2 use Scalar::Util 'blessed';
5 use Math::GSL::Errno qw/:all/;
6 use Math::GSL::BLAS qw/gsl_blas_ddot/;
8 '*' => \&_multiplication,
15 @EXPORT_all = qw/fopen fclose
16 gsl_vector_alloc gsl_vector_calloc gsl_vector_alloc_from_block gsl_vector_alloc_from_vector
17 gsl_vector_free gsl_vector_view_array gsl_vector_const_view_array gsl_vector_view_array_with_stride
18 gsl_vector_const_view_array_with_stride gsl_vector_subvector gsl_vector_subvector_wi gsl_vector_subvector_with_stride
19 gsl_vector_const_subvec gsl_vector_const_subvec gsl_vector_get gsl_vector_set
20 gsl_vector_ptr gsl_vector_const_ptr gsl_vector_set_zero gsl_vector_set_all
21 gsl_vector_set_basis gsl_vector_fread gsl_vector_fwrite gsl_vector_fscanf
22 gsl_vector_fprintf gsl_vector_memcpy gsl_vector_reverse gsl_vector_swap
23 gsl_vector_swap_elements gsl_vector_max gsl_vector_min gsl_vector_minmax
24 gsl_vector_max_index gsl_vector_min_index gsl_vector_minmax_index
25 gsl_vector_add gsl_vector_sub gsl_vector_mul gsl_vector_div
26 gsl_vector_scale gsl_vector_add_constant gsl_vector_isnull
27 gsl_vector_ispos gsl_vector_isneg gsl_vector_isnonneg
28 gsl_vector_float_alloc gsl_vector_float_calloc gsl_vector_float_alloc_from_block
29 gsl_vector_float_alloc_from_vector gsl_vector_float_free gsl_vector_float_view_array
30 gsl_vector_float_view_array_with_stride gsl_vector_float_const_view_array gsl_vector_float_const_view_array_with_stride
31 gsl_vector_float_subvector gsl_vector_float_subvector_with_stride gsl_vector_float_const_subvector
32 gsl_vector_float_const_subvector_with_stride gsl_vector_float_get gsl_vector_float_set gsl_vector_float_ptr
33 gsl_vector_float_const_ptr gsl_vector_float_set_zero gsl_vector_float_set_all gsl_vector_float_set_basis
34 gsl_vector_float_fread gsl_vector_float_fwrite gsl_vector_float_fscanf gsl_vector_float_fprintf
35 gsl_vector_float_memcpy gsl_vector_float_reverse gsl_vector_float_swap gsl_vector_float_swap_elements
36 gsl_vector_float_max gsl_vector_float_min gsl_vector_float_minmax gsl_vector_float_max_index gsl_vector_float_min_index
37 gsl_vector_float_minmax_index gsl_vector_float_add gsl_vector_float_sub gsl_vector_float_mul gsl_vector_float_div gsl_vector_float_scale
38 gsl_vector_float_add_constant gsl_vector_float_isnull gsl_vector_float_ispos gsl_vector_float_isneg gsl_vector_float_isnonneg
41 @EXPORT_file =qw/ fopen fclose/;
42 @EXPORT_OK = (@EXPORT_all, @EXPORT_file);
43 %EXPORT_TAGS = ( file => \@EXPORT_file, all => \@EXPORT_all );
47 Math::GSL::Vector - Functions concerning vectors
51 use Math::GSL::Vector qw/:all/;
52 my $vec1 = Math::GSL::Vector->new([1, 7, 94, 15 ]);
54 my $vec3 = Math::GSL::Vector>new(10); # 10 element zero vector
55 my $vec4 = $vec1 + $vec2;
57 # set the element at index 1 to 9
58 # and the element at index 3 to 8
59 $vec3->set([ 1, 3 ], [ 9, 8 ]);
61 my @vec = $vec2->as_list; # return elements as Perl list
63 my $dot_product = $vec1 * $vec2;
64 my $length = $vec2->length;
65 my $first = $vec1->get(0);
70 =head1 Objected Oriented Interface to GSL Math::GSL::Vector
72 =head2 Math::GSL::Vector->new()
74 Creates a new Vector of the given size.
76 my $vector = Math::GSL::Vector->new(3);
78 You can also create and set directly the values of the vector like this :
80 my $vector = Math::GSL::Vector->new([2,4,1]);
85 my ($class, $values) = @_;
86 my $length = $#$values;
89 if ( ref $values eq 'ARRAY' ){
90 die __PACKAGE__.'::new($x) - $x must be a nonempty array reference' if $length == -1;
91 $vector = gsl_vector_alloc($length+1);
92 map { gsl_vector_set($vector, $_, $values->[$_] ) } (0 .. $length);
93 $this->{_length} = $length+1;
94 } elsif ( (int($values) == $values) && ($values > 0)) {
95 $vector = gsl_vector_alloc($values);
96 gsl_vector_set_zero($vector);
97 $this->{_length} = $values;
99 die __PACKAGE__.'::new($x) - $x must be an int or array reference';
101 $this->{_vector} = $vector;
106 Get the underlying GSL vector object created by SWIG, useful for using gsl_vector_* functions which do not have an OO counterpart.
