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우선 Tcl 라이브러인 Tcllib를 http://www.tcl.tk/software/tcllib/ 에서 내려 받은 다음, 아래의 일련의 명령어들을 실행함으로서 라이브러리를 설치한다. 이 때, 관리자 계정으로 로그인 한 상태이어야 한다.  

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 

Matrix.tcl

#!/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 ]"



# Is a given matrix symmetric?

puts "isSymmetric( At * A ) = [::math::linearalgebra::symmetric $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]"

위 스크립트를 실행시키면 그 결과가 아래와 같이 출력이 된다. 

$ ./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 



isSymmetric( At * A ) = 1

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