2 use Scalar::Util 'blessed';
5 use Math::GSL::Errno qw/:all/;
6 use Math::GSL::BLAS qw/gsl_blas_ddot/;
7 use Math::GSL::Test qw/is_similar/;
9 '*' => \&_multiplication,
18 @EXPORT_all = qw/fopen fclose
19 gsl_vector_alloc gsl_vector_calloc gsl_vector_alloc_from_block gsl_vector_alloc_from_vector
20 gsl_vector_free gsl_vector_view_array gsl_vector_const_view_array gsl_vector_view_array_with_stride
21 gsl_vector_const_view_array_with_stride gsl_vector_subvector gsl_vector_subvector_wi gsl_vector_subvector_with_stride
22 gsl_vector_const_subvec gsl_vector_const_subvec gsl_vector_get gsl_vector_set
23 gsl_vector_ptr gsl_vector_const_ptr gsl_vector_set_zero gsl_vector_set_all
24 gsl_vector_set_basis gsl_vector_fread gsl_vector_fwrite gsl_vector_fscanf
25 gsl_vector_fprintf gsl_vector_memcpy gsl_vector_reverse gsl_vector_swap
26 gsl_vector_swap_elements gsl_vector_max gsl_vector_min gsl_vector_minmax
27 gsl_vector_max_index gsl_vector_min_index gsl_vector_minmax_index
28 gsl_vector_add gsl_vector_sub gsl_vector_mul gsl_vector_div
29 gsl_vector_scale gsl_vector_add_constant gsl_vector_isnull
30 gsl_vector_ispos gsl_vector_isneg gsl_vector_isnonneg
31 gsl_vector_float_alloc gsl_vector_float_calloc gsl_vector_float_alloc_from_block
32 gsl_vector_float_alloc_from_vector gsl_vector_float_free gsl_vector_float_view_array
33 gsl_vector_float_view_array_with_stride gsl_vector_float_const_view_array gsl_vector_float_const_view_array_with_stride
34 gsl_vector_float_subvector gsl_vector_float_subvector_with_stride gsl_vector_float_const_subvector
35 gsl_vector_float_const_subvector_with_stride gsl_vector_float_get gsl_vector_float_set gsl_vector_float_ptr
36 gsl_vector_float_const_ptr gsl_vector_float_set_zero gsl_vector_float_set_all gsl_vector_float_set_basis
37 gsl_vector_float_fread gsl_vector_float_fwrite gsl_vector_float_fscanf gsl_vector_float_fprintf
38 gsl_vector_float_memcpy gsl_vector_float_reverse gsl_vector_float_swap gsl_vector_float_swap_elements
39 gsl_vector_float_max gsl_vector_float_min gsl_vector_float_minmax gsl_vector_float_max_index gsl_vector_float_min_index
40 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
41 gsl_vector_float_add_constant gsl_vector_float_isnull gsl_vector_float_ispos gsl_vector_float_isneg gsl_vector_float_isnonneg
44 @EXPORT_file =qw/ fopen fclose/;
45 @EXPORT_OK = (@EXPORT_all, @EXPORT_file);
46 %EXPORT_TAGS = ( file => \@EXPORT_file, all => \@EXPORT_all );
50 Math::GSL::Vector - Functions concerning vectors
54 use Math::GSL::Vector qw/:all/;
55 my $vec1 = Math::GSL::Vector->new([1, 7, 94, 15 ]);
57 my $vec3 = Math::GSL::Vector>new(10); # 10 element zero vector
58 my $vec4 = $vec1 + $vec2;
60 # set the element at index 1 to 9
61 # and the element at index 3 to 8
62 $vec3->set([ 1, 3 ], [ 9, 8 ]);
64 my @vec = $vec2->as_list; # return elements as Perl list
66 my $dot_product = $vec1 * $vec2;
67 my $length = $vec2->length;
68 my $first = $vec1->get(0);
73 =head1 Objected Oriented Interface to GSL Math::GSL::Vector
75 =head2 Math::GSL::Vector->new()
77 Creates a new Vector of the given size.
79 my $vector = Math::GSL::Vector->new(3);
81 You can also create and set directly the values of the vector like this :
83 my $vector = Math::GSL::Vector->new([2,4,1]);
88 my ($class, $values) = @_;
89 my $length = $#$values;
92 if ( ref $values eq 'ARRAY' ){
93 die __PACKAGE__.'::new($x) - $x must be a nonempty array reference' if $length == -1;
94 $vector = gsl_vector_alloc($length+1);
95 map { gsl_vector_set($vector, $_, $values->[$_] ) } (0 .. $length);
96 $this->{_length} = $length+1;
97 } elsif ( (int($values) == $values) && ($values > 0)) {
98 $vector = gsl_vector_alloc($values);
99 gsl_vector_set_zero($vector);
100 $this->{_length} = $values;
102 die __PACKAGE__.'::new($x) - $x must be an int or array reference';
104 $this->{_vector} = $vector;
109 Get the underlying GSL vector object created by SWIG, useful for using gsl_vector_* functions which do not have an OO counterpart.
