pdl::opt::simplex(3) [suse man page]
Simplex(3) User Contributed Perl Documentation Simplex(3) NAME
PDL::Opt::Simplex -- Simplex optimization routines SYNOPSIS
use PDL::Opt::Simplex; ($optimum,$ssize) = simplex($init,$initsize,$minsize, $maxiter, sub {evaluate_func_at($_[0])}, sub {display_simplex($_[0])} ); DESCRIPTION
This package implements the commonly used simplex optimization algorithm. The basic idea of the algorithm is to move a "simplex" of N+1 points in the N-dimensional search space according to certain rules. The main benefit of the algorithm is that you do not need to calculate the derivatives of your function. $init is a 1D vector holding the initial values of the N fitted parameters, $optimum is a vector holding the final solution. $initsize is the size of $init (more...) $minsize is some sort of convergence criterion (more...) - e.g. $minsize = 1e-6 The sub is assumed to understand more than 1 dimensions and threading. Its signature is 'inp(nparams); [ret]out()'. An example would be sub evaluate_func_at { my($xv) = @_; my $x1 = $xv->slice("(0)"); my $x2 = $xv->slice("(1)"); return $x1**4 + ($x2-5)**4 + $x1*$x2; } Here $xv is a vector holding the current values of the parameters being fitted which are then sliced out explicitly as $x1 and $x2. $ssize gives a very very approximate estimate of how close we might be - it might be miles wrong. It is the euclidean distance between the best and the worst vertices. If it is not very small, the algorithm has not converged. FUNCTIONS
simplex Simplex optimization routine ($optimum,$ssize) = simplex($init,$initsize,$minsize, $maxiter, sub {evaluate_func_at($_[0])}, sub {display_simplex($_[0])} ); See module "PDL::Opt::Simplex" for more information. CAVEATS
Do not use the simplex method if your function has local minima. It will not work. Use genetic algorithms or simulated annealing or conjugate gradient or momentum gradient descent. They will not really work either but they are not guaranteed not to work ;) (if you have infinite time, simulated annealing is guaranteed to work but only after it has visited every point in your space). SEE ALSO
Ron Shaffer's chemometrics web page and references therein: "http://chem1.nrl.navy.mil/~shaffer/chemoweb.html". Numerical Recipes (bla bla bla XXX ref). The demonstration (Examples/Simplex/tsimp.pl and tsimp2.pl). AUTHOR
Copyright(C) 1997 Tuomas J. Lukka. All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. perl v5.12.1 2009-10-17 Simplex(3)
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Matrix(3) User Contributed Perl Documentation Matrix(3) NAME
PDL::Matrix -- a derived matrix class that implements column-major constructors and methods VERSION
This document refers to version PDL::Matrix 0.01 of PDL::Matrix SYNOPSIS
use PDL::Matrix; $m = mpdl [[1,2,3],[4,5,6]]; $m = PDL::Matrix->pdl([[1,2,3],[4,5,6]]); $m = msequence(4,3); @dimsa = $a->mdims; # 'dims' is not overloaded $v = vpdl [0,1,2,3] $v = vzeroes(4); DESCRIPTION
Overview This package tries to help people who want to use PDL for 2D matrix computation with lots of indexing involved . It provides a PDL subclass so one- and two-dimensional piddles that are used as vectors resp. matrices can be typed in using traditional matrix convention. The original pdl class refers to the first index as the first row, the second index as the first column of a matrix. Consider print $B = sequence(3,2) [ [0 1 2] [3 4 5] ] which gives a 2x3 matrix in terms of the matrix convention, but the constructor used (3,2). This might get more confusing when using slices like sequence(3,2)->slice("1:2,(0)") : with traditional matrix convention one would expect [2 4] instead of [1 2]. This subclass PDL::Matrix overloads the constructors and indexing functions of pdls so that they are compatible with the usual matrix con- vention, where the first dimension refers to the row of a matrix. So now, the above example would be written as print $B = PDL::Matrix->sequence(3,2) # or $B = msequence(3,2) [ [0 1] [2 3] [4 5] ] Routines like eigenvalue or matrix inversion can be used without any changes. Furthermore one can construct and use vectors as n x 1 matrices without mentioning the second index '1'. Implementation "PDL::Matrix" works by overloading a number of PDL constructors and methods such that first and second args (corresponding to first and second dims of corresponding matrices) are effectively swapped. It is not yet clear if PDL::Matrix achieves a consistent column major look-and-feel in this way. FUNCTIONS
mpdl, PDL::Matrix::pdl constructs an object of class PDL::Matrix which is a piddle child class, where the first index refers to the first column of the two-dimen- sional piddle. $m = mpdl [[1,2,3],[4,5,6]]; $m = PDL::Matrix->pdl([[1,2,3],[4,5,6]]); mzeroes, mones, msequence constructs a PDL::Matrix object similar to the piddle constructors zeroes, ones, sequence vpdl constructs an object of class PDL::Matrix which is of matrix dimensions (n x 1) print $v = vpdl [0,1]; [ [0] [1] ] vzeroes, vones, vsequence constructs a PDL::Matrix object with matrix dimensions (n x 1), therefore only the first scalar argument is used. print $v = vsequence(2); [ [0] [1] ] PDL::Matrix::slice, PDL::Matrix::dice same as slice, dice for normal piddles, but reflecting the matrix convention by swapping the first two arguments. print sequence(3,2)->slice("1:2,(0)") # piddle [1 2] print msequence(3,2)->slice("1:2,(0)") # PDL::Matrix [2 4] PDL::Matrix::at same as at for piddles, but reflecting the matrix convention by swapping the first two arguments If only one scalar argument is used, we assume the object to be a vector and look only at the first column. PDL::Matrix::set set a particular value in a PDL::Matrix object. Note that this has to be called as an object method rather than a function print msequence(3,3)->set(2,0,-1) # ok with PDL::Matrix convention [ [ 0 1 2] [ 3 4 5] [-1 7 8] ] print set msequence(3,3), 2,0,-1 # does not conform with PDL::Matrix convention [ [ 0 1 -1] [ 3 4 5] [ 6 7 8] ] PDL::Matrix::reshape same as reshape for piddles, but reflecting the matrix convention by swapping the first two arguments mdims returns the dimensions of the PDL::Matrix object in matrix convention "dims" is NOT overloaded by PDL::Matrix to make sure that methods like PDL::transpose still work. So use "mdims" to get the dims in the PDL::Matrix notation. print msequence(3,2)->mdims 3 2 kroneckerproduct returns kroneckerproduct of two matrices. This is not efficiently implemented. det_general returns a generalized determinant of a matrix. If the matrix is not regular, one can specify the rank of the matrix and the corresponding subdeterminant is returned. This is implemented using the "eigens" function. trace returns the trace of a matrix (sum of diagonals) vcrossp, PDL::Matrix::crossp similar to PDL::crossp, however reflecting PDL::Matrix notations BUGS AND PROBLEMS
Because we change the way piddles are constructed, not all pdl operators may be applied to piddle-matrices. The inner product is not rede- fined. We might have missed some functions/methods. Internal consistency of our approach needs yet to be established. TODO
check all PDL functions, benchmarks, optimization, lots of other things ... AUTHOR(S) Stephan Heuel (stephan@heuel.org), Christian Soeller (c.soeller@auckland.ac.nz). COPYRIGHT
All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated from the PDL distribution, the copyright notice should be included in the file. perl v5.8.0 2001-12-03 Matrix(3)