Ted Pedersen

# 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

# adds binary equivalent of v2 to v1
# 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

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";``````
``````         Similar to v1+=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.

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)
v1 will be (1, 1, , 1, 1, , 1, , 1).

If v1 = (1,  , , 1, 1, ,  , , 1)
&  v2 = ( , 1, , 3,  , , 5, , 9)
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 (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.``````

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