111 my $vector = Math::GSL::Vector->new(3);
112 my $gsl_vector = $vector->raw;
113 my $stuff = gsl_vector_get($gsl_vector, 1);
119 return $self->{_vector};
124 Exchanges the values in the vectors $v with $w by copying.
126 my $v = Math::GSL::Vector->new([1..5]);
127 my $w = Math::GSL::Vector->new([3..7]);
133 my ($self,$other) = @_;
134 croak "Math::GSL::Vector: \$v->swap(\$w) : \$w must be a Math::GSL::Vector"
135 unless ref $other eq 'Math::GSL::Vector';
136 gsl_vector_swap( $self->raw, $other->raw );
142 Reverse the elements in the vector.
150 gsl_vector_reverse($self->raw);
156 Returns the minimum value contained in the vector.
158 my $vector = Math::GSL::Vector->new([2,4,1]);
159 my $minimum = $vector->min;
165 return gsl_vector_min($self->raw);
170 Returns the minimum value contained in the vector.
172 my $vector = Math::GSL::Vector->new([2,4,1]);
173 my $maximum = $vector->max;
179 return gsl_vector_max($self->raw);
184 Returns the number of elements contained in the vector.
186 my $vector = Math::GSL::Vector->new([2,4,1]);
187 my $length = $vector->length;
191 sub length { my $self=shift; $self->{_length} }
195 Returns the p-norm of $v, which defaults to the Euclidean (p=2) norm when no argument is given.
197 my $euclidean_distance = $v->norm;
207 map { $norm += $p == 1 ? abs $_ : $_ ** $p } ($self->as_list);
208 return $norm ** (1 / $p);
213 Divide each element of a vector by it's norm, hence creating a unit vector. Returns the vector for chaining.
214 If you just want the value of the norm without changing the vector, use C<norm()>. The default value for C<$p>
215 is 2, which gives the familiar Euclidean distance norm.
217 my $unit_vector = $vector->normalize(2);
221 my $unit_vector = $vector->normalize;
229 my $norm = $self->norm($p);
230 return $self if ($norm == 0);
232 my $status = gsl_vector_scale( $self->raw, 1/$norm );
233 croak "Math::GSL::Vector - could not scale vectr" unless $status == $GSL_SUCCESS;
239 Gets the content of a Math::GSL::Vector object as a Perl list.
241 my $vector = Math::GSL::Vector->new(3);
243 my @values = $vector->as_list;
249 $self->get( [ 0 .. $self->length - 1 ] );
254 Gets the value of an of a Math::GSL::Vector object.
256 my $vector = Math::GSL::Vector->new(3);
258 my @values = $vector->get(2);
260 You can also enter an array of indices to receive their corresponding values:
262 my $vector = Math::GSL::Vector->new(3);
264 my @values = $vector->get([0,2]);
269 my ($self, $indices) = @_;
270 return map { gsl_vector_get($self->raw, $_ ) } @$indices ;
275 Sets values of an of a Math::GSL::Vector object.
277 my $vector = Math::GSL::Vector->new(3);
278 $vector->set([1,2], [8,23]);
280 This sets the second and third value to 8 and 23.
285 my ($self, $indices, $values) = @_;
286 die (__PACKAGE__.'::set($indices, $values) - $indices and $values must be array references of the same length')
287 unless ( ref $indices eq 'ARRAY' && ref $values eq 'ARRAY' && $#$indices == $#$values );
289 map { gsl_vector_set($self->{_vector}, $indices->[$_], $values->[$_] ) } (0..$#$indices);
