remove zero lines 2-D numpy array

Question

I run a qr factorization in numpy which returns a list of ndarrays, namely Qand R:

>>> [q,r] = np.linalg.qr(np.array([1,0,0,0,1,1,1,1,1]).reshape(3,3))

R is a two-dimensional array, having pivoted zero-lines at the bottom (even proved for all examples in my test set):

>>> print r
[[ 1.41421356  0.70710678  0.70710678]
 [ 0.          1.22474487  1.22474487]
 [ 0.          0.          0.        ]]

. Now, I want to divide R in two matrices R_~:

[[ 1.41421356  0.70710678  0.70710678]
 [ 0.          1.22474487  1.22474487]]

and R_0:

[[ 0.          0.          0.        ]]

(extracting all zero-lines). It seems to be close to this solution: deleting rows in numpy array.

EDIT:
Even more interesting: np.linalg.qr() returns a n x n-matrix. Not, what I would have expected:

A := n x m
Q := n x m
R := n x m

ecatmur · Accepted Answer · 2012-06-25 11:59:49Z

107

Use np.all with an axis argument:

>>> r[np.all(r == 0, axis=1)]
array([[ 0.,  0.,  0.]])
>>> r[~np.all(r == 0, axis=1)]
array([[-1.41421356, -0.70710678, -0.70710678],
       [ 0.        , -1.22474487, -1.22474487]])

answered Jun 25, 2012 at 11:59

ecatmur

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4 Comments

ecatmur Over a year ago

@denfromufa axis=0 would remove all-zero columns.

den.run.ai Over a year ago

that is obvious, what is problematic is that this filtering cannot be applied as is for axis=0, instead transpose is necessary

ecatmur Over a year ago

@denfromufa oh yeah, you need to do the subscript on the 1 axis: r[:, np.all(r == 0, axis=0)]

ecatmur Over a year ago

@denfromufa or s.compress(np.all(s == 0, axis=0), axis=1)

HYRY · Accepted Answer · 2012-06-25 12:02:54Z

5

Because the data are not equal zero exactly, we need set a threshold value for zero such as 1e-6, use numpy.all with axis=1 to check the rows are zeros or not. Use numpy.where and numpy.diff to get the split positions, and call numpy.split to split the array into a list of arrays.

import numpy as np
[q,r] = np.linalg.qr(np.array([1,0,0,0,1,1,1,1,1]).reshape(3,3))
mask = np.all(np.abs(r) < 1e-6, axis=1)
pos = np.where(np.diff(mask))[0] + 1
result = np.split(r, pos)

answered Jun 25, 2012 at 12:02

HYRY

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3 Comments

Milla Well Over a year ago

You think, 1e-6 should be precise enough for most purposes? Should I learn this paramater?

heltonbiker Over a year ago

@MillaWell the precision always depend on application. For example, a precision of one milimeter is very good for civil engineering, but very poor for mechanical engineering, and somewhat absurd for astronomy, for example.

oak Over a year ago

numpy now has np.allclose function which can make the code more readable docs.scipy.org/doc/numpy/reference/generated/…

yspreen · Accepted Answer · 2021-01-19 19:44:37Z

5

Since this is among the first google results to trim a 2D array of zero lines, I want to add my implementation to only remove leading and trailing zeros, in two dimensions:

p = np.where(t != 0)
t = t[min(p[0]) : max(p[0]) + 1, min(p[1]) : max(p[1]) + 1]

This assumes your array is called t and numpy is imported as np.

answered Jan 19, 2021 at 19:44

yspreen

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Comments

travelingbones · Accepted Answer · 2017-05-01 13:54:10Z

2

If you want to eliminate rows that have negligible entries, i'd use np.allclose.

zero_row_indices = [i for i in r.shape[0] if np.allclose(r[i,:],0)]
nonzero_row_indices =[i for i in r.shape[0] if not np.allclose(r[i,:],0)]
r_new = r[nonzero_row_indices,:]

answered May 1, 2017 at 13:54

travelingbones

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