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I don't understand broadcasting. The documentation explains the rules of broadcasting but doesn't seem to define it in English. My guess is that broadcasting is when NumPy fills a smaller dimensional array with dummy data in order to perform an operation. But this doesn't work:
>>> x = np.array([1,3,5])
>>> y = np.array([2,4])
>>> x+y
*** ValueError: operands could not be broadcast together with shapes (3,) (2,)
The error message hints that I'm on the right track, though. Can someone define broadcasting and then provide some simple examples of when it works and when it doesn't?
The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations.
It's basically a way numpy can expand the domain of operations over arrays.
The only requirement for broadcasting is a way aligning array dimensions such that either:
Aligned dimensions are equal.
One of the aligned dimensions is 1.
So, for example if:
x = np.ndarray(shape=(4,1,3))
y = np.ndarray(shape=(3,3))
You could not align x and y like so:
4 x 1 x 3
3 x 3
But you could like so:
4 x 1 x 3
3 x 3
How would an operation like this result?
Suppose we have:
x = np.ndarray(shape=(1,3), buffer=np.array([1,2,3]),dtype='int')
array([[1, 2, 3]])
y = np.ndarray(shape=(3,3), buffer=np.array([1,1,1,1,1,1,1,1,1]),dtype='int')
array([[1, 1, 1],
[1, 1, 1],
[1, 1, 1]])
The operation x + y would result in:
array([[2, 3, 4],
[2, 3, 4],
[2, 3, 4]])
I hope you caught the drift. If you did not, you can always check the official documentation here.
Cheers!
1.What is Broadcasting?
Broadcasting is a Tensor operation. Helpful in Neural Network (ML, AI)
2.What is the use of Broadcasting?
Without Broadcasting addition of only identical Dimension(shape) Tensors is supported.
Broadcasting Provide us the Flexibility to add two Tensors of Different Dimension.
for Example: adding a 2D Tensor with a 1D Tensor is not possible without broadcasting see the image explaining Broadcasting pictorially
Run the Python example code understand the concept
x = np.array([1,3,5,6,7,8])
y = np.array([2,4,5])
X=x.reshape(2,3)
x is reshaped to get a 2D Tensor X of shape (2,3), and adding this 2D Tensor X with 1D Tensor y of shape(1,3) to get a 2D Tensor z of shape(2,3)
print("X =",X)
print("\n y =",y)
z=X+y
print("X + y =",z)
You are almost correct about smaller Tensor, no ambiguity, the smaller tensor will be broadcasted to match the shape of the larger tensor.(Small vector is repeated but not filled with Dummy Data or Zeros to Match the Shape of larger).
3. How broadcasting happens?
Broadcasting consists of two steps:
1 Broadcast axes are added to the smaller tensor to match the ndim of
the larger tensor.
2 The smaller tensor is repeated alongside these new axes to match the full shape
of the larger tensor.
4. Why Broadcasting not happening in your code?
your code is working but Broadcasting can not happen here because both Tensors are different in shape but Identical in Dimensional(1D).
Broadcasting occurs when dimensions are nonidentical.
what you need to do is change Dimension of one of the Tensor, you will experience Broadcasting.
5. Going in Depth.
Broadcasting(repetition of smaller Tensor) occurs along broadcast axes but since both the Tensors are 1 Dimensional there is no broadcast Axis.
Don't Confuse Tensor Dimension with the shape of tensor,
Tensor Dimensions are not same as Matrices Dimension.
Broadcasting is numpy trying to be smart when you tell it to perform an operation on arrays that aren't the same dimension. For example:
2 + np.array([1,3,5]) == np.array([3, 5, 7])
Here it decided you wanted to apply the operation using the lower dimensional array (0-D) on each item in the higher-dimensional array (1-D).
You can also add a 0-D array (scalar) or 1-D array to a 2-D array. In the first case, you just add the scalar to all items in the 2-D array, as before. In the second case, numpy will add row-wise:
In [34]: np.array([1,2]) + np.array([[3,4],[5,6]])
Out[34]:
array([[4, 6],
[6, 8]])
There are ways to tell numpy to apply the operation along a different axis as well. This can be taken even further with applying an operation between a 3-D array and a 1-D, 2-D, or 0-D array.
>>> x = np.array([1,3,5])
>>> y = np.array([2,4])
>>> x+y
*** ValueError: operands could not be broadcast together with shapes (3,) (2,)
Broadcasting is how numpy do math operations with array of different shapes. Shapes are the format the array has, for example the array you used, x , has 3 elements of 1 dimension; y has 2 elements and 1 dimension.
