COPYRIGHT NOTICE
Photonic - A perl package for calculations on photonics and metamaterials.
Copyright (C) 2016 by W. Luis Mochán
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 1, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston MA 02110-1301 USA
mochan@fis.unam.mx
Instituto de Ciencias Físicas, UNAM
Apartado Postal 48-3
62251 Cuernavaca, Morelos
México
NAME
Photonic::Utils
VERSION
version 0.015
SYNOPSIS
use Photonic::Utils qw(cmatmult);
$c=cmatmult($a, $b);
DESCRIPTION
Utility functions that may be useful.
Exportable Functions
$r=linearCombine($c, $s)
Complex linear combination of states. $c is an arrayref of 'complex' pdl scalars and $s is an arrayref of 'complex' states ('complex' multidimensional pdl).
$r=linearCombineIt($c, $it)
Complex linear combination of states from iterator. $c is an arrayref of 'complex' pdl scalars and $it is an iterator for the corresponding states.
$p=HProd($a, $b, $skip)
Hermitean product <a|b> of two 2x.... 'complex' multidimensional pdls $a and $b. If $skip is present, preserve the first 1+$skip _dimensions (the first dimension is RorI) before adding up.
$p=MHProd($a, $b, $m, $skip)
Hermitean product <a|m|b> of two 2x.... 'complex' multidimensional pdls $a and $b representing vector fields using metric $m. If $skip is present, preserve the first 1+$skip dimensions (the first dimension is RorI) before adding up. (Might not be functional yet, or might be wrong)
$p=EProd($a, $b, $skip)
Euclidean product <a|b> of two 2x.... 'complex' multidimensional pdls $a and $b in reciprocal space. If $skip is present, preserve the first 1+$skip dimensions (the first dimension is RorI) before adding up.
$p=SProd($a, $b, $skip)
Spinor product <a|b> of two 2x.... 'complex' multidimensional pdls $a and $b in reciprocal space. If $skip is present, preserve the first 2+$skip dimensions (the first dimension is RorI and the second the spinor dimension) before adding up.
$p=VSProd($a, $b)
Vector-Spinor product <a|b> of two 2x...'complex' multidimensional pdls $a and $b in reciprocal space. For the vector-spinor field dimensions are like ri:xy:pm:nx:ny.
$psiG = RtoG($psiR, $ndims, $skip)
Transforms a $ndims-dimensional 'complex' scalar, vector or tensor field $psiR that is a function of position within the unit cell to a complex field $psiG that is a function of the reciprocal vectors. The first dimension must be 2, as the values are complex. The next $skip dimensions are skiped (0 for a scalar, 1 for a vector, 2 for a 2-tensor field). The Fourier transform is performed over the following $ndims dimensions.
$psiR = GtoR($psiG, $ndims, $skip)
The opposite transformation to RtoG. Transform a 'complex' scalar, vector or tensorial field from reciprocal to real space.
$c=lentzCF($as, $bs, $max, $small)
Compute a continued fraction a0+b1/a1+b2+... using the Lentz algorithm. $as and $bs are given in a PDL. $max is maximum number of iterations. $small is a small convergence criterium.
$b=tile($a, $nx, $ny,...)
Returns $a repeated periodically $nx times along the x direction, $ny along the y direction, etc. Useful for making plots.
@l=vectors2Dlist($f, $s, $d)
Returns a 2D vector field ready for gnuplotting from a vector field $f scaling the result by $s and decimating the field by $d. The vectors are centered on the decimated lattice points.
$c=cmatmult($a, $b)
Returns the matrix product of the complex matrices $a times $b, with signatures a(2,j,i), b(2,k,j), c(2,k,i). The first index is 2, corresponding to the real and imaginary parts, j denotes columns of a, rows of b, i denotes rows of a and of the result c, k denotes columns of b and the result c. Recall that in pdl the first (row) index is faster. May thread over extra dimensions.