Cloning row or column vectors

Question

Sometimes it is useful to  quot clone quot  a row or column vector to a matrix  By cloning I mean converting a row vector such as  1  2  3   Into a matrix   1  2  3     1  2  3     1  2  3    or a column vector such as   1     2     3    into   1  1  1    2  2  2    3  3  3    In MATLAB or octave this is done pretty easily   x    1  2  3   a   ones 3  1    x  a        1   2   3     1   2   3     1   2   3       b    x     ones 1  3   b        1   1   1     2   2   2     3   3   3  I want to repeat this in numpy  but unsuccessfully In  14   x   array  1  2  3   In  14   ones  3  1     x Out 14   array    1    2    3             1    2    3             1    2    3       so far so good In  16   x transpose     ones  1  3   Out 16   array    1    2    3       DAMN   I end up with  In  17    ones  3  1     x  transpose   Out 17   array    1    1    1             2    2    2             3    3    3      Why wasn t the first method  In  16   working  Is there a way to achieve this task in python in a more elegant way

User · Answer

If you have a pandas dataframe and want to preserve the dtypes  even the categoricals  this is a fast way to do it   import numpy as np import pandas as pd df   pd DataFrame  1   1  2  3   2   4  5  6    number repeats   50 new df   df reindex np tile df index  number repeats

User · Answer

One clean solution is to use NumPy s outer-product function with a vector of ones   np outer np ones n   x    gives n repeating rows  Switch the argument order to get repeating columns  To get an equal number of rows and columns you might do  np outer np ones like x   x

User · Answer

I think using the broadcast in numpy is the best  and faster  I did a compare as following  import numpy as np b   np random randn 1000  In  105    timeit c   np tile b    newaxis    1 100   1000 loops  best of 3  354   s per loop  In  106    timeit c   np repeat b    newaxis   100  axis 1  1000 loops  best of 3  347   s per loop  In  107    timeit c   np array  b   100  transpose   100 loops  best of 3  5 56 ms per loop   about 15 times faster using broadcast

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Here s an elegant  Pythonic way to do it    gt  gt  gt  array   1 2 3    3  array   1  2  3           1  2  3           1  2  3      gt  gt  gt  array   1 2 3    3  transpose   array   1  1  1           2  2  2           3  3  3      the problem with  16  seems to be that the transpose has no effect for an array  you re probably wanting a matrix instead    gt  gt  gt  x   array  1 2 3    gt  gt  gt  x array  1  2  3    gt  gt  gt  x transpose   array  1  2  3    gt  gt  gt  matrix  1 2 3   matrix   1  2  3     gt  gt  gt  matrix  1 2 3   transpose   matrix   1            2            3

User · Answer

You can use   np tile x 3  reshape  4 3     tile will generate the reps of the vector   and reshape will give it the shape you want

User · Answer

Let    gt  gt  gt  n   1000  gt  gt  gt  x   np arange n   gt  gt  gt  reps   10000   Zero-cost allocations  A view does not take any additional memory  Thus  these declarations are instantaneous     New axis x np newaxis          Broadcast to specific shape np broadcast to x   reps  n     Forced allocation  If you want force the contents to reside in memory    gt  gt  gt   timeit np array np broadcast to x   reps  n    10 2 ms    62 3   s per loop  mean    std  dev  of 7 runs  100 loops each    gt  gt  gt   timeit np repeat x np newaxis      reps  axis 0  9 88 ms    52 4   s per loop  mean    std  dev  of 7 runs  100 loops each    gt  gt  gt   timeit np tile x   reps  1   9 97 ms    77 3   s per loop  mean    std  dev  of 7 runs  100 loops each    All three methods are roughly the same speed   Computation   gt  gt  gt  a   np arange reps   n  reshape reps  n   gt  gt  gt  x tiled   np tile x   reps  1     gt  gt  gt   timeit np broadcast to x   reps  n     a 17 1 ms    284   s per loop  mean    std  dev  of 7 runs  100 loops each    gt  gt  gt   timeit x np newaxis       a 17 5 ms    300   s per loop  mean    std  dev  of 7 runs  100 loops each    gt  gt  gt   timeit x tiled   a 17 6 ms    240   s per loop  mean    std  dev  of 7 runs  100 loops each    All three methods are roughly the same speed     Conclusion  If you want to replicate before a computation  consider using one of the  zero-cost allocation  methods  You won t suffer the performance penalty of  forced allocation

User · Answer

To answer the actual question  now that nearly a dozen approaches to working around a solution have been posted  x transpose reverses the shape of x  One of the interesting side-effects is that if x ndim    1  the transpose does nothing  This is especially confusing for people coming from MATLAB  where all arrays implicitly have at least two dimensions  The correct way to transpose a 1D numpy array is not x transpose   or x T  but rather x    None   or x reshape -1  1   From here  you can multiply by a matrix of ones  or use any of the other suggested approaches  as long as you respect the  subtle  differences between MATLAB and numpy

User · Answer

import numpy as np x np array  1 2 3   y np multiply np ones  len x  len x    x  T print y    yields      1   1   1      2   2   2      3   3   3

User · Answer

First note that with numpy s broadcasting operations it s usually not necessary to duplicate rows and columns   See this and this for descriptions   But to do this  repeat and newaxis are probably the best way  In  12   x   array  1 2 3    In  13   repeat x   newaxis   3  1  Out 13    array   1  1  1           2  2  2           3  3  3     In  14   repeat x newaxis     3  0  Out 14    array   1  2  3           1  2  3           1  2  3      This example is for a row vector  but applying this to a column vector is hopefully obvious   repeat seems to spell this well  but you can also do it via multiplication as in your example  In  15   x   array   1  2  3       note the double brackets  In  16    ones  3 1   x  transpose   Out 16    array    1    1    1             2    2    2             3    3    3

User · Answer

Use numpy tile    gt  gt  gt  tile array  1 2 3     3  1   array   1  2  3           1  2  3           1  2  3      or for repeating columns    gt  gt  gt  tile array   1 2 3    transpose     1  3   array   1  1  1           2  2  2           3  3  3

[python] "Cloning" row or column vectors

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