To perform broadcasting there are 2 rules:
1) Array have the same dimensions(shape) or
2)The dimension that doesn't match equals one.
for example x has shape(2,3) [or 2 lines and 3 columns];
y has shape(2,1) [or 2 lines and 1 column]
Can you add them? x + y?
Answer: Yes, because the mismatched dimension is equal to 1 (the column in y). If y had shape(2,4) broadcasting would not be possible, because the mismatched dimension is not 1.
In the case you posted:
operands could not be broadcast together with shapes (3,) (2,);
it is because 3 and 2 mismatched altough both have 1 line.
I would like to suggest to try the np.broadcast_arrays, run some demos may give intuitive ideas. Official Document is also helpful. From my current understanding, numpy will compare the dimension from tail to head. If one dim is 1, it will broadcast in the dimension, if one array has more axes, such (256*256*3) multiply (1,), you can view (1) as (1,1,1). And broadcast will make (256,256,3).
I have found myself needing to add features to existing numpy arrays which has led to a question around what the last portion of the following code is actually doing:
np.ones(shape=feature_set.shape)[...,None]
Set-up
As an example, let's say I wish to solve for linear regression parameter estimates by using numpy and solving:
Assume I have a feature set shape (50,1), a target variable of shape (50,), and I wish to use the shape of my target variable to add a column for intercept values.
It would look something like this:
# Create random target & feature set
y_train = np.random.randint(0,100, size = (50,))
feature_set = np.random.randint(0,100,size=(50,1))
# Build a set of 1s after shape of target variable
int_train = np.ones(shape=y_train.shape)[...,None]
# Able to then add int_train to feature set
X = np.concatenate((int_train, feature_set),1)
What I Think I Know
I see the difference in output when I include [...,None] vs when I leave it off. Here it is:
The second version returns an error around input arrays needing the same number of dimensions, and eventually I stumbled on the solution to use [...,None].
Main Question
While I see the output of [...,None] gives me what I want, I am struggling to find any information on what it is actually supposed to do. Can anybody walk me through what this code actually means, what the None argument is doing, etc?
Thank you!
The slice of [..., None] consists of two "shortcuts":
The ellipsis literal component:
The dots (...) represent as many colons as needed to produce a complete indexing tuple. For example, if x is a rank 5 array (i.e., it has 5 axes), then
x[1,2,...] is equivalent to x[1,2,:,:,:],
x[...,3] to x[:,:,:,:,3] and
x[4,...,5,:] to x[4,:,:,5,:].
(Source)
The None component:
numpy.newaxis
The newaxis object can be used in all slicing operations to create an axis of length one. newaxis is an alias for ‘None’, and ‘None’ can be used in place of this with the same result.
(Source)
So, arr[..., None] takes an array of dimension N and "adds" a dimension "at the end" for a resulting array of dimension N+1.
Example:
import numpy as np
x = np.array([[1,2,3],[4,5,6]])
print(x.shape) # (2, 3)
y = x[...,None]
print(y.shape) # (2, 3, 1)
z = x[:,:,np.newaxis]
print(z.shape) # (2, 3, 1)
a = np.expand_dims(x, axis=-1)
print(a.shape) # (2, 3, 1)
print((y == z).all()) # True
print((y == a).all()) # True
Consider this code:
np.ones(shape=(2,3))[...,None].shape
As you see the 'None' phrase change the (2,3) matrix to a (2,3,1) tensor. As a matter of fact it put the matrix in the LAST index of the tensor.
If you use
np.ones(shape=(2,3))[None, ...].shape
it put the matrix in the FIRST index of the tensor
To my knowledge, I haven't seen any posts regrading this, if any, please note me.
According to SciPy website, numpy.matrix.A1 is equivalent to np.asarray(x).ravel().
One example will be enough to illustrate the problem:
x = np.matrix(np.arange(12).reshape((1, -1)))
print("Shape of x: ", x.shape)
print("Shape of x with asarray: ", np.asarray(x).shape)
print("Equality: ", np.array_equal(x, np.asarray(x)))
print("Shape of x ravel flatten: ", x.ravel().shape)
print("Shape of x ravel flatten with asarray: ", np.asarray(x).ravel().shape)
Prints:
Shape of x: (1, 12)
Shape of x with asarray: (1, 12)
Equality: True
Shape of x ravel flatten: (1, 12)
Shape of x ravel flatten with asarray: (12,)
Problem:
As observed, the dimension of flattened array is different with asarray, just wondered why it's being presenting such inconsistencies in dimensions?
