From e10a52ebe817fe7ff0235c066d83f51f39d3e023 Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Fri, 10 Feb 2023 03:01:41 +0000 Subject: CTAN sync 202302100301 --- macros/latex/contrib/ut-thesis/README | 4 +- macros/latex/contrib/ut-thesis/ut-thesis.dtx | 29 +- macros/latex/contrib/ut-thesis/ut-thesis.pdf | Bin 140497 -> 135197 bytes macros/luatex/latex/lualinalg/2dvec.jpg | Bin 0 -> 17528 bytes macros/luatex/latex/lualinalg/3dvec.jpg | Bin 0 -> 17920 bytes macros/luatex/latex/lualinalg/README.txt | 24 + macros/luatex/latex/lualinalg/luacomplex.lua | 298 +++++ macros/luatex/latex/lualinalg/lualinalg.pdf | Bin 0 -> 345798 bytes macros/luatex/latex/lualinalg/lualinalg.sty | 1685 ++++++++++++++++++++++++++ macros/luatex/latex/lualinalg/lualinalg.tex | 1084 +++++++++++++++++ macros/optex/README | 6 + macros/optex/base/alloc.opm | 6 +- macros/optex/base/basic-macros.opm | 5 +- macros/optex/base/doc.opm | 20 +- macros/optex/base/f-heros.opm | 8 +- macros/optex/base/fonts-resize.opm | 2 +- macros/optex/base/fonts-select.opm | 6 +- macros/optex/base/hisyntax-c.opm | 2 +- macros/optex/base/if-macros.opm | 20 +- macros/optex/base/keyval.opm | 99 +- macros/optex/base/lists.opm | 8 +- macros/optex/base/math-macros.opm | 4 +- macros/optex/base/more-macros.opm | 28 +- macros/optex/base/optex.ini | 2 +- macros/optex/base/others.opm | 6 +- macros/optex/base/parameters.opm | 12 +- macros/optex/base/prefixed.opm | 153 +-- macros/optex/base/references.opm | 3 +- macros/optex/base/sections.opm | 2 +- macros/optex/base/slides.opm | 2 +- macros/optex/base/table.opm | 9 +- macros/optex/base/unimath-codes.opm | 265 ++-- macros/optex/base/unimath-macros.opm | 123 +- macros/optex/doc/optex-doc.pdf | Bin 1484007 -> 1505109 bytes macros/optex/doc/optex-doc.tex | 4 +- macros/optex/doc/optex-userdoc.tex | 26 +- macros/optex/pkg/math.opm | 378 ++++-- macros/xetex/latex/xduts/xduts.dtx | 244 ++-- macros/xetex/latex/xduts/xduts.pdf | Bin 333533 -> 331822 bytes 39 files changed, 4031 insertions(+), 536 deletions(-) create mode 100644 macros/luatex/latex/lualinalg/2dvec.jpg create mode 100644 macros/luatex/latex/lualinalg/3dvec.jpg create mode 100644 macros/luatex/latex/lualinalg/README.txt create mode 100644 macros/luatex/latex/lualinalg/luacomplex.lua create mode 100644 macros/luatex/latex/lualinalg/lualinalg.pdf create mode 100644 macros/luatex/latex/lualinalg/lualinalg.sty create mode 100644 macros/luatex/latex/lualinalg/lualinalg.tex (limited to 'macros') diff --git a/macros/latex/contrib/ut-thesis/README b/macros/latex/contrib/ut-thesis/README index 880fe06c31..785d74c606 100644 --- a/macros/latex/contrib/ut-thesis/README +++ b/macros/latex/contrib/ut-thesis/README @@ -5,8 +5,8 @@ as of Fall 2020: [https://www.sgs.utoronto.ca/academic-progress/program-completion/formatting] Copyright (c) 1998-2013 Francois Pitt , - 2020-2021 Jesse Knight -last updated at 13:00 (EST) on Thu 26 Aug 2021 + 2020-2023 Jesse Knight +last updated at 13:00 (EST) on Wed 08 Feb 2023 This work may be distributed and/or modified under the conditions of the LaTeX Project Public Licence, either version 1.3c of this licence diff --git a/macros/latex/contrib/ut-thesis/ut-thesis.dtx b/macros/latex/contrib/ut-thesis/ut-thesis.dtx index fa8b3a4c31..873f0bd2c5 100644 --- a/macros/latex/contrib/ut-thesis/ut-thesis.dtx +++ b/macros/latex/contrib/ut-thesis/ut-thesis.dtx @@ -5,7 +5,7 @@ %\NeedsTeXFormat{LaTeX2e}[1999/12/01] %\ProvidesClass{ut-thesis} %<*class> -[2022/06/21 v3.1.6 University of Toronto thesis class] +[2023/02/08 v3.1.7 University of Toronto thesis class] % % %<*driver> @@ -16,7 +16,7 @@ \usepackage[margin=3cm,inner=5cm]{geometry} \usepackage{xcolor} \definecolor{code}{HTML}{990033} -\definecolor{link}{HTML}{000066} +\definecolor{link}{HTML}{006699} \let\ottfamily\ttfamily \renewcommand{\ttfamily}{\color{code}\ottfamily} \renewcommand{\MacroFont}{\ttfamily\color{code}} @@ -32,7 +32,7 @@ % % \GetFileInfo{ut-thesis.dtx} % -% \title{The \texttt{ut-thesis} class +% \title{The \textit{ut-thesis} class % \thanks{\fileversion~[\filedate] CTAN repository: % \href{https://ctan.org/pkg/ut-thesis} % {\texttt{https://ctan.org/pkg/ut-thesis}}}} @@ -47,7 +47,7 @@ % \maketitle % % \begin{abstract}\noindent -% The |ut-thesis| document class implements the formatting requirements of +% The \textit{ut-thesis} document class implements the formatting requirements of % the University of Toronto School of Graduate Studies (SGS), % as of Fall 2020. % \end{abstract} @@ -57,16 +57,19 @@ % % \section{Installation}\label{inst} % -% To use the |ut-thesis| class, -% you must first make the file |ut-thesis.cls| visible to your current \LaTeX\ distribution. -% There are two ways to do this: +% There are two main options to start using the class: % \begin{itemize} -% \item \textbf{local file}: Place the file |ut-thesis.cls| in your project directory. -% This works if you don't have write access -% in the \LaTeX\ distribution, such as if you use Overleaf. -% \item \textbf{installing}: Installation steps will depend on your \LaTeX\ distribution. -% Some helpful instructions can be found +% \item \textbf{installing}: The \textit{ut-thesis} class is available +% under the major \LaTeX\ distributions (Linux: TeX Live, macOS: MacTeX, Windows: MiKTeX). +% Installation steps will depend on the distribution; some helpful information is % \href{https://en.wikibooks.org/wiki/LaTeX/Installing_Extra_Packages}{here}. +% Within TeX Live, \textit{ut-thesis} is part of the +% \href{https://packages.ubuntu.com/kinetic/all/texlive-publishers/filelist} +% {publishers} bundle, so it should be available on Overleaf. +% \item \textbf{local file}: Place the file |ut-thesis.cls| in your project directory. +% The class will only be available in this directory. +% This works if you don't have write access in the \LaTeX\ distribution, +% or if you want to use an updated version of the class. % \end{itemize} % % \section{Usage}\label{use} @@ -76,6 +79,8 @@ % % The default options produce a final copy, ready for submission to % the University of Toronto School of Graduate Studies (SGS). +% Some examples are available on +% \href{https://github.com/jessexknight/ut-thesis/tree/master/test}{GitHub}. % % \subsection{Options}\label{use:opt} % diff --git a/macros/latex/contrib/ut-thesis/ut-thesis.pdf b/macros/latex/contrib/ut-thesis/ut-thesis.pdf index 88b20d0dfb..8f055d54d0 100644 Binary files a/macros/latex/contrib/ut-thesis/ut-thesis.pdf and b/macros/latex/contrib/ut-thesis/ut-thesis.pdf differ diff --git a/macros/luatex/latex/lualinalg/2dvec.jpg b/macros/luatex/latex/lualinalg/2dvec.jpg new file mode 100644 index 0000000000..7b857ab6d0 Binary files /dev/null and b/macros/luatex/latex/lualinalg/2dvec.jpg differ diff --git a/macros/luatex/latex/lualinalg/3dvec.jpg b/macros/luatex/latex/lualinalg/3dvec.jpg new file mode 100644 index 0000000000..1f84c4044f Binary files /dev/null and b/macros/luatex/latex/lualinalg/3dvec.jpg differ diff --git a/macros/luatex/latex/lualinalg/README.txt b/macros/luatex/latex/lualinalg/README.txt new file mode 100644 index 0000000000..fc33bfedec --- /dev/null +++ b/macros/luatex/latex/lualinalg/README.txt @@ -0,0 +1,24 @@ +# Introduction +The lualinalg package is developed to perform operations on vectors and matrices defined over the field of real or complex numbers inside LaTeX documents. +It provides flexible ways for defining and displaying vectors and matrices. +No particular environment of LaTeX is required to use commands in the package. +The package is written in Lua, and tex file is to be compiled with the LuaLaTeX engine. +The time required for calculations is not an issue while compiling with LuaLaTeX. +There is no need to install Lua on the user's system as TeX distributions (TeXLive or MikTeX) come bundled with LuaLaTeX. +It may also save users' efforts to copy vectors and matrices from other software (which may not be in latex-compatible format) and to use them in a tex file. +The vectors and matrices of reasonable size can be handled with ease. +The package can be modified or extended by writing custom Lua programs. + +# License +The \verb|lualinalg| package is released under the LaTeX Project Public License v1.3c or later. +The complete license text is available at \url{http://www.latex-project.org/lppl.txt}. +It is developed in Lua. Lua is available as a certified open-source software. +Its license is simple and liberal, which is compatible with GPL. +The package makes use of \verb|complex.lua| file which is available on \url{https://github.com/davidm/lua-matrix/blob/master/lua/matrix.lua}. +It is available under the same licensing as that of Lua. +The package also loads the luamaths package, which is available under the LaTeX Project Public License v1.3c or later. +This package is loaded to use the standard mathematical functions and for computations on real numbers while performing operations on vectors and matrices. + +#Installation and Inclusion +The installation of lualinalg package is similar to plain latex package, where the .sty file is in LaTeX directory of texmf tree. +The package can be included with \usepackage{lualinalg} command in the preamble of the LaTeX document. \ No newline at end of file diff --git a/macros/luatex/latex/lualinalg/luacomplex.lua b/macros/luatex/latex/lualinalg/luacomplex.lua new file mode 100644 index 0000000000..b817ce66b6 --- /dev/null +++ b/macros/luatex/latex/lualinalg/luacomplex.lua @@ -0,0 +1,298 @@ + +--Version=1.0, Date=31-Jan-2023 +-- provides module for complex numbers + +--Contains a modified version of the file complex.lua. It is availalbe on the link https://github.com/davidm/lua-matrix/blob/master/lua/matrix.lua. This is licensed under the same terms as Lua itself. This license allows to freely copy, modify and distribute the file for any purpose and without any restrictions. + +--Licensed under the same terms as Lua itself. This license allows to freely copy, modify and distribute the file for any purpose and without any restrictions. + + + +complex = {} + +local complex_meta = {} + +local function parse_scalar(s, pos0) + local x, n, pos = s:match('^([+-]?[%d%.]+)(.?)()', pos0) + if not x then return end + if n == 'e' or n == 'E' then + local x2, n2, pos2 = s:match('^([+-]?%d+)(.?)()', pos) + if not x2 then error 'number format error' end + x = tonumber(x..n..x2) + if not x then error 'number format error' end + return x, n2, pos2 + else + x = tonumber(x) + if not x then error 'number format error' end + return x, n, pos + end +end +local function parse_component(s, pos0) + local x, n, pos = parse_scalar(s, pos0) + if not x then + local x2, n2, pos2 = s:match('^([+-]?)(i)()$', pos0) + if not x2 then error 'number format error' end + return (x2=='-' and -1 or 1), n2, pos2 + end + if n == '/' then + local x2, n2, pos2 = parse_scalar(s, pos) + x = x / x2 + return x, n2, pos2 + end + return x, n, pos +end +local function parse_complex(s) + local x, n, pos = parse_component(s, 1) + if n == '+' or n == '-' then + local x2, n2, pos2 = parse_component(s, pos) + if n2 ~= 'i' or pos2 ~= #s+1 then error 'number format error' end + if n == '-' then x2 = - x2 end + return x, x2 + elseif n == '' then + return x, 0 + elseif n == 'i' then + if pos ~= #s+1 then error 'number format error' end + return 0, x + else + error 'number format error' + end +end + +function complex.to( num ) + -- check for table type + if type( num ) == "table" then + -- check for a complex number + if getmetatable( num ) == complex_meta then + return num + end + local real,imag = tonumber( num[1] ),tonumber( num[2] ) + if real and imag then + return setmetatable( { real,imag }, complex_meta ) + end + return + end + local isnum = tonumber( num ) + if isnum then + return setmetatable( { isnum,0 }, complex_meta ) + end + if type( num ) == "string" then + local real, imag = parse_complex(num) + return setmetatable( { real, imag }, complex_meta ) + end +end + +setmetatable( complex, { __call = function( _,num ) return complex.to( num ) end } ) + + +function complex.new( ... ) + return setmetatable( { ... }, complex_meta ) +end + + +function complex.type( arg ) + if getmetatable( arg ) == complex_meta then + return "complex" + end +end + + +function complex.convpolar( radius, phi ) + return setmetatable( { radius * math.cos( phi ), radius * math.sin( phi ) }, complex_meta ) +end + +function complex.convpolardeg( radius, phi ) + phi = phi/180 * math.pi + return setmetatable( { radius * math.cos( phi ), radius * math.sin( phi ) }, complex_meta ) +end + +function complex.tostring( cx,formatstr ) + local real,imag = cx[1],cx[2] + if formatstr then + if imag == 0 then + return string.format( formatstr, real ) + elseif real == 0 then + return string.format( formatstr, imag ).."i" + elseif imag > 0 then + return string.format( formatstr, real ).."+"..string.format( formatstr, imag ).."i" + end + return string.format( formatstr, real )..string.format( formatstr, imag ).."i" + end + if imag == 0 then + return real + elseif real == 0 then + return ((imag==1 and "") or (imag==-1 and "-") or imag).."i" + elseif imag > 0 then + return real.."+"..(imag==1 and "" or imag).."i" + end + return real..(imag==-1 and "-" or imag).."i" +end + +function complex.print( ... ) + print( complex.tostring( ... ) ) +end + +function complex.polar( cx ) + return math.sqrt( cx[1]^2 + cx[2]^2 ), math.atan2( cx[2], cx[1] ) +end + +function complex.polardeg( cx ) + return math.sqrt( cx[1]^2 + cx[2]^2 ), math.atan2( cx[2], cx[1] ) / math.pi * 180 +end + +function complex.norm2( cx ) + return cx[1]^2 + cx[2]^2 +end + +function complex.abs( cx ) + return math.sqrt( cx[1]^2 + cx[2]^2 ) +end + +function complex.get( cx ) + return cx[1],cx[2] +end + + +function complex.set( cx,real,imag ) + cx[1],cx[2] = real,imag +end + +function complex.is( cx,real,imag ) + if cx[1] == real and cx[2] == imag then + return true + end + return false +end + + +function complex.copy( cx ) + return setmetatable( { cx[1],cx[2] }, complex_meta ) +end + + +function complex.add( cx1,cx2 ) + return setmetatable( { cx1[1]+cx2[1], cx1[2]+cx2[2] }, complex_meta ) +end + + +function complex.sub( cx1,cx2 ) + return setmetatable( { cx1[1]-cx2[1], cx1[2]-cx2[2] }, complex_meta ) +end + +function complex.mul( cx1,cx2 ) + return setmetatable( { cx1[1]*cx2[1] - cx1[2]*cx2[2],cx1[1]*cx2[2] + cx1[2]*cx2[1] }, complex_meta ) +end + + +function complex.mulnum( cx,num ) + return setmetatable( { cx[1]*num,cx[2]*num }, complex_meta ) +end + +function complex.div( cx1,cx2 ) + local val = cx2[1]^2 + cx2[2]^2 + return setmetatable( { (cx1[1]*cx2[1]+cx1[2]*cx2[2])/val,(cx1[2]*cx2[1]-cx1[1]*cx2[2])/val }, complex_meta ) +end + +function complex.divnum( cx,num ) + return setmetatable( { cx[1]/num,cx[2]/num }, complex_meta ) +end + + +function complex.pow( cx,num ) + if math.floor( num ) == num then + if num < 0 then + local val = cx[1]^2 + cx[2]^2 + cx = { cx[1]/val,-cx[2]/val } + num = -num + end + local real,imag = cx[1],cx[2] + for i = 2,num do + real,imag = real*cx[1] - imag*cx[2],real*cx[2] + imag*cx[1] + end + return setmetatable( { real,imag }, complex_meta ) + end + local length,phi = math.sqrt( cx[1]^2 + cx[2]^2 )^num, math.atan2( cx[2], cx[1] )*num + return setmetatable( { length * math.cos( phi ), length * math.sin( phi ) }, complex_meta ) +end + +function complex.sqrt( cx ) + local len = math.sqrt( cx[1]^2+cx[2]^2 ) + local sign = (cx[2]<0 and -1) or 1 + return setmetatable( { math.sqrt((cx[1]+len)/2), sign*math.sqrt((len-cx[1])/2) }, complex_meta ) +end + + +function complex.ln( cx ) + return setmetatable( { math.log(math.sqrt( cx[1]^2 + cx[2]^2 )), + math.atan2( cx[2], cx[1] ) }, complex_meta ) +end + +function complex.exp( cx ) + local expreal = math.exp(cx[1]) + return setmetatable( { expreal*math.cos(cx[2]), expreal*math.sin(cx[2]) }, complex_meta ) +end + + +function complex.conjugate( cx ) + return setmetatable( { cx[1], -cx[2] }, complex_meta ) +end + +function complex.round( cx,idp ) + local mult = 10^( idp or 0 ) + return setmetatable( { math.floor( cx[1] * mult + 0.5 ) / mult, + math.floor( cx[2] * mult + 0.5 ) / mult }, complex_meta ) +end + + +complex.zero = complex.new(0, 0) +complex.one = complex.new(1, 0) + + + +complex_meta.__add = function( cx1,cx2 ) + local cx1,cx2 = complex.to( cx1 ),complex.to( cx2 ) + return complex.add( cx1,cx2 ) +end +complex_meta.__sub = function( cx1,cx2 ) + local cx1,cx2 = complex.to( cx1 ),complex.to( cx2 ) + return complex.sub( cx1,cx2 ) +end +complex_meta.__mul = function( cx1,cx2 ) + local cx1,cx2 = complex.to( cx1 ),complex.to( cx2 ) + return complex.mul( cx1,cx2 ) +end +complex_meta.__div = function( cx1,cx2 ) + local cx1,cx2 = complex.to( cx1 ),complex.to( cx2 ) + return complex.div( cx1,cx2 ) +end +complex_meta.