Kwkang at 09:03, 1 March 2009

2009-03-01T09:03:07Z

← Older revision		Revision as of 09:03, 1 March 2009
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	If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I introduce Tcl standard library that can ~~alleviate~~ our ~~burdens~~.		If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some vector or matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I introduce Tcl standard library, '''Tcllib''' that can resolve our troubles.

	Install		==Install==

	Download Tcllib from http://www.tcl.tk/software/tcllib/ and install it		Download Tcllib from http://www.tcl.tk/software/tcllib/ and install it
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	# ./installer.tcl		# ./installer.tcl

	Usage		==Usage==

	There are on-line documentations at http://tcllib.sourceforge.net/doc/ . Below is shown a sample Tcl script, ~~matrix~~.tcl to show how ~~we can~~ use ~~Tcl~~ linear algebra library.		There are on-line documentations at http://tcllib.sourceforge.net/doc/ . Below is shown a sample Tcl script, [[Media:Matrix.tcl \| Matrix.tcl]] to show how to use linear algebra library in Tcl.

	<pre>		<pre>
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	set AtA [::math::linearalgebra::matmul $At $A]		set AtA [::math::linearalgebra::matmul $At $A]
	puts "[::math::linearalgebra::show $AtA ]"		puts "[::math::linearalgebra::show $AtA ]"

			# Is a given matrix symmetric?
			puts "isSymmetric( At * A ) = [::math::linearalgebra::symmetric $AtA]"

	# Matrix determinant		# Matrix determinant
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	If you run the script, the result will look like the following.		If you run the script, the result will look like the following.
	<pre>		<pre>
	$ ./~~matrix~~.tcl		$ ./Matrix.tcl
	Tcl script name: ./~~matrix~~.tcl, with 0 arguments		Tcl script name: ./Matrix.tcl, with 0 arguments

	Durer's magic square		Durer's magic square
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	360.0000 206.0000 212.0000 378.0000		360.0000 206.0000 212.0000 378.0000

			isSymmetric( At * A ) = 1
	det(A) = 0.		det(A) = 0.

Kwkang: New page: If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I i...

2009-03-01T08:36:55Z

New page: If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I i...

New page

If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I introduce Tcl standard library that can alleviate our burdens.

Install

Download Tcllib from http://www.tcl.tk/software/tcllib/ and install it

# mv tcllib-1.11.1.tar.gz /usr/local/src/
# cd /usr/local/src/
# tar -zxvf tcllib-1.11.1.tar.gz
# cd tcllib-1.11.1
# ./installer.tcl

Usage

There are on-line documentations at http://tcllib.sourceforge.net/doc/ . Below is shown a sample Tcl script, matrix.tcl to show how we can use Tcl linear algebra library.

<pre>
#!/bin/sh
# the next line is executed by /bin/sh, but not tcl \
echo Tcl script name: $0, with $# arguments; echo ; exec tclsh "$0" "$@"

#*******************************************
# Call necessary pacakges
#*******************************************
package require math::linearalgebra

#*******************************************
# Definition of procedures
#*******************************************
proc det matrix {
if {[llength $matrix] != [llength [lindex $matrix 0]]} {
error "non-square matrix"
}
switch [llength $matrix] {
2 {
foreach {a b c d} [join $matrix] break
expr {$a*$d - $b*$c}
} default {
set i 0
set mat2 [lrange $matrix 1 end]
set res 0
foreach element [lindex $matrix 0] {
if $element {
set sign [expr {$i%2? -1: 1}]
set res [expr {$res + $sign*$element* [det [cancelcol $i $mat2]]}]
}
incr i
}
set res
}
}
}
proc cancelcol {n matrix} {
set res {}
foreach row $matrix {
lappend res [lreplace $row $n $n]
}
set res
}

#*******************************************
# Main program starts here
#*******************************************
# Durer's magic square
puts "Durer's magic square"
set A {{16 3 2 13} {5 10 11 8} {9 6 7 12} {4 15 14 1}}
puts "A = \n[::math::linearalgebra::show $A %2d]"

# Transpose the matrix A
puts "Transpose of the matrix A, At ="
set At [::math::linearalgebra::transpose $A]
puts "[::math::linearalgebra::show $At %2d]"

# Matrix Summation
puts "A + At ="
puts "[::math::linearalgebra::show \
[::math::linearalgebra::add $A $At] %2d]"

# Matrix multiplication
puts "At * A ="
set AtA [::math::linearalgebra::matmul $At $A]
puts "[::math::linearalgebra::show $AtA ]"

# Matrix determinant
set detA [det $A]
puts "det(A) = $detA.\n"

# Create a 3X3 matrix O whose elements are all zeros.
puts "Create a 3X3 matrix O whose elements are all zeros."
set O [::math::linearalgebra::mkMatrix 3 3 0]
puts "O = \n[::math::linearalgebra::show $O]"

# Create a 3X3 identity matrix I
puts "Create a 3X3 identity matrix I."
set I [::math::linearalgebra::mkIdentity 3]
puts "I = \n[::math::linearalgebra::show $I]"

# Create a 3X3 random matrix R
puts "Create a 3X3 random matrix R."
set R [::math::linearalgebra::mkRandom 3]
puts "R = \n[::math::linearalgebra::show $R]"

# Get the 2nd column from the matrix R.
puts "Get the 2nd column from the matrix R."
set c2 [::math::linearalgebra::getcol $R 1]
puts "c2 = \n[::math::linearalgebra::show $c2]"
</pre>

If you run the script, the result will look like the following.
<pre>
$ ./matrix.tcl
Tcl script name: ./matrix.tcl, with 0 arguments

Durer's magic square
A =
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1

Transpose of the matrix A, At =
16 5 9 4
3 10 6 15
2 11 7 14
13 8 12 1

A + At =
32 8 11 17
8 20 17 23
11 17 14 26
17 23 26 2

At * A =
378.0000 212.0000 206.0000 360.0000
212.0000 370.0000 368.0000 206.0000
206.0000 368.0000 370.0000 212.0000
360.0000 206.0000 212.0000 378.0000

det(A) = 0.

Create a 3X3 matrix O whose elements are all zeros.
O =
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000
0.0000 0.0000 0.0000

Create a 3X3 identity matrix I.
I =
1.0000 0.0000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.0000

Create a 3X3 random matrix R.
R =
0.3562 0.3277 0.0830
0.6627 0.9329 0.0609
0.9916 0.1730 0.3524

Get the 2nd column from the matrix R.
c2 =
0.3277
0.9329
0.1730
</pre>

Tcl library can do more than what is explained here. Refer its documentation.

Standard Tcl Library - Revision history

Kwkang at 09:03, 1 March 2009

Kwkang: New page: If you've used Tcl, sometimes you may feel that Tcl would be more convenient if it can support some matrix operations such as matrix summation, transpose, dot/cross product, norm, etc. I i...