108 my $vector = Math::GSL::Vector->new(3);
109 my $gsl_vector = $vector->raw;
110 my $stuff = gsl_vector_get($gsl_vector, 1);
116 return $self->{_vector};
121 Exchanges the values in the vectors $v with $w by copying.
123 my $v = Math::GSL::Vector->new([1..5]);
124 my $w = Math::GSL::Vector->new([3..7]);
130 my ($self,$other) = @_;
131 croak "Math::GSL::Vector: \$v->swap(\$w) : \$w must be a Math::GSL::Vector"
132 unless ref $other eq 'Math::GSL::Vector';
133 gsl_vector_swap( $self->raw, $other->raw );
139 Reverse the elements in the vector.
147 gsl_vector_reverse($self->raw);
153 Returns the minimum value contained in the vector.
155 my $vector = Math::GSL::Vector->new([2,4,1]);
156 my $minimum = $vector->min;
162 return gsl_vector_min($self->raw);
167 Returns the minimum value contained in the vector.
169 my $vector = Math::GSL::Vector->new([2,4,1]);
170 my $maximum = $vector->max;
176 return gsl_vector_max($self->raw);
181 Returns the number of elements contained in the vector.
183 my $vector = Math::GSL::Vector->new([2,4,1]);
184 my $length = $vector->length;
188 sub length { my $self=shift; $self->{_length} }
192 Returns the p-norm of $v, which defaults to the Euclidean (p=2) norm when no argument is given.
194 my $euclidean_distance = $v->norm;
204 map { $norm += $p == 1 ? abs $_ : $_ ** $p } ($self->as_list);
205 return $norm ** (1 / $p);
210 Divide each element of a vector by it's norm, hence creating a unit vector. Returns the vector for chaining.
211 If you just want the value of the norm without changing the vector, use C<norm()>. The default value for C<$p>
212 is 2, which gives the familiar Euclidean distance norm.
214 my $unit_vector = $vector->normalize(2);
218 my $unit_vector = $vector->normalize;
226 my $norm = $self->norm($p);
227 return $self if ($norm == 0);
229 my $status = gsl_vector_scale( $self->raw, 1/$norm );
230 croak "Math::GSL::Vector - could not scale vectr" unless $status == $GSL_SUCCESS;
236 Gets the content of a Math::GSL::Vector object as a Perl list.
238 my $vector = Math::GSL::Vector->new(3);
240 my @values = $vector->as_list;
246 $self->get( [ 0 .. $self->length - 1 ] );
251 Gets the value of an of a Math::GSL::Vector object.
253 my $vector = Math::GSL::Vector->new(3);
255 my @values = $vector->get(2);
257 You can also enter an array of indices to receive their corresponding values:
259 my $vector = Math::GSL::Vector->new(3);
261 my @values = $vector->get([0,2]);
266 my ($self, $indices) = @_;
267 return map { gsl_vector_get($self->raw, $_ ) } @$indices ;
272 Sets values of an of a Math::GSL::Vector object.
274 my $vector = Math::GSL::Vector->new(3);
275 $vector->set([1,2], [8,23]);
277 This sets the second and third value to 8 and 23.
282 my ($self, $indices, $values) = @_;
283 die (__PACKAGE__.'::set($indices, $values) - $indices and $values must be array references of the same length')
284 unless ( ref $indices eq 'ARRAY' && ref $values eq 'ARRAY' && $#$indices == $#$values );
286 map { gsl_vector_set($self->{_vector}, $indices->[$_], $values->[$_] ) } (0..$#$indices);