__pow = function( cx,num ) + if num == "*" then + return complex.conjugate( cx ) + end + return complex.pow( cx,num ) +end +complex_meta.__unm = function( cx ) + return setmetatable( { -cx[1], -cx[2] }, complex_meta ) +end +complex_meta.__eq = function( cx1,cx2 ) + if cx1[1] == cx2[1] and cx1[2] == cx2[2] then + return true + end + return false +end +complex_meta.__tostring = function( cx ) + return tostring( complex.tostring( cx ) ) +end +complex_meta.__concat = function( cx,cx2 ) + return tostring(cx)..tostring(cx2) +end +-- cx( cx, formatstr ) +complex_meta.__call = function( ... ) + print( complex.tostring( ... ) ) +end +complex_meta.__index = {} +for k,v in pairs( complex ) do + complex_meta.__index[k] = v +end + +return complex + diff --git a/macros/luatex/latex/lualinalg/lualinalg.pdf b/macros/luatex/latex/lualinalg/lualinalg.pdf new file mode 100644 index 0000000000..bdc2769722 Binary files /dev/null and b/macros/luatex/latex/lualinalg/lualinalg.pdf differ diff --git a/macros/luatex/latex/lualinalg/lualinalg.sty b/macros/luatex/latex/lualinalg/lualinalg.sty new file mode 100644 index 0000000000..53fe7fd688 --- /dev/null +++ b/macros/luatex/latex/lualinalg/lualinalg.sty @@ -0,0 +1,1685 @@ + +% The lualinalg package +% Authors: Chetan Shirore and Ajit Kumar +% version 1.0 +% Licensed under LaTeX Project Public License v1.3c or later. The complete license text is available at http://www.latex-project.org/lppl.txt. + + +\ProvidesPackage{lualinalg}[1.0] +\RequirePackage{xkeyval} +\RequirePackage{amsmath} +\RequirePackage{luamaths} +\RequirePackage{luacode} +\begin{luacode*} +local complex = require "luacomplex" + +-- matrices part +matrices = {} + +matrix = {} --module + +local matrix_meta = {} + +function matrix.new(matrix, rows, columns) + if type(rows) == "table" then + for i = 1, #rows do + if #rows[1] ~= #rows[i] then + error("Check input matrix.") + end + end + return setmetatable(rows, matrix_meta) + end + local mtx = {} + if columns == "I" then + for i = 1, rows do + mtx[i] = {} + for j = 1, rows do + if i == j then + mtx[i][j] = 1 + else + mtx[i][j] = 0 + end + end + end + return setmetatable(mtx, matrix_meta) + end +end + +setmetatable( + matrix, + {__call = function(...) + return matrix.new(...) + end} +) + +function matrix.add(m1, m2) + local mtx = {} + for i = 1, #m1 do + local m3i = {} + mtx[i] = m3i + for j = 1, #m1[1] do + m3i[j] = m1[i][j] + m2[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end +function matrix.sub(m1, m2) + local mtx = {} + for i = 1, #m1 do + local m3i = {} + mtx[i] = m3i + for j = 1, #m1[1] do + m3i[j] = m1[i][j] - m2[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mulnum(m1, num) + local mtx = {} + -- multiply elements with number + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] * num + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mul(m1, m2) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m2[1] do + local num = m1[i][1] * m2[1][j] + for n = 2, #m1[1] do + num = num + m1[i][n] * m2[n][j] + end + mtx[i][j] = num + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.swapRows(m1, p, q) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1[1] do + rowHold = m1[p][j] + mtx[p][j] = m1[q][j] + mtx[q][j] = rowHold + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.swapCols(m1, p, q) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1 do + rowHold = m1[j][p] + mtx[j][p] = m1[j][q] + mtx[j][q] = rowHold + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mulRow(m1, p, k) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1[1] do + mtx[p][j] = k * m1[p][j] + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mulAddRow(m1, k, p, q) + if p == q then + error("Can't operate on same row.") + end + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1[1] do + mtx[q][j] = k * (mtx[p][j]) + mtx[q][j] + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mulCol(m1, p, k) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1 do + mtx[j][p] = k * m1[j][p] + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.mulAddCol(m1, k, p, q) + if p == q then + error("Can't operate on same column.") + end + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + for j = 1, #m1 do + mtx[j][q] = k * mtx[j][p] + mtx[j][q] + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.transpose(m1) + local mtx = {} + for i = 1, #m1[1] do + mtx[i] = {} + for j = 1, #m1 do + mtx[i][j] = m1[j][i] + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.subm(m1, i1, j1, i2, j2) + local mtx = {} + for i = i1, i2 do + local _i = i - i1 + 1 + mtx[_i] = {} + for j = j1, j2 do + local _j = j - j1 + 1 + mtx[_i][_j] = m1[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.concath(m1, m2) + if #m1 ~= #m2 then + error("No. of rows must be equal.") + end + local mtx = {} + local offset = #m1[1] + for i = 1, #m1 do + mtx[i] = {} + for j = 1, offset do + mtx[i][j] = m1[i][j] + end + for j = 1, #m2[1] do + mtx[i][j + offset] = m2[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.concatv(m1, m2) + if #m1[1] ~= #m2[1] then + error("No. of columns must be equal.") + end + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + local offset = #mtx + for i = 1, #m2 do + local _i = i + offset + mtx[_i] = {} + for j = 1, #m2[1] do + mtx[_i][j] = m2[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.rows(mtx) + return #mtx +end + +function matrix.columns(mtx) + return #mtx[1] +end + +setmetatable( + matrix, + {__call = function(...) + return matrix.new(...) + end} +) + +function matrix.getelement(mtx, i, j) + if mtx[i] and mtx[i][j] then + return mtx[i][j] + end +end + +function matrix.setelement(mtx, i, j, value) + if matrix.getelement(mtx, i, j) then + mtx[i][j] = value + return value + end +end + +function matrix.invert(m1) + if #m1 ~= #m1[1] then + error("matrix not square") + end + if matrix.det(m1) == 0 then + error("matrix not invertible") + end + local mtx = {} + local idnt = matrix(#m1, "I") + mtx = matrix.subm(matrix.rref(matrix.concath(m1, idnt)), 1, #m1 + 1, #m1, #m1 + #m1) + return mtx +end + +function matrix.trace(m1) + if #m1 ~= #m1[1] then + error("matrix not square") + end + local sum = 0 + + for i = 1, #m1 do + for j = 1, #m1[1] do + if i == j then + sum = sum + m1[i][j] + end + end + end + + return sum +end + +function matrix.normF(mtx) + local result = 0 + for i = 1, #mtx do + for j = 1, #mtx[1] do + local e = mtx[i][j] + result = result + complex.abs(complex(e)) ^ 2 + end + end + return complex.sqrt(complex(result)) +end + +function matrix.normmax(mtx) + local result = 0 + for i = 1, #mtx do + for j = 1, #mtx[1] do + local e = complex.abs(complex(mtx[i][j])) + if e > result then + result = e + end + end + end + return result +end + +function matrix.norminfty(mtx) + local e = 0 + local result = 0 + for i = 1, #mtx do + local e = 0 + for j = 1, #mtx[1] do + e = e + complex.abs(complex(mtx[i][j])) + end + if e > result then + result = e + end + end + return result +end + +function matrix.norm1(mtx) + local e = 0 + local result = 0 + for i = 1, #mtx[1] do + local e = 0 + for j = 1, #mtx do + e = e + complex.abs(complex(mtx[j][i])) + end + if e > result then + result = e + end + end + return result +end + +function matrix.conjugate(m1) + local mtx = matrix.copy(m1) + for i = 1, #mtx do + for j = 1, #mtx[1] do + mtx[i][j] = complex.conjugate(complex(mtx[i][j])) + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.conjugateT(m1) + local mtx = {} + for i = 1, #m1[1] do + mtx[i] = {} + for j = 1, #m1 do + mtx[i][j] = complex.conjugate(complex(m1[j][i])) + end + end + return setmetatable(mtx, matrix_meta) +end + +function copy(x) + return type(x) == "table" and x.copy(x) or x +end + +function matrix.pow(m1, num) + assert(num == math.floor(num), "exponent not an integer") + if num == 0 then + return matrix:new(#m1, "I") + end + if num < 0 then + local rank + m1, rank = matrix.invert(m1) + if not m1 then + return m1, rank + end -- singular + num = -num + end + local mtx = matrix.copy(m1) + for i = 2, num do + mtx = matrix.mul(mtx, m1) + end + return mtx +end + +function matrix.createrandom(nrow, ncol, start, stop) + mtx = {} + for i = 1, nrow do + mtx[i] = {} + for j = 1, ncol do + mtx[i][j] = math.random(start, stop) + mtx[i][j] = mtx[i][j] + math.min(math.random(), math.abs(mtx[i][j] - start), math.abs(stop - mtx[i][j])) + end + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.process(m1) + --m1=load("return "..m1)() + return matrix.mulnum(m1, 1.0) +end + +function matrix.det(m1) + assert(#m1 == #m1[1], "matrix not square") + + local size = #m1 + + if size == 1 then + return m1[1][1] + end + + if size == 2 then + return m1[1][1] * m1[2][2] - m1[2][1] * m1[1][2] + end + + if size == 3 then + return (m1[1][1] * m1[2][2] * m1[3][3] + m1[1][2] * m1[2][3] * m1[3][1] + m1[1][3] * m1[2][1] * m1[3][2] - + m1[1][3] * m1[2][2] * m1[3][1] - + m1[1][1] * m1[2][3] * m1[3][2] - + m1[1][2] * m1[2][1] * m1[3][3]) + end + + local e = m1[1][1] + local zero = type(e) == "table" and e.zero or 0 + local norm2 = type(e) == "table" and e.norm2 or number_norm2 + + local mtx = matrix.copy(m1) + local det = 1 + + for j = 1, #mtx[1] do + local rows = #mtx + local subdet, xrow + for i = 1, rows do + local e = mtx[i][j] + if not subdet then + if e ~= zero then + subdet, xrow = e, i + end + elseif e ~= zero and math.abs(norm2(e) - 1) < math.abs(norm2(subdet) - 1) then + subdet, xrow = e, i + end + end + if subdet then + if xrow ~= rows then + mtx[rows], mtx[xrow] = mtx[xrow], mtx[rows] + det = -det + end + + for i = 1, rows - 1 do + if mtx[i][j] ~= zero then + local factor = mtx[i][j] / subdet + for n = j + 1, #mtx[1] do + mtx[i][n] = mtx[i][n] - factor * mtx[rows][n] + end + end + end + if math.fmod(rows, 2) == 0 then + det = -det + end + det = det * subdet + table.remove(mtx) + else + return det * 0 + end + end + + return det +end + +function matrix.copy(m1) + local mtx = {} + for i = 1, #m1 do + mtx[i] = {} + for j = 1, #m1[1] do + mtx[i][j] = m1[i][j] + end + end + return setmetatable(mtx, matrix_meta) +end + +norm2 = type(e) == "table" and e.norm2 or number_norm2 + +function number_norm2(x) + return x * x +end + +function matrix.op(exp) + return load("return " .. exp, exp, "t", matrices)() +end + +function matrix.rref(mtx) + local mtx = matrix.copy(mtx) + step = 1 + lead = 1 + rowCount = #mtx + columnCount = #mtx[1] + for r = 1, rowCount do + if lead > columnCount then + return mtx + end + i = r + while (mtx[i][lead] == 0) do + i = i + 1 + if (i - 1 == rowCount) then + i = r + if (columnCount == lead) then + return mtx + end + lead = lead + 1 + end + end + + if i ~= r then + mtx = matrix.swapRows(mtx, i, r) + end + + local m = mtx[r][lead] + if (mtx[r][lead] ~= 0) then + for u = 1, columnCount do + mtx[r][u] = mtx[r][u] / m + end + end + for i = 1, rowCount do + local m = mtx[i][lead] + if (i ~= r) then + for v = 1, columnCount do + mtx[i][v] = mtx[i][v] - m * mtx[r][v] + end + end + end + lead = lead + 1 + end + return mtx +end + +function matrix.rref0E(mtx, fom, dignum) + local strng = "" + truncate = truncate or 6 + local mtx = matrix.copy(mtx) + step = 1 + lead = 1 + stepCnt = 0 + rowCount = #mtx + columnCount = #mtx[1] + for r = 1, rowCount do + if lead > columnCount then + return mtx + end + i = r + while (mtx[i][lead] == 0) do + i = i + 1 + if (i - 1 == rowCount) then + i = r + if (columnCount == lead) then + if stepCnt == 0 then + stepCnt = stepCnt + 1 + strng = strng .. "Step " .. tostring(stepCnt) ".$$" .. tostring(matrix.show(mtx, fom, dignum)) + return strng + end + return strng + end + lead = lead + 1 + end + end + + if i ~= r then + mtx = matrix.swapRows(mtx, i, r) + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Interchange rows " .. + tostring(i) .. + " and " .. tostring(r) .. ".$$" .. tostring(matrix.show(mtx, fom, dignum)) .. "$$" + end + + local m = mtx[r][lead] + if (mtx[r][lead] ~= 0) then + for u = 1, columnCount do + mtx[r][u] = mtx[r][u] / m + end + if m ~= 1.0 then + if m ~= complex("1.0") then + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Divide row " .. + tostring(r) .. + " by " .. + tostring(complex.round(complex(m), dignum)) .. + ".$$" .. tostring(matrix.show(mtx, fom, dignum)) .. "$$" + end + end + end + for i = 1, rowCount do + local m = mtx[i][lead] + if (i ~= r) then + for v = 1, columnCount do + mtx[i][v] = mtx[i][v] - m * mtx[r][v] + end + if m ~= 0 then + if m ~= complex("0.0") then + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Multiply row " .. + tostring(r) .. + " by " .. + tostring(complex.round(complex(m), dignum)) .. + " and subtract it from row " .. + tostring(i) .. + ".$$" .. tostring(matrix.show(mtx, fom, dignum)) .. "$$" + end + end + end + end + lead = lead + 1 + end + return strng +end + +function matrix.GaussJordan(mtx, augmt) + local mtx = matrix.copy(mtx) + local augmt = matrix.copy(augmt) + step = 1 + lead = 1 + rowCount = #mtx + columnCount = #mtx[1] + for r = 1, rowCount do + if lead > columnCount then + return matrix.concath(mtx, augmt) + end + i = r + while (mtx[i][lead] == 0) do + i = i + 1 + if (i - 1 == rowCount) then + i = r + if (columnCount == lead) then + return matrix.concath(mtx, augmt) + end + lead = lead + 1 + end + end + + if i ~= r then + mtx = matrix.swapRows(mtx, i, r) + augmt = matrix.swapRows(augmt, i, r) + end + + local m = mtx[r][lead] + if (mtx[r][lead] ~= 0) then + for u = 1, columnCount do + mtx[r][u] = mtx[r][u] / m + end + augmt[r][1] = augmt[r][1] / m + end + for i = 1, rowCount do + local m = mtx[i][lead] + if (i ~= r) then + for v = 1, columnCount do + mtx[i][v] = mtx[i][v] - m * mtx[r][v] + end + augmt[i][1] = augmt[i][1] - m * augmt[r][1] + end + end + lead = lead + 1 + end + return matrix.concath(mtx, augmt) +end + +function matrix.gauss0E(mtx, augmt, fom, dignum) + local strng = "" + truncate = truncate or 6 + local mtx = matrix.copy(mtx) + local augmt = matrix.copy(augmt) + if matrix.columns(augmt) ~= 1 then + error("The second matrix should have only 1 column.") + end + step = 1 + lead = 1 + stepCnt = 0 + rowCount = #mtx + columnCount = #mtx[1] + for r = 1, rowCount do + if lead > columnCount then + return mtx + end + i = r + while (mtx[i][lead] == 0) do + i = i + 1 + if (i - 1 == rowCount) then + i = r + if (columnCount == lead) then + if stepCnt == 0 then + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) ".$$" .. + tostring(matrix.show(matrix.concath(mtx, augmt), fom, dignum)) + return strng + end + return strng + end + lead = lead + 1 + end + end + + if i ~= r then + mtx = matrix.swapRows(mtx, i, r) + augmt = matrix.swapRows(augmt, i, r) + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Interchange rows " .. + tostring(i) .. + " and " .. tostring(r) .. ".$$" .. tostring(matrix.show(mtx, fom, dignum)) .. "$$" + end + + local m = mtx[r][lead] + if (mtx[r][lead] ~= 0) then + for u = 1, columnCount do + mtx[r][u] = mtx[r][u] / m + end + augmt[r][1] = augmt[r][1] / m + if m ~= 1.0 then + if m ~= complex("1.0") then + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Divide row " .. + tostring(r) .. + " by " .. + tostring(complex.round(complex(m), dignum)) .. + ".$$" .. + tostring(matrix.show(matrix.concath(mtx, augmt), fom, dignum)) .. + "$$" + end + end + end + for i = 1, rowCount do + local m = mtx[i][lead] + if (i ~= r) then + for v = 1, columnCount do + mtx[i][v] = mtx[i][v] - m * mtx[r][v] + end + augmt[i][1] = augmt[i][1] - m * augmt[r][1] + if m ~= 0 then + if m ~= complex("0.0") then + stepCnt = stepCnt + 1 + strng = + strng .. + "Step " .. + tostring(stepCnt) .. + ": Multiply row " .. + tostring(r) .. + " by " .. + tostring(complex.round(complex(m), dignum)) .. + " and subtract it from row " .. + tostring(i) .. + ".$$" .. + tostring( + matrix.show(matrix.concath(mtx, augmt), fom, dignum) + ) .. + "$$" + end + end + end + end + lead = lead + 1 + end + return strng +end + +function matrix.rank(m1) + local mtx = {} + mtx = matrix.rref(m1) + rank = #mtx + for i = 1, #mtx do + if CheckEqual(mtx[i], 0) then + rank = rank - 1 + end + end + return rank +end + +function CheckEqual(Values, Number) + local CheckEqual = true + local i = 1 + + while (CheckEqual and (i <= #Values)) do + if Values[i] == Number then + i = i + 1 + else + CheckEqual = false + end + end + + return CheckEqual +end + +function matrix.replace(m1, func, ...) + local mtx = {} + for i = 1, #m1 do + local m1i = m1[i] + local mtxi = {} + for j = 1, #m1i do + mtxi[j] = func(m1i[j], ...) + end + mtx[i] = mtxi + end + return setmetatable(mtx, matrix_meta) +end + +function matrix.show(mtx, format, dig) + mtx = matrix.process(mtx) + local format = format or "bmatrix" + local dig = dig or 6 + local str = "\\begin{" .. format .. "}" + for i = 1, #mtx do + str = str .. "\t" .. complex.round(complex(mtx[i][1]), dig) + for j = 2, #mtx[1] do + str = str .. " & " .. complex.round(complex(mtx[i][j]), dig) + end + if i == #mtx then + str = str .. " \\\\ " + else + str = str .. " \\\\ " + end + end + return str .. "\\end{" .. format .. "} " +end + +matrix_meta.