# [NTG-context] Simple command with variable number of arguments

Hans Hagen pragma at wxs.nl
Fri May 23 20:00:39 CEST 2014

On 5/23/2014 3:48 PM, Jeong Dal wrote:
> Dear Luigi and listers,
>
> Last year, I need to write a text for a linear algebra class.
> Since there are many \startmatrix … \stopmatrix and matrix calculations, I wrote a lua code which did matrix calculations and writing with a lot of help from this list.
> Using the code, I can write class materials easily. It is good enough for my purpose.
> I am not good in Lua coding, so there may be many things to be checked for efficiency and for stability.
>
> However, I attached the code because there may be someone who need it.
> It is also good thing to return what I get from the list back.
>
> I hope that you enhance the code for better performance since you are an expert in Lua.

matrixOP.symMatrix = function(sym, x, y, nx ,ny) -- symMatrix("a", "m", "n")
local nx = nx or 2
local ny = ny or nx
local function filled(i,y)
local mrow = { }
for j=1,nx do
table.insert(mrow, string.formatters["%s_{%s%s}"](sym,i,j))
end
table.insert(mrow,"\\cdots")
table.insert(mrow,string.formatters["%s_{%s%s}"](sym,i,y))
return mrow
end
local function dummy()
local mrow = { }
for j=1,nx do
table.insert(mrow,"\\vdots")
end
table.insert(mrow,"\\ddots")
table.insert(mrow,"\\vdots")
return mrow
end
--
local mm = { }
for i=1,ny do
table.insert(mm,filled(i,y))
end
table.insert(mm,dummy())
table.insert(mm,filled(x,y))
return mm
end

Also, variable nx, ny:

\ctxlua{matrixOP.write(matrixOP.symMatrix("a","m","n",4,8))}

Maybe this too:

local default = {
left  = [[\left(\,]],
right = [[\,\right)]],
}

matrixOP.write = function (t)
context.startmatrix(default)
for _, r in ipairs(t) do
for _, c in ipairs(r) do
context.NC(c)
end
context.NR()
end
context.stopmatrix()
end

matrixOP.writeDet = function(t)
context.startmatrix(default)
for _, r in ipairs(t) do
for _, c in ipairs(r) do
context.NC(c)
end
context.NR()
end
context.stopmatrix()
end

And:

matrixOP.rowMult = function(t, i, m) -- replace i-th row with m*(i-th row)
for k = 1, #t[i] do t[i][k] =  m*t[i][k] end
end

matrixOP.rowMultSum = function(t, i, j, m) -- replace i-th row with i-th
row + m*(j-th row)
for k = 1, #t do t[i][k] = t[i][k] + m*t[j][k] end
end

(no need for further speedup as it't non-critical code with neglectable
runtime)

More Luaish (local usage):

matrixOP.transpose = function(m) -- transpose of a matrix
local mT={}
for j = 1, #m do
local mTrow={}
for i=1, #m do
local temp = m[i][j]
table.insert(mTrow, temp)
end
table.insert(mT, mTrow)
end
return mT
end

Don't forget the local here:

matrixOP.inner = function (u, v) -- inner product of two vectors
local temp=0
if #u == #v then
for i=1, #u do
temp = temp + u[i]*v[i]
end
end
return temp
end

and here:

matrixOP.product = function(m1, m2) -- product of two matrices
local m3={}
if #m1 == #m2 then
for i = 1, #m1 do
local mrow={}
for j=1, #m2 do
local temp = 0
for k=1, #m1 do
u = m1[i][k]*m2[k][j]
temp = temp + u
end
table.insert(mrow, temp)
end
table.insert(m3, mrow)
end
end
return m3
end

less code:

matrixOP.searchRow = function(m, i)
local pr = #m + 1
for k=i+1, #m do
if m[k][i] == 0 then
k = k+1
else
pr = k
break
end
end
if pr <= #m then
return pr
else
return 0
end
end

Are you sure this is ok? I've added a copy as you might want to keep the
original table:

matrixOP.upperTri = function(m)
local temp = table.copy(m)
for i=1, #temp-1 do
local pivot = temp[i][i]
if pivot == 0 then
local pRow = matrixOP.searchRow(temp, i)
if pRow==0 then
break
end
matrixOP.rowChange(temp, i, pRow)
sgn=(-1)*sgn
end
for k=i+1, #temp do
matrixOP.rowMultSum(temp, k, i,-temp[k][i]/temp[i][i])
end
end
return temp
end

So then, watch how we use the return value of this one:

matrixOP.determinant = function(m)
if #m ==#mthen
local det = 1
local t = matrixOP.upperTri(m)
for i=1,#t do
det = det * t[i][i]
end
return det
else
return 0
end
end

> I always thank to this list and to developers of ConTeXt.

Based on the attached I can make a more efficient version that we can
then add to the distribution (maybe you need more than this?)

Hans

> Best regards,
>
> Dalyoung
>
>
>
>
>
>
>
>
>>
>> Message: 1
>> Date: Fri, 23 May 2014 13:44:30 +0200
>> From: luigi scarso <luigi.scarso at gmail.com>
>> To: mailing list for ConTeXt users <ntg-context at ntg.nl>
>> Subject: Re: [NTG-context] Simple command with variable number of
>> 	arguments
>> Message-ID:
>> Content-Type: text/plain; charset="utf-8"
>>
>> On Fri, May 23, 2014 at 11:54 AM, Matthias Weber <matweber at indiana.edu>wrote:
>>
>>> Dear All,
>>>
>>> I would like to define a command that expands
>>>
>>> \vector{2,4} % or vector[2,4] if that?s easier
>>>
>>> to
>>>
>>> \startpmatrix
>>> \NC 2 \NR
>>> \NC 4 \NR
>>> \stoppmatrix
>>>
>>> and more generally
>>>
>>> \vector{2,4,1,7}
>>>
>>> to
>>>
>>> \startpmatrix
>>> \NC 2 \NR
>>> \NC 4 \NR
>>> \NC 1 \NR
>>> \NC 7 \NR
>>> \stoppmatrix
>>>
>>> Any hints how to achieve this?
>>>
>>> Thanks,
>>>
>>
>>
>>
>> \definemathmatrix
>>   [pmatrix]
>>   [left={\left(\,},right={\,\right)}]
>>
>> \startluacode
>> document = document or {}
>> document.matthias =  document.matthias or {}
>> local function lua_columnvector(a)
>> context.startpmatrix()
>>   for i,v in ipairs(a) do
>>      context.NC() context(tostring(v))  context.NR()
>> end
>> context.stoppmatrix()
>> end
>> document.matthias.lua_columnvector = document.matthias.lua_columnvector  or
>> lua_columnvector
>> \stopluacode
>>
>> \def\columnvector#1{\ctxlua{document.matthias.lua_columnvector(#1)}}
>>
>> \starttext
>> \startformula
>> \columnvector{{1,2,3}} %% watch the double { !
>> \stopformula
>>
>>
>> \stoptext
>>
>> --
>> luigi
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>
>
>
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
>
> maillist : ntg-context at ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
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> wiki     : http://contextgarden.net
> ___________________________________________________________________________________
>

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