296 Returns a copy of the vector, which has the same length and values but resides at a different location in memory.
298 my $vector = Math::GSL::Vector->new([10 .. 20]);
299 my $copy = $vector->copy;
306 my $copy = Math::GSL::Vector->new( $self->length );
307 if ( gsl_vector_memcpy($copy->raw, $self->raw) != $GSL_SUCCESS ) {
308 croak "Math::GSL - error copying memory, aborting";
313 sub _multiplication {
314 my ($left,$right) = @_;
315 my $lcopy = $left->copy;
317 if ( blessed $right && $right->isa('Math::GSL::Vector') ) {
318 return $lcopy->dot_product($right);
320 gsl_vector_scale($lcopy->raw, $right);
326 my ($left, $right, $flip) = @_;
329 my $lcopy = $left->copy;
330 gsl_vector_scale($lcopy->raw, -1 );
331 gsl_vector_add_constant($lcopy->raw, $right);
334 return _addition($left, -1.0*$right);
344 my ($left, $right, $flip) = @_;
346 my $lcopy = $left->copy;
348 if ( blessed $right && $right->isa('Math::GSL::Vector') && blessed $left && $left->isa('Math::GSL::Vector') ) {
349 if ( $left->length == $right->length ) {
350 gsl_vector_add($lcopy->raw, $right->raw);
352 croak "Math::GSL - addition of vectors must be called with two objects vectors and must have the same length";
355 gsl_vector_add_constant($lcopy->raw, $right);
361 my ($left,$right) = @_;
363 if ( blessed $right && $right->isa('Math::GSL::Vector') &&
364 $left->length == $right->length ) {
365 my @l = $left->as_list;
366 my @r = $right->as_list;
367 map { $sum += $l[$_] * $r[$_] } (0..$#l);
370 croak "dot_product() must be called with two vectors";
375 my ($left,$right) = @_;
377 my ($status, $product) = gsl_blas_ddot($left->raw,$right->raw);
378 croak sprintf "Math::GSL::dot_product - %s", gsl_strerror($status) if ($status != $GSL_SUCCESS);
383 my ($left,$right) = @_;
384 if ($left->length != $right->length)
388 return is_similar( [$left->as_list ],
393 my ($left, $right) = @_;
394 return !_equal($left,$right);
399 Here is a list of all the functions included in this module :
403 =item C<gsl_vector_alloc($x)> - create a vector of size $x
405 =item C<gsl_vector_calloc($x)> - create a vector of size $x and initializes all the elements of the vector to zero
407 =item C<gsl_vector_alloc_from_block>
409 =item C<gsl_vector_alloc_from_vector>
411 =item C<gsl_vector_free($v)> - free a previously allocated vector $v
413 =item C<gsl_vector_view_array($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 $n-1. The array containing the elements of v is not owned by the new vector view. When the view goes out of scope the original array will continue to exist. The original memory can only be deallocated by freeing the original pointer base. Of course, the original array should not be deallocated while the view is still in use.
415 =item C<gsl_vector_const_view_array($base, $n)> - This function is equivalent to gsl_vector_view_array but can be used for arrays which are declared const.
417 =item C<gsl_vector_view_array_with_stride($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 $view->{vector}.
419 =item C<gsl_vector_const_view_array_with_stride($base, $stride, $n)> - This function is equivalent to gsl_vector_view_array_with_stride but can be used for arrays which are declared const.
421 =item C<gsl_vector_subvector($v, $offset, $n)> - return a vector_view type which contains a subvector of $v, with a size of $size, starting from the $offset position
423 =item C<gsl_vector_subvector_with_stride($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 $v
425 =item C<gsl_vector_const_subvector>
427 =item C<gsl_vector_get($v, $i)> - return the $i-th element of a vector $v
429 =item C<gsl_vector_set($v, $i, $x)> - return the vector $v with his $i-th element set to $x
431 =item C<gsl_vector_ptr>
433 =item C<gsl_vector_const_ptr>
435 =item C<gsl_vector_set_zero($v)> - set all the elements of $v to 0
437 =item C<gsl_vector_set_all($v, $x)> - set all the elements of $v to $x
439 =item C<gsl_vector_set_basis($v, $i)> - set all the elements of $v to 0 except for the $i-th element which is set to 1 and return 0 if the operation succeded, 1 otherwise.
441 =item C<gsl_vector_fread($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 $v to determine how many bytes to read. The return value is 0 for success and 1 if there was a problem reading from the file.
443 =item C<gsl_vector_fwrite($file, $v)> - This function writes the elements of the vector $v to the stream $file opened with gsl_fopen function from the Math::GSL module in binary format. The return value is 0 for success and 1 if there was a problem writing to the file. Since the data is written in the native binary format it may not be portable between different architectures.
445 =item C<gsl_vector_fscanf($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 $v to determine how many numbers to read. The function returns 0 for success and 1 if there was a problem reading from the file.
