Polyfit with scaling - Q regarding polyconf

[Ben Abbott]

I've completed the change to polyfit() and polyval(). However, the  
tolerance/prediction intervals calculated by my polyconf() need to be  
compared to Matlab (I've modified polyval to depend upon polyconf).

Thomas, can you run the script below in Matlab and post the result?

r = 0:10:50;
p = poly (r);
p = p / max(abs(p));
x = linspace(0,50,11);
y = polyval(p,x) + 0.25*sin(100*x);
[pf, s] = polyfit (x, y, numel(r));
[y1, delta1] = polyval (pf, x, s);
[y2, delta2] = polyconf (pf, x, s, 'alpha', 0.5, 'predopt', 'curve',  
'simopt', 'off');
[y3, delta3] = polyconf (pf, x, s, 'alpha', 0.5, 'predopt', 'curve',  
'simopt', 'on');
[y4, delta4] = polyconf (pf, x, s, 'alpha', 0.5, 'predopt',  
'observation', 'simopt', 'off');
[y5, delta5] = polyconf (pf, x, s, 'alpha', 0.5, 'predopt',  
'observation', 'simopt', 'on');

disp (num2str([delta1; delta2; delta3; delta4; delta5]'))

The polyconf() I've written is attached.

What I get using the attached is ...

0.18832    0.13296    0.09848    0.18832    0.13949
0.18134    0.12286   0.091006    0.18134    0.13431
0.16301   0.093733   0.069428    0.16301    0.12074
0.16411   0.095626    0.07083    0.16411    0.12155
0.15845   0.085546   0.063364    0.15845    0.11736
0.16203   0.092008    0.06815    0.16203    0.12001
0.15845   0.085546   0.063364    0.15845    0.11736
0.16411   0.095626    0.07083    0.16411    0.12155
0.16301   0.093733   0.069428    0.16301    0.12074
0.18134    0.12286   0.091006    0.18134    0.13431
0.18832    0.13296    0.09848    0.18832    0.13949

Regarding polyval(), I'm hoping to determine variety of inputs for  
polyconf() it is equivalent to.

Regarding polyconf(), I'm hoping to determine if I've inferred its  
operation correctly.

Ben

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