PolyCoef(data,φ(x))

a547043f-0fa9-4b85-814a-4d3ed3b6c2c6 22 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

x y n PolyFit r 1 x length range : c 1 n 1 + (range : A 0 : M 0 : 14 mat #x f 10 #x * + 11 mat : n 0 ≡ #x f 1 #x 1 n range^vectorize stack 11 line : cases M x f vectorize : A r c el M r el c el : A transpose A * (1 -^A transpose y * (* 51 line :

Data 0 0.9 2 2.4 3154 17.4 5 30.5 6 48.3 62 mat :

n 0 :

Data 6002150 Random.N 1 rsort :

X Data 1 col : Y Data 2 col : 12 mat

C X Y n PolyFit :

C #

Data 0 0.9 2 2.4 3154 17.4 5 30.5 6 48.3 62 mat m * :

n 2 :

X Data 1 col : Y Data 2 col : 12 mat

C X Y n PolyFit :

(symbolically evaluated)

C #

PolyCoef(data,φ(x))

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

data # Φ PolyCoef X data 1 col : Y data 2 col : 12 mat j 1 x Φ length range i 1 X length range M i j el X i el Φ j el : for for M transpose M * (1 -^M transpose Y * (* eval 31 line :

data 111123571010910910910914914919121322429 mat transpose :

x Φ 1 x x 2^x 3^14 mat transpose :

sub 2 :

xy data sub data rows range 12 range el :

XY data o 6 red plot :

c x f c k el x k 1 -^* k 1 x Φ rows sum :

reduce order here rows(Φ(x))-1

clean export wrt x^c x f c 1 el x 11 -^* c 2 el x 21 -^* + c 3 el x 31 -^* + c 4 el x 41 -^* +

c xy x Φ PolyCoef :

c 80.6308588626697 32.1406690780869 2.24995858241394 - 0.047294281151809 41 mat

c x f XY 2 1 sys

c 80.6308588626706 32.1406690780845 2.24995858241355 - 0.047294281151785 41 mat :

c x f c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + :

. . . Revisit Polyfit . . .

]]> PolyCoef(data,φ(x))

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

data # Φ PolyCoef X data 1 col : Y data 2 col : 12 mat j 1 x Φ length range i 1 X length range N i j el X i el Φ j el : for for N transpose N * (1 -^N transpose Y * (* eval 31 line :

data 0 2113.3 1 2111.7 2 2109.2 3 2105.2 4 2099.4 5 2092.1 6 2084.7 7 2078.6 8 2075.1 9 2073.9 10 2074.1 11 2074.4 12207413 2072.5 14 2070.1 15 2067.2 16 2064.4 17206218 2060.5 19 2059.6 202 mat :

Corn Thermies Project

order 10 :

x Φ n 1 order 1 + (range f n el 1 n 0 ≡ x n 1 -^cases : for f 21 line :

x n 1 -^polynomials ≡

x n - 1 +^reciprocals ≡

x Φ transpose 1 x x 2^x 3^x 4^x 5^x 6^x 7^x 8^x 9^x 10^111 mat

add/delete best fit x Φ 1 x x 2^x 3^x 4^x 5^x 6^x 7^x 8^19 mat transpose :

c data x Φ PolyCoef :

c 2113.41999326691 4.42983970617582 - 3.74798136100075 1.77302641221344 - 0.309157197465638 0.025515825694903 - 0.001041304917005 0.000018690339511 - 0.000000085149056 91 mat

data c x Φ * 2 1 sys