# [Numpy-discussion] SVD problem - matrices are not aligned

Sun Oct 24 09:16:04 CDT 2010

```On Oct 24, 2010, at 4:29 AM, josef.pktd@gmail.com wrote:

> On Sat, Oct 23, 2010 at 11:47 PM, Daniel Wagner
>>
>> On Oct 23, 2010, at 11:25 PM, Charles R Harris wrote:
>>
>>
>> On Sat, Oct 23, 2010 at 9:21 PM, Daniel Wagner
>>>
>>> On Oct 23, 2010, at 10:48 PM, Charles R Harris wrote:
>>>
>>>
>>> On Sat, Oct 23, 2010 at 8:33 PM, Daniel Wagner
>>>>
>>>> On Sat, Oct 23, 2010 at 7:00 PM, Daniel Wagner
>>>>>
>>>>> Hi,
>>>>>
>>>>> I'm a new subscriber of this list. I hope to directly start with a
>>>>> question is ok...
>>>>>
>>>>> My question or problem:
>>>>> I've a matrix A which is calculated from the data b. The shapes of these
>>>>> matrices are:
>>>>>>>> A.shape
>>>>> (954, 9)
>>>>>>>> b.shape
>>>>> (954,)
>>>>>
>>>>> I calculate the SVD of A:
>>>>>>>> U, w, V = numpy.linalg.svd(A, full_matrices="True")
>>>>>>>> U.shape
>>>>> (954, 954)
>>>>
>>>> You want full_matrices set false so that U has shape (954, 9).
>>>>
>>>>
>>>> thanks! I tried it before with "False" as a string but of course this
>>>> couldn't work. omgh. (no error message?)
>>>> Now I'm using:
>>>>>>> U, w, V = numpy.linalg.svd(yz_matrix_by, full_matrices=False)
>>>>>
>>>>>>>> W.diag(w)
>>>>>>>> W.shape
>>>>> (9,9)
>>>>>>>> V.shape
>>>>> (9,9)
>>>>>
>>>>> If I'm doing the check of the SVD results using:
>>>>>>>> numpy.allclose(A, numpy.dot(U, numpy.dot(W, V)))
>>>>> I get this error:
>>>>
>>>> easier, allclose(A, dot(U*w, V) )
>>>>
>>>> That's right!
>>>>
>>>>> "ValueError: matrices are not aligned"
>>>>>
>>>>
>>>> Mismatched dimensions.
>>>>
>>>> Yeah, this error is away. Now I get:
>>>>  >>>print(numpy.allclose(U_by*w_by, V_by))
>>>> False
>>>
>>> Seems to be a missing "dot" in there.
>>>
>>> The following works:
>>>>>> numpy.allclose(A, numpy.dot(U, numpy.dot(W, V)))
>>> True
>>> But now I've a new problem problem:
>>> When I'm using:
>>>>>> A.shape
>>> (954, 9)
>>>>>> b.shape
>>> (954, )
>>>>>> temp = numpy.linalg.pinv(A, rcond=1.0000000000000001e-15)
>>>>>> temp.shape
>>> (9, 954)
>>> to multiply this with my data b
>>>>>> x = numpy.dot(temp, b)
>>> ValueError: matrices are not aligned
>>> I've missmatched dimensions again....
>>
>> Looks like you might want to look at lstsq.
>>
>> It works like a charm! The next time I really should use the already
>> implemented functions and if I'm unsure how they work I still can take a
>> look into their source code...
>> Thank you for the hint!
>
>
> I'm just going the other way, using pinv and leastsq, and now switch
> to decomposition directly.
>
>> From what I can see the main difference  in your example to what I
> have is to use linalg.diagsvd
>
>    u,s,v = np.linalg.svd(x, full_matrices=1)
>    Sig = linalg.diagsvd(s,*x.shape)
>
>>>> np.max(np.abs(np.dot(u, np.dot(Sig, v)) - x))
>    3.1086244689504383e-015
>
> for the correct shapes of the sqrt of the x'x and xx':
>
>>>> us = np.dot(u, Sig)
>>>> np.max(np.abs(np.dot(us, us.T) - np.dot(x, x.T)))
>    1.0658141036401503e-014
>
>>>> sv = np.dot(Sig, v)
>>>> np.max(np.abs(np.dot(sv.T, sv) - np.dot(x.T, x)))
>    1.1368683772161603e-013
>
>
> I'm still trying to collect these things into a class.
>
> statsmodels is doing all the least square calculations with
> linalg.pinv directly,
>
> I thought your pinv example should work, you could also try with
> explicit 2dimensional b
>
>>>> x = numpy.dot(temp, b{:,None)
Thanks, this works:
>>>x2 = x = numpy.dot(temp, b[:,None])

Greetings,
Daniel
```