__tostring = function(...) + return matrix.show(...) +end + +matrix_meta.__add = function(...) + return matrix.add(...) +end + +matrix_meta.__sub = function(...) + return matrix.sub(...) +end + +matrix_meta.__mul = function(m1, m2) + if getmetatable(m1) ~= matrix_meta then + return matrix.mulnum(m2, m1) + elseif getmetatable(m2) ~= matrix_meta then + return matrix.mulnum(m1, m2) + end + return matrix.mul(m1, m2) +end + +matrix_meta.__div = function(m1, m2) + if getmetatable(m1) ~= matrix_meta then + return matrix.mulnum(matrix.invert(m2), m1) + elseif getmetatable(m2) ~= matrix_meta then + return matrix.divnum(m1, m2) + end + return matrix.div(m1, m2) +end + +matrix_meta.__unm = function(mtx) + return matrix.mulnum(mtx, -1) +end + +local option = { + ["*"] = function(m1) + return matrix.conjugate(m1) + end, + ["T"] = function(m1) + return matrix.transpose(m1) + end +} +matrix_meta.__pow = function(m1, opt) + return option[opt] and option[opt](m1) or matrix.pow(m1, opt) +end + +-- vector part + +vectors = {} + +vector = {} --module + +local vector_meta = {} + +function vector.new(vector, rows, columns, n) + if columns ~= "e" then + local tbl = {} + for i = 1, #rows do + tbl[i] = rows[i] + end + return setmetatable(tbl, vector_meta) + end + local vec = {} + if columns == "e" then + for i = 1, rows do + if i == n then + vec[i] = 1 + else + vec[i] = 0 + end + end + return setmetatable(vec, vector_meta) + end +end + +setmetatable( + vector, + {__call = function(...) + return vector.new(...) + end} +) + +function vector.add(v1, v2) + if #v1 ~= #v2 then + return error("Vectors should be of same dimension.") + end + local vec = {} + for i = 1, #v1 do + vec[i] = v1[i] + v2[i] + end + return setmetatable(vec, vector_meta) +end + +function vector.sub(v1, v2) + if #v1 ~= #v2 then + return error("Vectors should be of same dimension.") + end + local vec = {} + for i = 1, #v1 do + vec[i] = v1[i] - v2[i] + end + return setmetatable(vec, vector_meta) +end + +function vector.dot(v1, v2) + if #v1 ~= #v2 then + return error("Vectors should be of same dimension") + end + local sum = 0 + for i = 1, #v1 do + sum = sum + v1[i] * complex.conjugate(complex(v2[i])) + end + return sum +end + +function vector.mulnum(v1, num) + local vec = {} + -- multiply elements with number + for i = 1, #v1 do + vec[i] = v1[i] * num + end + return setmetatable(vec, vector_meta) +end + +function vector.sumnorm(v1) + local norm = 0 + for i = 1, #v1 do + norm = norm + complex.abs(complex(v1[i])) + end + return norm +end + +function vector.euclidnorm(v1) + return complex.sqrt(vector.dot(v1, v1)) +end + +function vector.pnorm(v1, p) + if math.floor(p) ~= math.abs(p) or p <= 1 then + return error("Invalid value of p") + end + local sum = 0 + for i = 1, #v1 do + sum = sum + complex.abs(complex(v1[i])) ^ p + end + return sum ^ (1 / p) +end + +function vector.supnorm(v1) + local result = 0 + for i = 1, #v1 do + local e = complex.abs(complex(v1[i])) + if e > result then + result = e + end + end + return result +end + +function vector.cross(v1, v2) + if #v1 ~= 3 or #v2 ~= 3 then + return error("Vectors should be of dimension 3") + end + local vec = {} + vec[1] = v1[2] * v2[3] - v1[3] * v2[2] + vec[2] = v1[3] * v2[1] - v1[1] * v2[3] + vec[3] = v1[1] * v2[2] - v1[2] * v2[1] + return setmetatable(vec, vector_meta) +end + +function vector.createrandom(n, start, stop) + start = start or 0 + stop = stop or 10 + vec = {} + for i = 1, n do + vec[i] = math.random(start, stop) + vec[i] = vec[i] + math.min(math.random(), math.abs(vec[i] - start), math.abs(stop - vec[i])) + end + return setmetatable(vec, vector_meta) +end + +function vector.getcoordinate(vec, i) + if vec[i] then + return vec[i] + end +end + +function vector.setcoordinate(vec, i, val) + if vec[i] then + vec[i] = val + return val + end +end + +function vector.getangle(v1, v2) + if #v1 ~= #v2 then + return error("Vectors should be of same dimension") + end + local x = complex.get(vector.dot(v1, v2) / (vector.euclidnorm(v1) * vector.euclidnorm(v2))) + return math.acos(mathround(x, 15)) +end + +function vector.copy(v1) + local vec = {} + for i = 1, #v1 do + vec[i] = v1[i] + end + return setmetatable(vec, vector_meta) +end + +function vector.op(exp) + return load("return " .. exp, exp, "t", vectors)() +end + +function vector.process(v1) + --v1=load("return "..v1)() + return vector.mulnum(v1, 1.0) +end + +function vector.show(vec, dig) + vec = vector.process(vec) + local dig = dig or 6 + local str = "" + for i = 1, #vec do + if i == 1 then + str = str .. complex.round(complex(vec[i]), dig) + else + str = str .. "," .. complex.round(complex(vec[i]), dig) + end + end + return str .. "" +end + +function vector.parse(vec) + local tbl = {} + for i = 1, #vec do + tbl[i] = vec[i] + end + return "(" .. table.concat(tbl, ",") .. ")" +end + +function vector.gs(inptTbl, brckt, dignum) + local brcktR = "" + brckt = brckt or "round" + if brckt == "round" then + brcktL = "(" + brcktR = ")" + end + if brckt == "square" then + brcktL = "[" + brcktR = "]" + end + if brckt == "curly" then + brcktL = "\\{" + brcktR = "\\}" + end + + local tbl = {} + local str = "" + k = #inptTbl + + if vector.euclidnorm(inptTbl[1]) ~= complex(0.0) then + tbl[1] = vector.mulnum(inptTbl[1], 1 / vector.euclidnorm(inptTbl[1])) + else + tbl[1] = vector.mulnum(inptTbl[1], 1.0) + end + setmetatable(tbl[1], vector_meta) + str = str .. "$\\left" .. brcktL .. vector.show(tbl[1], dignum) .. "\\right" .. brcktR + for i = 2, k do + tbl[i] = inptTbl[i] + setmetatable(tbl[i], vector_meta) + for j = 1, i - 1 do + setmetatable(tbl[j], vector_meta) + tbl[i] = vector.sub(tbl[i], vector.mulnum(tbl[j], vector.dot(tbl[i], tbl[j]))) + end + if vector.euclidnorm(tbl[i]) ~= complex(0.0) then + tbl[i] = vector.mulnum(tbl[i], 1 / vector.euclidnorm(tbl[i])) + end + tbl[i] = vector.mulnum(tbl[i], 1.0) + str = str .. ",\\left" .. brcktL .. vector.show(tbl[i], dignum) .. "\\right" .. brcktR + end + str = str .. "$" + return str +end + +function vector.gsX(inptTbl, brckt, dignum) + local brcktR = "" + local cnt = 1 + brckt = brckt or "round" + if brckt == "round" then + brcktL = "\\left(" + brcktR = "\\right)$$" + end + if brckt == "square" then + brcktL = "\\left[" + brcktR = "\\right]$$" + end + if brckt == "curly" then + brcktL = "\\left\\{" + brcktR = "\\right\\}$$" + end + + local tbl = {} + local tmpTbl = {} + local str = "" + k = #inptTbl + str = str .. "\\ \\newline Take given vectors as $v_1,\\ldots, v_" .. k .. "$ in order." + + if vector.euclidnorm(inptTbl[1]) ~= complex(0.0) then + tbl[1] = vector.mulnum(inptTbl[1], 1 / vector.euclidnorm(inptTbl[1])) + else + tbl[1] = vector.mulnum(inptTbl[1], 1.0) + end + setmetatable(tbl[1], vector_meta) + str = str .. "\\ \\newline Step " .. cnt .. ": $$ u_" .. cnt .. "=v_" .. cnt .. "=" + str = str .. brcktL .. vector.show(inptTbl[1], dignum) .. brcktR + str = str .. " $$ e_" .. cnt .. "=" + if vector.euclidnorm(tbl[1]) ~= complex(0.0) then + str = str .. "\\frac{u_{" .. cnt .. "}}" .. "{||u_{" .. cnt .. "}||} =" + end + str = str .. brcktL .. vector.show(tbl[1], dignum) .. brcktR + for i = 2, k do + tbl[i] = inptTbl[i] + setmetatable(tbl[i], vector_meta) + for j = 1, i - 1 do + setmetatable(tbl[j], vector_meta) + tmpTbl[i] = vector.sub(tbl[i], vector.mulnum(tbl[j], vector.dot(tbl[i], tbl[j]))) + tbl[i] = vector.sub(tbl[i], vector.mulnum(tbl[j], vector.dot(tbl[i], tbl[j]))) + end + if vector.euclidnorm(tbl[i]) ~= complex(0.0) then + tbl[i] = vector.mulnum(tbl[i], 1 / vector.euclidnorm(tbl[i])) + else + tbl[i] = vector.mulnum(tbl[i], 1.0) + end + + cnt = cnt + 1 + str = str .. " Step " .. cnt + str = str .. ": $$ u_" .. cnt .. "=" + str = str .. "v_" .. cnt .. "-\\sum_{j=1}^{" .. (cnt - 1) .. "}{{proj_{u_j}(v_" .. cnt .. ")}}=" + str = str .. brcktL .. vector.show(tmpTbl[i], dignum) .. brcktR + str = str .. " $$ e_" .. cnt .. "=" + if vector.euclidnorm(tbl[i]) ~= complex(0.0) then + str = str .. "\\frac{u_{" .. cnt .. "}}" .. "{||u_{" .. cnt .. "}||} =" + end + str = str .. brcktL .. vector.show(tbl[i], dignum) .. brcktR + end + + return str +end + +vector_meta.__tostring = function(...) + return vector.show(...) +end + +vector_meta.__add = function(...) + return vector.add(...) +end + +vector_meta.__sub = function(...) + return vector.sub(...) +end + +vector_meta.__unm = function(vec) + return vector.mulnum(vec, -1) +end + +vector_meta.__mul = function(v1, v2) + if getmetatable(v1) ~= vector_meta then + return vector.mulnum(v2, v1) + elseif getmetatable(v2) ~= vector_meta then + return vector.mulnum(v1, v2) + end + return vector.dot(v1, v2) +end + +function mathround(num, numDecimalPlaces) + local mult = 10 ^ (numDecimalPlaces or 0) + return math.floor(num * mult + 0.5) / mult +end + + +\end{luacode*} + +% matrix latex commands + +\newcommand\matrixNew[2]{% + \directlua{% + matrices['#1'] = matrix(#2) + }% +} + +% ========= KEY DEFINITIONS ========= +\define@key{matrixop}{type}{\def\mop@type{#1}} +\define@key{matrixop}{truncate}{\def\mop@truncate{#1}} + +% ========= KEY DEFAULTS ========= +\setkeys{matrixop}{type=bmatrix,truncate=6}% + +\newcommand{\matrixPrint}[2][]{% + \begingroup% + \setkeys{matrixop}{#1} + \directlua{tex.sprint(matrix.show(matrices['#2'],"\mop@type",\mop@truncate))} + % + \endgroup% +} + +\newcommand\matrixOp[2]{% + \directlua{% + matrices['#1'] = matrix.op('#2') + }% +} + + +\newcommand\matrixAdd[3]{% + \directlua{% + matrices['#1'] = matrix.add(matrices['#2'],matrices['#3']) + }% +} + +\newcommand\matrixSub[3]{% + \directlua{% + matrices['#1'] = matrix.sub(matrices['#2'],matrices['#3']) + }% +} + +\newcommand\matrixMulNum[3]{% + \directlua{% + matrices['#1'] = matrix.mulnum(matrices['#3'],#2) + }% +} + +\newcommand\matrixMul[3]{% + \directlua{% + matrices['#1'] = matrix.mul(matrices['#2'],matrices['#3']) + }% +} + +\newcommand\matrixSwapRows[4]{% + \directlua{% + matrices['#1'] = matrix.swapRows(matrices['#2'],#3,#4) + }% +} + +\newcommand\matrixSwapCols[4]{% + \directlua{% + matrices['#1'] = matrix.swapCols(matrices['#2'],#3,#4) + }% +} + +\newcommand\matrixMulRow[4]{% + \directlua{% + matrices['#1'] = matrix.mulRow(matrices['#2'],#3,#4) + }% +} + +\newcommand\matrixMulCol[4]{% + \directlua{% + matrices['#1'] = matrix.mulCol(matrices['#2'],#3,#4) + }% +} + +\newcommand\matrixMulAddRow[5]{% + \directlua{% + matrices['#1'] = matrix.mulAddRow(matrices['#2'],#4,#3,#5) + }% +} + +\newcommand\matrixMulAddCol[5]{% + \directlua{% + matrices['#1'] = matrix.mulAddCol(matrices['#2'],#4,#3,#5) + }% +} + +\newcommand\matrixTranspose[2]{% + \directlua{% + matrices['#1'] = matrix.transpose(matrices['#2']) + }% +} + +\newcommand\matrixSubmatrix[6]{% + \directlua{% + matrices['#1'] = matrix.subm(matrices['#2'],#3,#4,#5,#6) + }% +} + +\newcommand\matrixConcatH[3]{% + \directlua{% + matrices['#1'] = matrix.concath(matrices['#2'],matrices['#3']) + }% +} + +\newcommand\matrixConcatV[3]{% + \directlua{% + matrices['#1'] = matrix.concatv(matrices['#2'],matrices['#3']) + }% +} + +\newcommand\matrixNumRows[1]{% + \directlua{% + tex.sprint(tostring(matrix.rows(matrices['#1']))) + }% +} + +\newcommand\matrixNumCols[1]{% + \directlua{% + tex.sprint(tostring(matrix.columns(matrices['#1']))) + }% +} + +\newcommand\matrixGetElement[3]{% + \directlua{% + tex.sprint(tostring(matrix.getelement(matrices['#1'],#2,#3))) + }% +} + +\newcommand\matrixSetElement[4]{% + \directlua{% + matrix.setelement(matrices['#1'],#2,#3,#4) + }% +} + +\newcommand\matrixInvert[2]{% + \directlua{% + matrices['#1'] = matrix.invert(matrices['#2']) + }% +} + +\newcommand\matrixPow[3]{% + \directlua{% + matrices['#1'] = matrix.pow(matrices['#2'],#3) + }% +} + +\newcommand\matrixCreateRandom[5]{% + \directlua{% + matrices['#1'] = matrix.createrandom(#2,#3,#4,#5) + }% +} + +\newcommand\matrixDet[1]{% + \directlua{% + tex.sprint(tostring(matrix.det(matrices['#1']))) + }% +} + +\newcommand\matrixTrace[1]{% + \directlua{% + tex.sprint(tostring(matrix.trace(matrices['#1']))) + }% +} + +\newcommand\matrixNormOne[1]{% + \directlua{% + tex.sprint(tostring(matrix.norm1(matrices['#1']))) + }% +} + +\newcommand\matrixNormInfty[1]{% + \directlua{% + tex.sprint(tostring(matrix.norminfty(matrices['#1']))) + }% +} + +\newcommand\matrixNormMax[1]{% + \directlua{% + tex.sprint(tostring(matrix.normmax(matrices['#1']))) + }% +} + +\newcommand\matrixNormF[1]{% + \directlua{% + tex.sprint(tostring(matrix.normF(matrices['#1']))) + }% +} + +\newcommand\matrixCopy[2]{% + \directlua{% + matrices['#1'] = matrix.copy(matrices['#2']) + }% +} + +\newcommand\matrixRREF[2]{% + \directlua{% + matrices['#1'] = matrix.rref(matrices['#2']) + }% +} + +\newcommand\matrixConjugate[2]{% + \directlua{% + matrices['#1'] = matrix.conjugate(matrices['#2']) + }% +} + +\newcommand\matrixConjugateT[2]{% + \directlua{% + matrices['#1'] = matrix.conjugateT(matrices['#2']) + }% +} + +\newcommand\matrixRank[1]{% + \directlua{% + tex.sprint(tostring(matrix.rank(matrices['#1']))) + }% +} + +\newcommand\matrixRREFERR[1]{% + \directlua{% + tex.sprint(tostring(matrix.rref0E(matrices['#1']))) + }% +} + +\newcommand\matrixRREFE[1]{% + \directlua{% + tex.sprint(tostring(matrix.rref0E(matrices['#1']))) + }% +} + +% ========= KEY DEFINITIONS ========= +\define@key{matrixrr}{type}{\def\moprr@type{#1}} +\define@key{matrixrr}{truncate}{\def\moprr@truncate{#1}} + +% ========= KEY DEFAULTS ========= +\setkeys{matrixrr}{type=bmatrix,truncate=6}% + +\newcommand{\matrixRREFSteps}[2][]{% + \begingroup% + \setkeys{matrixrr}{#1} + \directlua{% + tex.sprint(matrix.rref0E(matrices['#2'],"\moprr@type",\moprr@truncate))} + % + \endgroup% +} + +\newcommand\matrixGaussJordan[3]{% + \directlua{% + matrices['#1'] = matrix.GaussJordan(matrices['#2'],matrices['#3']) + }% +} + +\newcommand{\matrixGaussJordanSteps}[3][]{% + \begingroup% + \setkeys{matrixrr}{#1} + \directlua{% + tex.sprint(matrix.gauss0E(matrices['#2'],matrices['#3'],"\moprr@type",\moprr@truncate))} + % + \endgroup% +} + +% vector latex commands + +\newcommand\vectorNew[2]{% + \directlua{% + vectors['#1'] = vector(#2) + }% +} + +% ========= KEY DEFINITIONS ========= +\define@key{vectorop}{truncate}{\def\vop@truncate{#1}} + +% ========= KEY DEFAULTS ========= +\setkeys{vectorop}{truncate=6}% + +\newcommand{\vectorPrint}[2][]{% + \begingroup% + \setkeys{vectorop}{#1} + \directlua{tex.sprint(vector.show(vectors['#2'],\vop@truncate))} + % + \endgroup% +} + +\newcommand\vectorParse[1]{% + \directlua{% + tex.sprint(tostring(vector.parse(vectors['#1']))) + }% +} + +\newcommand\vectorOp[2]{% + \directlua{% + vectors['#1'] = vector.op('#2') + }% +} + +\newcommand\vectorAdd[3]{% + \directlua{% + vectors['#1'] = vector.add(vectors['#2'],vectors['#3']) + }% +} + +\newcommand\vectorSub[3]{% + \directlua{% + vectors['#1'] = vector.sub(vectors['#2'],vectors['#3']) + }% +} + +\newcommand\vectorDot[2]{% + \directlua{% + tex.sprint(tostring(vector.dot(vectors['#1'],vectors['#2']))) + }% +} + +\newcommand\vectorMulNum[3]{% + \directlua{% + vectors['#1'] = vector.mulnum(vectors['#2'],#3) + }% +} + +\newcommand\vectorCross[3]{% + \directlua{% + vectors['#1'] = vector.cross(vectors['#2'],vectors['#3']) + }% +} + +\newcommand\vectorSumNorm[1]{% + \directlua{% + tex.sprint(tostring(vector.sumnorm(vectors['#1']))) + }% +} + +\newcommand\vectorEuclidNorm[1]{% + \directlua{% + tex.sprint(tostring(vector.euclidnorm(vectors['#1']))) + }% +} + +\newcommand\vectorSupNorm[1]{% + \directlua{% + tex.sprint(tostring(vector.supnorm(vectors['#1']))) + }% +} + +\newcommand\vectorpNorm[2]{% + \directlua{% + tex.sprint(tostring(vector.pnorm(vectors['#1'],#2))) + }% +} + +\newcommand\vectorCreateRandom[4]{% + \directlua{% + vectors['#1'] = vector.createrandom(#2,#3,#4) + }% +} + +\newcommand\vectorCopy[2]{% + \directlua{% + vectors['#1'] = vector.copy(vectors['#2']) + }% +} + +\newcommand\vectorGetCoordinate[2]{% + \directlua{% + tex.sprint(tostring(vector.getcoordinate(vectors['#1'],#2))) + }% +} + +\newcommand\vectorSetCoordinate[3]{% + \directlua{% + tex.sprint(tostring(vector.setcoordinate(vectors['#1'],#2,#3))) + }% +} + +\newcommand\vectorGetAngle[2]{% + \directlua{% + tex.sprint(tostring(vector.getangle(vectors['#1'],vectors['#2']))) + }% +} + +\newcommand\complexRound[2]{% + \directlua{% + tex.sprint(tostring(complex.round(complex('#1'),#2))) + }% +} + +% ========= KEY DEFINITIONS ========= +\define@key{vecrr}{brckt}{\def\voprr@brckt{#1}} +\define@key{vecrr}{truncate}{\def\voprr@truncate{#1}} + +% ========= KEY