# [Numpy-discussion] Efficient orthogonalisation with scipy/numpy

josef.pktd@gmai... josef.pktd@gmai...
Tue Jan 19 14:52:54 CST 2010

```On Tue, Jan 19, 2010 at 3:47 PM, Gael Varoquaux
<gael.varoquaux@normalesup.org> wrote:
> On Tue, Jan 19, 2010 at 02:22:30PM -0600, Robert Kern wrote:
>> > y = y - np.dot(confounds.T, linalg.lstsq(confounds.T, y)[0])
>
>> > with np = numpy and linalg = scipy.linalg where scipy calls ATLAS.
>
>> For clarification, are you trying to find the components of the y
>> vectors that are perpendicular to the space spanned by the 10
>> orthonormal vectors in confounds?
>
> Yes. Actually, what I am doing is calculating partial correlation between
> x and y conditionally to confounds, with the following code:
>
> def cond_partial_cor(y, x, confounds=[]):
>    """ Returns the partial correlation of y and x, conditionning on
>        confounds.
>    """
>    # First orthogonalise y and x relative to confounds
>    if len(confounds):
>        y = y - np.dot(confounds.T, linalg.lstsq(confounds.T, y)[0])
>        x = x - np.dot(confounds.T, linalg.lstsq(confounds.T, x)[0])

you can  combine x, and y for one call to leastsq, if it makes a difference
linalg.lstsq(confounds.T, [x,y])  #format? columnstack?

I don't see anything else yet

Josef

>    return np.dot(x, y)/sqrt(np.dot(y, y)*np.dot(x, x))
>
> I am not sure that what I am doing is optimal.
>
>> > Most of the time is spent in linalg.lstsq. The length of the vectors is
>> > 810, and there are about 10 confounds.
>
>> Exactly what are the shapes? y.shape = (810, N); confounds.shape = (810, 10)?
>
> Sorry, I should have been more precise:
>
> y.shape = (810, )
> confounds.shape = (10, 810)
>
> Thanks,
>
> Gaël
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>
```