.\" Automatically generated by Pod::Man 2.22 (Pod::Simple 3.07)
.\"
.\" Standard preamble:
.\" ========================================================================
.de Sp \" Vertical space (when we can't use .PP)
.if t .sp .5v
.if n .sp
..
.de Vb \" Begin verbatim text
.ft CW
.nf
.ne \\$1
..
.de Ve \" End verbatim text
.ft R
.fi
..
.\" Set up some character translations and predefined strings.  \*(-- will
.\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left
.\" double quote, and \*(R" will give a right double quote.  \*(C+ will
.\" give a nicer C++.  Capital omega is used to do unbreakable dashes and
.\" therefore won't be available.  \*(C` and \*(C' expand to `' in nroff,
.\" nothing in troff, for use with C<>.
.tr \(*W-
.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
.ie n \{\
.    ds -- \(*W-
.    ds PI pi
.    if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
.    if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\"  diablo 12 pitch
.    ds L" ""
.    ds R" ""
.    ds C` ""
.    ds C' ""
'br\}
.el\{\
.    ds -- \|\(em\|
.    ds PI \(*p
.    ds L" ``
.    ds R" ''
'br\}
.\"
.\" Escape single quotes in literal strings from groff's Unicode transform.
.ie \n(.g .ds Aq \(aq
.el       .ds Aq '
.\"
.\" If the F register is turned on, we'll generate index entries on stderr for
.\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index
.\" entries marked with X<> in POD.  Of course, you'll have to process the
.\" output yourself in some meaningful fashion.
.ie \nF \{\
.    de IX
.    tm Index:\\$1\t\\n%\t"\\$2"
..
.    nr % 0
.    rr F
.\}
.el \{\
.    de IX
..
.\}
.\"
.\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2).
.\" Fear.  Run.  Save yourself.  No user-serviceable parts.
.    \" fudge factors for nroff and troff
.if n \{\
.    ds #H 0
.    ds #V .8m
.    ds #F .3m
.    ds #[ \f1
.    ds #] \fP
.\}
.if t \{\
.    ds #H ((1u-(\\\\n(.fu%2u))*.13m)
.    ds #V .6m
.    ds #F 0
.    ds #[ \&
.    ds #] \&
.\}
.    \" simple accents for nroff and troff
.if n \{\
.    ds ' \&
.    ds ` \&
.    ds ^ \&
.    ds , \&
.    ds ~ ~
.    ds /
.\}
.if t \{\
.    ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
.    ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
.    ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
.    ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
.    ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
.    ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
.\}
.    \" troff and (daisy-wheel) nroff accents
.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
.ds ae a\h'-(\w'a'u*4/10)'e
.ds Ae A\h'-(\w'A'u*4/10)'E
.    \" corrections for vroff
.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
.    \" for low resolution devices (crt and lpr)
.if \n(.H>23 .if \n(.V>19 \
\{\
.    ds : e
.    ds 8 ss
.    ds o a
.    ds d- d\h'-1'\(ga
.    ds D- D\h'-1'\(hy
.    ds th \o'bp'
.    ds Th \o'LP'
.    ds ae ae
.    ds Ae AE
.\}
.rm #[ #] #H #V #F C
.\" ========================================================================
.\"
.IX Title "Math::SparseVector 3pm"
.TH Math::SparseVector 3pm "2008-03-25" "perl v5.10.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.SH "NAME"
Math::SparseVector \- Supports sparse vector operations such as 
setting a value in a vector, reading a value at a given index,
obtaining all indices, addition and dot product of two sparse vectors, 
and vector normalization.
.SH "MODULE HISTORY"
.IX Header "MODULE HISTORY"
This module is the successor to Sparse::Vector, which was re-cast 
into this new namespace in order to introduce another module 
Math::SparseMatrix, which makes use of this module.
