CODEWITHSUNDEEP
pythonrnumpy
irritable_phd_syndrome
irritable_phd_syndrome

Reputation: 5067

Differences between R's and Numpy's QR decomposition

I'm working through a large R (v3.6.0) codebase and trying to understand what it is doing. To do this, I'm translating some of the R code into Python (v3.6.5) using Numpy (v1.14.3). I have a piece of R code that appears to work just fine:

> v<-c(1,1,1,1)
> qrout<-qr(v)
> qr.Q(qrout)
     [,1]
[1,] -0.5
[2,] -0.5
[3,] -0.5
[4,] -0.5
> qr.R(qrout)
     [,1]
[1,]   -2

The Python equivalent is not fine :

>>> import numpy as np
>>> v=np.ones(4)
>>> v
array([1., 1., 1., 1.])
>>> np.linalg.qr(v)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/opt/python/3.6.5/lib/python3.6/site-packages/numpy/linalg/linalg.py", line 753, in qr
    _assertRank2(a)
  File "/opt/python/3.6.5/lib/python3.6/site-packages/numpy/linalg/linalg.py", line 195, in _assertRank2
    'two-dimensional' % a.ndim)
numpy.linalg.linalg.LinAlgError: 1-dimensional array given. Array must be two-dimensional

Looking at the docs it appears that in R uses LAPACK's DQRDC(2)/DGEQP3/ZGEQP3, while Numpy uses LAPACK's dgeqrf, zgeqrf, dorgqr, and zungqr. Clearly R is happy with a 1 dimensional matrix, while Numpy is not.

QUESTION

How do I replicate R's QR factorization using Numpy?

Upvotes: 1

Views: 487

Answers (1)

gboffi
gboffi

Reputation: 25033

As stated in the error message

Array must be two-dimensional 

In [7]: qr(v[:,None])                                                                     
Out[7]: 
(array([[-0.5],
        [-0.5],
        [-0.5],
        [-0.5]]), array([[-2.]]))

Edit
What follows is not different from the striked code above, but who knows...

In [28]: from numpy.linalg import qr 
    ...: from numpy import ones

In [29]: v = ones(4) ; print(v.shape) ; print(v[:,None].shape) # adding a dimension
(4,)
(4, 1)

In [30]: q, r = qr(v[:, None])

In [31]: print(q) ; print() ; print(r)                 
[[-0.5]
 [-0.5]
 [-0.5]
 [-0.5]]

[[-2.]]

In [32]:

In Python/Numpy arrays can have just one dimension, but qr requires a 2-dimensional array.

E.g., in Python transposition doesn't modify the dimensions of what is, in its essence, a 1D vector.

In [9]: print(v); print(v.T)                                                              
[1 1 1 1]
[1 1 1 1]

[10]: print(v.shape); print((v.T).shape)                                                
(4,)
(4,)

In R, qr() attempts to coerce its input to a 2-dimensional array (matrix), so qr() does this step for you, while in Python you have to do it explicitly.

The most idiomatic way to add a dimension to a Numpy array being to use None in a slice object to signify the addition of a dummy dimension to it.

Upvotes: 1

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