From np implementation of asarray function, I didn't see any thing might cause a dimension problem, plus it passes the equality test (x == np.asarray(x)). But other than this, what could be possibly making implicit changes to the array.
def asarray(a, dtype=None, order=None):
return array(a, dtype, copy=False, order=order)
Edited:
This could be confusing
plus it passes the equality test (x == np.asarray(x))
to be more precise, I mean, it passes the equality test (np.array_equal(x, np.asarray(x)))
NumPy matrices (np.matrix) are always 2D. (Mathematically, the strict definition of a matrix, rather than a matrix or vector.)
From np.matrix.ravel:
Return the matrix flattened to shape (1, N) where N is the number
of elements in the original matrix.
Some motivation for NumPy matrices is for Matlab users. See here for some of the finer points on NumPy matrix versus array.
In brief, a NumPy array (the result of asarray(x) here) can be a 1-dimensional structure. Matrices can be a minimum of 2d. type(np.asarray(x)) is, not shockingly, an array. (Not to be confused with np.asanyarray(), for which your result would be a matrix because it's an array subclass.
Lastly, you noted:
it passes the equality test (x == np.asarray(x))
I see how this could be a bit confusing. Technically, you want to use np.array_equal(x, np.asarray(x)), although that still evaluates to True. However, NumPy logic testing is generally meant to be data-structure agnostic, in general:
np.array_equal([1, 2, 3], np.array([1, 2, 3]))
# True
(Here is the source for array_equal()--both are cast to arrays.)
The bottom line is that their "minimum dimensionalities" are different, and one is a subclass of the other.
issubclass(np.matrix, np.ndarray)
# True
I have a matrix X which has len(X) equal to 13934 and len(X[i]), for all i, equal to 74, and I have an array Y which has len(Y) equal to 13934 and len(Y[i]) equal to TypeError: object of type 'numpy.int64' has no len() for all i.
When I try np.vstack((X,Y)) or result = np.concatenate((X, Y.T), axis=1)
I get ValueError: all the input array dimensions except for the concatenation axis must match exactly
What is the problem?
When I print out Y it says array([1,...], dtype=int64) and when I print out X it says array([data..]) with no dtype. Could this be the problem?
I tried converting them both to float32 by doing X.view('float32') and this did not help.
Since X is a numpy array, you can do X.shape instead of the repeated len. I expect it to show (13934, 74).
I expect Y.shape to be (13934,). It's a 1d array, which is why Y[0] is a number, numpy.int64. And since it is 1d, transpose (swapping axes) doesn't do anything. (this isn't MATLAB where everything has at least 2 dimensions.)
It looks like you want to create an array that has shape (13934, 75). To do that you'll need to add a dimension to Y. Y[:,None] is a concise way of doing that. The shape of that is (13934,1), which will concatenate with X. If that None syntax is puzzling, try, Y.reshape(-1,1) (or reshape(13934,1)).
You can try this:
# use Y[:,None] to make Y 2d array so it can be concatenated with X which is also 2d
np.concatenate((X, Y[:,None]), axis=1)
Or:
np.hstack((X,Y[:,None]))
I don't understand broadcasting. The documentation explains the rules of broadcasting but doesn't seem to define it in English. My guess is that broadcasting is when NumPy fills a smaller dimensional array with dummy data in order to perform an operation. But this doesn't work:
>>> x = np.array([1,3,5])
>>> y = np.array([2,4])
>>> x+y
*** ValueError: operands could not be broadcast together with shapes (3,) (2,)
The error message hints that I'm on the right track, though. Can someone define broadcasting and then provide some simple examples of when it works and when it doesn't?
The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations.
It's basically a way numpy can expand the domain of operations over arrays.
The only requirement for broadcasting is a way aligning array dimensions such that either:
Aligned dimensions are equal.
One of the aligned dimensions is 1.
So, for example if:
x = np.ndarray(shape=(4,1,3))
y = np.ndarray(shape=(3,3))
You could not align x and y like so:
4 x 1 x 3
3 x 3
But you could like so:
4 x 1 x 3
3 x 3
How would an operation like this result?