DEFAULTS ========= +\setkeys{vecrr}{brckt=round,truncate=6}% +\newcommand{\vectorGramSchmidt}[2][]{% + \begingroup% + \setkeys{vecrr}{#1} + \directlua{% + local tbl = #2 + local outTbl={} + local sum = 0 + for i=1,table.getn(tbl) do + outTbl[i] = vectors[tbl[i]] + end + + tex.sprint(vector.gs(outTbl,"\voprr@brckt",\voprr@truncate))} + % + \endgroup% +} + +\newcommand{\vectorGramSchmidtSteps}[2][]{% + \begingroup% + \setkeys{vecrr}{#1} + \directlua{% + local tbl = #2 + local outTbl={} + local sum = 0 + for i=1,table.getn(tbl) do + outTbl[i] = vectors[tbl[i]] + end + tex.sprint(vector.gsX(outTbl,"\voprr@brckt",\voprr@truncate))} + % + \endgroup% +} + +\endinput diff --git a/macros/luatex/latex/lualinalg/lualinalg.tex b/macros/luatex/latex/lualinalg/lualinalg.tex new file mode 100644 index 0000000000..fa7c9fa4ea --- /dev/null +++ b/macros/luatex/latex/lualinalg/lualinalg.tex @@ -0,0 +1,1084 @@ +\documentclass{article} +\usepackage{listings,color,parskip,booktabs,longtable,array, +hyperref,multirow,multicol,url,amsmath,amssymb,framed,graphicx} +\usepackage[top=1.1in, bottom=1.1in, left=1in, right=1in]{geometry} +\hypersetup{colorlinks,urlcolor=blue} +\lstset{frame=none, + language=[LaTeX]{TeX}, + aboveskip=3mm, + belowskip=3mm, + showstringspaces=false, + columns=flexible, + basicstyle={\ttfamily}, + numbers=none, + numberstyle=\tiny\color{gray}, + stringstyle=\color{mauve}, + breaklines=true, + breakatwhitespace=true, + tabsize=1, + upquote=true +} +\begin{document} +\title{The lualinalg Package} +\author{Chetan Shirore and Ajit Kumar} +\maketitle + +\section{Introduction} + +The \verb|lualinalg| package is developed to perform operations on vectors and matrices defined over the field of real or complex numbers inside LaTeX documents. It provides flexible ways for defining and displaying vectors and matrices. No particular environment of LaTeX is required to use commands in the package. The package is written in Lua, and tex file is to be compiled with the LuaLaTeX engine. The time required for calculations is not an issue while compiling with LuaLaTeX. There is no need to install Lua on the user's system as TeX distributions (TeXLive or MikTeX) come bundled with LuaLaTeX. It may also save users' efforts to copy vectors and matrices from other software (which may not be in latex-compatible format) and to use them in a tex file. The vectors and matrices of reasonable size can be handled with ease. The package can be modified or extended by writing custom Lua programs (Section \ref{customuse}). + +\section{Installation and License} +The installation of the \verb|lualinalg| package is similar to the plain latex package, where the \verb|.sty| file is in the LaTeX directory of the texmf tree. The package can be included with \verb|\usepackage{lualinalg}| command in the preamble of the LaTeX document. + +The \verb|lualinalg| package is released under the LaTeX Project Public License v1.3c or later. The complete license text is available at \url{http://www.latex-project.org/lppl.txt}. It is developed in Lua. Lua is available as a certified open-source software. Its license is simple and liberal, which is compatible with GPL. The package makes use of \verb|complex.lua| file which is available on \url{https://github.com/davidm/lua-matrix/blob/master/lua/matrix.lua}. It is available under the same licensing as that of Lua. The package also loads the \href{https://ctan.org/pkg/luamaths}{luamaths} package, which is available under the LaTeX Project Public License v1.3c or later. This package is loaded to use the standard mathematical functions and for computations on real numbers while performing operations on vectors and matrices. +\section{Defining vectors and performing operations on vectors} +\subsection{Defining Vectors} Vectors are defined with the \verb|\vectornew| command. +\begin{verbatim} +\vectorNew{vector name}{coordinates} +\end{verbatim} + This command has two compulsory arguments: \verb|vector name| and \verb|coordinates|. Coordinates of vectors are enclosed in curly braces. A comma separates coordinates. The complex numbers are to be enclosed in single or double quotes inside the \verb|complex()| function. The following are a few valid ways of defining vectors. +\begin{lstlisting} +\vectorNew{v1}{{1,2,3,4,5,6}} +\vectorNew{v2}{{3,6,complex('6+6i')}} +\end{lstlisting} +The standard vector of dimension \(n \) with \(i^{th}\) coordinate \(1\) can be produced by using the following command. +\begin{lstlisting} +\vectorNew{e}{n,'e',i} +\end{lstlisting} +For example, the following commands +\begin{lstlisting} +\vectorNew{e_1}{3,'e',1} +\(e_1=\left(\vectorPrint{e}\right)\) +\end{lstlisting} +output to \(e_1 = \left(1.0,0.0,0.0\right) \). +\subsection{Commands for operations on vectors} +Table \ref{tbl:luavector} lists commands for operations on vectors. +\begin{longtable}{m{7cm}m{7cm}} +\toprule +\multicolumn{1}{c}{\textcolor{blue}{Command Format}} & \multicolumn{1}{c}{\textcolor{blue}{Description}} \\ +\toprule +\begin{lstlisting} +\vectorPrint[truncate]{vector} +\end{lstlisting} & Prints vector. Accepts one \emph{optional} argument: \verb|truncate|. It specifies the number of digits up to which vector coordinates must be truncated. The value of \verb|truncate| may be 0,1,2,\ldots\\ +\midrule +\begin{lstlisting} +\vectorGetCoordinate{vector}{i} +\end{lstlisting} +& +Gives the \(i^{th}\) coordinate of vector. \\ +\midrule + \begin{lstlisting} +\vectorSetCoordinate +{vector}{i}{val} +\end{lstlisting} +& +Sets the \(i^{th}\) coordinate of vector as \verb|val|. \\ +\midrule +\begin{lstlisting} +\vectorCopy{v}{w} +\end{lstlisting}& +Defines a new vector \(v\) obtained by copying coordinates of vector \(w\). \\ +\midrule +\begin{lstlisting} +\vectorAdd{vector}{v1}{v2} +\end{lstlisting}& +Defines a new vector as the addition of vectors \(v1\) and \(v2\). Both vectors \(v1\) and \(v2\) should be of the same dimension. The addition is done coordinate-wise.\\ +\midrule + \begin{lstlisting} +\vectorSub{vector}{v1}{v2} +\end{lstlisting}& +Defines a new vector as the subtraction of vectors \(v1\) and \(v2\). Both vectors \(v1\) and \(v2\) should be of the same dimension. The subtraction is done coordinate-wise. \\ +\midrule + \begin{lstlisting} +\vectorMulNum{vector}{v}{num} +\end{lstlisting}& +Defines a new vector obtained by multiplying each coordinate of a vector by number \verb|num|. It can be a real or complex number (scalar). \\ +\midrule +\begin{lstlisting} +\vectorDot{v}{w} +\end{lstlisting}& +Gives the dot product of two vectors: \(v\) and \(w\). If \(v=\left(v_1, \ldots, v_n \right)\) and \(w =\left(w_1, \ldots, w_n \right)\) are defined over the field of real numbers, then it is evaluated as \(v_1\cdot w_1 + \cdots + v_n \cdot w_n\). If they are defined over the field of complex numbers, then it is evaluated as \(v_1\cdot \bar{w_1} + \cdots + v_n \cdot \bar{w_n}\). \(\bar{w_i}\) denotes the complex conjugate of complex number \(w_i\). \\ +\midrule +\begin{lstlisting} +\vectorCross{vector}{v}{w} +\end{lstlisting}& +Defines a new vector obtained by taking the cross product of vectors \(v\) and \(w\) of dimension 3. If \(v=\left(v_1, v_2, v_3 \right)\) and \(w =\left(w_1, w_2, w_3 \right)\), then the cross product of these two vectors is the vector \((v_2w_3-v_3w_2, v_3w_1-v_1w_3,\) \( v_1w_2-v_2w_1 ) \). \\ +\midrule + \begin{lstlisting} +\vectorSumNorm{v} +\end{lstlisting}& +Calculates the sum norm of a vector \(v\). If \(v=\left(v_1, \ldots, v_n \right)\) then it is given by \(|v_1| + \cdots + |v_n| \). \\ +\midrule + \begin{lstlisting} +\vectorEuclidNorm{v} +\end{lstlisting}& +Calculates the Euclidean norm of a vector \(v\). If \(v=\left(v_1, \ldots, v_n \right)\) then it is given by \(\sqrt{|v_1|^2 + \cdots + |v_n|^2} \). \\ +\midrule + \begin{lstlisting} +\vectorpNorm{v} +\end{lstlisting}& +Calculates the \(p\) \((p > 1)\) norm of a vector \(v\). If \(v=\left(v_1, \ldots, v_n \right)\) then it is given by \(\sqrt[p]{|v_1|^2 + \cdots + |v_n|^2} \). \\ +\midrule +\begin{lstlisting} +\vectorSupNorm{v} +\end{lstlisting}& +Calculates the sup norm of a vector \(v\). If \(v=\left(v_1, \ldots, v_n \right)\) then it is given by \(\max\{|v_1| , \ldots , |v_n| \} \). \\ +\midrule + \begin{lstlisting} +\vectorCreateRandom{v}{n}{a}{b} +\end{lstlisting}& +Creates a new vector \(v\) of dimension \(n\) with coordinates as random numbers from the interval \([a,b]\). \\ +\midrule +\begin{lstlisting} +\vectorOp{vector}{expression} +\end{lstlisting}& +Defines a new vector obtained by evaluating an expression. The expression supports all standard operations such as \(+,-,* \). \\ +\midrule + \begin{lstlisting} + \vectorGetAngle{v}{w} +\end{lstlisting}& +Gives the angle between two vectors \(v\) and \(w\) in radians. If \(v\) and \(w \) are defined over the field of real numbers, then it is evaluated as \(\cos^{-1}\left(\frac{v \cdot w}{|v| |w|}\right)\). If they are defined over the field of complex numbers, then it is evaluated as \(\cos^{-1}\left(\frac{Re (v \cdot w) }{|v| |w|}\right)\). Here \(v \cdot w\) denotes the dot product of vectors \(v\) and \(w\), \(Re (v \cdot w)\) denotes real part of the dot product \(v \cdot w\), and \(|v|\) and \(|w|\) denote Euclidean norms of vectors \(v\) and \(w\) respectively. \\ +\midrule + \begin{lstlisting} +\vectorParse{vector} +\end{lstlisting}& +Parses the coordinates of a vector defined over the field of real numbers. The command helps to plot vectors with different packages. \\ +\midrule +\begin{lstlisting} +\vectorGramSchmidt[brckt, +truncate]{list of vectors} +\end{lstlisting} & Performs Gram Schmidt orthogonalisation process on a list of vectors. Accepts two \emph{optional} arguments: \verb|brckt| and \verb|truncate|. The \verb|brckt| is type of parenthesis to be used for displaying vectors. It can be `round', `square' or `curly'. The truncate is number of digits up to which vector coordinates are to be truncated. The value of \verb|truncate| can be 0,1,2,\ldots\\ +\midrule +\begin{lstlisting} +\vectorGramSchmidtSteps[brckt, +truncate]{list of vectors} +\end{lstlisting} & Performs Gram Schmidt orthogonalisation process on a list of vectors in a step-by-step manner. Accepts two \emph{optional} arguments: \verb|brckt| and \verb|truncate|. The \verb|brckt| is type of parenthesis to be used for displaying vectors. It can be `round', `square' or `curly'. The truncate is number of digits up to which vector coordinates are to be truncated. The value of \verb|truncate| can be 0,1,2,\ldots\\ +\bottomrule \\ +\caption{Commands for operations on vectors} +\label{tbl:luavector} +\end{longtable} +\subsection{Illustrations of commands for operations on vectors} +The following commands define vectors \(v,w,x,\) and \(y\). +\begin{lstlisting} +\vectorNew{v}{{1,2,complex('3+3i')}} +\vectorNew{w}{{3,6,complex('6+6i')}} +\vectorNew{x}{{1.12345678,6,complex('6+6i')}} +\vectorNew{y}{{1,2,3}} +\end{lstlisting} +Table \ref{tbl:illluavector} illustrates various operations on vectors \(v,w,x\) and \(y\). +\begin{longtable}{lc} +\toprule +Commands & Output Produced\\ +\toprule +\begin{lstlisting} +\(v=\left(\vectorPrint{v}\right)\) +\(w=\left(\vectorPrint{w}\right)\) +\end{lstlisting} & +\(v=\left(1.0,2.0,3.0+3.0i\right)\) \\ +& +\(w=\left(3.0,6.0,6.0+6.0i\right)\) +\\ +\midrule +\begin{lstlisting} +\(x=\left(\vectorPrint +[truncate=3]{x}\right)\) +\end{lstlisting} & +\(x=\left(1.123,6.0,6.0+6.0i\right)\) +\\ +\midrule +\begin{lstlisting} +third coordinate of vector +\(v = \vectorGetCoordinate{v}{3}\) +\end{lstlisting} & +third coordinate of vector \(v = 3 + 3i\) +\\ +\midrule +\begin{lstlisting} +\(y = \vectorCopy{y}{w}\) +\(\left(\vectorPrint{y}\right)\) +\end{lstlisting} & +\(y = \left( 3.0,6.0,6.0+6.0i\right)\) +\\ +\midrule +\begin{lstlisting} +new third coordinate of vector +\(y = \vectorSetCoordinate{y}{3}{9.3}\) +\(y=\left(\vectorPrint{y}\right)\) +\end{lstlisting} & +new third coordinate of vector \(y = 9.3\) \\ +& \(y = \left( 3.0,6.0,9.3\right)\) +\\ +\midrule +\begin{lstlisting} +\vectorAdd{v1}{v}{w} +\(v1 = v+w =\left(\vectorPrint{v1}\right)\) +\end{lstlisting} & +\(v1 = v+w =\left(4.0, 8.0, 9.0 + 9.0i\right)\) +\\ +\midrule +\begin{lstlisting} +\vectorSub{v2}{v}{w} +\(v2 = v-w =\left(\vectorPrint{v2}\right)\) +\end{lstlisting} & +\(v2 = v-w =\left(-2.0, -4.0, -3.0 -3.0i\right)\) +\\ +\midrule +\begin{lstlisting} +\vectorMulNum{v3}{v}{complex('3+i')} +\(v3 = 3v =\left(\vectorPrint{v3}\right)\) +\end{lstlisting} & +\(v3 = 3v =\left(3.0 + i, 6.0 + 2.0i, 6.0 + 12.0i\right)\) +\\ +\midrule +\begin{lstlisting} +\vectorDot{v}{w} +\(v \cdot w =\vectorDot{v}{w}\) +\end{lstlisting} & +\(v \cdot w = 51\) +\\ +\midrule +\begin{lstlisting} +\vectorCross{v4}{v}{w} +\(v \times w =\left(\vectorPrint{v4}\right)\) +\end{lstlisting} & +\(v \times w = \left(-6.0 - 6.0i, 3.0 + 3.0i, 0.0\right)\) +\\ +\midrule +\begin{lstlisting} + Sum norm of a vector \(v = \vectorSumNorm{v}\) +\end{lstlisting} & + Sum norm of a vector \(v = 7.2426406871193\) +\\ +\midrule +\begin{lstlisting} +Euclidean norm of a vector + \(v = \vectorEuclidNorm{v}\) +\end{lstlisting} & +Euclidean norm of a vector \(v = 4.7958315233127\) +\\ +\midrule +\begin{lstlisting} +p norm of a vector \(v = \vectorpNorm{v}{3}\) +\end{lstlisting} & +p norm of a vector \(v = 4.4031577258332\) +\\ +\midrule +\begin{lstlisting} +Sup norm of a vector \(v = \vectorSupNorm{v}\) +\end{lstlisting} & +Sup norm of a vector \(v = 4.2426406871193\) +\\ +\midrule +\begin{lstlisting} +\vectorCreateRandom{v5}{3}{9}{90} +\(v5 =\left(\vectorPrint{v5}\right)\) +\end{lstlisting} & +\(v5 =\left(18.290405, 23.356018, 49.966278\right)\) +\\ +\midrule +\begin{lstlisting} +\vectorOp{v6}{v+w-2*v} +\(v6 =\left(\vectorPrint{v7}\right)\) +\end{lstlisting} & +\(v6=\left(2.0, 4.0, 27.0 + 27.0i \right)\) +\\ +\midrule +\begin{lstlisting} + angle between vector \(v\) and \(w\) is + \( \vectorGetAngle{v}{w}\). +\end{lstlisting} & +angle between vector \(v\) and \(w\) is + \( 0.32823410158508\). +\\ +\midrule +\begin{lstlisting} +\vectorParse{y} +\end{lstlisting} & +\(\left(1,2,3 \right)\) +\\ +\bottomrule \\ +\caption{Illustration of commands for operations on vectors} +\label{tbl:illluavector} +\end{longtable} +The package has commands for performing Gram Schmidt Orthogonalisation process. It can also produce the computations in a step-by step manner. +\begin{framed} +\begin{lstlisting}[label={code:luavecgs}, caption={Gram Schmidt Orthogonalisation process in the lualinalgpackage}] +\vectorNew{v1}{{1,2,3}} +\vectorNew{v2}{{4,5,6}} +\vectorNew{v3}{{7,8,90}} +\[v1=\left(\vectorPrint{v1}\right)\] +\[v2=\left(\vectorPrint{v2}\right)\] +\[v3=\left(\vectorPrint{v3}\right)\] +Gram Schmidt on \(v1,v2,v3\): \vectorGramSchmidt[brckt=round,truncate=3]{{'v1','v2','v3'}} +\vectorGramSchmidtSteps[brckt=round,truncate=3]{{'v1','v2','v3'}} +\end{lstlisting} +\end{framed} +Listing \ref{code:luavecgs} outputs the following. +\begin{framed} +\[v1=\left(1,2,3\right)\] +\[v2=\left(4,5,6\right)\] +\[v3=\left(7,8,90\right)\] +Gram Schmidt on \(v1,v2,v3\): $\left(0.267,0.535,0.802\right),\left(0.873,0.218,-0.436\right),\left(0.408,-0.816,0.408\right)$ + +Take given vectors as $v_1,\ldots, v_3$ in order.