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 re-cast 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 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.\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 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;
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 = $spvec->get(12);
3. keys() - Returns the indices of all non-zero values in the vector
# equivalent to @keys=sort {$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 non-zero
'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 non-zero 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, Carnegie-Mellon University maheshj at cmu.edu
COPYRIGHT AND LICENSE
Copyright (c) 2006-2008, 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 02111-1307, USA.