Suppose we have:
x = np.ndarray(shape=(1,3), buffer=np.array([1,2,3]),dtype='int')
array([[1, 2, 3]])
y = np.ndarray(shape=(3,3), buffer=np.array([1,1,1,1,1,1,1,1,1]),dtype='int')
array([[1, 1, 1],
[1, 1, 1],
[1, 1, 1]])
The operation x + y would result in:
array([[2, 3, 4],
[2, 3, 4],
[2, 3, 4]])
I hope you caught the drift. If you did not, you can always check the official documentation here.
Cheers!
1.What is Broadcasting?
Broadcasting is a Tensor operation. Helpful in Neural Network (ML, AI)
2.What is the use of Broadcasting?
Without Broadcasting addition of only identical Dimension(shape) Tensors is supported.
Broadcasting Provide us the Flexibility to add two Tensors of Different Dimension.
for Example: adding a 2D Tensor with a 1D Tensor is not possible without broadcasting see the image explaining Broadcasting pictorially
Run the Python example code understand the concept
x = np.array([1,3,5,6,7,8])
y = np.array([2,4,5])
X=x.reshape(2,3)
x is reshaped to get a 2D Tensor X of shape (2,3), and adding this 2D Tensor X with 1D Tensor y of shape(1,3) to get a 2D Tensor z of shape(2,3)
print("X =",X)
print("\n y =",y)
z=X+y
print("X + y =",z)
You are almost correct about smaller Tensor, no ambiguity, the smaller tensor will be broadcasted to match the shape of the larger tensor.(Small vector is repeated but not filled with Dummy Data or Zeros to Match the Shape of larger).
3. How broadcasting happens?
Broadcasting consists of two steps:
1 Broadcast axes are added to the smaller tensor to match the ndim of
the larger tensor.
2 The smaller tensor is repeated alongside these new axes to match the full shape
of the larger tensor.
4. Why Broadcasting not happening in your code?
your code is working but Broadcasting can not happen here because both Tensors are different in shape but Identical in Dimensional(1D).
Broadcasting occurs when dimensions are nonidentical.
what you need to do is change Dimension of one of the Tensor, you will experience Broadcasting.
5. Going in Depth.
Broadcasting(repetition of smaller Tensor) occurs along broadcast axes but since both the Tensors are 1 Dimensional there is no broadcast Axis.
Don't Confuse Tensor Dimension with the shape of tensor,
Tensor Dimensions are not same as Matrices Dimension.
Broadcasting is numpy trying to be smart when you tell it to perform an operation on arrays that aren't the same dimension. For example:
2 + np.array([1,3,5]) == np.array([3, 5, 7])
Here it decided you wanted to apply the operation using the lower dimensional array (0-D) on each item in the higher-dimensional array (1-D).
You can also add a 0-D array (scalar) or 1-D array to a 2-D array. In the first case, you just add the scalar to all items in the 2-D array, as before. In the second case, numpy will add row-wise:
In [34]: np.array([1,2]) + np.array([[3,4],[5,6]])
Out[34]:
array([[4, 6],
[6, 8]])
There are ways to tell numpy to apply the operation along a different axis as well. This can be taken even further with applying an operation between a 3-D array and a 1-D, 2-D, or 0-D array.
>>> x = np.array([1,3,5])
>>> y = np.array([2,4])
>>> x+y
*** ValueError: operands could not be broadcast together with shapes (3,) (2,)
Broadcasting is how numpy do math operations with array of different shapes. Shapes are the format the array has, for example the array you used, x , has 3 elements of 1 dimension; y has 2 elements and 1 dimension.
To perform broadcasting there are 2 rules:
1) Array have the same dimensions(shape) or
2)The dimension that doesn't match equals one.
for example x has shape(2,3) [or 2 lines and 3 columns];
y has shape(2,1) [or 2 lines and 1 column]
Can you add them? x + y?
Answer: Yes, because the mismatched dimension is equal to 1 (the column in y). If y had shape(2,4) broadcasting would not be possible, because the mismatched dimension is not 1.
In the case you posted:
operands could not be broadcast together with shapes (3,) (2,);
it is because 3 and 2 mismatched altough both have 1 line.
I would like to suggest to try the np.broadcast_arrays, run some demos may give intuitive ideas. Official Document is also helpful. From my current understanding, numpy will compare the dimension from tail to head. If one dim is 1, it will broadcast in the dimension, if one array has more axes, such (256*256*3) multiply (1,), you can view (1) as (1,1,1). And broadcast will make (256,256,3).