Difference between numpy array shape R 1 and R

Question

In numpy  some of the operations return in shape  R  1  but some return  R    This will make matrix multiplication more tedious since explicit reshape is required  For example  given a matrix M  if we want to do numpy dot M   0   numpy ones  1  R    where R is the number of rows  of course  the same issue also occurs column-wise   We will get matrices are not aligned error since M   0  is in shape  R   but numpy ones  1  R   is in shape  1  R    So my questions are    What s the difference between shape  R  1  and  R    I know literally it s list of numbers and list of lists where all list contains only a number  Just wondering why not design numpy so that it favors shape  R  1  instead of  R   for easier matrix multiplication  Are there better ways for the above example  Without explicitly reshape like this  numpy dot M   0  reshape R  1   numpy ones  1  R

User · Answer

The difference between  R   and  1 R  is literally the number of indices that you need to use   ones  1 R   is a 2-D array that happens to have only one row   ones R  is a vector   Generally if it doesn t make sense for the variable to have more than one row column  you should be using a vector  not a matrix with a singleton dimension   For your specific case  there are a couple of options   1  Just make the second argument a vector   The following works fine       np dot M   0   np ones R     2  If you want matlab like matrix operations  use the class matrix instead of ndarray   All matricies are forced into being 2-D arrays  and operator   does matrix multiplication instead of element-wise  so you don t need dot    In my experience  this is more trouble that it is worth  but it may be nice if you are used to matlab

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The shape is a tuple  If there is only 1 dimension the shape will be one number and just blank after a comma  For 2  dimensions  there will be a number after all the commas     1 dimension with 2 elements  shape    2       Note there s nothing after the comma  z np array      start dimension     10          not a dimension     20          not a dimension                 end dimension print z shape        2       2 dimensions  each with 1 element  shape    2 1  w np array      start outer dimension       10         element is in an inner dimension      20         element is in an inner dimension                 end outer dimension print w shape        2 1

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There are a lot of good answers here already  But for me it was hard to find some example  where the shape or array can break all the program   So here is the one   import numpy as np a   np array  1 2 3 4   b   np array  10 20 30 40     from sklearn linear model import LinearRegression regr   LinearRegression   regr fit a b    This will fail with error      ValueError  Expected 2D array  got 1D array instead   but if we add reshape to a   a   np array  1 2 3 4   reshape -1 1    this works correctly

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The data structure of shape  n   is called a rank 1 array  It doesn t behave consistently as a row vector or a column vector which makes some of its operations and effects non intuitive  If you take the transpose of this  n   data structure  it ll look exactly same and the dot product will give you a number and not a matrix  The vectors of shape  n 1  or  1 n  row or column vectors are much more intuitive and consistent

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For its base array class  2d arrays are no more special than 1d or 3d ones   There are some operations the preserve the dimensions  some that reduce them  other combine or even expand them   M np arange 9  reshape 3 3  M   0  shape    3   selects one column  returns a 1d array M 0    shape   same  one row  1d array M    0   shape    3 1   index with a list  or array   returns 2d M    0 1   shape    3 2   In  20   np dot M   0  reshape 3 1  np ones  1 3     Out 20    array    0    0    0             3    3    3             6    6    6      In  21   np dot M    0   np ones  1 3    Out 21    array    0    0    0             3    3    3             6    6    6       Other expressions that give the same array  np dot M   0    np newaxis  np ones  1 3    np dot np atleast 2d M   0   T np ones  1 3    np einsum  i j  M   0  np ones  3    M1 M   0   R np ones  3    np dot M1   None   R None       MATLAB started out with just 2D arrays   Newer versions allow more dimensions  but retain the lower bound of 2   But you still have to pay attention to the difference between a row matrix and column one  one with shape  1 3  v  3 1    How often have you written  1 2 3      I was going to write row vector and column vector  but with that 2d constraint  there aren t any vectors in MATLAB - at least not in the mathematical sense of vector as being 1d   Have you looked at np atleast 2d  also  1d and  3d versions

