Looks neat. I think it has to be square, and it doesn't need to be
non-singular:
eg,
Here, y = x is a straight line, and 5 data points overspecify it! ...
(,:(X np X)&p.) steps _1.5 1.5 5
_1.5 _0.9 _0.3 0.3 0.9 1.5
_1.5 _0.9 _0.3 0.3 0.9 1.5
Oddly enough, I tried it out first on my iPad, running J701. On that
tablet I got :
~. X np Y in J701/iPad !!! ~. to save lines
_14.1014
I thought that was it for discrepancies. I haven't kept J7.01 on the
laptop,
but I do still have J8.07. I've just checked and find the same result
there!
JVERSION
Engine: j807/j64/windows
Release-e: commercial/2019-11-04T09:51:03
Library: 8.07.26
Qt IDE: 1.7.9/5.9.6
Platform: Win 64
Installer: J807 install
InstallPath: c:/d/j807
Contact: www.jsoftware.com
~. X np Y NB. in J807...
_14.1014
Old J - odd/old results. I expect others will see why,
Cheers,
Mike
On 17/10/2020 23:10, Raul Miller wrote:
For what it's worth, here's an example of a "quite straightforward"
translation of the original 'np' to tacit form (assuming that the
newton matrix is always square -- I didn't spend enough time studying
here to feel comfortable leaving that assumption unstated, though I
did force a length error should that not be a valid assumption):
NB. divided differences
dd=: (2 -~/\ ]) % [ ({: - {.)\~ 2 + -&#
NB. Coefficients are the topmost entries
np=: [: {."1 dd ^:(i.@#@+)
X=: _3r2 _3r4 0 3r4 3r2
Y=: 3 o. X
load'plot stats'
plot(;(X np Y)&p.) steps _1.5 1.5 30
I hope this helps,
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