\ \newline Step 1: $$ u_1=v_1=\left(1.0,2.0,3.0\right)$$ $$ e_1=\frac{u_{1}}{||u_{1}||} =\left(0.267,0.535,0.802\right)$$ Step 2: $$ u_2=v_2-\sum_{j=1}^{1}{{proj_{u_j}(v_2)}}=\left(1.714,0.429,-0.857\right)$$ $$ e_2=\frac{u_{2}}{||u_{2}||} =\left(0.873,0.218,-0.436\right)$$ Step 3: $$ u_3=v_3-\sum_{j=1}^{2}{{proj_{u_j}(v_3)}}=\left(13.5,-27.0,13.5\right)$$ $$ e_3=\frac{u_{3}}{||u_{3}||} =\left(0.408,-0.816,0.408\right)$$ +\end{framed} + +In addition to \verb|\mathRound|, the command \verb|complexRound| is also available. It has the following syntax. +\begin{verbatim} +\complexRound{complex number}{number of decimal places} +\end{verbatim} + +This command has two compulsory arguments. The complex number and number of decimal places to which number should be rounded off. For example, + \verb| \complexRound{3.3333666+6.777666i}{3}| outputs to \(3.333+6.778i\). This command can be nested with other commands in the package. + +\subsection{Plotting vectors} +The \verb|lualinalg| package can be used with other packages that have facility to plot vectors defined over the field of real numbers in 2 or 3 dimensions. Listing \ref{code:luavecplot} illustrates plotting of vectors in 2-D plane by using \verb|lualinalg| and \verb|tikz| package. +\begin{lstlisting}[label={code:luavecplot}, caption={Plotting vectors in 2-dimensions with the lualinalg and tikz packages}] +\begin{document} +\tdplotsetmaincoords{0}{0} +\begin{tikzpicture}[scale=1, + tdplot_main_coords, + axis/.style={->,blue,thick}, + vector/.style={-stealth,red,very thick}, + vector guide/.style={dashed,red,thick}] +\vectorNew{o}{{0,0}} +\vectorNew{e1}{{4,0}} +\vectorNew{e2}{{0,4}} +\vectorNew{f}{{2,1}} +\vectorNew{g}{{1,2}} +% Axes +\draw [axis] \vectorParse{o}-- \vectorParse{e1} node [below left] {$x$}; +\draw [axis] \vectorParse{o}-- \vectorParse{e2} node [right] {$y$}; +% Plotting Vectors +\draw [vector] \vectorParse{o} --\vectorParse{f}; +\draw [vector] \vectorParse{o} --\vectorParse{g}; +\vectorOp{h}{f+g} +\draw [vector] \vectorParse{o} --\vectorParse{h}; +\draw [vector,dashed,black] \vectorParse{f} --\vectorParse{h}; +\draw [vector,dashed,black] \vectorParse{g} --\vectorParse{h}; +% Labels + \node [below right] at \vectorParse{f} {$f$}; + \node [above left] at \vectorParse{g} {$g$}; +\node [above left] at \vectorParse{h} {$f+g$}; + \draw[vector guide, black] \vectorParse{h} -- (\vectorGetCoordinate{h}{1},0) node [below] {$x=\vectorGetCoordinate{h}{1}$}; + \draw[vector guide, black] \vectorParse{h} -- (0,\vectorGetCoordinate{h}{2}) node [left] {$y=\vectorGetCoordinate{h}{2}$}; +\end{tikzpicture} +\end{document} +\end{lstlisting} +Listing \ref{code:luavecplot} produces figure \ref{fig:2dvecplot}. +\begin{figure}[!ht] % or [H] to turn off float + \centering + \includegraphics[scale=0.9]{2dvec.jpg} + \caption{Plotting of 3-D Vectors with lualinalg and tikz packages} + \label{fig:2dvecplot} +\end{figure} +Listing \ref{code:luavecplot2} illustrates plotting of vectors in 3-D plane by using \verb|lualinalg| and \verb|tikz| package. +\begin{lstlisting}[label={code:luavecplot2}, caption={Plotting vectors in 3-dimensions with the lualinalg and tikz packages}] +\documentclass{article} +\usepackage{tikz,tikz-3dplot,lualinalg} +\begin{document} +\tdplotsetmaincoords{60}{120} +\begin{tikzpicture}[scale=1, + tdplot_main_coords, + axis/.style={->,blue,thick}, + vector/.style={-stealth,red,very thick}, + vector guide/.style={dashed,red,thick}] +\vectorNew{o}{{0,0,0}} +\vectorNew{e1}{{3,0,0}} +\vectorNew{e2}{{0,5,0}} +\vectorNew{e3}{{0,0,4}} +\vectorNew{f}{{2,2,0}} +\vectorNew{g}{{-1,2,2}} +% Axes +\draw [axis] \vectorParse{o}-- \vectorParse{e1} node [below left] {$x$}; +\draw [axis] \vectorParse{o}-- \vectorParse{e2} node [right] {$y$}; +\draw [axis] \vectorParse{o}-- \vectorParse{e3} node [above] {$z$}; +% Plotting Vectors +\draw [vector] \vectorParse{o} --\vectorParse{f}; +\draw [vector] \vectorParse{o} --\vectorParse{g}; +\vectorOp{h}{f+g} +\draw [vector] \vectorParse{o} --\vectorParse{h}; +% Labels + \node [below right] at \vectorParse{f} {$f$}; + \node [above left] at \vectorParse{g} {$g$}; +\node [right] at \vectorParse{h} {$f+g$}; + \draw[vector guide, black] \vectorParse{h} -- (\vectorGetCoordinate{h}{1},0,0) node [left] {$x=\vectorGetCoordinate{h}{1}$}; + \draw[vector guide, black] \vectorParse{h} -- (0,\vectorGetCoordinate{h}{2},0) node [below] {$y=\vectorGetCoordinate{h}{2}$}; + \draw[vector guide, black] \vectorParse{h} -- (0,0,\vectorGetCoordinate{h}{3}) node [left] {$z=\vectorGetCoordinate{h}{3}$}; +\end{tikzpicture} +\end{document} +\end{lstlisting} + +Listing \ref{code:luavecplot2} produces figure \ref{fig:3dvecplot}. +\begin{figure}[!ht] % or [H] to turn off float + \centering + \includegraphics[scale=0.9]{3dvec.jpg} + \caption{Plotting of Vectors with lualinalg and tikz packages} + \label{fig:3dvecplot} +\end{figure} + +\section{Defining matrices and operations on matrices} +Matrices are defined with the \verb|\matrixNew| command. +\begin{lstlisting} +\matrixNew{matrix name}{row entries} +\end{lstlisting} +This command has two compulsory arguments: \verb|matrix name| and \verb|row entries|. Each row of the matrix is enclosed in curly brackets. A comma separates numbers in rows. Rows are also separated by a comma. The whole matrix is then enclosed in curly brackets. The complex numbers are to be enclosed in single or double quotes inside the parenthesis of the \verb|complex()| function. The following are a few valid ways of defining matrices. + +\begin{lstlisting} +\def\n{{{1,2,3},{4,5,6},{7,8,complex('9+3i')}}} +\def\s{{{1,2,3},{4,5,6},{7,8,10}}} +\matrixNew{m}{\n} +\matrixNew{n}{\s} +% an alternative way +\matrixNew{m}{{{1,2,3},{4,5,6},{7,8,complex('9+3i')}}} +\matrixNew{n}{{{1,2,3},{4,5,6},{7,8,10}}} +\end{lstlisting} + +The identity matrix can be defined as well by using the \verb|\matrixNew| command. For example, the following commands +\begin{lstlisting} +\matrixNew{mtx}{3,'I'} +I = \(\matrixPrint{mtx}\) +\end{lstlisting} +output to +\[I = \begin{bmatrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0\\\end{bmatrix} \] + +\subsection{Commands for operations on matrices} +Table \ref{tbl:luamtxcmd} lists all commands for operations on matrices in the \verb|lualinalg| package. +\begin{longtable}{m{7cm}m{7cm}} +\toprule + \multicolumn{1}{c}{\textcolor{blue}{Command Format}} & \multicolumn{1}{c}{\textcolor{blue}{Description}} \\ +\toprule +\multicolumn{2}{c}{Printing Matrices}\\ +\midrule +\begin{lstlisting} +\matrixPrint[type,truncate]{mtx} +\end{lstlisting} & Prints matrix. Accepts two \emph{optional} arguments: \verb|type| and \verb|truncate|. The \verb|type| may be one of the values \verb|pmatrix,bmatrix, vmatrix,Vmatrix|. +The default type is \verb|bmatrix|. The \verb|truncate| specifies the number of digits up to which matrix entries are to be truncated. The value of \verb|truncate| may be 0,1,2,\ldots.\\ +\midrule +\multicolumn{2}{c}{Some parameters of defined matrices} \\ +\midrule +\begin{lstlisting} +\matrixNumRows{matrix} +\end{lstlisting} & +Gives the number of rows in a matrix.\\ +\midrule +\begin{lstlisting} +\matrixNumCols{matrix} +\end{lstlisting}& +Gives the number of columns in a matrix.\\ +\midrule +\begin{lstlisting} +\matrixGetElement{matrix}{i}{j} +\end{lstlisting} +& +Gives an entry of matrix in the \(i^{th} \) row and the \(j^{th} \) column. \\ +\midrule +\multicolumn{2}{c}{Algebraic operations on matrices} \\ +\midrule + \begin{lstlisting} +\matrixAdd{matrix}{m1}{m2} +\end{lstlisting}& +Defines a new matrix as the addition of matrices m1 and m2. The second matrix may have more rows and\textbackslash or columns.\\ +\midrule + \begin{lstlisting} +\matrixSub{matrix}{m1}{m2} +\end{lstlisting}& +Defines a new matrix as the subtraction of matrices m1 and m2. The second matrix may have more rows and\textbackslash or columns.\\ +\midrule + \begin{lstlisting} +\matrixMulNum{matrix}{number}{m1} +\end{lstlisting}& +Defines a new matrix obtained by multiplying each entry of matrix m1 by s real or complex number. \\ +\midrule +\begin{lstlisting} +\matrixMul{matrix}{m1}{m2} +\end{lstlisting}& +Defines a new matrix obtained by multiplying matrix m1 by matrix m2. The number of rows in matrix m2 must equal the number of columns in matrix m1.\\ +\midrule + \begin{lstlisting} +\matrixPow{matrix}{m1}{power} +\end{lstlisting}& +Defines a new matrix obtained by taking the \(i^{th}\) power of matrix m11 (multiplying matrix1 \(i\) times with itself). \\ +\midrule + \begin{lstlisting} +\matrixInvert{matrix}{matrix1} +\end{lstlisting}& +Defines a new matrix obtained by taking the inverse of matrix1. It throws an error if matrix is not invertible. \\ +\midrule +\begin{lstlisting} +\matrixTrace{matrix} +\end{lstlisting}& +Gives the trace (sum of diagonal entries) of a square matrix. It throws an error if the matrix is not square. \\ +\midrule + +\begin{lstlisting} +\matrixConjugate{matrix}{m1} +\end{lstlisting}& +Defines a new matrix obtained by taking the complex conjugate of each entry of matrix m1. \\ +\midrule + \begin{lstlisting} +\matrixConjugateT{matrix}{m1} +\end{lstlisting}& +Defines a new matrix obtained by taking the transpose of matrix m1 and then the complex conjugate of each matrix entry. \\ +\midrule +\begin{lstlisting} +\matrixNormOne{matrix} +\end{lstlisting}& +Calculates the norm1 of a matrix. For matrix \(A\) of size \(m \times n\), it is given by +\[ \|A\|_{1}=\max _{1 \leqslant j \leqslant n} \sum_{i=1}^{m}\left|a_{i j}\right| \] \\ +\midrule +\begin{lstlisting} +\matrixNormInfty{matrix} +\end{lstlisting}& +Calculates the infinity norm of a matrix. For matrix \(A\) of size \(m \times n\), it is given by +\[ \|A\|_{\infty}=\max _{1 \leqslant i \leqslant m} \sum_{j=1}^{n}\left|a_{i j}\right| \] \\ +\midrule +\begin{lstlisting} +\matrixNormMax{matrix} +\end{lstlisting}& +Calculates the max norm of a matrix. For matrix \(A\) of size \(m \times n\), it is given by +\[ \|A\|_{\max }=\max _{i,j}\left|a_{i j}\right| \] \\ +\midrule + \begin{lstlisting} +\matrixNormF{matrix} +\end{lstlisting}& +Calculates the Frobenius norm of a matrix. For matrix \(A\) of size \(m \times n\), it is given by +\[\|A\|_{F}=\sqrt{\sum_{i=1}^{m} \sum_{j=1}^{n}\left|a_{i j}\right|^{2}} \] \\ +\midrule + \begin{lstlisting} +\matrixRank{matrix} +\end{lstlisting}& +Gives the rank of matrix \(m\). It also supports matrices of complex numbers. \\ +\midrule + \begin{lstlisting} +\matrixDet{matrix} +\end{lstlisting}& +Gives the determinant of matrix \(m\). It also supports matrices of complex numbers. \\ +\midrule + \begin{lstlisting} +\matrixTranspose{matrix}{m1} +\end{lstlisting}& +Defines a new matrix obtained by taking the transpose of matrix m1. \\ +\midrule + \begin{lstlisting} +\matrixSetElement{matrix}{i}{j}{val} +\end{lstlisting} +& +Set entry of a matrix in the \(i^{th} \) row and \(j^{th} \) column as \verb|val|. \\ +\midrule + \begin{lstlisting} +\matrixSubmatrix{sm}{m}{i}{j}{k}{l} +\end{lstlisting}& +Defines a new matrix sm obtained by taking a submatrix of matrix m. Here \(i,j\) denotes the start row and start column, and \(k,l\) denotes the end row and end column for obtaining the submatrix. \\ +\midrule + \begin{lstlisting} +\matrixConcatH{matrix}{m1}{m2} +\end{lstlisting}& +Defines a new matrix obtained by augmenting matrix m1 with matrix m2 horizontally. \\ +\midrule + \begin{lstlisting} +\matrixConcatV{matrix}{m1}{m2} +\end{lstlisting}& +Defines a new matrix obtained by augmenting matrix m1 with matrix m2 vertically. \\ +\midrule +\begin{lstlisting} +\matrixOp{matrix}{expression} +\end{lstlisting}& +Defines a new matrix obtained by evaluating an expression. The expression supports all standard operations such as \(+,*, \) \^ \ . \\ +\midrule +\begin{lstlisting} +\matrixCopy{matrix}{matrix1} +\end{lstlisting}& +Defines a new matrix obtained by copying values from matrix1. \\ +\midrule + \begin{lstlisting} +\matrixCreateRandom +{m}{i}{j}{k}{l} +\end{lstlisting}& +Creates a new matrix m with random numbers. Here \(i,j\) denotes the number of rows and columns, and \(k, l\) denotes the start and end integers between which random numbers are generated. \\ +\midrule +\multicolumn{2}{c}{Elementary row operations on matrices} \\ +\midrule + \begin{lstlisting} +\matrixSwapRows{mtx}{m1}{i}{j} +\end{lstlisting}& +Defines a new matrix mtx obtained by swapping the \(i^{th}\) and \(j^{th}\) rows of matrix m1. \\ +\midrule + \begin{lstlisting} +\matrixMulRow{matrix}{m}{i}{no} +\end{lstlisting}& +Defines a new matrix obtained by multiplying the \(i^{th}\) row of matrix1 by a real or complex number. \\ +\midrule +\begin{lstlisting} +\matrixMulAddRow{mtx}{m}{i}{no}{j} +\end{lstlisting}& +Defines a new matrix mtx obtained by multiplying the \(i^{th}\) row of matrix1 by a real or complex number and adding it to the \(j^{th}\) row. \\ +\midrule +\multicolumn{2}{c}{Elementary column operations on matrices} \\ +\midrule +\begin{lstlisting} +\matrixSwapCols{mtx}{m}{i}{j} +\end{lstlisting}& +Defines a new matrix mtx obtained by swapping the \(i^{th}\) and \(j^{th}\) columns of matrix m. \\ +\midrule +\begin{lstlisting} +\matrixMulCol{matrix}{m}{i}{no} +\end{lstlisting}& +Defines a new matrix obtained by multiplying the \(i^{th}\) column of matrix1 by a real or complex number. \\ +\midrule + \begin{lstlisting} +\matrixMulAddCol{mtx}{m}{i}{no}{j} +\end{lstlisting}& +Defines a new matrix mtx obtained by multiplying the \(i^{th}\) column of matrix1 by a real or complex number and adding it to the \(j^{th}\) column. \\ +\midrule +\multicolumn{2}{c}{Reduced row echelon form of matrix} \\ +\midrule + \begin{lstlisting} +\matrixRREF{matrix}{matrix1} +\end{lstlisting}& +Defines a new matrix obtained by taking the reduced row echelon form of matrix1. It supports matrices of complex numbers as well. \\ +\midrule +\begin{lstlisting} +\matrixRREFSteps[type,truncate] +{matrix} +\end{lstlisting}& +Obtains reduced row echelon form of matrix in a step-by-step manner. The command has two optional parameters \verb|type| and \verb|truncate|. It supports matrices with complex numbers as well. \verb|type| may be one of the values \verb|pmatrix,bmatrix, vmatrix,Vmatrix|. +The default type is \verb|bmatrix|. \verb|truncate| specifies number of digits up to which matrix entries are to be truncated. \verb|truncate| may be 0,1,2,\ldots. \\ +\midrule +\multicolumn{2}{c}{Gauss-Jordan Elimination} \\ +\midrule +\begin{lstlisting} +\matrixGaussJordan{matrix} +{m1}{m2} +\end{lstlisting}& +Defines new matrix obtained by performing Gauss-Jordan elimination on augmented matrix \(m1|m2\). \\ +\midrule +\begin{lstlisting} +\matrixGaussJordanSteps[type,truncate] +{matrix}{m1}{m2} +\end{lstlisting}& +Defines new matrix obtained by performing Gauss-Jordan elimination on augmented matrix \(m1|m2\) in a step-by-step manner. The command has two optional parameters \verb|type| and \verb|truncate|. \verb|type| may be one of the values \verb|pmatrix, bmatrix, vmatrix,| \verb |Vmatrix|. The default type is \verb|bmatrix|. \verb|truncate| specifies number of digits up to which matrix entries are to be truncated. \verb|truncate| may be 0,1,2,\ldots. \\ +\bottomrule \\ +\caption{Commands for operations on matrices} +\label{tbl:luamtxcmd} +\end{longtable} +\subsection{Illustrations of matrix operations} +The following commands define matrices \(m,n,\) and \(r\). +\begin{lstlisting} +\def\r{{{1,2,3},{4,5,6},{7,8,complex('9+3i')}}} +\def\s{{{1,2,3},{4,5,6},{7,8,10}}} +\def\t{{{1,2,3},{4,5,6},{7,8,9}}} +\def\u{{{1},{2},{3}}} + +\matrixNew{m}{\r} +\matrixNew{n}{\s} +\matrixNew{p}{\t} +\matrixNew{q}{\u} +\end{lstlisting} +Table \ref{tbl:illluamatrix} illustrates various operations on matrices \(m,n,p,\) and \(q\). +\begin{center} +\begin{longtable}{lc} +\toprule +Commands & Output Produced\\ +\toprule +\multicolumn{2}{c}{Printing matrices}\\ +\midrule +\begin{lstlisting} +\(m=\matrixPrint{\m}\) +\end{lstlisting} & +\(m=\begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 9.0+3.0i\end{bmatrix}\) +\\ +\midrule +\begin{lstlisting} +\(m=\matrixPrint[type=pmatrix]{\m}\) +\end{lstlisting} & +\(m=\begin{pmatrix} 1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 9.0+3.0i\end{pmatrix}\) +\\ +\midrule +\multicolumn{2}{c}{Some parameters of defined matrices}\\ +\midrule +\begin{lstlisting} +\(No. or rows in matrix m += \matrixNumRows{m}\) +\end{lstlisting} & +No. or rows in matrix \(m = 3\)\\ +\midrule +\begin{lstlisting} +\(No. or columns in matrix m += \matrixNumCols{m}\) +\end{lstlisting} & +No. or columns in matrix \(m = 3\)\\ +\midrule +\begin{lstlisting} +\(Element of matrix m at (3,3) = + \matrixGetElement{m}{3}{3}\) +\end{lstlisting} & +\(9+3i\)\\ +\midrule +\multicolumn{2}{c}{Algebraic operations on matrices}\\ +\midrule +\begin{lstlisting} +\matrixAdd{m1}{m}{p} +\(m1 = \matrixPrint{m1}\) +\end{lstlisting} & +\(m1 = \begin{bmatrix} 2.0 & 4.0 & 6.0 \\ 8.0 & 10.0 & 12.0 \\ 14.0 & 16.0 & 18.0+3.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixSub{m2}{m}{p} +\(m2 = \matrixPrint{m2}\) +\end{lstlisting} & +\(m2 = \begin{bmatrix} 0.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 3.0i \end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixMulNum{m3}{3}{m} +\(m3 = \matrixPrint{m3}\) +\end{lstlisting} & +\(m3 = \begin{bmatrix} 3.0 & 6.0 & 9.0 \\ 12.0 & 15.0 & 18.0 \\ 21.0 & 24.0 & 27.0+9.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixMul{m4}{m}{p} +\(m4 = \matrixPrint{m4}\) +\end{lstlisting} & +\(m4 = \begin{bmatrix} 30.0 & 36.0 & 42.0 \\ 66.0 & 81.0 & 96.0 \\ 102.0+21.0i & 126.0+24.0i & 150.0+27.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixPow{m5}{m}{2} +\(m5 = \matrixPrint{m5}\) +\end{lstlisting} & +\(m5 = \begin{bmatrix} 30.0 & 36.0 & 42.0+9.0i \\ 66.0 & 81.0 & 96.0+18.0i \\ 102.0+21.0i & 126.0+24.0i & 141.0+54.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixInvert{m6}{m} +\(m6 = \matrixPrint[truncate=4]{m6}\) +\end{lstlisting} & +\(m6 = \begin{bmatrix} -1.6667-0.3333i & 0.6667+0.6667i & -0.3333i \\ 1.3333+0.6667i & -0.3333-1.3333i & 0.6667i \\ -0.3333i & 0.6667i & -0.3333i\end{bmatrix} +\)\\ +\midrule + +\begin{lstlisting} +Rank of matrix \(m =\matrixRank{m}\) + +\end{lstlisting} & +Rank of matrix \(m = 3\)\\ +\midrule +\begin{lstlisting} +Determinant of matrix \(m =\matrixDet{m}\) +\end{lstlisting} & +Determinant of matrix \(m = -9i\)\\ +\midrule +\begin{lstlisting} +\matrixTranspose{m7}{m} +\(m7 = \matrixPrint{m7}\) +\end{lstlisting} & +\(m7 = \begin{bmatrix}1.0 & 4.0 & 7.0 \\ 2.0 & 5.0 & 8.0 \\ 3.0 & 6.0 & 9.0+3.