## 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

\$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 (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 \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.

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.

You should have received a copy of the \s-1GNU\s0 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.

## POD ERRORS

Hey! The above document had some coding errors, which are explained below:

Around line 464:

=back doesn't take any parameters, but you said =back =back

Around line 467:

You forgot a '=back' before '=head1'