If we look closer to see how the rearrangement exactly happened arrays of numbers seems to have changed in a particular pattern.
We changed the 1st and 2nd, so it becomes (3, 2, 4) in size. Here, original array sizes are (2, 3, 4). If we try a different example with a 3 dimensional array with each dimension having a different size, the rearrangement part becomes more clear. So the end result doesn't seem to change except the reordering of rows arr and arr. The example in the book with a (2, 2, 4) sized array is not very clear since 1st and 2nd axes has the same size. transpose(0, 1, 2), the array will stay the same because there is nothing to change it is the default order. transpose(1, 0, 2), we mean, "Change the 1st axis with the 2nd." If we use. transpose(1, 0, 2) determines how the order of axes are changed compared to the original. Here "permute" means "rearrange", so rearranging the order of axes. Transposing Arrays and Swapping Axes.įor higher dimensional arrays, transpose will accept a tuple of axis numbers to permute the axes (for extra mind bending). This feature of transpose is mentioned in Chapter 4.1. It seems the question and the example originates from the book Python for Data Analysis by Wes McKinney. And you had 2 papers, so now you have 2 elements going from left to right. You had 4 elements going from left to right, so now you have four pieces of paper instead. By transposing (2, 1, 0) you're saying that you want the direction of paper-to-paper to now march along the paper from left to right, and the direction of left to right to now go from paper to paper. Why is the first inner element ? Because if you visualize your 3D array as two sheets of paper, 0 and 8 are lined up, one on one paper and one on the other paper, both in the upper left. You'll probably get better understanding if all dimensions were of different size, so you could see where each axis went. Read off the tuple in that order: (2, 1, 0). More interesting is a transpose by (2, 1, 0) which gives you an array of. In this case your new array dimensions are again, only because axes 0 and 1 had the same size (2). Read off the tuple in that order: (1, 0, 2). The destination axes are always in order, so all you need is to specify the source axes. You are effectively permuting the axes: 0 -\/-> 0 So, arr.transpose((1, 0, 2)) would take axis 1 and put it in position 0, axis 0 and put it in position 1, and axis 2 and leave it in position 2. This is exactly how numpy treats the axes of an N-dimensional array. The axes are 0, 1, 2, with sizes 2, 2, 4. Each of those 2D arrays has 2 1D array, each of those 1D arrays has 4 elements. In C notation, your array would be: int arr
#6 PERMUTE 3 CODE#
The actual code that handles the transpose is written in C and can be found here. This basic concept works for any permutation of an array's axes. Now we must jump further to move along axis 1 than axis 0: The transposed array looks like this:Īll that NumPy needs to do is to swap the stride information for axis 0 and axis 1 (axis 2 is unchanged). When we write arr.transpose(1, 0, 2) we are swapping axes 0 and 1. For instance, to move along axis 1, four values (32 bytes) are jumped, and to move along axis 0, eight values (64 bytes) need to be jumped. Since each integer takes up 8 bytes of memory (we're using the int64 dtype), the stride value for each dimension is 8 times the number of values that we need to jump. To interpret it as a 3D object, NumPy must jump over a certain constant number of bytes in order to move along one of the three axes: This array is stored in a contiguous block of memory essentially it is one-dimensional. Now, our 3D array arr looks this (with labelled axes): The stride value represents the number of bytes that must be travelled in memory in order to reach the next value of an axis of an array. No data needs to be copied for this to happen NumPy can simply change how it looks at the underlying memory to construct the new array. The lengths of these axes were also swapped (both lengths are 2 in this example). Notice that the transpose operation swapped the strides for axis 0 and axis 1. To transpose an array, NumPy just swaps the shape and stride information for each axis.
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