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixSetElement{n}{3}{3}{300} +\(n= \matrixPrint{n}\) +\end{lstlisting} & +\(n = \begin{bmatrix}1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 300.0\end{bmatrix} +\)\\ +\midrule + +\begin{lstlisting} +\matrixSubmatrix{m8}{m}{1}{2}{2}{3} +\(m8 = \matrixPrint{m8}\) +\end{lstlisting} & +\(m8 = \begin{bmatrix} 2.0 & 3.0 \\ 5.0 & 6.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixConcatH{m9}{m}{q} +\(m9= \matrixPrint{m9}\) +\end{lstlisting} & +\(m9 = \begin{bmatrix}1.0 & 2.0 & 3.0 & 1.0 \\ 4.0 & 5.0 & 6.0 & 2.0 \\ 7.0 & 8.0 & 9.0+3.0i & 3.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixConcatV{m10}{m}{n} +\(m10= \matrixPrint{m10}\) +\end{lstlisting} & +\(m10= \begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 9.0+3.0i \\ 1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 300.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixOp{m11}{m*m+2*m} +\(\matrixPrint[truncate=4]{m11}\) +\end{lstlisting} & +\(m11 = \begin{bmatrix} 32.0 & 40.0 & 48.0+9.0i \\ 74.0 & 91.0 & 108.0+18.0i \\ 116.0+21.0i & 142.0+24.0i & 159.0+60.0i\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixCopy{m12}{m} +\(m12 = \matrixPrint{m12}\) +\end{lstlisting} & +\(m12 = \begin{bmatrix}1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 9.0+3.0i\end{bmatrix} +\)\\ + +\midrule +\begin{lstlisting} +trace of matrix \( m = \matrixTrace{m}\) +\end{lstlisting} & +trace of matrix \( m = 15+3i\) \\ + +\midrule +\begin{lstlisting} +\matrixConjugate{mc}{m} +\(mc = \matrixPrint{mc}\) +\end{lstlisting} & +\(mc = \begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 7.0 & 8.0 & 9.0-3.0i\end{bmatrix} +\)\\ +\midrule + +\begin{lstlisting} +\matrixConjugateT{mct}{m} +\(mct = \matrixPrint{mct}\) +\end{lstlisting} & +\(mct = \begin{bmatrix} 1.0 & 4.0 & 7.0 \\ 2.0 & 5.0 & 8.0 \\ 3.0 & 6.0 & 9.0-3.0i\end{bmatrix} +\)\\ +\midrule + +\begin{lstlisting} + \(\matrixNormOne{m}\) +\end{lstlisting} & + \(18.486832980505\) \\ + +\midrule +\begin{lstlisting} + \(\matrixNormInfty{m}\) +\end{lstlisting} & + \(24.486832980505\) \\ + +\midrule +\begin{lstlisting} + \(\matrixNormMax{m}\) +\end{lstlisting} & + \(9.4868329805051\) \\ + +\midrule +\begin{lstlisting} + \(\matrixNormF{m}\) +\end{lstlisting} & +\( 17.146428199482\) \\ + +\midrule +\multicolumn{2}{c}{Elementary row operations on matrices}\\ +\midrule +\begin{lstlisting} +\matrixSwapRows{m13}{m}{2}{3} +\(m13 = \matrixPrint{m13}\) +\end{lstlisting} & +\(m13 = \begin{bmatrix}1.0 & 2.0 & 3.0 \\ 7.0 & 8.0 & 9.0+3.0i \\ 4.0 & 5.0 & 6.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixMulRow{m14}{m}{3}{300} +\(m14 = \matrixPrint{m14}\) +\end{lstlisting} & +\(m14 = \begin{bmatrix}1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 2100.0 & 2400.0 & 2700.0+900.0i \end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixMulAddRow{m15}{m}{2}{10}{3} +\(m15 = \matrixPrint{m15}\) +\end{lstlisting} & +\(m15 = \begin{bmatrix}1.0 & 2.0 & 3.0 \\ 4.0 & 5.0 & 6.0 \\ 47.0 & 58.0 & 69.0+3.0i\end{bmatrix} +\)\\ +\midrule +\multicolumn{2}{c}{Elementary column operations on matrices}\\ +\midrule +\begin{lstlisting} +\matrixSwapCols{m16}{m}{2}{3} +\(m16 = \matrixPrint{m16}\) +\end{lstlisting} & +\(m16 = \begin{bmatrix}1.0 & 3.0 & 2.0 \\ 4.0 & 6.0 & 5.0 \\ 7.0 & 9.0+3.0i & 8.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixMulCol{m17}{m}{3}{300} +\(m17 = \matrixPrint{m17}\) +\end{lstlisting} & +\(m17 = \begin{bmatrix} 1.0 & 2.0 & 900.0 \\ 4.0 & 5.0 & 1800.0 \\ 7.0 & 8.0 & 2700.0+900.0i \end{bmatrix} +\)\\ +\midrule + +\begin{lstlisting} +\matrixMulAddCol{m18}{m}{2}{10}{3} +\(m18 = \matrixPrint{m18}\) +\end{lstlisting} & +\(m18 = \begin{bmatrix}1.0 & 2.0 & 23.0 \\ 4.0 & 5.0 & 56.0 \\ 7.0 & 8.0 & 89.0+3.0i\end{bmatrix} +\)\\ +\midrule + +\multicolumn{2}{c}{Reduced row echelon form of a matrix}\\ +\midrule +\begin{lstlisting} +\matrixRREF{m19}{p} +\(m19 = \matrixPrint{m19}\) +\end{lstlisting} & +\(m19 = \begin{bmatrix}1.0 & 0.0 & -1.0 \\ 0.0 & 1.0 & 2.0 \\ 0.0 & 0.0 & 0.0\end{bmatrix} +\)\\ +\midrule +\begin{lstlisting} +\matrixRREF{m20}{m} +\(m20 = \matrixPrint{m20}\) +\end{lstlisting} & +\(m20 = \begin{bmatrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0\end{bmatrix} +\)\\ +\bottomrule \\ +\caption{Illustration of commands for operations on matrices} +\label{tbl:illluamatrix} +\end{longtable} +\end{center} + +The package has command \verb|\matrixRREFSteps| to produce step-by-step computation of reduced row echelon form of a matrix. The command \verb|\matrixRREFSteps{p}| outputs the following. +\begin{framed}Step 1:Multiply row 1 by 4.0 and subtract it from row 2.$$\begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 0.0 & -3.0 & -6.0 \\ 7.0 & 8.0 & 9.0 \\ \end{bmatrix} $$Step 2:Multiply row 1 by 7.0 and subtract it from row 3.$$\begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 0.0 & -3.0 & -6.0 \\ 0.0 & -6.0 & -12.0 \\ \end{bmatrix} $$Step 3:Divide row 2 by -3.0.$$\begin{bmatrix} 1.0 & 2.0 & 3.0 \\ 0.0 & 1.0 & 2.0 \\ 0.0 & -6.0 & -12.0 \\ \end{bmatrix} $$Step 4:Multiply row 2 by 2.0 and subtract it from row 1.$$\begin{bmatrix} 1.0 & 0.0 & -1.0 \\ 0.0 & 1.0 & 2.0 \\ 0.0 & -6.0 & -12.0 \\ \end{bmatrix} $$Step 5:Multiply row 2 by -6.0 and subtract it from row 3.$$\begin{bmatrix} 1.0 & 0.0 & -1.0 \\ 0.0 & 1.0 & 2.0 \\ 0.0 & 0.0 & 0.0 \\ \end{bmatrix} $$ +\end{framed} + +The command \verb|\matrixGaussJordan| is used to obtain Gauss-Jordan elimination of an augmented matrix. + +\begin{lstlisting} +\def\a{{{1,1,1},{2,-1,-1},{1,-1,1}}} +\def\b{{{3},{3},{9}}} +\matrixNew{S}{\a} +\matrixNew{T}{\b} +\matrixConcatH{W}{S}{T} +$$W = \matrixPrint{W}$$ +\matrixGaussJordan{U}{S}{T} +$$U = \matrixPrint{U}$$ +\end{lstlisting} + +The above code produces the following output. +\begin{framed} +$$W =\begin{bmatrix} 1.0 & 1.0 & 1.0 & 3.0 \\ 2.0 & -1.0 & -1.0 & 3.0 \\ 1.0 & -1.0 & 1.0 & 9.0 \\ \end{bmatrix} $$ +$$U = \begin{bmatrix} 1.0 & 0.0 & 0.0 & 2.0 \\ 0.0 & 1.0 & 0.0 & -3.0 \\ 0.0 & 0.0 & 1.0 & 4.0 \\ \end{bmatrix}$$ +\end{framed} + +The package also has a command \verb|\matrixGaussJordanSteps| to produce step-by-step computation of Gauss-Jordan elimination of an augmented matrix. The command \verb|\matrixGaussJordanSteps{S}{T}| produces the following output. + +\begin{framed} +$$W =\begin{bmatrix} 1.0 & 1.0 & 1.0 & 3.0 \\ 2.0 & -1.0 & -1.0 & 3.0 \\ 1.0 & -1.0 & 1.0 & 9.0 \\ \end{bmatrix} $$ +Step 1:Multiply row 1 by 2.0 and subtract it from row 2.$$\begin{bmatrix} 1.0 & 1.0 & 1.0 & 3.0 \\ 0.0 & -3.0 & -3.0 & -3.0 \\ 1.0 & -1.0 & 1.0 & 9.0 \\ \end{bmatrix} $$Step 2:Multiply row 1 by 1.0 and subtract it from row 3.$$\begin{bmatrix} 1.0 & 1.0 & 1.0 & 3.0 \\ 0.0 & -3.0 & -3.0 & -3.0 \\ 0.0 & -2.0 & 0.0 & 6.0 \\ \end{bmatrix} $$Step 3:Divide row 2 by -3.0.$$\begin{bmatrix} 1.0 & 1.0 & 1.0 & 3.0 \\ 0.0 & 1.0 & 1.0 & 1.0 \\ 0.0 & -2.0 & 0.0 & 6.0 \\ \end{bmatrix} $$Step 4:Multiply row 2 by 1.0 and subtract it from row 1.$$\begin{bmatrix} 1.0 & 0.0 & 0.0 & 2.0 \\ 0.0 & 1.0 & 1.0 & 1.0 \\ 0.0 & -2.0 & 0.0 & 6.0 \\ \end{bmatrix} $$Step 5:Multiply row 2 by -2.0 and subtract it from row 3.$$\begin{bmatrix} 1.0 & 0.0 & 0.0 & 2.0 \\ 0.0 & 1.0 & 1.0 & 1.0 \\ 0.0 & 0.0 & 2.0 & 8.0 \\ \end{bmatrix} $$Step 6:Divide row 3 by 2.0.$$\begin{bmatrix} 1.0 & 0.0 & 0.0 & 2.0 \\ 0.0 & 1.0 & 1.0 & 1.0 \\ 0.0 & 0.0 & 1.0 & 4.0 \\ \end{bmatrix} $$Step 7:Multiply row 3 by 1.0 and subtract it from row 2.$$\begin{bmatrix} 1.0 & 0.0 & 0.0 & 2.0 \\ 0.0 & 1.0 & 0.0 & -3.0 \\ 0.0 & 0.0 & 1.0 & 4.0 \\ \end{bmatrix} $$ +\end{framed} + +\section{Customized usage}\label{customuse} +The commands available in the package can be used for performing further operations on vectors and matrices. The command \verb|\vectorAdd| can be extended to add more than two vectors. The latex document (listing \ref{code:custluavec}) provides some instances of such usage. +\begin{lstlisting}[label={code:custluavec}, caption={Customized usage of the lualinalg package}] +\documentclass{article} +\usepackage{lualinalg} +\begin{document} +\begin{luacode} +function sumcoordinates(v1) +local sum = 0 +for i = 1,#v1 do + sum = sum + v1[i] + end +return sum +end + +function vector.addmulti(...) + p=table.pack(...) + s=vector(p[1]) + for i=2,#p do +s=vector.add(s,vector(p[i])) +end + return s +end +\end{luacode} +\vectorNew{v}{{1,2,complex('3+3i')}} +The sum of coordinates of vector + \(v = \directlua{tex.sprint(tostring( sumcoordinates(v)))}\). + +\newcommand\vectorAddmulti[2]{% + \directlua{% + vectors['#1'] = vector.addmulti(#2) + }% +} + +\vectorNew{w}{{3,6,complex('6+6i')}} +\vectorNew{x}{{9,12,complex('12+12i')}} +\vectorAddmulti{y}{v,w,x} +The sum of vectors \(v,w \text{ and } x =\left( \vectorPrint{y} \right)\). +\end{document} +\end{lstlisting} + +The latex document (listing \ref{code:custluavec}) outputs the following on compilation. +\begin{framed} +The sum of coordinates of vector \(v = 6 + 3i\). + +The sum of vectors \(v,w \text{ and } x = \left(13.0, 20.0, 21.0 + 21.0i \right) \). +\end{framed} + + +The command \verb|\matrixAdd| can be extended to add more than two matrices. The latex document (listing \ref{code:custluamtx}) provides some instances of such usage. + +\begin{lstlisting}[label={code:custluamtx}, caption={Customized usage of the lualinalg package}] +\documentclass{article} +\usepackage{lualinalg} +\begin{document} +\begin{luacode} +function squareDiagEntries(m1) + if #m1 ~= #m1[1] then error( "matrix not square") end + local sum = 0 +for i = 1,#m1 do + for j = 1,#m1[1] do + if i == j then sum = sum + (m1[i][j])^2 end + end + end +return sum +end + +function matrix.addmulti(...) + p=table.pack(...) + s=matrix(p[1]) + for i=2,#p do +s=matrix.add(s,matrix(p[i])) +end + return s +end +\end{luacode} + +\def\r{{{1,2,3},{4,5,6},{7,8,complex('9+3i')}}} +\matrixNew{m}{\r} +The sum of squares of diagonal entries of matrix + \(m = \directlua{tex.sprint(tostring(squareDiagEntries(m)))}\). + +\def\s{{{1,2,3},{4,5,complex('6+6i')}}} +\def\t{{{10,20,30},{40,50,complex('60+60i')}}} +\def\u{{{100,200,300},{400,500,complex('600+600i')}}} +\matrixNew{m1}{\s} +\matrixNew{m2}{\t} +\matrixNew{m3}{\u} +\newcommand\matrixAddmulti[2]{% + \directlua{% + matrices['#1'] = matrix.addmulti(#2) + }% +} +\matrixAddmulti{m4}{m1,m2,m3} +The sum of matrices \(m1,m2 \text{ and } m3 = \matrixPrint{m4}\). +\end{document} +\end{lstlisting} + +The latex document (listing \ref{code:custluamtx}) outputs the following on compilation. +\begin{framed} +The sum of squares of diagonal entries of matrix \(m = 98.0 + 54i\). + +The sum of matrices \(m1,m2 \text{ and } m3 =\begin{bmatrix} 111.0 & 222.0 & 333.0 \\ 444.0 & 555.0 & 666.0+666.0i \end{bmatrix} \). +\end{framed} + +\section{Known issues and limitations} +\begin{itemize} +\item The package supports small and big numbers. They can be input in the usual scientific notation. The math library in Lua defines constants with the maximum \verb|math.maxinteger| and the minimum \verb|math.mininteger| values for an integer. The result wraps around when there is a computational operation on integers that would result in a value smaller than the \verb|mininteger| or larger than the \verb|maxinteger|. It means that the computed result is the only number between the \verb|miniinteger| and \verb|maxinteger|. + +\item The package currently supports only numerical computations. The table in a Lua is a data type that implements an associative array. This feature is used in packages to define and store vectors and matrices. This approach is close to object-oriented programming. It will allow easy conversion of algorithms in packages for symbolic computations. Future package updates will consider algorithm conversions to support symbolic calculations. + +\item The error handling mechanism in the tool is not robust. There are some custom errors included in the package. However the package mostly depends on error handling mechanism of Lua. The error handling can be strengthened in future updates of the package. + +\end{itemize} +\end{document} \ No newline at end of file diff --git a/macros/optex/README b/macros/optex/README index f6a86e51d2..36c2c98bb1 100644 --- a/macros/optex/README +++ b/macros/optex/README @@ -22,6 +22,12 @@ doc/ ... PDF version of the OpTeX documentation and sources. History: +<1.10> Feb 2022: + key-values improved: \iskv, \kvx, \nokvx introduced. + unimath-codes: control sequences are macros, no \chardef. + \bp, \expr: optional syntax for setting the number of digits after decimal point. + \isnextchar is expandable. + math.opm: various improvements. <1.09> Dec 2022: New math.opm package: doing math more comfortable. The math.opm package can be a package template for macro writers. diff --git a/macros/optex/base/alloc.opm b/macros/optex/base/alloc.opm index d4f823fec4..fae88d286e 100644 --- a/macros/optex/base/alloc.opm +++ b/macros/optex/base/alloc.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \newdimen {Allocators for registers <2022-06-10>} % preloaded in format +\_codedecl \newdimen {Allocators for registers <2023-02-03>} % preloaded in format \_doc ----------------------------- The limits are set first. @@ -46,9 +46,10 @@ \_errmessage{No room for a new \_ea\_string\_csname #2\_endcsname}% \_else \_global#3#1=\_cs{_#2alloc}% - \_wlog{\_string#1=\_ea\_string\_csname #2\_endcsname\_the\_cs{_#2alloc}}% + \_wloga{\_string#1=\_ea\_string\_csname #2\_endcsname\_the\_cs{_#2alloc}}% \_fi } +\_let\_wloga=\_wlog % you can suppress the logging by \_let\_wloga=\_ignoreit \_doc ----------------------------- The allocation macros @@ -177,6 +178,7 @@ the array-like declarator of counters. \_endinput +2023-02-03 \_wloga introduced 2022-06-10 \_famalloc set to 42 (answer to the biggest fundamental question) 2022-03-07 \_noattr allocated 2022-02-19 \_newlanguage introduced diff --git a/macros/optex/base/basic-macros.opm b/macros/optex/base/basic-macros.opm index ae5c833140..9227505678 100644 --- a/macros/optex/base/basic-macros.opm +++ b/macros/optex/base/basic-macros.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \sdef {Basic macros for OpTeX <2022-11-22>} % preloaded in format +\_codedecl \sdef {Basic macros for OpTeX <2023-01-22>} % preloaded in format \_doc ------------------------------ \`\bgroup`, \`\egroup`, \`\empty`, \`\space`, and \`\null` @@ -73,7 +73,7 @@ \_cod ------------------------------ \_def \_cs #1{\_csname#1\_endcsname} -\_def \_trycs#1#2{\_ifcsname #1\_endcsname \_csname #1\_ea\_endcsname \_else #2\_fi} +\_def \_trycs#1#2{\_ifcsname #1\_endcsname \_csname #1\_ea\_endcsname \_else \_afterfi{#2}\_fi} \_public \cs \trycs ; \_doc ------------------------------ @@ -142,6 +142,7 @@ \_endcode % ------------------------------------- +2023-01-22: \trycs: afterfi used for second parameter 2022-11-22: \_banner definition moved here 2022-11-18: \ahead introduced 2022-10-29: \_fin introduced diff --git a/macros/optex/base/doc.opm b/macros/optex/base/doc.opm index dc5d037e72..fb96d35007 100644 --- a/macros/optex/base/doc.opm +++ b/macros/optex/base/doc.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \printdoc {Macros for documentation printing <2022-11-21>} % loaded on demand by \load[doc] +\_codedecl \printdoc {Macros for documentation printing <2022-12-11>} % loaded on demand by \load[doc] \_doc ----------------------------- General decalarations. @@ -204,7 +204,7 @@ \_doc ----------------------------- If this macro is loaded by \^`\load` then we need to initialize - catcodes using the `\_afteroad` macro. + catcodes using the `\_afterload` macro. \_cod ----------------------------- \_def\_afterload{\_catcode`\<=13 \_catcode`\`=13 @@ -229,26 +229,32 @@ Link to user documentation point: \code{\\~`\\foo}. \_cod ----------------------------- +\_def\_docrefcodes{\_catcode`\.