Reshape a 4D array to a 2D matrix where the size of the arrays vary

I have a 4D array

MM = [ 2.*N+1 , 2.*N+1 , Cylinder , Cylinder ] ;

where N is a scale for a contour plot and Cylinder defines the number of 2N+1 x 2N+1 arrays; so for example, N = 100 and Cylinder = 3 would produce an array of nine 201 x 201 square matrices. I want to reshape MM into a square 2D matrix, so the output always has a consistent format as the values of N and Cylinder vary.

For example, Cylinder = 2 would give MM the structure

val(:,:,1,1) = ...

val(:,:,2,1) = ...

val(:,:,1,2) = ...

val(:,:,2,2) = ...

I want to reshape it as

[ val(:,:,1,1) , val(:,:,2,1) ; ...
  val(:,:,1,2) , val(:,:,2,2) ] ;

So for Cylinder = 3, I want

[ val(:,:,1,1) , val(:,:,2,1) , val(:,:,3,1) ; ...
  val(:,:,1,2) , val(:,:,2,2) , val(:,:,3,2) ; ...
  val(:,:,1,3) , val(:,:,2,3) , val(:,:,3,3) ] ;

and Cylinder = 4,

[ val(:,:,1,1) , val(:,:,2,1) , val(:,:,3,1) , val(:,:,4,1) ; ...
  val(:,:,1,2) , val(:,:,2,2) , val(:,:,3,2) , val(:,:,4,2) ; ...
  val(:,:,1,3) , val(:,:,2,3) , val(:,:,3,3) , val(:,:,4,3) ; ...
  val(:,:,1,4) , val(:,:,2,4) , val(:,:,3,4) , val(:,:,4,4) ] ;

etc. How can this structure be achieved for any value of N and Cylinder?

Answer 1

[Stephen23]

You can use permute and reshape:

S = size(M);
Z = reshape(permute(M,[1,4,2,3]),cyl*S(1:2))

Here is a little test code for you to try:

% fake data:
N = 2;
cyl = 3;
M = zeros(2*N+1,2*N+1,cyl,cyl);
M(:) = 1:numel(M)
% reshape:
S = size(M);
Z = reshape(permute(M,[1,4,2,3]),cyl*S(1:2))

And you can see the input M and output Z:

M(:,:,1,1) =
     1     6    11    16    21
     2     7    12    17    22
     3     8    13    18    23
     4     9    14    19    24
     5    10    15    20    25
M(:,:,2,1) =
    26    31    36    41    46
    27    32    37    42    47
    28    33    38    43    48
    29    34    39    44    49
    30    35    40    45    50
M(:,:,3,1) =
    51    56    61    66    71
    52    57    62    67    72
    53    58    63    68    73
    54    59    64    69    74
    55    60    65    70    75
M(:,:,1,2) =
    76    81    86    91    96
    77    82    87    92    97
    78    83    88    93    98
    79    84    89    94    99
    80    85    90    95   100
M(:,:,2,2) =
   101   106   111   116   121
   102   107   112   117   122
   103   108   113   118   123
   104   109   114   119   124
   105   110   115   120   125
M(:,:,3,2) =
   126   131   136   141   146
   127   132   137   142   147
   128   133   138   143   148
   129   134   139   144   149
   130   135   140   145   150
M(:,:,1,3) =
   151   156   161   166   171
   152   157   162   167   172
   153   158   163   168   173
   154   159   164   169   174
   155   160   165   170   175
M(:,:,2,3) =
   176   181   186   191   196
   177   182   187   192   197
   178   183   188   193   198
   179   184   189   194   199
   180   185   190   195   200
M(:,:,3,3) =
   201   206   211   216   221
   202   207   212   217   222
   203   208   213   218   223
   204   209   214   219   224
   205   210   215   220   225

Z =
     1     6    11    16    21    26    31    36    41    46    51    56    61    66    71
     2     7    12    17    22    27    32    37    42    47    52    57    62    67    72
     3     8    13    18    23    28    33    38    43    48    53    58    63    68    73
     4     9    14    19    24    29    34    39    44    49    54    59    64    69    74
     5    10    15    20    25    30    35    40    45    50    55    60    65    70    75
    76    81    86    91    96   101   106   111   116   121   126   131   136   141   146
    77    82    87    92    97   102   107   112   117   122   127   132   137   142   147
    78    83    88    93    98   103   108   113   118   123   128   133   138   143   148
    79    84    89    94    99   104   109   114   119   124   129   134   139   144   149
    80    85    90    95   100   105   110   115   120   125   130   135   140   145   150
   151   156   161   166   171   176   181   186   191   196   201   206   211   216   221
   152   157   162   167   172   177   182   187   192   197   202   207   212   217   222
   153   158   163   168   173   178   183   188   193   198   203   208   213   218   223
   154   159   164   169   174   179   184   189   194   199   204   209   214   219   224
   155   160   165   170   175   180   185   190   195   200   205   210   215   220   225

[Michael Ransom]

Thank you for your answer and examples. It works perfectly.