Array2PagedMatrix - Transform an N-dimensional array into a paged matrix.
Vertically concatenate all pages in the array, and add N-1
columns listing the subscripts for all dimensions except the
second dimension (which is implicit, since it becomes the
second dimension of the output matrix).
USAGE
M = Array2Matrix(A)
A N-dimensional array
EXAMPLE
Consider the following example. Let A be the array:
A(:,:,1,1) =
1 2 3 4 5
6 7 8 9 0
A(:,:,2,1) =
0 9 8 7 6
5 4 3 2 1
A(:,:,1,2) =
4 4 4 4 4
5 5 5 5 5
A(:,:,2,2) =
6 6 6 6 6
7 7 7 7 7
A(:,:,1,3) =
8 8 8 8 8
9 9 9 9 9
A(:,:,2,3) =
0 0 0 0 0
6 5 6 5 6
Array2PagedMatrix concatenates each of the above pages vertically, and adds three
columns listing the first, third and fourth dimensions, yielding:
B =
1 2 3 4 5 1 1 1
6 7 8 9 0 2 1 1
0 9 8 7 6 1 2 1
5 4 3 2 1 2 2 1
4 4 4 4 4 1 1 2
5 5 5 5 5 2 1 2
6 6 6 6 6 1 2 2
7 7 7 7 7 2 2 2
8 8 8 8 8 1 1 3
9 9 9 9 9 2 1 3
0 0 0 0 0 1 2 3
6 5 6 5 6 2 2 30001 function M = Array2PagedMatrix(A) 0002 0003 %Array2PagedMatrix - Transform an N-dimensional array into a paged matrix. 0004 % 0005 % Vertically concatenate all pages in the array, and add N-1 0006 % columns listing the subscripts for all dimensions except the 0007 % second dimension (which is implicit, since it becomes the 0008 % second dimension of the output matrix). 0009 % 0010 % USAGE 0011 % 0012 % M = Array2Matrix(A) 0013 % 0014 % A N-dimensional array 0015 % 0016 % EXAMPLE 0017 % 0018 % Consider the following example. Let A be the array: 0019 % 0020 % A(:,:,1,1) = 0021 % 0022 % 1 2 3 4 5 0023 % 6 7 8 9 0 0024 % 0025 % 0026 % A(:,:,2,1) = 0027 % 0028 % 0 9 8 7 6 0029 % 5 4 3 2 1 0030 % 0031 % 0032 % A(:,:,1,2) = 0033 % 0034 % 4 4 4 4 4 0035 % 5 5 5 5 5 0036 % 0037 % 0038 % A(:,:,2,2) = 0039 % 0040 % 6 6 6 6 6 0041 % 7 7 7 7 7 0042 % 0043 % 0044 % A(:,:,1,3) = 0045 % 0046 % 8 8 8 8 8 0047 % 9 9 9 9 9 0048 % 0049 % 0050 % A(:,:,2,3) = 0051 % 0052 % 0 0 0 0 0 0053 % 6 5 6 5 6 0054 % 0055 % Array2PagedMatrix concatenates each of the above pages vertically, and adds three 0056 % columns listing the first, third and fourth dimensions, yielding: 0057 % 0058 % B = 0059 % 0060 % 1 2 3 4 5 1 1 1 0061 % 6 7 8 9 0 2 1 1 0062 % 0 9 8 7 6 1 2 1 0063 % 5 4 3 2 1 2 2 1 0064 % 4 4 4 4 4 1 1 2 0065 % 5 5 5 5 5 2 1 2 0066 % 6 6 6 6 6 1 2 2 0067 % 7 7 7 7 7 2 2 2 0068 % 8 8 8 8 8 1 1 3 0069 % 9 9 9 9 9 2 1 3 0070 % 0 0 0 0 0 1 2 3 0071 % 6 5 6 5 6 2 2 3 0072 % 0073 0074 0075 % Copyright (C) 2008-2011 by Michaël Zugaro 0076 % 0077 % This program is free software; you can redistribute it and/or modify 0078 % it under the terms of the GNU General Public License as published by 0079 % the Free Software Foundation; either version 3 of the License, or 0080 % (at your option) any later version. 0081 0082 % A(:,:,1,1) = [1 2 3 4 5;6 7 8 9 0]; 0083 % A(:,:,2,1) = [0 9 8 7 6;5 4 3 2 1]; 0084 % A(:,:,1,2) = [4 4 4 4 4;5 5 5 5 5]; 0085 % A(:,:,2,2) = [6 6 6 6 6;7 7 7 7 7]; 0086 % A(:,:,1,3) = [8 8 8 8 8;9 9 9 9 9]; 0087 % A(:,:,2,3) = [0 0 0 0 0;6 5 6 5 6]; 0088 0089 if nargin < 1, 0090 error('Incorrect number of parameters (type ''help <a href="matlab:help Array">Array</a>2PagedMatrix'' for details).'); 0091 end 0092 0093 if length(size(A)) <= 2 0094 M = A; 0095 return 0096 end 0097 0098 % The array A contains k pages, each of which is a m x n matrix. Let d be the number of 0099 % dimensions. The output matrix should have size k*m x (n+d-1) 0100 m = size(A,1); 0101 n = size(A,2); 0102 d = length(size(A)); 0103 k = prod(size(A))/(m*n); 0104 M = zeros((k*m),(n+d-1)); 0105 0106 % This string will be evaluated later to determine for each page the subscripts for the d extra dimensions 0107 % (we need to use this trick because we do not know how many extra dimensions there are) 0108 getSubscripts = '['; 0109 for i = 1:d, 0110 getSubscripts = [getSubscripts 'v' int2str(i) ',']; 0111 end 0112 getSubscripts = [getSubscripts(1:end-1) ']=ind2sub(size(A),i*s);']; 0113 0114 % This string will be evaluated later to set the last d columns (corresponding to the subscripts for the d extra dimensions) 0115 % (we need to use this trick because we do not know how many extra dimensions there are) 0116 setSubscripts = 'M((i-1)*m+1:i*m,n+2:end)=repmat(['; 0117 for i = 3:d, 0118 setSubscripts = [setSubscripts 'v' int2str(i) ',']; 0119 end 0120 setSubscripts = [setSubscripts(1:end-1) '],m,1);']; 0121 0122 s = m*n; 0123 for i = 1:k, 0124 % Get i-th page 0125 M((i-1)*m+1:i*m,1:n) = reshape(A((i-1)*s+1:i*s),m,n); 0126 % Set the last d columns (corresponding to the subscripts for the extra dimensions) 0127 eval(getSubscripts); 0128 eval(setSubscripts); 0129 end 0130 0131 M(:,n+1) = repmat((1:m)',k,1);