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\&  use Math::SparseVector;
\&
\&  # creating an empty sparse vector object
\&  $spvec=Math::SparseVector\->new;
\&
\&  # sets the value at index 12 to 5
\&  $spvec\->set(12,5);
\&
\&  # returns value at index 12
\&  $value = $spvec\->get(12);
\&
\&  # returns the indices of non\-zero values in sorted order
\&  @indices = $spvec\->keys;
\&
\&  # returns 1 if the vector is empty and has no keys
\&  if($spvec\->isnull) {
\&    print "vector is null.\en";
\&  }
\&  else  {
\&    print "vector is not null.\en";
\&  }
\&
\&  # print sparse vector to stdout
\&  $spvec\->print;
\&
\&  # returns the string form of sparse vector
\&  # same as print except the string is returned
\&  # rather than displaying on stdout
\&  $spvec\->stringify;
\&
\&  # adds sparse vectors v1, v2 and stores 
\&  # result into v1
\&  $v1\->add($v2);
\&
\&  # adds binary equivalent of v2 to v1
\&  $v1\->binadd($v2);
\&  # binary equivalnet treats all non\-zero values 
\&  # as 1s
\&
\&  # increments the value at index 12
\&  $spvec\->incr(12);
\&
\&  # divides each vector entry by a given divisor 4
\&  $spvec\->div(4);
\&
\&  # returns norm of the vector
\&  $spvec_norm = $spvec\->norm;
\&
\&  # normalizes a sparse vector
\&  $spvec\->normalize;
\&
\&  # returns dot product of the 2 vectors
\&  $dotprod = $v1\->dot($v2);
\&
\&  # deallocates all entries
\&  $spvec\->free;
.Ve
.SH "USAGE NOTES"
.IX Header "USAGE NOTES"
.IP "1. Loading Math::SparseVector Module" 4
.IX Item "1. Loading Math::SparseVector Module"
To use this module, you must insert the following line in your Perl program
before using any of the supported methods.
.Sp
.Vb 1
\&    use Math::SparseVector;
.Ve
.IP "2. Creating a Math::SparseVector Object" 4
.IX Item "2. Creating a Math::SparseVector Object"
The following line creates a new object of Math::SparseVector class referred 
with the name 'spvec'.
.Sp
.Vb 1
\&    $spvec=Math::SparseVector\->new;
.Ve
.Sp
The newly created 'spvec' vector will be initially empty.
.IP "3. Using Methods" 4
.IX Item "3. Using Methods"
Now you can use any of the following methods on this 'spvec' Math::SparseVector
object.
.RS 4
.IP "1. set(i,n) \- Sets the value at index i to n" 4
.IX Item "1. set(i,n) - Sets the value at index i to n"
.Vb 2
\&         # equivalent to $spvec{12}=5;
\&         $spvec\->set(12,5);
.Ve
.IP "2. get(i)    \- Returns the value at index i" 4
.IX Item "2. get(i)    - Returns the value at index i"
.Vb 2
\&         # equivalent to $value=$spvec{12};
\&         $value = $spvec\->get(12);
.Ve
.IP "3. \fIkeys()\fR    \- Returns the indices of all non-zero values in the vector" 4
.IX Item "3. keys()    - Returns the indices of all non-zero values in the vector"
.Vb 2
\&         # equivalent to @keys=sort {$a <=> $b} keys %spvec;
\&         @indices = $spvec\->keys;
.Ve
.IP "4. \fIisnull()\fR  \- Returns 1 if the vector is empty and has no keys" 4
.IX Item "4. isnull()  - Returns 1 if the vector is empty and has no keys"
.Vb 3
\&         # similar to
\&         # if(scalar(keys %spvec)==0) {print "vector is null.\en";}
\&         if($spvec\->isnull) { print "vector is null.\en"; }
.Ve
.IP "5. \fIprint()\fR   \- Prints the sparse vector to stdout \- Output will show a list of space separated 'index value' pairs for each non-zero 'value' in the vector." 4
.IX Item "5. print()   - Prints the sparse vector to stdout - Output will show a list of space separated 'index value' pairs for each non-zero 'value' in the vector."
.Vb 4
\&         # similar to
\&         # foreach $ind (sort {$a<=>$b} keys %spvec)
\&             # { print "$ind " . $spvec{$ind} . " "; }
\&         $spvec\->print;
.Ve
.IP "6. \fIstringify()\fR \- Returns the vector in a string form. Same as \fIprint()\fR method except the vector is written to a string that is returned instead of displaying onto stdout" 4
.IX Item "6. stringify() - Returns the vector in a string form. Same as print() method except the vector is written to a string that is returned instead of displaying onto stdout"
.Vb 3
\&         # the below will do exactly same as $spvec\->print;
\&         $string=$spvec\->stringify;
\&         print "$string\en";
.Ve
.IP "7. v1\->add(v2) \- Adds contents of v2 to vector v1." 4
.IX Item "7. v1->add(v2) - Adds contents of v2 to vector v1."
.Vb 1
\&         Similar to v1+=v2
\&
\&         $v1\->add($v2);
\&         If v1 = (2,  , , 5, 8, ,  , , 1)
\&         &  v2 = ( , 1, , 3,  , , 5, , 9)
\&         where blanks show the 0 values that are not stored in 
\&         Math::SparseVector.