=11\_relax} + \_verbchar` -\_def\`#1`{\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% - \_ifcsname cs:\_tmp\_endcsname\_else \_dest[cs:\_tmp]\_fi +\_def\`{\_bgroup \_docrefcodes \_mainpoint} +\_def\_mainpoint #1`{\_egroup\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% + \_ifcsname cs:\_tmp\_endcsname \_moremainpoints \_else \_dest[cs:\_tmp]\_fi \_sxdef{cs:\_tmp}{}% \_hbox{\_ifcsname cs:^\_tmp\_endcsname \_link[cs:^\_tmp]{\mlinkcolor}{\_tt\_csstring\\\_tmp}\_else {\_tt\mlinkcolor\_csstring\\\_tmp}\_fi}% } -\_def\^`#1{\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% +\_def\^`{\_bgroup \_docrefcodes \_docpoint} +\_def\_docpoint #1{\_egroup\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% \_hbox{\_ifcsname cs:^\_tmp\_endcsname \_else \_dest[cs:^\_tmp]\_sxdef{cs:^\_tmp}{}\_fi \_link[cs:\_tmp]{\ulinkcolor}{\_tt\_string#1}}% \_futurelet\_next\_cslinkA } \_def\_cslinkA{\_ifx\_next`\_ea\_ignoreit \_else \_ea\_ea\_ea`\_ea\_string\_fi} -\_def\~`#1{\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% +\_def\~`{\_bgroup \_docrefcodes \_doctpoint} +\_def\_doctpoint #1{\_egroup\_leavevmode\_edef\_tmp{\_csstring#1}\_iindex{\_tmp}% \_hbox{\_link[cs:^\_tmp]{\ulinkcolor}{\_tt\_string#1}}% \_futurelet\_next\_cslinkA } +\_def\_moremainpoints{\_opwarning{Second main documentation point \_bslash\_tmp}} \_doc ----------------------------- The \`\fw` macro for forward links to user documentation point (given later) @@ -357,6 +363,8 @@ have the same meaning: `\optexdoclink` in this example. And \endinput +2022-12-11 \_opwaning "Second main documentation point" introduced. +2022-12-11 \_docrefcodes added (bug due to 2022-11-13 fixed). 2022-11-21 magenta color for internal links instead green. 2022-11-13 \catcode`.=11: only local settings 2022-07-01 \_printii improved, colors declaration part added. diff --git a/macros/optex/base/f-heros.opm b/macros/optex/base/f-heros.opm index 2531573ca4..d749553882 100644 --- a/macros/optex/base/f-heros.opm +++ b/macros/optex/base/f-heros.opm @@ -193,12 +193,16 @@ so the first font from the new family is loaded and it is ready to use it. \seccc Name conventions -Create font modifiers, new variants, and the `\` only as public, i.e. -in user namespace without `_` prefix. We assume that if a user re-defines them then he/she needs +Create font modifiers, new variants, and the `\` only in +public namespace without `_` prefix. We assume that if a user re-defines them then he/she needs not them, so we have no problems. If the user's definition was done before loading the font family file then it is re-defined and \OpTeX/ warns about it. See the end of section~\ref[fontcommands]. +If you need to use an internal control sequence declared in your fontfile, +use the reserved name space with names starting with two `_` followed by family +indentifier or by `vf` if it relates to variable fonts. + The name of `\` should begin with an uppercase letter. Please, look at diff --git a/macros/optex/base/fonts-resize.opm b/macros/optex/base/fonts-resize.opm index 34885d44bd..e76596611b 100644 --- a/macros/optex/base/fonts-resize.opm +++ b/macros/optex/base/fonts-resize.opm @@ -107,7 +107,7 @@ The \`\_regtfm` ` ` registers optical sizes data directly by the font file names. This can be used for `tfm` files or OpenType files without - various font features. See also \`\_regoptsizes` in section~\ref[optsizes]. + various font features. See also \^`\_regoptsizes` in section~\ref[optsizes]. The `\_regtfm` command saves the concerned to the ``. The `` is in the form as shown below in the code where `\_regtfm` is used. diff --git a/macros/optex/base/fonts-select.opm b/macros/optex/base/fonts-select.opm index 7e00c9baea..6b10f75aff 100644 --- a/macros/optex/base/fonts-select.opm +++ b/macros/optex/base/fonts-select.opm @@ -733,10 +733,10 @@ Compare ex-height of Termes \rmsans with Heros \rm and Termes. \endtt The variant selectors (declared by \~`\famvardef`) or font -modifiers (declared by \~`\moddef`) are (typically) control sequences in user name -space (`\mf`, `\caps`). They are most often declared in font family files and +modifiers (declared by \~`\moddef`) are (typically) control sequences in the public +namespace (`\mf`, `\caps`). They are most often declared in font family files and they are loaded by \^`\fontfam`. A conflict with such names in -user namespace can be here. For example: if `\mf` is defined by a user and then +the public namespace can be here. For example: if `\mf` is defined by a user and then `\fontfam[Roboto]` is used then `\famvardef\mf` is performed for Roboto family and the original meaning of `\mf` is lost. But \OpTeX/ prints warning about it. There are two cases: diff --git a/macros/optex/base/hisyntax-c.opm b/macros/optex/base/hisyntax-c.opm index 3c1f228f88..d0a4217b31 100644 --- a/macros/optex/base/hisyntax-c.opm +++ b/macros/optex/base/hisyntax-c.opm @@ -52,7 +52,7 @@ User can re-declare his/her own colors by `\hicolors` which has precedence before `\_hicolors`. The public variants can be declared if you want to give these token lists to -the user namespace. But it is not explicitly needed. +the public namespace. But it is not explicitly needed. All settings must be global here because the file is typically read inside a group and we need not read it repeatedly before each code chunk diff --git a/macros/optex/base/if-macros.opm b/macros/optex/base/if-macros.opm index 9113b5f8be..148c855941 100644 --- a/macros/optex/base/if-macros.opm +++ b/macros/optex/base/if-macros.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \newif {Special if-macros, is-macros and loops <2022-12-02>} % preloaded in format +\_codedecl \newif {Special if-macros, is-macros and loops <2023-01-16>} % preloaded in format \_doc ---------------------------- \secc Classical \code{\\newif} @@ -64,6 +64,7 @@ \_def \_iterate {\_body \_ea \_iterate \_fi} \_doc ----------------------------- + {\_let\_moremainpoints=\_relax \`\foreach` ``\`\do` `{}` repeats `` for each element of the ``. The `` can include `#1` which is substituted by each @@ -82,7 +83,7 @@ Recommendation: it is better to use private variants of \`\_foreach`. When the user writes `\input tikz` then `\foreach` macro is redefined in each TikZ environment. - The private variants use \`\_do` separator instead `\do` separator. + The private variants use \`\_do` separator instead `\do` separator.} \_cod ----------------------------- \_newcount\_frnum % the numeric variable used in \fornum @@ -101,6 +102,7 @@ \_afterfi{\_foreachA{#1}{##1}}\_else\_afterfi{\_foreachA{#1}{#2}}\_fi} \_doc ----------------------------- + {\_let\_moremainpoints=\_relax \`\fornum` `..` \`\do` `{}` or \`\fornumstep` `: ..` \`\do` `{}` repeats `` for each number from `` to `` (with step `` @@ -110,7 +112,7 @@ The test in the \`\_fornumB` says: if ( $\string<$ AND is positive) or if ( $>$ AND is negative) then close loop by `\_getforstack`. Sorry, the condition is - writen by somewhat cryptoid \TeX/ language. + writen by somewhat cryptoid \TeX/ language.} \_cod ----------------------------- \_def\_fornum#1..#2\_do{\_fornumstep 1:#1..#2\_do} @@ -292,16 +294,17 @@ \_public \isfont ; \_doc ---------------------------- - The last macro \`\isnextchar` `{}{}` + The macro \`\isnextchar` `{}{}` has a different syntax than all other is-macros. It executes `` if next character is equal to . - Else the `` is executed. The macro is not expandable. + Else the `` is executed. The macro is expandable. \_cod ---------------------------- -\_long\_def\_isnextchar#1#2#3{\_begingroup\_toks0={\_endgroup#2}\_toks1={\_endgroup#3}% - \_let\_tmp= #1\_futurelet\_next\_isnextcharA +\_long\_def\_isnextchar#1#2#3{\_immediateassignment + \_def\_isnextcharA{\_isnextcharB{#1}{#2}{#3}}% + \_immediateassignment\_futurelet \_next \_isnextcharA } -\_def\_isnextcharA{\_the\_toks\_ifx\_tmp\_next0\_else1\_fi\_space} +\_long\_def\_isnextcharB#1{\_ifx\_next#1\_ea\_ignoresecond\_else\_ea\_usesecond\_fi} \_public \isnextchar ; @@ -359,6 +362,7 @@ \_endcode +2023-01-16 \isnextchar created expandable. 2022-12-02 \xcasesof: its first parameter is \long too. 2022-11-29 renamed to \casesof, \xcasesof. 2022-11-26 \casesby, \casesbyif introduced. diff --git a/macros/optex/base/keyval.opm b/macros/optex/base/keyval.opm index 7d089ce6b1..21e6f9acf3 100644 --- a/macros/optex/base/keyval.opm +++ b/macros/optex/base/keyval.opm @@ -1,26 +1,39 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \readkv {Key-value dictionaries <2020-12-21>} % preloaded in format +\_codedecl \readkv {Key-value dictionaries <2023-01-14>} % preloaded in format \_doc ---------------------------- - {\bf Implementation.} + {\bf Implementation.}\nl The \`\readkv``` expands its parameter and does replace-strings in order to - remove spaces around equal signs and after commas. Double commas are - removed. Then \`\_kvscan` reads the parameters list finished by the double - comma and saves values to `\_kv:` macros.\nl - The \`\kv``{}` expands the `\_kv:` macro. If this macro isn't - defined then \`\_kvunknown` is processed. You can re-define it if you want. + remove spaces around equal signs and after commas. + Then \`\_kvscan` reads the parameters list finished by `,\_fin,` + and saves values to `\_kv::` macros. + The `\_kvx::` is processed (if it is defined) with parameter + after it.\nl + The \`\kvx``{}{}` defines the `\_kvx::#1` macro + and \`\nokvx``{}` defines the `\_nokvx::` macro.\nl + The \`\kv``{}` expands the `\_kv::` macro. If this macro isn't + defined then \`\_kvunknown` is processed. You can re-define it if you want.\nl + The \`\iskv``{}\iftrue` (or `\iffalse`) is the test, + if the `` is defined in current . \_cod ---------------------------- \_def\_readkv#1{\_ea\_def\_ea\_tmpb\_ea{#1}% - \_replstring\_tmpb{= }{=}\_replstring\_tmpb{ =}{=}% - \_replstring\_tmpb{, }{,}\_replstring\_tmpb{,,}{,}% - \_ea \_kvscan \_tmpb,,=,} -\_def\_kvscan #1#2=#3,{\_ifx#1,\_else \_sdef{_kv:#1#2}{#3}\_ea\_kvscan\_fi} -\_def\_kv#1{\_trycs{_kv:#1}{\_kvunknown}} + \_replstring\_tmpb{= }{=}\_replstring\_tmpb{ =}{=}\_replstring\_tmpb{, }{,}% + \_ea \_kvscan\_tmpb,\_fin,} +\_def\_kvscan#1,{\_ifx\_fin#1\_empty\_ea\_ignoreit \_else\_ea\_useit \_fi + {\_kvsd #1==\_fin \_kvscan}} +\_def\_kvsd#1=#2=#3\_fin{\_sdef{\_kvcs#1}{#2}% + \_trycs{_kvx:\_the\_kvdict:#1}% + {\_trycs{_nokvx:\_the\_kvdict}{\_ea\_ignoreit}{#1}\_ea\_ignoreit}{#2}} +\_def\_kvx#1#2{\_sdef{_kvx:\_the\_kvdict:#1}##1{#2}} +\_def\_nokvx#1{\_sdef{_nokvx:\_the\_kvdict}##1\_ea\_ignoreit\_fi##2{\_fi#1}} +\_def\_kv#1{\_trycs{\_kvcs#1}{\_kvunknown}} +\_def\_iskv#1#2{#2\_else\_ea\_unless\_fi \_ifcsname\_kvcs#1\_endcsname} +\_def\_kvcs{_kv:\_the\_kvdict:} \_def\_kvunknown{???} -\public \readkv \kv ; +\public \readkv \kvx \nokvx \kv \iskv ; \_endcode @@ -43,7 +56,7 @@ or simply `\myframe {text3}`. You can define `\myframe` as follows: \begtt \def\myframedefaults{% defaults: frame-color=\Black, % color of frame rules - text-color=\Black, % color ot text inside the frame + text-color=\Black, % color of text inside the frame rule-width=0.4pt, % width of rules used in the frame margins=2pt, % space between text inside and rules. } @@ -64,18 +77,54 @@ The last setting wins. Third: the values can be used by the expandable \^`\kv{}` macro. The \^`\kv{}` returns `???` if such key is not declared. -You can use keys without values in the parameters list too, but with -additional care. For example, suppose `draft` option without parameter. -If a user writes `\myframe [..., draft, ...]{text}` then `\myframe` should behave differently. -We have to add `DRAFTv=0,` in `\myframedefault` macro. -Moreover, `\myframe` macro must include preprocessing of `\myframedefault` using -\^`\replstring` which replaces the occurrence of `draft` by `DRAFTv=1`. +You can use keys without values in the parameters list too. +Then you can ask if the key is declared by \^`\iskv``{}\iftrue` +or the key is undeclared by \^`\iskv``{}\iffalse`. +For example, you write to your documentation of your code that +user can set the `draft` option without the value. Then you can do \begtt \optdef\myframe [] #1{... - \ea\addto\ea\myframedefaults\ea{\the\opt}% - \replstring\myframedefaults{draft}{DRAFTv=1}% - \readkv\myframedefaults - ... - \ifnum\kv{DRAFTv}=1 draft mode\else normal mode\fi + \readkv\myframedefaults \readkv{\the\opt}% + \iskv{draft}\iftrue ...draft mode... \else ...final mode... \fi + ...} +\endtt +Maybe, you want to allow not ony `draft` option but `final` option (which is +opposite to `draft`) too and you want to apply the result from the last given +option. Then `\iskv` doesn't work because you can only check if both options +are declared but you don't know what one is given as last. But you can +use \^`\kvx``{}{}` to declare which is processed +immediately when the `` is processed by `\readkv`. For example +\begtt +\newcount\mydraftmode +\kvx{draft}{\mydraftmode=1 } +\kvx{final}{\mydraftmode=0 } +\optdef\myframe [] #1{... + \readkv\myframedefaults \readkv{\the\opt}% + \ifnum\mydraftmode=1 ...draft mode... \else ...final mode... \fi ...} \endtt +The syntax of \^`\kvx` `{}{}` allows to use `#1` inside the code. +It is replaced by the actual ``. Example: `\kvx{opt}{\message{opt is #1}}`, +then `\readkv{opt=HELLO}` prints \"opt is HELLO". + +The \^`\nokvx` `{}` can declare a processed for all +undeclared by \^`\kvx`. The `#1` and `#2` can be used in the , +`#1` is , `#2` is . If `\nokvx` is unused then nothing is done +for undeclared . Example: `\nokvx{\opwarnig{Unknown option "#1"}}`. + +The default dictionary name (where key-value pairs are processed) is +empty. You can use your specific dictionary by +\^`\kvdict``={}`. Then `\redakv`, `\kv`, `\iskv`, `\kvx` and `\nokvx` +macros use this named dictionary of / pairs. +Package options can be processed when +`\kvdict={pkg:}`, example is the `\mathset` macro in +\ulink[https://petr.olsak.net/ftp/olsak/optex/math-doc.pdf]{{\tt math.opm} package}. + +Recommendation: If the value of the key-value pair includes `=` or `,` or +`]`, then use the syntax `={}`. + +\_endinput + +2023-01-13 \kvx parameter added, \nokvx introduced. +2023-01-07 \kvdict, \kvx, \iskv added. +2020-12-21 Released diff --git a/macros/optex/base/lists.opm b/macros/optex/base/lists.opm index 189719302d..57b057d6c8 100644 --- a/macros/optex/base/lists.opm +++ b/macros/optex/base/lists.opm @@ -61,7 +61,7 @@ \_public \begitems \enditems \itemnum ; \_doc ---------------------------- - \`\novspaces` sets \`\listskipamount` to 0pt. + \`\novspaces` sets \^`\listskipamount` to 0pt. \_cod ---------------------------- \_def\_novspaces {\_removelastskip \_listskipamount=0pt \_relax} @@ -71,9 +71,9 @@ Various item marks are saved in `\_item:` macros. You can re-define then or define more such macros. The \`\style` `` does \`\_printitem``={\_item:}`. - More exactly: \^`\begitems` does `\_printitem=`\^`\defaultitem` first, - then \`\style` `` does \`\_printitem``={\_item:}` - when it is used and finally, `\_startitem` alias `*` uses `\_printitem`. + More exactly: \^`\begitems` does \^`\_printitem=`\^`\defaultitem` first, + then \^`\style` `` does \^`\_printitem``={\_item:}` + when it is used and finally, `\_startitem` alias `*` uses \^`\_printitem`. \_cod ----------------------------- \_def\_style#1{% diff --git a/macros/optex/base/math-macros.opm b/macros/optex/base/math-macros.opm index 83d3c5ab51..6e2365c9cc 100644 --- a/macros/optex/base/math-macros.opm +++ b/macros/optex/base/math-macros.opm @@ -368,7 +368,7 @@ \_doc ----------------------------- \`\big`, \`\Big`, \`\bigg`, \`\Bigg`, \`\bigl`, \`\bigm`, \`\bigr`, \`\Bigl`, \`\Bigm`, - \`\Bigr`, \`\biggl`, \`\biggm`, \`\biggr`, \`\Biggl`, \`\Biggm`, \`\Bigg`, \`\Biggr` + \`\Bigr`, \`\biggl`, \`\biggm`, \`\biggr`, \`\Biggl`, \`\Biggm`, \`\Biggr` are based on the \`\_scalebig` macro because we need the dependency on the various sizes of the fonts. \_cod ----------------------------- @@ -703,7 +703,7 @@ \_public\displaylines ; \_doc ----------------------------- - \`\openup`, \`\eqalignno` and `\leqalignno` macros are copied from + \`\openup`, \`\eqalignno` and \`\leqalignno` macros are copied from Plain \TeX/ unchanged. \_cod ----------------------------- diff --git a/macros/optex/base/more-macros.opm b/macros/optex/base/more-macros.opm index 418e71b774..8c62243234 100644 --- a/macros/optex/base/more-macros.opm +++ b/macros/optex/base/more-macros.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \eoldef {OpTeX useful macros <2022-11-24>} % preloaded in format +\_codedecl \eoldef {OpTeX useful macros <2023-01-18>} % preloaded in format \_doc ----------------------------- We define \`\opinput` `{}` macro which @@ -261,7 +261,7 @@ \_public \cstochar ; \_doc ----------------------------- - You can use expandable \`\bp``{}` convertor from + You can use expandable \`\bp``{}` converter from \TeX/ `` (or from an expression accepted by `\dimexpr` primitive) to a decimal value in big points (used as natural unit in the PDF format). So, you can write, for example: @@ -269,21 +269,32 @@ \pdfliteral{q \_bp{.3\hsize-2mm} \_bp{2mm} m 0 \_bp{-4mm} l S Q} \endtt You can use expandable \`\expr``{}` for analogical purposes. - It expands to the value of the `` at expand processor level - with \`\_decdigits` digits after the decimal point. + It expands to the value of the `` at expand processor level. The `` can include `+-*/()` and decimal numbers in common syntax. + The math functions (and pi constant) have to be prefixed by `math.