math::matrix Class Reference

Public Member Functions
static function	__add (local a, local b)
static function	__concat (local a, local b)
static function	__div (local a, local b)
static function	__eq (local a, local b)
static function	__mul (local a, local b)
static function	__pow (local a, local b)
static function	__sub (local a, local b)
static function	__tostring (local a)
static function	abs (local a)
	applies abs function to symbol More...
static function	add (local m1, local m2)
	functions are designed to be light on checks More...
static function	columns (local mtx)
static function	concath (local m1, local m2)
static function	concatv (local m1, local m2)
static function	copy (local m1)
	local functions to copy matrix values More...
static function	cross (local m1, local m2)
function	det ()
static function	div (local m1, local m2)
static function	divnum (local m1, local num)
function	dogauss ()
	locals More...
static function	elementstostrings (local mtx)
static function	getelement (local mtx, local i, local j)
function	gsub (local from, local to)
	Performs string.gsub on symbol. More...
function	invert ()
static function	ipairs (local mtx)
static function	latex (local mtx, local align)
static function	len (local m1)
static function	makereplacer (local ...)
	creates function that replaces one letter by something else More...
static function	mul (local m1, local m2)
static function	mulnum (local m1, local num)
static function	new (local o)
	note '...' is always faster than 'arg1,arg2,...' if it can be used More...
function	new (local rows, local columns, local value)
	access to the metatable we set at the end of the file More...
static function	normf (local mtx)
static function	normmax (local mtx)
static function	pow (local m1, local num)
static function	print (local ...)
static function	random (local mtx, local start, local stop, local idp)
static function	replace (local m1, local func, local ...)
static function	root (local m1, local root, local iters)
static function	rotl (local m1)
static function	rotr (local m1)
static function	round (local mtx, local idp)
	Functions changing the matrix itself. More...
static function	rows (local mtx)
static function	scalar (local m1, local m2)
	a vector is defined as a 3x1 matrix More...
static function	setelement (local mtx, local i, local j, local value)
static function	size (local mtx)
static function	solve (local m1)
static function	sqrt (local a)
	applies sqrt function to symbol More...
static function	sqrt (local m1, local iters)
	you have to determin for yourself if the result is sufficent enough for you More...
static function	sub (local m1, local m2)
static function	subm (local m1, local i1, local j1, local i2, local j2)
static function	tostring (local mtx, local formatstr)
	symbol( arg ) More...
static function	transpose (local m1)
function	type ()
	Returns "symbol" if object is a symbol type, else nothing. More...
static function	type (local mtx)

Public Attributes
string	_NAME
string	_TYPE
string	_VERSION
table	symbol

Member Function Documentation

__add()

static function __add	(	local	a,
		local	b
	)

__concat()

static function __concat	(	local	a,
		local	b
	)

__div()

static function __div	(	local	a,
		local	b
	)

__eq()

static function __eq	(	local	a,
		local	b
	)

__mul()

static function __mul	(	local	a,
		local	b
	)

__pow()

static function __pow	(	local	a,
		local	b
	)

__sub()

static function __sub	(	local	a,
		local	b
	)

__tostring()

static function __tostring

(

local

a

)

abs()

static function abs

(

local

a

)

applies abs function to symbol

add()

static function add	(	local	m1,
		local	m2
	)

functions are designed to be light on checks

matrix ( rows [, comlumns [, value]] )

set __call behaviour of matrix

for matrix( ... ) as matrix.new( ... )so we get Lua errors instead on wrong input

matrix.<functions> should handle any table of structure t[i][j] = value

we always return a matrix with scripts metatable

cause its faster than setmetatable( mtx, getmetatable( input matrix ) )

for real, complex and symbolic matrices //–

note: real and complex matrices may be added, subtracted, etc.

matrix.add ( m1, m2 )

Add two matrices; m2 may be of bigger size than m1

columns()

static function columns

(

local

mtx

)

matrix.columns ( mtx )

return number of columns

concath()

static function concath	(	local	m1,
		local	m2
	)

matrix.concath( m1, m2 )

Concatenate two matrices, horizontal

will return m1 m2; rows have to be the same

e.g.: #m1 == #m2

concatv()

static function concatv	(	local	m1,
		local	m2
	)

matrix.concatv ( m1, m2 )

Concatenate two matrices, vertical

will return m1

              m2

columns have to be the same; e.g.: #m1[1] == #m2[1]

copy()

static function copy

(

local

m1

)

local functions to copy matrix values

matrix.copy ( m1 )

Copy a matrix

simple copy, one can write other functions oneself

cross()

static function cross	(	local	m1,
		local	m2
	)

matrix.cross ( m1, m2 )

returns the Cross Product of two 3x1 matrices (vectors)

det()

function det

(

)

matrix.det ( m1 )