293 Returns a copy of the vector, which has the same length and values but resides at a different location in memory.
295 my $vector = Math::GSL::Vector->new([10 .. 20]);
296 my $copy = $vector->copy;
303 my $copy = Math::GSL::Vector->new( $self->length );
304 if ( gsl_vector_memcpy($copy->raw, $self->raw) != $GSL_SUCCESS ) {
305 croak "Math::GSL - error copying memory, aborting";
310 sub _multiplication {
311 my ($left,$right) = @_;
312 my $lcopy = $left->copy;
314 if ( blessed $right && $right->isa('Math::GSL::Vector') ) {
315 return $lcopy->dot_product($right);
317 gsl_vector_scale($lcopy->raw, $right);
323 my ($left, $right, $flip) = @_;
326 my $lcopy = $left->copy;
327 gsl_vector_scale($lcopy->raw, -1 );
328 gsl_vector_add_constant($lcopy->raw, $right);
331 return _addition($left, -1.0*$right);
341 my ($left, $right, $flip) = @_;
343 my $lcopy = $left->copy;
345 if ( blessed $right && $right->isa('Math::GSL::Vector') && blessed $left && $left->isa('Math::GSL::Vector') ) {
346 if ( $left->length == $right->length ) {
347 gsl_vector_add($lcopy->raw, $right->raw);
349 croak "Math::GSL - addition of vectors must be called with two objects vectors and must have the same length";
352 gsl_vector_add_constant($lcopy->raw, $right);
358 my ($left,$right) = @_;
360 if ( blessed $right && $right->isa('Math::GSL::Vector') &&
361 $left->length == $right->length ) {
362 my @l = $left->as_list;
363 my @r = $right->as_list;
364 map { $sum += $l[$_] * $r[$_] } (0..$#l);
367 croak "dot_product() must be called with two vectors";
372 my ($left,$right) = @_;
374 my ($status, $product) = gsl_blas_ddot($left->raw,$right->raw);
375 croak sprintf "Math::GSL::dot_product - %s", gsl_strerror($status) if ($status != $GSL_SUCCESS);
381 Here is a list of all the functions included in this module :
385 =item C<gsl_vector_alloc($x)> - create a vector of size $x
387 =item C<gsl_vector_calloc($x)> - create a vector of size $x and initializes all the elements of the vector to zero
389 =item C<gsl_vector_alloc_from_block>
391 =item C<gsl_vector_alloc_from_vector>
393 =item C<gsl_vector_free($v)> - free a previously allocated vector $v
395 =item C<gsl_vector_view_array($base, $n)> - This function returns a vector view of an array reference $base. The start of the new vector is given by $base and has $n elements. Mathematically, the i-th element of the new vector v' is given by, v'(i) = $base->[i] where the index i runs from 0 to $n-1. The array containing the elements of v is not owned by the new vector view. When the view goes out of scope the original array will continue to exist. The original memory can only be deallocated by freeing the original pointer base. Of course, the original array should not be deallocated while the view is still in use.
397 =item C<gsl_vector_const_view_array($base, $n)> - This function is equivalent to gsl_vector_view_array but can be used for arrays which are declared const.
399 =item C<gsl_vector_view_array_with_stride($base, $stride, $n)> - This function returns a vector view of an array reference $base with an additional $stride argument. The subvector is formed in the same way as for gsl_vector_view_array but the new vector has $n elements with a step-size of $stride from one element to the next in the original array. Mathematically, the i-th element of the new vector v' is given by, v'(i) = $base->[i*$stride] where the index i runs from 0 to $n-1. Note that the view gives direct access to the underlying elements of the original array. A vector view $view can be passed to any subroutine which takes a vector argument just as a directly allocated vector would be, using $view->{vector}.
401 =item C<gsl_vector_const_view_array_with_stride($base, $stride, $n)> - This function is equivalent to gsl_vector_view_array_with_stride but can be used for arrays which are declared const.
403 =item C<gsl_vector_subvector($v, $offset, $n)> - return a vector_view type which contains a subvector of $v, with a size of $size, starting from the $offset position
405 =item C<gsl_vector_subvector_with_stride($v, $offset, $stride, $size)> - return a vector_view type which contains a subvector of $v, with a size of $size, starting from the $offset position and with a $stride step between each element of $v
407 =item C<gsl_vector_const_subvector>
409 =item C<gsl_vector_get($v, $i)> - return the $i-th element of a vector $v
411 =item C<gsl_vector_set($v, $i, $x)> - return the vector $v with his $i-th element set to $x
413 =item C<gsl_vector_ptr>
415 =item C<gsl_vector_const_ptr>
417 =item C<gsl_vector_set_zero($v)> - set all the elements of $v to 0
419 =item C<gsl_vector_set_all($v, $x)> - set all the elements of $v to $x
421 =item C<gsl_vector_set_basis($v, $i)> - set all the elements of $v to 0 except for the $i-th element which is set to 1 and return 0 if the operation succeded, 1 otherwise.
423 =item C<gsl_vector_fread($file, $v)> - This function reads into the vector $v from the open stream $file opened with gsl_fopen function from the Math::GSL module in binary format. The vector $v must be preallocated with the correct length since the function uses the size of $v to determine how many bytes to read. The return value is 0 for success and 1 if there was a problem reading from the file.
425 =item C<gsl_vector_fwrite($file, $v)> - This function writes the elements of the vector $v to the stream $file opened with gsl_fopen function from the Math::GSL module in binary format. The return value is 0 for success and 1 if there was a problem writing to the file. Since the data is written in the native binary format it may not be portable between different architectures.
