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.
MODULE HISTORY
This module is the successor to Sparse::Vector, which was recast into this new namespace in order to introduce another module Math::SparseMatrix, which makes use of this module.
SYNOPSIS
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 nonzero 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.\n";
}
else {
print "vector is not null.\n";
}
# 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 nonzero 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;
USAGE NOTES
 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.
use Math::SparseVector;
 2. Creating a Math::SparseVector Object

The following line creates a new object of Math::SparseVector class referred with the name 'spvec'.
$spvec=Math::SparseVector>new;
The newly created 'spvec' vector will be initially empty.
 3. Using Methods

Now you can use any of the following methods on this 'spvec' Math::SparseVector object.
 1. set(i,n)  Sets the value at index i to n

# equivalent to $spvec{12}=5; $spvec>set(12,5);
 2. get(i)  Returns the value at index i

# equivalent to $value=$spvec{12}; $value = $spvec>get(12);
 3. keys()  Returns the indices of all nonzero values in the vector

# equivalent to @keys=sort {$a <=> $b} keys %spvec; @indices = $spvec>keys;
 4. isnull()  Returns 1 if the vector is empty and has no keys

# similar to # if(scalar(keys %spvec)==0) {print "vector is null.\n";} if($spvec>isnull) { print "vector is null.\n"; }
 5. print()  Prints the sparse vector to stdout  Output will show a list of space separated 'index value' pairs for each nonzero 'value' in the vector.

# similar to # foreach $ind (sort {$a<=>$b} keys %spvec) # { print "$ind " . $spvec{$ind} . " "; } $spvec>print;
 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

# the below will do exactly same as $spvec>print; $string=$spvec>stringify; print "$string\n";
 7. v1>add(v2)  Adds contents of v2 to vector v1.

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
 8. v1>binadd(v2)  Binary equivalent of v2 is added into v1. Binary equivalent of a vector is obtained by setting all nonzero values to 1s.

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).
 9. incr(i)  Increments the value at index i

# is similar to $spvec{12}++; $spvec>incr(12);
 10. div(n)  Divides each vector entry by a given divisor n

$spvec>div(4); If spvec = (2, , , 5, 8, , , , 1) Then, $spvec>div(4) will set spvec to (0.5, , , 1.25, 2, , , , 0.25)
 11. norm()  Returns the norm of a given vector

$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
 12. v1>dot(v2)  Returns the dot product of two vectors

$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
 13. free()  Deallocates all entries and makes the vector empty

$spvec>free; will set spvec to null vector ()
AUTHORS
Amruta Purandare, University of Pittsburgh amruta at cs.pitt.edu
Ted Pedersen, University of Minnesota, Duluth tpederse at d.umn.edu
Mahesh Joshi, CarnegieMellon University maheshj at cmu.edu
COPYRIGHT AND LICENSE
Copyright (c) 20062008, Amruta Purandare, Ted Pedersen, Mahesh Joshi
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program; if not, write to
The Free Software Foundation, Inc.,
59 Temple Place  Suite 330,
Boston, MA 021111307, USA.
2 POD Errors
The following errors were encountered while parsing the POD:
 Around line 464:
=back doesn't take any parameters, but you said =back =back
 Around line 467:
You forgot a '=back' before '=head1'