Description of slallcombs

Home > sltoolbox > utils > slallcombs.m

slallcombs

PURPOSE

SLALLCOMBS Generate all combination of numbers

SYNOPSIS

function A = slallcombs(nums)

DESCRIPTION

SLALLCOMBS Generate all combination of numbers

 $ Syntax $
   - A = slallcombs(nums)

 $ Arguments $
   - nums:         the numbers of component sets
   - A:            the resultant indices matrix

 $ Description $
   - A = slallcombs(nums) generates the set of all possible index-vectors
     for a d1 x d2 x ... x dK array, where d1, d2, ... dK are stored in 
     the K-dim vector nums. Then the resultant matrix A would be of size
     K x dK x ... d2 x d1.

 $ Remarks $
   # If the number in some dimensions equals zero, then an empty array
     will be returned.

 $ Examples $
   - Generate all indices for 3D array,
     \{
           A = slallcombs([3 2 4]);
     \}
     Then A is a 3 x 3 x 2 x 4 matrix, with 
     A(:, i3, i2, i1) = [i1 i2 i3]'

 $ History $
   - Created by Dahua Lin on Nov 19th, 2005

CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

• slcartprod SLCARTPROD Get the Cartesian product of a series of sets
• slgridsamples SLGRIDSAMPLES Generate the sample vectors on grid points

SOURCE CODE

0001 function A = slallcombs(nums)
0002 %SLALLCOMBS Generate all combination of numbers
0003 %
0004 % $ Syntax $
0005 %   - A = slallcombs(nums)
0006 %
0007 % $ Arguments $
0008 %   - nums:         the numbers of component sets
0009 %   - A:            the resultant indices matrix
0010 %
0011 % $ Description $
0012 %   - A = slallcombs(nums) generates the set of all possible index-vectors
0013 %     for a d1 x d2 x ... x dK array, where d1, d2, ... dK are stored in
0014 %     the K-dim vector nums. Then the resultant matrix A would be of size
0015 %     K x dK x ... d2 x d1.
0016 %
0017 % $ Remarks $
0018 %   # If the number in some dimensions equals zero, then an empty array
0019 %     will be returned.
0020 %
0021 % $ Examples $
0022 %   - Generate all indices for 3D array,
0023 %     \{
0024 %           A = slallcombs([3 2 4]);
0025 %     \}
0026 %     Then A is a 3 x 3 x 2 x 4 matrix, with
0027 %     A(:, i3, i2, i1) = [i1 i2 i3]'
0028 %
0029 % $ History $
0030 %   - Created by Dahua Lin on Nov 19th, 2005
0031 %
0032 
0033 %% parse input arguments
0034 nums = nums(:);
0035 K = length(nums);
0036 n = prod(nums);
0037 if n == 0
0038     A = [];
0039     return;
0040 end
0041 
0042 %% prepare storage
0043 A = zeros(K, n);
0044 
0045 %% get organization tables
0046 cprods = cumprod(nums);
0047 n_grps = [1; cprods(1:end-1)];
0048 n_ins = cprods(end) ./ cprods;
0049 
0050 %% organize
0051 for i = 1 : K
0052     
0053     r = n_ins(i);
0054     s = nums(i);
0055     g = n_grps(i);
0056     
0057     P = (1:s);
0058     P = P(ones(r, 1), :);
0059     P = P(:);
0060     P = P(:, ones(1, g));
0061     
0062     A(i, :) = P(:)';
0063 end
0064 
0065 A = reshape(A, [K, nums(end:-1:1)']);
0066

---

Generated on Wed 20-Sep-2006 12:43:11 by m2html © 2003