Calculate the determinant of a matrix

m1 needs to be square

Can calc the det for symbolic matrices up to 3x3 too

The function to calculate matrices bigger 3x3

is quite fast and for matrices of medium size ~(100x100)

and average values quite accurate

here we try to get the nearest element to |1|, (smallest pivot element)

os that usually we have |mtx[i][j]/subdet| > 1 or mtx[i][j];

with complex matrices we use the complex.abs function to check if it is bigger or smaller

div()

static function div	(	local	m1,
		local	m2
	)

matrix.div ( m1, m2 )

Divide two matrices; m1 columns must be equal to m2 rows

m2 must be square, to be inverted,

if that fails returns the rank of m2 as second argument

e.g. #m1[1] == #m2; #m2 == #m2[1]

divnum()

static function divnum	(	local	m1,
		local	num
	)

matrix.divnum ( m1, num )

Divide matrix by a number

num may be of type 'number' or 'complex number'

strings get converted to complex number, if that fails then to symbol

dogauss()

function dogauss

(

)

locals

matrix.dogauss ( mtx )

Gauss elimination, Gauss-Jordan Method

this function changes the matrix itself

returns on success: true,

returns on failure: false,'rank of matrix'checking here for the element nearest but not equal to zero (smallest pivot element).

This way the factor in dogauss will be >= 1, which

can give better results. note: in –// ... //– we have a way that does no divison,

however with big number and matrices we get problems since we do no reducing

elementstostrings()

static function elementstostrings

(

local

mtx

)

matrix.remcomplex ( mtx )

set the matrix elements to strings

IMPROVE: tostring v.s. tostringelements confusing

getelement()

static function getelement	(	local	mtx,
		local	i,
		local	j
	)

matrix.getelement ( mtx, i, j )

return specific element ( row,column )

returns element on success and nil on failure

gsub()

function gsub	(	local	from,
		local	to
	)

Performs string.gsub on symbol.

for use in matrix.replace

invert()

function invert

(

)

matrix.invert ( m1 )

Get the inverted matrix or m1

matrix must be square and not singular

on success: returns inverted matrix

on failure: returns nil,'rank of matrix'

ipairs()

static function ipairs

(

local

mtx

)

matrix.ipairs ( mtx )

iteration, same for complex

latex()

static function latex	(	local	mtx,
		local	align
	)

matrix.latex ( mtx [, align] )

LaTeX output

len()

static function len

(

local

m1

)

matrix.len ( m1 )

returns the Length of a 3x1 matrix (vector)

makereplacer()

static function makereplacer

(

local ...

)

creates function that replaces one letter by something else

makereplacer( "a",4,"b",7, ... )(x)

will replace a with 4 and b with 7 in symbol x.

for use in matrix.replace

mul()

static function mul	(	local	m1,
		local	m2
	)

matrix.mul ( m1, m2 )

Multiply two matrices; m1 columns must be equal to m2 rows

e.g. #m1[1] == #m2

mulnum()

static function mulnum	(	local	m1,
		local	num
	)

matrix.mulnum ( m1, num )

Multiply matrix with a number

num may be of type 'number' or 'complex number'

strings get converted to complex number, if that fails then to symbol

new() [1/2]

static function new

(

local

o

)

note '...' is always faster than 'arg1,arg2,...' if it can be used

MetaTable

as we declaired on top of the page

local/shared metatable

matrix_meta Set add "+" behaviour Set subtract "-" behaviour Set multiply "*" behaviour Set division "/" behaviour Set unary minus "-" behavior Set power "^" behaviour

if opt is any integer number will do mtx^opt

(returning nil if answer doesn't exist)

if opt is 'T' then it will return the transpose matrix

only for complex:

if opt is '*' then it returns the complex conjugate matrix Set equal "==" behaviour Set tostring "tostring( mtx )" behaviour set __call "mtx( [formatstr] )" behaviour, mtx [, formatstr]

__index handling

access to the symbolic metatable

new() [2/2]

function new	(	local	rows,
		local	columns,
		local	value
	)

access to the metatable we set at the end of the file

matrix:new ( rows [, columns [, value]] )

if rows is a table then sets rows as matrix

if rows is a table of structure {1,2,3} then it sets it as a vector matrix

if rows and columns are given and are numbers, returns a matrix with size rowsxcolumns

if num is given then returns a matrix with given size and all values set to num

if rows is given as number and columns is "I", will return an identity matrix of size rowsxrows

Returns

math.matrix

normf()

static function normf

(

local

mtx

)

matrix.normf ( mtx )

calculates the Frobenius norm of the matrix.

||mtx||_F = sqrt(SUM_{i,j} |a_{i,j}|^2)

http://en.wikipedia.org/wiki/Frobenius_norm#Frobenius_norm

normmax()

static function normmax

(

local

mtx

)

matrix.normmax ( mtx )

calculates the max norm of the matrix.

||mtx||_{max} = max{|a_{i,j}|}

Does not work with symbolic matrices

http://en.wikipedia.org/wiki/Frobenius_norm#Max_norm

pow()

static function pow	(	local	m1,
		local	num
	)

for real and complex matrices only //–

matrix.pow ( m1, num )

Power of matrix; mtx^(num)

num is an integer and may be negative

m1 has to be square

if num is negative and inverting m1 fails

returns the rank of matrix m1 as second argument

print()

static function print

(

local ...

