a7b32e81-1365-4d65-80ad-5f1d6bc3105e 8 6 12 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]
 <p> HadCRU [797 months] </p> XY

ChebyShev poly order

order 5 : <p> All LinfitCheby collapsed </p>

0. reserve for backscale in original domain

xy XY : minXd xy 1 1 el : maxXd xy xy rows 1 el : Origin XY . 10 red plot : 4 1 line 1950 2016.3333 2 1 mat

1. Convert Original XY => Cheby domain [±1]

v i 1 XY rows range v i el i : for v 2 v * v Min - v Max - v Max v Min - / : 2 1 line : XY v XY 2 col augment : vx XY 1 col : vy XY 2 col : data XY o 5 black plot : 5 1 line

2. Create ChebyShev ... Symbolic spool to file

x p n 0 order range F n 1 + el n x acos * cos : for F 2 1 line : iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAAA9SURBVEhLY/hPZcAABCCCbIwOKHLhqIFgMGogaWCEGoiMwWJgkkxAUwNhYIQYiAxGDSQNoBsGAlQ28P9/ACFKisraGHSGAAAAAElFTkSuQmCC 1

0. Create the original reserve 1. The original XY is converted in ChebyShev domain. 2. The ChebyShev vector function is created. 3. Collect the model f(x,β). 4. Cheby coefficients are spooled to file. 5. Collocate the "linfitCheby" Colln(x) 6. Reverse back the fit & the data set

Optimiz ... SYMBOLIC

x p 1 x 2 x acos * cos 3 x acos * cos 4 x acos * cos 5 x acos * cos 6 1 mat

Cholesky companion solver ........ NUMERIC ........

j 1 x p length range i 1 X length range M i j el X i el p j el : for for Φ M transpose M * : d M transpose Y * : β Φ 1 - ^ eval d * : 4 1 line

NUMERIC ... spool to file

c ct 1 : j 1 β rows range u ct el β j el 6 round : ct ct 1 + : 2 1 line for u 3 1 line : 1

5. Collocate the "linfitCheby"

x Colln c k el x p k el * ( k 1 order sum 1 1 line :

6. reverse scale 'x domain'

ω X 2 ω * minXd - maxXd - maxXd minXd - / :
Observe: the scalar plot is auto-bounded
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5. Data set & the fit in ChebyShev domain [-1..1]

 data x Colln 2 1 sys

6. reverse scale 'x domain'

ω scale 2 ω * minXd - maxXd - maxXd minXd - / :

6. Global Warming HadCRUt4 linfitCheby in the original domain. 1994: year the rate global warming reversed [started decreasing]. 2010: year accumulated global warming started cooling down.

 HadCRUt4 x scale Colln 10 x D1 * 100 x D2 * 1994 0 + 20 red 1 5 mat 2010 0 + 20 red 1 5 mat 7 1 sys

---------- linfitCheby ----------- HadCRUt4 January 1950 ... May 2016

https://en.wikipedia.org/wiki/HadCRUT
HadCRU . . . Hadley Cimate Research Unit [East Anglia University Norfolk]
]]> HadCRUt4 GW axes 2010 1.5 2010 2 - 2 2 mat 4 1 sys