Tcl Library Source Code

'\"
'\" Generated from file 'linalg\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004-2008 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>
'\" Copyright (c) 2004 Ed Hume <http://www\&.hume\&.com/contact\&.us\&.htm>
'\" Copyright (c) 2008 Michael Buadin <relaxkmike@users\&.sourceforge\&.net>
'\"
.TH "math::linearalgebra" n 1\&.1\&.5 tcllib "Tcl Math Library"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
math::linearalgebra \- Linear Algebra
.SH SYNOPSIS
package require \fBTcl  ?8\&.4?\fR
.sp
package require \fBmath::linearalgebra  ?1\&.1\&.5?\fR
.sp
\fB::math::linearalgebra::mkVector\fR \fIndim\fR \fIvalue\fR
.sp
\fB::math::linearalgebra::mkUnitVector\fR \fIndim\fR \fIndir\fR
.sp
\fB::math::linearalgebra::mkMatrix\fR \fInrows\fR \fIncols\fR \fIvalue\fR
.sp

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 ] <hr>
<h1 class="title">math::linearalgebra(n) 1.1.5 tcllib &quot;Tcl Math Library&quot;</h1>
<div id="name" class="section"><h2><a name="name">Name</a></h2>
<p>math::linearalgebra - Linear Algebra</p>
</div>
<div id="toc" class="section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="toc">
<li class="section"><a href="#toc">Table Of Contents</a></li>
<li class="section"><a href="#synopsis">Synopsis</a></li>

<li class="section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="synopsis">
<ul class="requirements">
<li>package require <b class="pkgname">Tcl <span class="opt">?8.4?</span></b></li>
<li>package require <b class="pkgname">math::linearalgebra <span class="opt">?1.1.5?</span></b></li>
</ul>
<ul class="syntax">
<li><a href="#1"><b class="cmd">::math::linearalgebra::mkVector</b> <i class="arg">ndim</i> <i class="arg">value</i></a></li>
<li><a href="#2"><b class="cmd">::math::linearalgebra::mkUnitVector</b> <i class="arg">ndim</i> <i class="arg">ndir</i></a></li>
<li><a href="#3"><b class="cmd">::math::linearalgebra::mkMatrix</b> <i class="arg">nrows</i> <i class="arg">ncols</i> <i class="arg">value</i></a></li>
<li><a href="#4"><b class="cmd">::math::linearalgebra::getrow</b> <i class="arg">matrix</i> <i class="arg">row</i> <span class="opt">?imin?</span> <span class="opt">?imax?</span></a></li>
<li><a href="#5"><b class="cmd">::math::linearalgebra::setrow</b> <i class="arg">matrix</i> <i class="arg">row</i> <i class="arg">newvalues</i> <span class="opt">?imin?</span> <span class="opt">?imax?</span></a></li>

[comment {-*- tcl -*- doctools manpage}]
[vset VERSION 1.1.5]
[manpage_begin math::linearalgebra n [vset VERSION]]
[keywords {least squares}]
[keywords {linear algebra}]
[keywords {linear equations}]
[keywords math]
[keywords matrices]
[keywords matrix]
[keywords vectors]
[copyright {2004-2008 Arjen Markus <[email protected]>}]
[copyright {2004 Ed Hume <http://www.hume.com/contact.us.htm>}]
[copyright {2008 Michael Buadin <[email protected]>}]
[moddesc   {Tcl Math Library}]
[titledesc {Linear Algebra}]
[category  Mathematics]
[require Tcl [opt 8.4]]
[require math::linearalgebra [opt [vset VERSION]]]
[description]
[para]
This package offers both low-level procedures and high-level algorithms
to deal with linear algebra problems:

[list_begin itemized]
[item]

    # Determine the shift h so that the matrix A+hI is positive
    # definite (the Gershgorin region)
    #
    set h {}
    set i 0
    foreach row $A {
        set aii [lindex $row $i]
        set sum [expr {$aii + abs($aii) - [norm_one $row]}]
        incr i

        if { $h == {} || $sum < $h } {
            set h $sum
        }
    }
    if { $h <= $eps } {

    return $result
}

#
# Announce the package's presence
#
package provide math::linearalgebra 1.1.5

if { 0 } {
Te doen:
behoorlijke testen!
matmul
solveGauss_band
join_col, join_row

    set b {}
    foreach {Ar br} $Ab {
        lappend A $Ar
        lappend b $br
    }
    set x [::math::linearalgebra::leastSquaresSVD $A $b]
} -result {1.0 1.0 0.1}


test eigenvectors-1.0 "Eigenvectors solution" -match numbers -body {
    #
    # Matrix:
    #    /2   1\
    #    \1   2/
    # has eigenvalues 3 and 1 with eigenvectors:
    #    / 1\      /1\
    #    \-1/  and \1/
    # (so include a factor 1/sqrt(2) in the answer)
    #
    set A  { {2 1}
             {1 2} } ;# Note: integer coefficients!

    ::math::linearalgebra::eigenvectorsSVD $A
} -cleanup {
    unset A
} -result {{{0.7071068 -0.7071068} {0.7071068 0.7071068}} {3.0 1.0}}

test eigenvectors-1.1-tkt7f082f8667 {Eigenvector signs} -setup {
    # Test case derived from the example code found in ticket [7f082f8667].
    set A {
	{2.7563361585555084  0.02600440980933252 0.0}
	{0.02600440980933252 2.785766824118953   0.0}
	{0.0                 0.0                -5.542102982674461}
    }
} -body {
    lindex [::math::linearalgebra::eigenvectorsSVD $A] 1
} -cleanup {
    unset A
} -match numbers -result {2.80093075418638 2.7411722284880806 -5.542102982674461}


test mkHilbert-1.0 "Hilbert matrix" -match numbers -body {
    set computed [mkHilbert 3]
    set expected {{1.0 0.5 0.333333333333} {0.5 0.333333333333 0.25} {0.333333333333 0.25 0.2}}
    set diff [sub $computed $expected]
    set norm [normMatrix $diff max]
    set result [expr {$norm<1.e-10}]

if {![package vsatisfies [package provide Tcl] 8.4]} {return}
# statistics depends on linearalgebra (for multi-variate linear regression).
package ifneeded math::statistics        0.9.2 [list source [file join $dir statistics.tcl]]
package ifneeded math::optimize          1.0.1 [list source [file join $dir optimize.tcl]]
package ifneeded math::calculus          0.8   [list source [file join $dir calculus.tcl]]
package ifneeded math::interpolate       1.1   [list source [file join $dir interpolate.tcl]]
package ifneeded math::linearalgebra     1.1.5 [list source [file join $dir linalg.tcl]]
package ifneeded math::bignum            3.1.1 [list source [file join $dir bignum.tcl]]
package ifneeded math::bigfloat          1.2.2 [list source [file join $dir bigfloat.tcl]]
package ifneeded math::machineparameters 0.1   [list source [file join $dir machineparameters.tcl]]

if {![package vsatisfies [package provide Tcl] 8.5]} {return}
package ifneeded math::calculus::symdiff 1.0   [list source [file join $dir symdiff.tcl]]
package ifneeded math::bigfloat          2.0.2 [list source [file join $dir bigfloat2.tcl]]