User · Answer

1  The meaning of shapes in NumPy  You write   I know literally it s list of numbers and list of lists where all list contains only a number  but that s a bit of an unhelpful way to think about it   The best way to think about NumPy arrays is that they consist of two parts  a data buffer which is just a block of raw elements  and a view which describes how to interpret the data buffer   For example  if we create an array of 12 integers    gt  gt  gt  a   numpy arange 12   gt  gt  gt  a array   0   1   2   3   4   5   6   7   8   9  10  11     Then a consists of a data buffer  arranged something like this    -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    and a view which describes how to interpret the data    gt  gt  gt  a flags   C CONTIGUOUS   True   F CONTIGUOUS   True   OWNDATA   True   WRITEABLE   True   ALIGNED   True   UPDATEIFCOPY   False  gt  gt  gt  a dtype dtype  int64    gt  gt  gt  a itemsize 8  gt  gt  gt  a strides  8    gt  gt  gt  a shape  12     Here the shape  12   means the array is indexed by a single index which runs from 0  to  11  Conceptually  if we label this single index i  the array a looks like this   i  0    1    2    3    4    5    6    7    8    9   10   11  -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    If we reshape an array  this doesn t change the data buffer  Instead  it creates a new view that describes a different way to interpret the data  So after    gt  gt  gt  b   a reshape  3  4     the array b has the same data buffer as a  but now it is indexed by two indices which run from 0  to  2 and 0  to  3 respectively  If we label the two indices i and j  the array b looks like this   i  0    0    0    0    1    1    1    1    2    2    2    2 j  0    1    2    3    0    1    2    3    0    1    2    3  -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    which means that    gt  gt  gt  b 2 1  9   You can see that the second index changes quickly and the first index changes slowly  If you prefer this to be the other way round  you can specify the order parameter    gt  gt  gt  c   a reshape  3  4   order  F     which results in an array indexed like this   i  0    1    2    0    1    2    0    1    2    0    1    2 j  0    0    0    1    1    1    2    2    2    3    3    3  -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    which means that    gt  gt  gt  c 2 1  5   It should now be clear what it means for an array to have a shape with one or more dimensions of size  1  After    gt  gt  gt  d   a reshape  12  1     the array d is indexed by two indices  the first of which runs from 0  to  11  and the second index is always  0   i  0    1    2    3    4    5    6    7    8    9   10   11 j  0    0    0    0    0    0    0    0    0    0    0    0  -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    and so    gt  gt  gt  d 10 0  10   A dimension of length  1 is  free   in some sense   so there s nothing stopping you from going to town    gt  gt  gt  e   a reshape  1  2  1  6  1     giving an array indexed like this   i  0    0    0    0    0    0    0    0    0    0    0    0 j  0    0    0    0    0    0    1    1    1    1    1    1 k  0    0    0    0    0    0    0    0    0    0    0    0 l  0    1    2    3    4    5    0    1    2    3    4    5 m  0    0    0    0    0    0    0    0    0    0    0    0  -----------------------------------------------------------      0     1     2     3     4     5     6     7     8     9    10    11     -----------------------------------------------------------    and so    gt  gt  gt  e 0 1 0 0 0  6   See the NumPy internals documentation for more details about how arrays are implemented   2  What to do   Since numpy reshape just creates a new view  you shouldn t be scared about using it whenever necessary  It s the right tool to use when you want to index an array in a different way   However  in a long computation it s usually possible to arrange to construct arrays with the  right  shape in the first place  and so minimize the number of reshapes and transposes  But without seeing the actual context that led to the need for a reshape  it s hard to say what should be changed   The example in your question is   numpy dot M   0   numpy ones  1  R      but this is not realistic  First  this expression   M   0  sum     computes the result more simply  Second  is there really something special about column 0  Perhaps what you actually need is   M sum axis 0

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1  The reason not to prefer a shape of  R  1  over  R   is that it unnecessarily complicates things  Besides  why would it be preferable to have shape  R  1  by default for a length-R vector instead of  1  R   It s better to keep it simple and be explicit when you require additional dimensions   2  For your example  you are computing an outer product so you can do this without a reshape call by using np outer   np outer M   0   numpy ones  1  R

[python] Difference between numpy.array shape (R, 1) and (R,)

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