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RE: unpartition

• To: mathgroup at smc.vnet.net
• Subject: [mg45954] RE: [mg45899] unpartition
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 30 Jan 2004 04:17:09 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: steven.burger at duke.edu [mailto:steven.burger at duke.edu]
To: mathgroup at smc.vnet.net
>Sent: Thursday, January 29, 2004 11:35 AM
>To: mathgroup at smc.vnet.net
>Subject: [mg45954] [mg45899] unpartition
>
>
>How do you unpartition a matrix?
>
>For example: Starting with, 
>
>Partition[Table[4*(i - 1) + j, {i, 4}, {j, 4}],{2,2}]
>
>
>how do you go back to,
>
>Table[4*(i - 1) + j, {i, 4}, {j, 4}]
>

In principle, the inverse to Partition is Flatten.


The problem is to get the dimensions right!
Lets first consider your example:
 
In[15]:= Table[4*(i - 1) + j, {i, 4}, {j, 4}]
Out[15]=
{{1, 2, 3, 4}, {5, 6, 7, 8},
 {9, 10, 11, 12}, {13, 14, 15, 16}}

In[16]:= Partition[%, {2, 2}]
Out[16]=
{{{{1, 2}, {5, 6}}, {{3, 4}, {7, 8}}},
 {{{9, 10}, {13, 14}}, {{11, 12}, {15, 16}}}}

In[17]:= Dimensions[%]
Out[17]= {2, 2, 2, 2}

In[18]:= Transpose[%%, {1, 3, 2, 4}]
Out[18]=
{{{{1, 2}, {3, 4}}, {{5, 6}, {7, 8}}},
 {{{9, 10}, {11, 12}}, {{13, 14}, {15, 16}}}}

In[19]:= Map[Flatten, %, {2}]
Out[19]= 
{{{1, 2, 3, 4}, {5, 6, 7, 8}},
 {{9, 10, 11, 12}, {13, 14, 15, 16}}}

In[20]:= Flatten[%, 1]
Out[20]=
{{1, 2, 3, 4}, {5, 6, 7, 8},
 {9, 10, 11, 12}, {13, 14, 15, 16}}



This sequence works in general:
 
In[25]:=
{k, l, m, n} = Prime /@ Table[Random[Integer, {1, 10}], {4}]
Out[25]= {3, 29, 11, 2}

In[26]:= t = Partition[Range[k*l*m*n], k*l];

In[27]:= Dimensions[t] == {m*n, k*l}
Out[27]= True

In[28]:= s = Partition[t, {m, k}];

In[29]:= Dimensions[s] == {n, l, m, k}
Out[29]= True

In[30]:= ss = Transpose[s, {1, 3, 2, 4}];

In[31]:= Dimensions[ss] == {n, m, l, k}
Out[31]= True

In[32]:= t == Flatten[Map[Flatten, ss, {2}], 1]
Out[32]= True


or also

In[33]:= s2 = Partition[t, {n, l}];

In[34]:= Dimensions[s2] == {m, k, n, l}
Out[34]= True

In[35]:= ss2 = Transpose[s2, {1, 3, 2, 4}];

In[36]:= Dimensions[ss2] == {m, n, k, l}
Out[36]= True

In[37]:= t == Flatten[Map[Flatten, ss2, {2}], 1]
Out[37]= True


Alternatively you may Flatten everything and then repartition with the
appropriate dimensions:

In[45]:=
t == Partition[Flatten[Transpose[s, {1, 3, 2, 4}]], 
    Times @@ Dimensions[s][[{2, 4}]]]
Out[45]= True

In[46]:=
t == Partition[Flatten[Transpose[s2, {1, 3, 2, 4}]], 
    Times @@ Dimensions[s2][[{2, 4}]]]
Out[46]= True


--
Hartmut Wolf