427 =item C<gsl_vector_fscanf($file, $v)> This function reads formatted data from the stream $file opened with gsl_fopen function from the Math::GSL module into the vector $v. The vector $v must be preallocated with the correct length since the function uses the size of $v to determine how many numbers to read. The function returns 0 for success and 1 if there was a problem reading from the file.
429 =item C<gsl_vector_fprintf($file, $v, $format)> -This function writes the elements of the vector $v line-by-line to the stream $file opened with gsl_fopen function from the Math::GSL module using the format specifier $format, which should be one of the "%g", "%e" or "%f" formats for floating point numbers and "%d" for integers. The function returns 0 for success and 1 if there was a problem writing to the file.
431 =item C<gsl_vector_memcpy($dest, $src)> - This function copies the elements of the vector $src into the vector $dest and return 0 if the opertaion succeded, 1 otherwise. The two vectors must have the same length.
433 =item C<gsl_vector_reverse($v)> - reverse the order of the elements of the vector $v and return 0 if the opertaion succeded, 1 otherwise
435 =item C<gsl_vector_swap($v, $v2)> - swap the values of the vectors $v and $v2 and return 0 if the opertaion succeded, 1 otherwise
437 =item C<gsl_vector_swap_elements($v, $i, $j)> - permute the elements at position $i and $j in the vector $v and return 0 if the operation succeded, 1 otherwise.
439 =item C<gsl_vector_max($v)> - return the maximum value in the vector $v
441 =item C<gsl_vector_min($v)> - return the minimum value in the vector $v
443 =item C<gsl_vector_minmax($v)> - return two values, the first is the minimum value in the vector $v and the second is the maximum value.
445 =item C<gsl_vector_max_index($v)> - return the position of the maximum value in the vector $v
447 =item C<gsl_vector_min_index($v)> - return the position of the minimum value in the vector $v
449 =item C<gsl_vector_minmax_index> - return two values, the first is the position of the minimum value in the vector $v and the second is the position of the maximum value.
451 =item C<gsl_vector_add($v, $v2)> - add the elements of $v2 to the elements of $v, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
453 =item C<gsl_vector_sub($v, $v2)> - substract the elements of $v2 from the elements of $v, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
455 =item C<gsl_vector_mul($v, $v2)> - multiply the elements of $v by the elements of $v2, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
457 =item C<gsl_vector_div($v, $v2)> - divides the elements of $v by the elements of $v2, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
459 =item C<gsl_vector_scale($v, $x)> - multiplty the elements of the vector $v by a constant $x and return 0 if the operation succeded, 1 otherwise.
461 =item C<gsl_vector_add_constant($v, $x)> - add a constant $x to the elements of the vector $v and return 0 if the operation succeded, 1 otherwise.
463 =item C<gsl_vector_isnull($v)> - verify if all the elements of the vector $v are null, return 0 if it's the case, 1 otherwise.
465 =item C<gsl_vector_ispos($v)> - verify if all the elements of the vector $v are positive, return 0 if it's the case, 1 otherwise.
467 =item C<gsl_vector_isneg($v)> - verify if all the elements of the vector $v are negative, return 0 if it's the case, 1 otherwise.
469 =item C<gsl_vector_isnonneg($v)> - verify if all the elements the vector $v are not negative, return 0 if it's the case, 1 otherwise.
473 Precision on the vector_view type : every modification you'll make on a vector_view will also modify the original vector.
474 For example, the following code will zero the even elements of the vector $v of length $size, while leaving the odd elements untouched :
478 =item C<$v_even= gsl_vector_subvector_with_stride ($v, 0, 2, $size/2);>
480 =item C<gsl_vector_set_zero ($v_even-E<gt>{vector});>
484 For more informations on the functions, we refer you to the GSL offcial documentation:
485 L<http://www.gnu.org/software/gsl/manual/html_node/>
487 Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
491 Here is an example using both interfaces.
493 use Math::GSL::Vector qw/:all/;
495 print "We'll create this vector : [0,1,4,9,16] \n";
496 my $vector = Math::GSL::Vector->new([0,1,4,9,16]);
497 my ($min, $max) = gsl_vector_minmax_index($vector->raw);
499 print "We then check the index value of the maximum and minimum values of the vector. \n";
500 print "The index of the maximum should be 4 and we received $max \n";
501 print "The index of the minimum should be 0 and we received $min \n";
502 print "We'll then swap the first and the third elements of the vector \n";
504 gsl_vector_swap_elements($vector->raw, 0, 3);
505 my @got = $vector->as_list;
506 print "The vector should now be like this : [9,1,4,0,16] \n";
507 print "and we received : [ @got ]\n";
511 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
513 =head1 COPYRIGHT AND LICENSE
515 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
517 This program is free software; you can redistribute it and/or modify it
518 under the same terms as Perl itself.