users.bigpond.net.au/amiller/elsunc.f90">elsunc.f90</A> 
  Per Lindstroem's package for non-linear least squares with upper &amp; lower 
  bounds on parameter values. <A 
  href="http://users.bigpond.net.au/amiller/d_elsunc.f90">d_elsunc.f90</A> 
  demonstrates this package. 
  <LI><A href="http://users.bigpond.net.au/amiller/solvopt.zip">solvopt.zip</A> 
  The SolvOpt package minimizes or maximizes nonlinear functions, which may be 
  nonsmooth and may have constraints, using the so-called method of exact 
  penalization. This is a zip file containing several driver programs. 
  <LI><A href="http://users.bigpond.net.au/amiller/ga.zip">ga.zip</A> A package 
  for global minimization using genetic algorithms. Please note the copyright 
  conditions if you want to use this for commercial purposes. This is a ZIP 
  file. 
  <LI><A href="http://users.bigpond.net.au/amiller/pikaia.zip">pikaia.zip</A> 
  Another genetic algorithm for global optimization without derivatives. This 
  one comes from the High Altitude Observatory of NCAR. This is a ZIP file, 
  containing a number of interesting examples. There is an excellent manual, but 
  you will have to download it from <A 
  href="http://www.hao.ucar.edu/public/research/si/pikaia/pikaia.html">their web 
  site</A>. N.B. The manual is 120 pages long, and in postscript. Where does the 
  name Pikaia come from? Pikaia gracilens is a flattened worm-like beast about 
  5cm long which crawled in the mud on the sea floor about 530 million years 
  ago! 
  <LI><A href="http://users.bigpond.net.au/amiller/cdfcor.zip">cdfcor.zip</A> A 
  package for rational (Pade) approximation in one and two dimensions. Includes 
  a driver for 9 test problems, input data and output. This is a ZIP file. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/sym_band.f90">sym_band.f90</A> Find 
  the eigenvalues/vectors of a symmetric banded matrix stored in compact form. 
  Based upon EISPACK code. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/strassen.f90">strassen.f90</A> The 
  Strassen fast matrix multiply algorithm for large matrices. Code downloaded 
  from the comp.lang.fortran newsgroup. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/varpro/varpro.f90">varpro.f90</A> 
  The VARPRO package for separable nonlinear least squares is for fitting models 
  of the kind<BR>Y = a1.F1(x, b) + a2.F2(x, b) + ...<BR>in which the a's are 
  linear parameters, the vector b is a vector of nonlinear parameters, and the 
  F's are nonlinear functions. An important application is fitting sums of 
  exponential decay terms. A driver program <A 
  href="http://users.bigpond.net.au/amiller/varpro/twoexp.f90">twoexp.f90</A> is 
  provided, as well as the <A 
  href="http://users.bigpond.net.au/amiller/varpro/a.dat">data</A>. 
  <LI><A href="http://users.bigpond.net.au/amiller/bvls.f90">bvls.f90</A> Fits a 
  linear model using least squares but with upper and lower bounds as 
  constraints on each regression coefficient. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/foldat73.f90">foldat73.f90</A> There 
  is a compiler which accepts Fortran code in fixed format extending beyond 
  column 72, other than sequence numbers which occupy these columns in fixed 
  form. This simple program takes such code as input data and breaks long lines 
  after column 72 starting with a continuation character in column 6. 
  <LI><A 
  href="http://users.bigpond.net.au/amiller/diehard/diehard.f90">DIEHARD</A> A 
  version of George Marsaglia's random number tests in standard Fortran. You 
  will also need the files <A 
  href="http://users.bigpond.net.au/amiller/diehard/tests.txt">tests.txt</A> and 
  <A