`, + because it is processed by Lua interpreter. For + example `\expr{math.pi*math.sqrt(2)}`. + The list of available functions is in + \ulink[https://www.lua.org/manual/5.3/manual.html\#6.7]{Lua manual}. + + You can set the number of decimal digits after decimal point of the + results of `\bp` and `\expr` + by optional syntax `\bp[]{}` and + `\expr[]{}`. Default is \`\_decdigits`. The usage of prefixed versions \`\_expr` or \`\_bp` is more recommended because a user can re-define the control sequences `\expr` or `\bp`. \_cod ----------------------------- \_def\_decdigits{3} % digits after decimal point in \_bp and \_expr outputs. -\_def\_pttopb{% - \_directlua{tex.print(string.format('\_pcent.\_decdigits f', +\_def\_pttopb#1{% + \_directlua{tex.print(string.format('\_pcent.#1f', token.scan_dimen()/65781.76))}% pt to bp conversion } -\def\_bp#1{\_ea\_pttopb\_dimexpr#1\_relax} -\def\_expr#1{\_directlua{tex.print(string.format('\_pcent.\_decdigits f',#1))}} +\_def\_bp{\_isnextchar[{\_bpA}{\_bpA[\_decdigits]}} +\_def\_bpA[#1]#2{\_pttopb{#1}\_dimexpr#2\_relax} +\_def\_expr{\_isnextchar[{\_exprA}{\_exprA[\_decdigits]}} +\_def\_exprA[#1]#2{\_directlua{tex.print(string.format('\_pcent.#1f',#2))}} \_public \expr \bp ; @@ -363,6 +374,7 @@ \_endcode % ------------------------------------- +2023-01-18 \bp, \expr have optional syntax for setting dec-digits 2022-11-24 \setpos, \posx, \posy moved from OpTeX trick here 2022-11-22 \docgen writes banner to log 2022-11-20 \docgen reads lines before \_codedecl in order to define pkg. version diff --git a/macros/optex/base/optex.ini b/macros/optex/base/optex.ini index 4941ead57c..3266cf0ab1 100644 --- a/macros/optex/base/optex.ini +++ b/macros/optex/base/optex.ini @@ -21,7 +21,7 @@ % OpTeX version -\def\optexversion{1.09 Dec 2022} +\def\optexversion{1.10 Feb 2023} \def\fmtname{OpTeX} \let\fmtversion=\optexversion diff --git a/macros/optex/base/others.opm b/macros/optex/base/others.opm index 98df836f76..cde2f02fa1 100644 --- a/macros/optex/base/others.opm +++ b/macros/optex/base/others.opm @@ -177,9 +177,9 @@ \_else % LuaTeX 1.14 or newer: \_doc ----------------------------- - We set `\partokenneame` to `\_par` in order to keep the name `\par` in - user name space. I.e. a user can say `\def\par{paragraph}` for example - without crash of processing the document. Se section~\ref[prefixed] for + We set `\partokenneame` to `\_par` in order to keep the name `\par` in the + public namespace for end users. I.e.\ a user can say `\def\par{paragraph}` for example + without crash of processing the document. Se section~\ref[namespaces] for more details about the name space concept.\nl Moreover, we set `\partokencontext` to one in order to the `\_par` token is inserted not only at empty lines, but also at the end of `\vbox`, `\vtop` and diff --git a/macros/optex/base/parameters.opm b/macros/optex/base/parameters.opm index 499aee8d45..855969f4de 100644 --- a/macros/optex/base/parameters.opm +++ b/macros/optex/base/parameters.opm @@ -204,6 +204,14 @@ \_newdimen\_picheight \_picheight=0pt \_public \picwidth \picheight ; + \_doc ----------------------------- + \`\kvdict` is dictionary name when \~`\readkv`, \~`\kvx`, \~`\kv`, and \~`\iskv` are + processed. The default is empty. + \_cod ----------------------------- + +\_newtoks \_kvdict +\_public \kvdict ; + \_doc ----------------------------- The \`\everytt` is the token list used in \^`\begtt`...\^`\endtt` environment and @@ -542,12 +550,10 @@ % \_shadow=N \_overlapmargins=N \_hhkern=3pt \_vvkern=3pt} \_newdimen \_roundness \_roundness=5mm % used in \clippingoval macro - \_public \ovalparams \circleparams \roundness ; \_doc ----------------------------- - \OpTeX/ defines \"Standard \OpTeX/ markup language"% - \fnote{Will be developed in 2021.} + \OpTeX/ defines \"Standard \OpTeX/ markup language" which lists selected commands from chapter~1 and gives their behavior when a converter from \OpTeX/ document to HTML or Markdown or \LaTeX/ is used. The structure-oriented commands are selected here, but the commands which diff --git a/macros/optex/base/prefixed.opm b/macros/optex/base/prefixed.opm index a599e0ec85..023f3bc4de 100644 --- a/macros/optex/base/prefixed.opm +++ b/macros/optex/base/prefixed.opm @@ -152,44 +152,70 @@ \_endcode %---------------------------------------------------- -\sec[prefixed] Concept of namespaces of control sequences +\sec[basic-code] Basic principles of \OpTeX/ sources -\secc Prefixing internal control sequences +\secc[namespaces] Concept of namespaces of control sequences -All control sequences used in \OpTeX/ are used and defined with `_` prefix. -The user can be sure that when he/she does `\def\foo` then neither internal macros of -\OpTeX/ nor \TeX/ primitives will be damaged. For example -`\def\if{...}` will not damage macros because \OpTeX/'s macros -are using `\_if` instead of `\if`. +\OpTeX/ sets the category code of the \"`_`" character to 11 (letter) +and it is never changed.\fnote +{This is only singular exception form category codes given by plain \TeX.} +So, we can always construct multiletter control sequence names from letters +`A`--`Z`, `a`--`z`, and `_`. The \"letter `_`" works in math mode as a subscript +constructor because it is set as math active character (see section~\ref[math-macros]). -All \TeX/ primitives are initialized with two representative control -sequences: `\word` and `\_word`, for example `\hbox` and `\_hbox`. -The first alternative is reserved for users or such control sequences -can be re-defined by a user. - -\OpTeX/ sets the character `_` as letter, so it can be used in -control sequences. When a control sequence begins with this character -then it means that it is a primitive or it is used in \OpTeX/ macros as -internal. User can redefine such prefixed control sequence only -if he/she explicitly knows what happens. - -We never change catcode of `_`, so internal macros can be -redefined by user without problems if it is desired. We don't need -something like `\makeatletter` from \LaTeX/. - -\OpTeX/ defines all new macros as prefixed. For public usage of such macros, -we need to set their non-prefixed versions. This is done by +We distinguish following namespaces for multiletter control sequences: +\begitems +* Only alphabetical names are in the {\em public namespace}. They are intended + for end users when creating a document. Sometimes it is called {\em user + namespace} too. For example `\hbox`, `\fontfam`, `\MyMacro`. +* Only alphabetical lowercase names prefixed by single \"`_`" are in the + {\em private namespace}. It is used in \OpTeX/ internal macros. + For example `\_hbox`, `\_fontsel`. +* Names in the form `\__` are in the {\em package namespace}, + see section~\ref[pkg-namespace]. For example `\_qr_size`, `\_math_alist`. +* Names starting with two \"`_`" are in the {\em reserved namespace}. They can be + used for internal control sequences in font family files or in similar cases. +* Other names which include \"`_`" but not as the first character can be used + too, but with care, see the end of this section. +\enditems +All \TeX/ primitives are initialized with two control sequences with the +same meaning: {\em prefixed} control sequence +(in private namespace, for example `\_hbox`) +and {\em unprefixed} control sequence (in public namespace, for example `\hbox`). +All \OpTeX/ macros intended for end users are initialized in these two forms +too, for example `\_ref` and `\ref`. + +Users can declare any control sequences in the public namespace without worrying +that \OpTeX/ behavior is changed. This is because \OpTeX/ uses exclusively +prefixed control sequences in its macros. For example, a user can declare +`\def\fi{finito}` and nothing bad happens, if the user doesn't use `\fi` in +its original primitive meaning. You don't have to know all \TeX/ primitives +and \OpTeX/ macros, you can declare control sequences for your use in the +public namespace without limitations and nothing bad will happen. + +You can use control sequences from private or package namespace in +a \"read-only manner" without changing \OpTeX/ behavior too. +On the other hand, if you re-define a control sequence in the private name +space, the \OpTeX/ behavior can be changed. You can do it +but we suppose that you know what you are doing and what \OpTeX/ +behavior is changed. + +All multiletter control sequences declared by \OpTeX/ are defined in the private +namespace first (`\_def\_macro{...}`). If the declared control sequences are +intended for end users too then they are exported to the public namespace +after that. It is done by the \^`\public` macro: \begtt \catcode`\<=13 \public ; \endtt - For example \^`\public`` \foo \bar ;` does `\let\foo=\_foo`, `\let\bar=\_bar`. -At the end of each code segment in \OpTeX/, the `\_public` macro is used. You -can see which macros are defined for public usage in that code segment. +There is an exception of the above mentioned principle. Control sequences +which are alternatives to math characters (`\alpha`, `\forall`, `\subset` etc.) +are declared only in public name space if they are not used in any internal +\OpTeX/ macros. -The macro \^`\private` does the reverse job of `\public` with the same syntax. +The macro \^`\private` does the reverse job of \^`\public` with the same syntax. For example `\private \foo \bar ;` does `\let\_foo=\foo`, `\let\_bar=\bar`. This should be used when an unprefixed variant of a control sequence is declared already but we need the prefixed variant too. @@ -199,45 +225,33 @@ In this documentation: if both variants of a control sequence are declared the unprefixed variant. The code typically defines the prefixed variant and then the \^`\public` (or `\_public`) macro is used. -\secc[user-ns] Namespace of control sequences for users - -Users can (re)define or (re)declare any control sequence with a name without any `_`. -This does not make any problem in internal \OpTeX/ macros.\fnote -{The token `\par` is in user name space too from \OpTeX/ 1.04+ and -Lua\TeX/ 1.14, see also the end of section~\ref[others].} - -User can define or declare control sequences with `_` character, for -example `\my_control_sequence`, but with the following exceptions: - -\begitems -* Control sequences which begin with `_` are reserved for \TeX/ primitives, - \OpTeX/ internal macros and packages internal macros. -* Multiletter control sequences in the form - `\_` or `\_`, where - is a sequence of letters, are inaccessible, because they - are interpreted as `\` followed by `_` or as `\` followed by - `_`. This is important for writing math, for example: -\begtt \adef-{_} - \int-a^b ... is interpreted as \int _a^b - \max-M ... is interpreted as \max _M - \alpha-{ij} ... is interpreted as \alpha _{ij} -\endtt - This feature is implemented using Lua code at input processor level, see - the section~\ref[math-macros] for more details. You can deactivate this feature by - \^`\mathsboff`. After this, you can still write - `$`$\int$`_a^b$` (Unicode) or `$\int _a^b$` % $∫_a^b$ (Unicode) or $\int _a^b$ - without problems but `\int``_a^b` yields to undefined control sequence - `\int``_a`. You can activate this feature again by \^`\mathsbon`. The - effect will take shape from next line read from input file. -* Control sequences in the form `\__` is intended for package - writers as internal macros for a package with `` identifier, - see section~\ref[pkg-namespace]. -\enditems - The single-letter control sequences like `\%`, `\$`, `\^` etc. are not used in internal macros. Users can redefine them, but (of course) some classical features can be lost (printing percent character by `\%` for example). +It is very tempting to use control sequence names with `_` in order to +distinguish more words in the sequence name. If the first character isn't +`_` then such a name is outside private and package namespaces, so they can +be used for various purposes. For example `\my_control_sequence`. But there +is an exception: control sequences in the form `\_` or `\_`, +where is a sequence of letters, are inaccessible, because they +are interpreted as `\` followed by `_` or as `\` followed by +`_`. This feature is activated because we want to write math +formulae as in plain \TeX, for example: +\begtt + \int_a^b ... is interpreted as \int _a^b + \max_M ... is interpreted as \max _M + \alpha_{ij} ... is interpreted as \alpha _{ij} +\endtt +It is implemented using Lua code at input processor level, see +the section~\ref[math-macros] for more details. You can deactivate this feature by +\^`\mathsboff`. After this, you can still write +`$`$\int$`_a^b$` (Unicode) or `$\int _a^b$` % $∫_a^b$ (Unicode) or $\int _a^b$ +without problems but `\int``_a^b` yields to undefined control sequence +`\int``_a`. You can activate this feature again by \^`\mathsbon`. The +effect will take shape from next line read from input file. + + \secc Macro files syntax Segments of \OpTeX/ macros or external macro packages @@ -272,7 +286,7 @@ put macros for creating your documentation between first pair of \^`\_doc` ... \^`\_cod` used after \^`\_endcode`. These macros should \^`\load[doc]` and must be finished by \^`\bye`. Then you have code+documentation together in a single file and -user can generate the documentation of our package by +user can generate the documentation of your package by \^`\docgen` used at command line: \begtt optex -jobname pkgname-doc '\docgen pkgname' @@ -307,10 +321,10 @@ does `\let\foo = \__foo` for each given sequence when \^`\_namespace{}` is declared. Moreover, it prints a warning if `\foo` is defined already. The \^`\_nsprivate` macro does reverse operation to it without warnings. Example: you can define `\def\.macro{...}` and then -set it to the user name space by `\_nspublic \macro;`. +set it to the public namespace by `\_nspublic \macro;`. It could happen that a package writer needs to declare a control sequence -(say `\foo`) directly without setting it in `\__foo` name space +(say `\foo`) directly without setting it in `\__foo` namespace followed by using \^`\_nspublic`. The \^`\newpublic` prefix should be used in this case, for example `\_newpublic\_def\foo` or `\_newpublic\_chardef\foo` or `\_newpublic{\_long\_def}\foo`. The \^`\newpublic``\` prints @@ -338,9 +352,9 @@ If you are writing a macro file that is intended to be published for \OpTeX/, then you are greatly welcome. You should follow these rules: \begitems -* Don't use control sequences from the user namespace in the macro +* Don't use control sequences from the public namespace in the macro bodies if there is no explicit and documented reason to do this. -* Don't declare control sequences in the user namespace if there are no +* Don't declare control sequences in the public namespace if there are no explicit and documented reasons to do this. * Use control sequences from \OpTeX/ and primitive namespace in read-only mode, if there is not an explicit and documented reason to @@ -368,11 +382,12 @@ used directly in \OpTeX/ and from other published macros. This extension `.opm` has precedence before `.tex` when the \^`\load` macro is used. -The `qrcode.opm` is the first example of how an external macro file for \OpTeX/ +The `math.opm` is a good example of how an external macro file for \OpTeX/ can look like. \endinput +2023-01-30 doc. about namespaces rewritten 2022-11-25 \_resetnamespace: moved \gdef\_namesp:#1 {} to \_namespace 2022-11-24 \newpublic introduced, \_checkexists with only two parameters. 2022-11-22 \currfile introduced and used in \_codedecl diff --git a/macros/optex/base/references.opm b/macros/optex/base/references.opm index 9da2bca30f..56ad7ad589 100644 --- a/macros/optex/base/references.opm +++ b/macros/optex/base/references.opm @@ -1,6 +1,6 @@ %% This is part of the OpTeX project, see http://petr.olsak.net/optex -\_codedecl \ref {References <2021-04-13>} % preloaded in format +\_codedecl \ref {References <2022-01-22>} % preloaded in format \_doc ---------------------------- \`\_Xpage` `{}{}` saves the parameter pair into \`\_currpage`. @@ -121,5 +121,6 @@ See section \ref[ref-file] for more information about `.ref` file concept. \_endinput +2022-01-22 ... extended format for \ref, \pgref 2021-04-13 ... \_slideshook introduced (used by \slides) 2020-03-03 ... released diff --git a/macros/optex/base/sections.opm b/macros/optex/base/sections.opm index 7d7a78232b..7940a47bfa 100644 --- a/macros/optex/base/sections.opm +++ b/macros/optex/base/sections.opm @@ -171,7 +171,7 @@ First, we read the optional parameter `[