I am working with the multinerf Framework from Google Research.
It's great to work with and things are actually pretty clear down to the paragraph existing data loaders under Intrinsic camera poses:
Intrinsic camera poses
pixtocams= [N, 3, 4] numpy array of inverse intrinsic matrices, OR [3,
4] numpy array of a single shared inverse intrinsic matrix. These
should be in OpenCV format, e.g.
camtopix = np.array([
[focal, 0, width/2],
[ 0, focal, height/2],
[ 0, 0, 1],
])
pixtocam = np.linalg.inv(camtopix)
I don't quite understand why they are talking about an inverse intrinsic matrix (or matrices) of the dimensions [3, 4]. The inverse intrinsic matrix should have the dimensions [3, 3], shouldn't it?
I think that it's a typo, since you can't really invert a 3x4 matrix (it must be singular). You're right that the dimensions should be 3x3. You can see that immediately below the passage you quoted, they give this example of an inverse intrinsic matrix:
camtopix = np.array([
[focal, 0, width/2],
[ 0, focal, height/2],
[ 0, 0, 1],
])
pixtocam = np.linalg.inv(camtopix)
which is 3x3.
In scientific computation, we often have to construct matrices that compute differential operators. It is often easier to write the code that applies the operator than to explicitly construct the matrix. Is there a library that takes the code (assuming it only uses linear operations) and outputs the matrix, ideally in sparse form?
Example:
# computes finite differences
def myop(a):
return a[1:]-a[:-1]
a = np.array(5)
myop(a)
computes the finite differences of the "a" vector. I now want to so something like
a = some_library.array(5)
op = myop(a)
print(op.as_matrix())
which should give me the matrix representation:
[[-1, 1, 0, 0, 0],
[0, -1, 1, 0, 0],
[0, 0, -1, 1, 0],
[0, 0, 0, -1, 1]]
Having the matrix is very useful, for example for computing the transposed operator or analyzing the sparsity patterns. Technically it should be possible to use automatic differentiation tools and extract the Jacobian of op(), but I didn't find any AD libraries that efficiently deal with the whole Jacobian, in particular if it is sparse. They all seem to either do one pass per row or one per column of the Jacobian, which is horribly slow even for only a few hundreds of variables.
One easy way:
In [568]: arr = np.zeros((4,5),int)
In [569]: arr[np.arange(4),np.arange(4)]=-1
In [570]: arr[np.arange(4),np.arange(1,5)]=1
In [571]: arr
Out[571]:
array([[-1, 1, 0, 0, 0],
[ 0, -1, 1, 0, 0],
[ 0, 0, -1, 1, 0],
[ 0, 0, 0, -1, 1]])
There are various np.diag... functions, but since your don't want a square matrix I though this would be easier.
The scipy.sparse library is often used for finite-difference problems, and has various dia constructors. But that requires more reading.
I have a numpy 2d array and i want to run a function that checks if values fron neighboring pixels are lowe than the given value (start value). If it’s i'm trying to run recursive function with this pixel and value from the first one
It works fine for small arrays, but with a big one i have memory errors.
I'm wondering if there is a better way to do this.
In result I'm trying to get numpy 2d array with values that met this criteria.
code:
def check_neighbours(point_position, arr, water_level):
locs = [[-1, -1], [-1, 0], [-1, 1], [0, -1],
[0, 1], [1, 1], [1, -1], [1, 0]]
if point in self.checked_cells:
return True
self.checked_cells.append(point)
neighbours = [self.get_locs(x, point) for x in locs]
for i in neighbours:
n_point = arr[i[0], i[1]]
if n_point <= water_level:
check_neighbours(i, arr, water_level)
check_neigbours([10,20], 2darray, 70)
Thanks everyone for the insights. Turned out the i was looking for something like a flood fill algorithm.
To avoid the stack overflow i had to use an queue within a while loop.
EDIT
I realized that I did not check my mwe very well and as such asked something of the wrong question. The main problem is when the numpy array is passed in as a 2d array instead of 1d (or even when a python list is passed in as 1d instead of 2d). So if we have
x = np.array([[1], [2], [3]])
then obviously if you try to index this then you will get arrays out (if you use item you do not). this same thing also applies to standard python lists.
Sorry about the confusion.
Original
I am trying to form a new numpy array from something that may be a numpy array or may be a standard python list.
for example
import numpy as np
x = [2, 3, 1]
y = np.array([[0, -x[2], x[1]], [x[2], 0, -x[0]], [-x[1], x[0], 0]])
Now I would like to form a function such that I can make y easily.
def skew(vector):
"""
this function returns a numpy array with the skew symmetric cross product matrix for vector.
the skew symmetric cross product matrix is defined such that
np.cross(a, b) = np.dot(skew(a), b)
:param vector: An array like vector to create the skew symmetric cross product matrix for
:return: A numpy array of the skew symmetric cross product vector
"""
return np.array([[0, -vector[2], vector[1]],
[vector[2], 0, -vector[0]],
[-vector[1], vector[0], 0]])
This works great and I can now write (assuming the above function is included)
import numpy as np
x=[2, 3, 1]
y = skew(x)
However, I would also like to be able to call skew on existing 1d or 2d numpy arrays. For instance
import numpy as np
x = np.array([2, 3, 1])
y = skew(x)
Unfortunately, doing this returns a numpy array where the elements are also numpy arrays, not python floats as I would like them to be.
