Combine matrices of equal height
in [Mathematica]
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From: Sam Takoy on 17 Jul 2010 08:16 Hi, Given two matrices of equal height, what's the best way to combine them. Here's what I did TF[m_] := Flatten[Transpose[m]] Combine[m1_, m2_] := Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T Surely there's a better way of doing it. Thanks!
From: David Park on 18 Jul 2010 01:02 Here are two sample matrices. m1 = Array[1 &, {3, 2}]; m2 = Array[2 &, {3, 3}]; Transpose[Join[Transpose[m1], Transpose[m2]]] // MatrixForm Another method that doesn't explicitly use Join and Transpose is to make a new blank matrix first and then fill in the parts using the Span notation. This might be more intuitive. m3 = Array[0 &, {3, 5}]; m3[[All, 1 ;; 2]] = m1; m3[[All, 3 ;; 5]] = m2; m3 // MatrixForm David Park djmpark(a)comcast.net http://home.comcast.net/~djmpark/ From: Sam Takoy [mailto:sam.takoy(a)yahoo.com] Hi, Given two matrices of equal height, what's the best way to combine them. Here's what I did TF[m_] := Flatten[Transpose[m]] Combine[m1_, m2_] := Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T Surely there's a better way of doing it. Thanks!
From: Leonid Shifrin on 18 Jul 2010 01:03 Hi, you did not provide a test example and your code does not seem to work for me so I can only guess what you meant by combining. The following function will combine together any number of matrices provided they all have the same length (number of rows): combine[x___?MatrixQ /; Equal @@ Map[Length, {x}]] := Flatten[Transpose[{x}], {{1}, {2, 3}}]; For example: In[19]:= tst1 = Partition[Range[12], 3] Out[19]= {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}} In[20]:= tst2 = Partition[Range[13, 24], 3] Out[20]= {{13, 14, 15}, {16, 17, 18}, {19, 20, 21}, {22, 23, 24}} In[21]:= combine[tst1, tst2] Out[21]= {{1, 2, 3, 13, 14, 15}, {4, 5, 6, 16, 17, 18}, {7, 8, 9, 19, 20, 21}, {10, 11, 12, 22, 23, 24}} Hope this helps. Regards, Leonid On Sat, Jul 17, 2010 at 4:16 PM, Sam Takoy <sam.takoy(a)yahoo.com> wrote: > Hi, > > Given two matrices of equal height, what's the best way to combine them. > Here's what I did > > TF[m_] := Flatten[Transpose[m]] > Combine[m1_, m2_] := > Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T > > > Surely there's a better way of doing it. > > Thanks! > >
From: Bill Rowe on 18 Jul 2010 01:04 On 7/17/10 at 8:16 AM, sam.takoy(a)yahoo.com (Sam Takoy) wrote: >Given two matrices of equal height, what's the best way to combine >them. Here's what I did >TF[m_] := Flatten[Transpose[m]] Combine[m1_, m2_] := >Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T I assume there is a typo here and the last portion of what you wrote above should be TF not just T. If so, joining two matrices can be done with ArrayFlatten. Taking your "equal height" to mean an equal number of rows, then =46latten(a)ArrayFlatten@{{m1,m2}} gives the same result as your code. For example, In[12]:= a = RandomInteger[1, {5, 2}]; b = RandomInteger[5, {5, 3}]; Combine[a, b] == Flatten(a)ArrayFlatten@{{a, b}} Out[14]= True Note, what I have done with ArrayFlatten requires the two matrices to have the same number of rows which is not true of your code. You can relax this requirement by using Riffle which will not care if the to matrices have the same number of rows. That is: In[15]:= Combine[a, b] == Flatten(a)Riffle[a, b] Out[15]= True
From: Ray Koopman on 18 Jul 2010 01:05
On Jul 17, 5:16 am, Sam Takoy <sam.ta...(a)yahoo.com> wrote: > Hi, > > Given two matrices of equal height, what's the best way to combine them. > Here's what I did > > TF[m_] := Flatten[Transpose[m]] > Combine[m1_, m2_] := > Partition[Join[m1 // TF, m2 // TF], Length[m1]] // T > > Surely there's a better way of doing it. > > Thanks! m1 = {{11,12}, {21,22}}; m2 = {{13,14,15}, {23,24,25}}; m3 = {{16,17}, {26,27}}; MapThread[Join,{m1,m2,m3}] {{11,12,13,14,15,16,17}, {21,22,23,24,25,26,27}} |