This and other RFCs are available on the web at http://dev.perl.org/rfc/ =head1 TITLE Arrays: transpose() =head1 VERSION Maintainer: Jeremy Howard <[EMAIL PROTECTED]> Date: 22 Sep 2000 Last Modified: 24 Sep 2000 Mailing List: [EMAIL PROTECTED] Number: 272 Version: 2 Status: Frozen =head1 DISCUSSION This RFC was modified to incorporate the functionality of PDL's xchg() and mv(), which are useful for acting on arbitrary dimensions of multidimensional arrays. Implementing aliasing was discussed in more detail than for RFCs 90, 91, and 148, including suggestions to learn from PDL's implementation (outlined in RFC 116), which are more sophisticated than simply keeping a list of mapped indices, instead actually storing information about the specific operations that have occured. =head1 ABSTRACT It is proposed that a new function C<transpose> be added to Perl. C<transpose($dim1, $dim2, @list)> would return @list with $dim1 and $dim2 switched. C<transpose(\@order, @list)> would return @list with dimensions in the order specified by @order. C<transpose> would return an alias into the original list, not a copy of the elements. =head1 DESCRIPTION =head2 Swapping Dimensions It is proposed that Perl implement a function called C<transpose> that transposes two dimensions of an array, and is evaluated lazily. L<RFC 202> gives an overview of the proposed multidimensional arrays that C<transpose> works with. For instance: @a = ([1,2],[3,4],[5,6]); @transposed_list = transpose(0,1,@a); # ([1,3,5],[2,4,6]) This is different to C<reshape> (see L<RFC 148>) which does not reorder its elements: @a = ([1,2],[3,4],[5,6]); @reshaped_list = reshape([3,2],@a); # ([1,2,3],[4,5,6]) C<transpose> is its own inverse: @transposed_list = transpose(0,1,@a); # ([1,3,5],[2,4,6]) @orig_list = transpose(0,1,@transposed_list); # (([1,2],[3,4],[5,6]) @a == @orig_list; # true If C<transpose> refers to a dimension that does not exist, empty dimensions autovivify as necessary: @row_vector = (1,2,3,4); @col_vector = transpose(0,1,@row_vector); # ([1],[2],[3],[4]) =head2 Reordering Dimensions An alternative form of C<transpose> uses the first argument as a list ref to specify a new order for the dimensions: transpose [0,3,4,1,2], @arr; If some dimensions are not specified in the first argument, those dimensions are left in their current order: # Where @arr is a rank 5 array... transpose ([3], @arr) == transpose ([3,0,1,2,4], @arr); transpose ([0,3], @arr) == transpose ([0,3,1,2,4], @arr); This syntax allows multidimensional arrays to be reduced along any dimension: @sumover_1st_dim = reduce ^_ + ^_, @arr[ 0..; |i; * ]; @sumover_3rd_dim = reduce ^_ + ^_, transpose([3],@arr)[0..; |i; * ]; Note that C<reduce> is from RFC 76, and C<|i> is from RFC 207. =head2 Aliasing C<transpose> does not make a copy of the elements of its arguments; it simply create an alias: @row_vector = (1,2,3,4); @col_vector = transpose(0,1,@row_vector); # ([1],[2],[3],[4]) $col_vector[[0,1]] = 0; @row_vector == (1,0,3,4); # True =head2 Optional Extra: Dimension Insert To move a dimension and insert it before some other dimension, the following syntax may be used: transpose ({3=>2}, @arr) == transpose ([0,1,3,2,4], @arr); which inserts dimension 3 in front of dimension 2. =head1 IMPLEMENTATION RFC 90 discusses possible approaches to implementing aliasing. =head1 REFERENCES RFC 76: Builtin: reduce RFC 90: Arrays: merge() and unmerge() RFC 148: Arrays: Add reshape() for multi-dimensional array reshaping RFC 207: Arrays: Efficient Array Loops