Is there an easy way to form a new numpy array like I have done from something that is either a python list or a numpy array and have the result be just a standard numpy array with floats in each element?
Now obviously one solution is to check to see if the input is a numpy array or not:
def skew(vector):
"""
this function returns a numpy array with the skew symmetric cross product matrix for vector.
the skew symmetric cross product matrix is defined such that
np.cross(a, b) = np.dot(skew(a), b)
:param vector: An array like vector to create the skew symmetric cross product matrix for
:return: A numpy array of the skew symmetric cross product vector
"""
if isinstance(vector, np.ndarray):
return np.array([[0, -vector.item(2), vector.item(1)],
[vector.item(2), 0, -vector.item(0)],
[-vector.item(1), vector.item(0), 0]])
else:
return np.array([[0, -vector[2], vector[1]],
[vector[2], 0, -vector[0]],
[-vector[1], vector[0], 0]])
however, it gets very tedious having to write these instance checks all over the place.
Another solution would be to cast everything to an array first and then just use the array call
def skew(vector):
"""
this function returns a numpy array with the skew symmetric cross product matrix for vector.
the skew symmetric cross product matrix is defined such that
np.cross(a, b) = np.dot(skew(a), b)
:param vector: An array like vector to create the skew symmetric cross product matrix for
:return: A numpy array of the skew symmetric cross product vector
"""
vector = np.array(vector)
return np.array([[0, -vector.item(2), vector.item(1)],
[vector.item(2), 0, -vector.item(0)],
[-vector.item(1), vector.item(0), 0]])
but I feel like this is inefficient as it requires creating a new copy of vector (in this case not a big deal since vector is small but this is just a simple example).
My question is, is there a different way to do this outside of what I've discussed or am I stuck using one of these methods?
Arrays are iterable. You can write in your skew function:
def skew(x):
return np.array([[0, -x[2], x[1]],
[x[2], 0, -x[0]],
[-x[1], x[0], 0]])
x = [1,2,3]
y = np.array([1,2,3])
>>> skew(y)
array([[ 0, -3, 2],
[ 3, 0, -1],
[-2, 1, 0]])
>>> skew(x)
array([[ 0, -3, 2],
[ 3, 0, -1],
[-2, 1, 0]])
In any case your methods ended with 1st dimension elements being numpy arrays containing floats. You'll need in any case a call on the 2nd dimension to get the floats inside.
Regarding what you told me in the comments, you may add an if condition for 2d arrays:
def skew(x):
if (isinstance(x,ndarray) and len(x.shape)>=2):
return np.array([[0, -x[2][0], x[1][0]],
[x[2][0], 0, -x[0][0]],
[-x[1][0], x[0][0], 0]])
else:
return np.array([[0, -x[2], x[1]],
[x[2], 0, -x[0]],
[-x[1], x[0], 0]])
You can implement the last idea efficiently using numpy.asarray():
vector = np.asarray(vector)
Then, if vector is already a NumPy array, no copying occurs.
You can keep the first version of your function and convert the numpy array to list:
def skew(vector):
if isinstance(vector, np.ndarray):
vector = vector.tolist()
return np.array([[0, -vector[2], vector[1]],
[vector[2], 0, -vector[0]],
[-vector[1], vector[0], 0]])
In [58]: skew([2, 3, 1])
Out[58]:
array([[ 0, -1, 3],
[ 1, 0, -2],
[-3, 2, 0]])
In [59]: skew(np.array([2, 3, 1]))
Out[59]:
array([[ 0, -1, 3],
[ 1, 0, -2],
[-3, 2, 0]])
This is not an optimal solution but is a very easy one.
You can just convert the vector into list by default.
def skew(vector):
vector = list(vector)
return np.array([[0, -vector[2], vector[1]],
[vector[2], 0, -vector[0]],
[-vector[1], vector[0], 0]])
It should be a standard question but I am not able find the answer :(
I have a numpy darray n samples (raw) and p variables (observation).
I would like to count how many times each variables is non 0.
I would use a function like
sum([1 for i in column if i!=0])
but how can I apply this function to all the columns of my matrix?
from this post: How to apply numpy.linalg.norm to each row of a matrix?
If the operation supports axis, use the axis parameter, it's usually faster,
Otherwise, np.apply_along_axis could help.
Here is the numpy.count_nonzero.
So here is the simple answer:
import numpy as np
arr = np.eye(3)
np.apply_along_axis(np.count_nonzero, 0, arr)
You can use np.sum over a boolean array created from comparing your original array to zero, using the axis keyword argument to indicate whether you want to count over rows or columns. In your case:
>>> a = np.array([[0, 1, 1, 0],[1, 1, 0, 0]])
>>> a
array([[0, 1, 1, 0],
[1, 1, 0, 0]])
>>> np.sum(a != 0, axis=0)
array([1, 2, 1, 0])