function rank = npart_rsf_lex_rank ( n, npart, a ) %*****************************************************************************80 % %% NPART_RSF_LEX_RANK computes the lex rank of an RSF NPART partition. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 25 January 2011 % % Author: % % John Burkardt % % Reference: % % Donald Kreher, Douglas Simpson, % Combinatorial Algorithms, % CRC Press, 1998, % ISBN: 0-8493-3988-X, % LC: QA164.K73. % % Parameters: % % Input, integer N, the integer to be partitioned. % N must be positive. % % Input, integer NPART, the number of parts of the partition. % 1 <= NPART <= N. % % Input, integer A(NPART), contains the partition. % A(1) through A(NPART) contain the nonzero integers which % sum to N. % % Output, integer RANK, the rank of the partition. % offset = 1; % % Check. % ierror = part_rsf_check ( n, npart, a ); if ( ierror ~= 0 ) fprintf ( 1, '\n' ); fprintf ( 1, 'NPART_RSF_LEX_RANK - Fatal error!\n' ); fprintf ( 1, ' The input array is illegal.\n' ); fprintf ( 1, ' IERROR = %d\n', ierror ) error ( 'NPART_RSF_LEX_RANK - Fatal error!' ); end % % Get the table of partitions of N with NPART parts. % p = npart_table ( n, npart ); % % Copy the partition "backwards". % b(1:npart) = a(npart:-1:1); rank = 0; while ( 0 < n && 0 < npart ) if ( b(npart) == 1 ) n = n - 1; npart = npart - 1; else b(1:npart) = b(1:npart) - 1; rank = rank + p(n-1+offset,npart-1+offset); n = n - npart; end end return end