447 =item C<gsl_vector_fprintf($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 $format, which should be one of the "%g", "%e" or "%f" formats for floating point numbers and "%d" for integers. The function returns 0 for success and 1 if there was a problem writing to the file.
449 =item C<gsl_vector_memcpy($dest, $src)> - This function copies the elements of the vector $src into the vector $dest and return 0 if the opertaion succeded, 1 otherwise. The two vectors must have the same length.
451 =item C<gsl_vector_reverse($v)> - reverse the order of the elements of the vector $v and return 0 if the opertaion succeded, 1 otherwise
453 =item C<gsl_vector_swap($v, $v2)> - swap the values of the vectors $v and $v2 and return 0 if the opertaion succeded, 1 otherwise
455 =item C<gsl_vector_swap_elements($v, $i, $j)> - permute the elements at position $i and $j in the vector $v and return 0 if the operation succeded, 1 otherwise.
457 =item C<gsl_vector_max($v)> - return the maximum value in the vector $v
459 =item C<gsl_vector_min($v)> - return the minimum value in the vector $v
461 =item C<gsl_vector_minmax($v)> - return two values, the first is the minimum value in the vector $v and the second is the maximum value.
463 =item C<gsl_vector_max_index($v)> - return the position of the maximum value in the vector $v
465 =item C<gsl_vector_min_index($v)> - return the position of the minimum value in the vector $v
467 =item C<gsl_vector_minmax_index> - return two values, the first is the position of the minimum value in the vector $v and the second is the position of the maximum value.
469 =item C<gsl_vector_add($v, $v2)> - add the elements of $v2 to the elements of $v, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
471 =item C<gsl_vector_sub($v, $v2)> - substract the elements of $v2 from the elements of $v, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
473 =item C<gsl_vector_mul($v, $v2)> - multiply the elements of $v by the elements of $v2, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
475 =item C<gsl_vector_div($v, $v2)> - divides the elements of $v by the elements of $v2, the two vectors must have the same lenght and return 0 if the operation succeded, 1 otherwise.
477 =item C<gsl_vector_scale($v, $x)> - multiplty the elements of the vector $v by a constant $x and return 0 if the operation succeded, 1 otherwise.
479 =item C<gsl_vector_add_constant($v, $x)> - add a constant $x to the elements of the vector $v and return 0 if the operation succeded, 1 otherwise.
481 =item C<gsl_vector_isnull($v)> - verify if all the elements of the vector $v are null, return 0 if it's the case, 1 otherwise.
483 =item C<gsl_vector_ispos($v)> - verify if all the elements of the vector $v are positive, return 0 if it's the case, 1 otherwise.
485 =item C<gsl_vector_isneg($v)> - verify if all the elements of the vector $v are negative, return 0 if it's the case, 1 otherwise.
487 =item C<gsl_vector_isnonneg($v)> - verify if all the elements the vector $v are not negative, return 0 if it's the case, 1 otherwise.
491 Precision on the vector_view type : every modification you'll make on a vector_view will also modify the original vector.
492 For example, the following code will zero the even elements of the vector $v of length $size, while leaving the odd elements untouched :
496 =item C<$v_even= gsl_vector_subvector_with_stride ($v, 0, 2, $size/2);>
498 =item C<gsl_vector_set_zero ($v_even-E<gt>{vector});>
502 For more informations on the functions, we refer you to the GSL offcial documentation:
503 L<http://www.gnu.org/software/gsl/manual/html_node/>
505 Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
509 Here is an example using both interfaces.
511 use Math::GSL::Vector qw/:all/;
513 print "We'll create this vector : [0,1,4,9,16] \n";
514 my $vector = Math::GSL::Vector->new([0,1,4,9,16]);
515 my ($min, $max) = gsl_vector_minmax_index($vector->raw);
517 print "We then check the index value of the maximum and minimum values of the vector. \n";
518 print "The index of the maximum should be 4 and we received $max \n";
519 print "The index of the minimum should be 0 and we received $min \n";
520 print "We'll then swap the first and the third elements of the vector \n";
522 gsl_vector_swap_elements($vector->raw, 0, 3);
523 my @got = $vector->as_list;
524 print "The vector should now be like this : [9,1,4,0,16] \n";
525 print "and we received : [ @got ]\n";
529 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
531 =head1 COPYRIGHT AND LICENSE
533 Copyright (C) 2008-2009 Jonathan Leto and Thierry Moisan
535 This program is free software; you can redistribute it and/or modify it
536 under the same terms as Perl itself.