\&
\&         After      $v1\->add($v2); 
\&         v1 = (2, 1, , 8, 8, , 5, , 10) and v2 remains same
.Ve
.IP "8. v1\->binadd(v2) \- Binary equivalent of v2 is added into v1. Binary equivalent of a vector is obtained by setting all non-zero values to 1s." 4
.IX Item "8. v1->binadd(v2) - Binary equivalent of v2 is added into v1. Binary equivalent of a vector is obtained by setting all non-zero values to 1s."
.Vb 4
\&         If v1 = (1,  , , 1, 1, ,  , , 1)
\&         &  v2 = ( , 1, , 1,  , , 1, , 1)
\&         Then, after v1\->binadd(v2),
\&         v1 will be (1, 1, , 1, 1, , 1, , 1).
\&
\&         If v1 = (1,  , , 1, 1, ,  , , 1)
\&         &  v2 = ( , 1, , 3,  , , 5, , 9)
\&         v1\->binadd(v2);
\&         will set v1 to (1, 1, , 1, 1, , 1, , 1).
.Ve
.IP "9. incr(i)   \- Increments the value at index i" 4
.IX Item "9. incr(i)   - Increments the value at index i"
.Vb 2
\&         # is similar to $spvec{12}++;
\&         $spvec\->incr(12);
.Ve
.IP "10. div(n)   \- Divides each vector entry by a given divisor n" 4
.IX Item "10. div(n)   - Divides each vector entry by a given divisor n"
.Vb 4
\&         $spvec\->div(4);
\&         If spvec = (2,  , , 5, 8, ,  , , 1)
\&         Then, $spvec\->div(4)
\&         will set spvec to (0.5, , , 1.25, 2, , , , 0.25)
.Ve
.IP "11. \fInorm()\fR   \- Returns the norm of a given vector" 4
.IX Item "11. norm()   - Returns the norm of a given vector"
.Vb 6
\&         $spvec_norm = $spvec\->norm;
\&         If spvec = (2,  , , 5, 8, ,  , , 1)
\&         $spvec\->norm will return the value 
\&         = sqrt(2^2 + 5^2 + 8^2 + 1)
\&         = sqrt(4 + 25 + 64 + 1)
\&         = 9.69536
.Ve
.IP "12. v1\->dot(v2) \- Returns the dot product of two vectors" 4
.IX Item "12. v1->dot(v2) - Returns the dot product of two vectors"
.Vb 5
\&         $dotprod = $v1\->dot($v2);
\&         If v1 = (2,  , , 5, 8, ,  , , 1)
\&                 &  v2 = ( , 1, , 3,  , , 5, , 9)
\&         v1\->dot(v2) returns
\&         5*3 + 1*9 = 15 + 9 = 24
.Ve
.IP "13. \fIfree()\fR   \- Deallocates all entries and makes the vector empty" 4
.IX Item "13. free()   - Deallocates all entries and makes the vector empty"
.Vb 2
\&         $spvec\->free;
\&         will set spvec to null vector ()
.Ve
.RE
.RS 4
.RE
.SH "AUTHORS"
.IX Header "AUTHORS"
Amruta Purandare, University of Pittsburgh
amruta at cs.pitt.edu
.PP
Ted Pedersen, University of Minnesota, Duluth
tpederse at d.umn.edu
.PP
Mahesh Joshi, Carnegie-Mellon University
maheshj at cmu.edu
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (c) 2006\-2008, Amruta Purandare, Ted Pedersen, Mahesh Joshi
.PP
This program is free software; you can redistribute it and/or modify it under
the terms of the \s-1GNU\s0 General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later
version.
.PP
This program is distributed in the hope that it will be useful, but \s-1WITHOUT\s0
\&\s-1ANY\s0 \s-1WARRANTY\s0; without even the implied warranty of \s-1MERCHANTABILITY\s0 or \s-1FITNESS\s0
\&\s-1FOR\s0 A \s-1PARTICULAR\s0 \s-1PURPOSE\s0. See the \s-1GNU\s0 General Public License for more details.
.PP
You should have received a copy of the \s-1GNU\s0 General Public License along with
this program; if not, write to
.PP
.Vb 3
\& The Free Software Foundation, Inc.,
\& 59 Temple Place \- Suite 330,
\& Boston, MA  02111\-1307, USA.
.Ve
.SH "POD ERRORS"
.IX Header "POD ERRORS"
Hey! \fBThe above document had some coding errors, which are explained below:\fR
.IP "Around line 464:" 4
.IX Item "Around line 464:"
=back doesn't take any parameters, but you said =back  =back
.IP "Around line 467:" 4
.IX Item "Around line 467:"
You forgot a '=back' before '=head1'