)

matrix.print ( mtx [, formatstr] )

print out the matrix, just calls tostring

random()

static function random	(	local	mtx,
		local	start,
		local	stop,
		local	idp
	)

matrix.random( mtx [,start] [, stop] [, idip] )

fillmatrix with random values

replace()

static function replace	(	local	m1,
		local	func,
		local ...
	)

matrix.replace (mtx, func, ...)

for each element e in the matrix mtx, replace it with func(mtx, ...).

root()

static function root	(	local	m1,
		local	root,
		local	iters
	)

matrix.root ( m1, root [,iters] )

calculate any root of a matrix

source: http://www.dm.unipi.it/~cortona04/slides/bruno.pdf

m1 and root have to be given;(m1 = matrix, root = number)

conditions same as matrix.sqrt

returns same values as matrix.sqrt

rotl()

static function rotl

(

local

m1

)

matrix.rotl ( m1 )

Rotate Left, 90 degrees

rotr()

static function rotr

(

local

m1

)

matrix.rotr ( m1 )

Rotate Right, 90 degrees

round()

static function round	(	local	mtx,
		local	idp
	)

Functions changing the matrix itself.

matrix.round ( mtx [, idp] )

perform round on elements

rows()

static function rows

(

local

mtx

)

matrix.rows ( mtx )

return number of rows

scalar()

static function scalar	(	local	m1,
		local	m2
	)

a vector is defined as a 3x1 matrix

get a vector; vec = matrix{{ 1,2,3 }}^'T'

matrix.scalar ( m1, m2 )

returns the Scalar Product of two 3x1 matrices (vectors)

setelement()

static function setelement	(	local	mtx,
		local	i,
		local	j,
		local	value
	)

matrix.setelement( mtx, i, j, value )

set an element ( i, j, value )

returns 1 on success and nil on failure

size()

static function size

(

local

mtx

)

matrix.size ( mtx )

get matrix size as string rows,columns

solve()

static function solve

(

local

m1

)

matrix.solve ( m1 )

solve; tries to solve a symbolic matrix to a number

sqrt() [1/2]

static function sqrt

(

local

a

)

applies sqrt function to symbol

sqrt() [2/2]

static function sqrt	(	local	m1,
		local	iters
	)

you have to determin for yourself if the result is sufficent enough for you

matrix.sqrt ( m1 [,iters] )

calculate the square root of a matrix using "Denman Beavers square root iteration"

condition: matrix rows == matrix columns; must have a invers matrix and a square root

if called without additional arguments, the function finds the first nearest square root to

input matrix, there are others but the error between them is very small

if called with agument iters, the function will return the matrix by number of iterations

the script returns:local average error square root function

sub()

static function sub	(	local	m1,
		local	m2
	)

matrix.sub ( m1 ,m2 )

Subtract two matrices; m2 may be of bigger size than m1

subm()

static function subm	(	local	m1,
		local	i1,
		local	j1,
		local	i2,
		local	j2
	)

matrix.subm ( m1, i1, j1, i2, j2 )

Submatrix out of a matrix

input: i1,j1,i2,j2

i1,j1 are the start element

i2,j2 are the end element

condition: i1,j1,i2,j2 are elements of the matrix

tostring()

static function tostring	(	local	e,
		local	fstr
	)

symbol( arg )

matrix.tostring ( mtx, formatstr )

tostring function

same as symbol.to( arg )

set __call behaviour of symbol Converts object to string, optionally with formatting.

transpose()

static function transpose

(

local

m1

)

matrix.transpose ( m1 )

Transpose a matrix

switch rows and columns

type() [1/2]

function type

(

)

Returns "symbol" if object is a symbol type, else nothing.

type() [2/2]

static function type

(

local

mtx

)

matrix.type ( mtx )

get type of matrix, normal/complex/symbol or tensor

Member Data Documentation

_NAME

string _NAME

_TYPE

string _TYPE

_VERSION

string _VERSION

symbol

table symbol

---

The documentation for this class was generated from the following file:

• src/math/matrix.lua.hpp