CHOLESKY FUNCTION

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CHOLESKY FUNCTION

Order Data CholeskyF i 1 Order 1 + (range i 1 ≡ φ i el 1 : φ i el x i 1 -^: if for x φ φ : k2 x φ length : X Data 1 col : n X length : Y Data 2 col : 14 mat j 1 k2 range i 1 n range Xi i j el X i el φ j el : for for M1 Xi transpose Xi * : M2 Xi transpose Y * : 12 mat B1 M1 1 -^eval M2 * : i 1 Order 1 + (range i 1 ≡ R B1 i el eval : R R B1 i el x i 1 -^* + : if for R 81 line :

plot function

X_a Y_a char_a size_a color_a plotG n_a X_a length : plot_a X_a 1 el Y_a 1 el char_a size_a color_a augment : i_a 2 n_a range plot_a plot_a X i_a el Y i_a el char_a size_a color_a augment stack : for plot_a 41 line :

2. Example on Quadratic Fit using Native SMath

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Data 1 0.9 2 2.4 374 17.4 5 30.5 6 48.3 62 mat :

QUADRATIC Order 2 :

x R Order Data CholeskyF :

FUNCTION t R 383100 / 340873147280716871947673600 / - (t 21 -^* + 2267742732287110995116277760 / t 31 -^* +

Graph the results

X Data 1 col :

Y Data 2 col :

fitdata X Y o 15 Blue plotG :

fitline x R :

fitdata fitline 2 1 sys

Native Smath X R vectorize 0.932143 2.15929 7.51143 16.9886 30.5907 48.3179 61 mat

Maxima Fit 0.9321 2.1593 7.5114 16.9886 30.5907 48.3179 61 mat

Same: compare

3. Example on Linear Fit using Native SMath

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Data1 0.5000 32.00 1.100 33.00 1.500 34.20 2.100 35.10 2.300 35.70 52 mat :

LINEAR Order 1 :

x R Order Data1 CholeskyF :

FUNCTION t R 30.9305555555562 5624816429132127487790694400 / t 21 -^* +

X Data1 1 col :

Y Data1 2 col :

XE X :

fitdata X Y o 15 Blue plotG :

Graph the results

fitline x R :

fitdata fitline 2 1 sys

Smath Fit X R vectorize 31.9537 33.1815 34.0000 35.2278 35.6370 51 mat

Excel Fit

xP 12345661 mat :

yP 0.9 2.4 7 17.4 30.5 48.3 61 mat :

Data2 1.000 0.9000 2.000 2.400 3.000 7.000 4.000 17.40 5.000 30.50 6.000 48.30 62 mat :

X Data2 1 col :

Y Data2 2 col :

X1 X :

Y1 Y :

fitdata2 X Y o 15 Blue plotG :

x y1 1 Data1 CholeskyF : 11 mat Linear ≡ x y2 2 Data2 CholeskyF : 11 mat 2nd\0020\order ≡ x y3 3 Data2 CholeskyF : 11 mat 3rd order ≡ x y4 4 Data2 CholeskyF : 11 mat 4th order ≡ x y5 5 Data2 CholeskyF : 11 mat 5th order ≡ 51 line

Linear Fit : x2, y2 XE y1 vectorize 31.9537 33.1815 34 35.2278 35.637 51 mat

(2 nd  order) :  x1, y1 X1 y2 vectorize 0.9321 2.1593 7.5114 16.9886 30.5907 48.3179 61 mat

(3 rd  order) :  x1, y1 X1 y3 vectorize 0.9683 2.1087 7.4825 17.0175 30.6413 48.2817 61 mat

(4 th  order) :  x1, y1 X1 y4 vectorize 0.9433 2.1837 7.4325 16.9675 30.7163 48.2567 61 mat

(5 th  order) :  x1, y1 X1 y5 vectorize 0.9 2.4 7 17.4 30.5 48.3 61 mat

NDTM Smath Fit 31.9537 33.1815 34 35.2278 35.637 51 mat

NDTM Smath Fit 0.9321 2.1593 7.5114 16.9886 30.5907 48.3179 61 mat

NDTM Smath Fit 0.9683 2.1087 7.4825 17.0175 30.6413 48.2817 61 mat

NDTM Smath Fit 0.9433 2.1837 7.4325 16.9675 30.7163 48.2567 61 mat

NDTM Smath Fit 0.9 2.4 7 17.4 30.5 48.3 61 mat

fitdata x R fitdata2 x y2 x y3 x y4 x y5 7 1 sys

EQUATIONS

x y1 30.9305555555559 1406204107283687194767360 / x 21 -^* +

x y2 383100 / 2726985178245549755813888 / - (x 21 -^* + 181419418582978796093022208 / x 31 -^* +

x y3 4.13333333334229 4698812390240260879609302220799 / - (x 21 -^* + 19253670281848387960930222080 / x 31 -^* + 33087155467927487790694400 / - (x 41 -^* +

x y4 3.08333333336048 2486548454293500703687441776637 / - (x 21 -^* + 570442921500672469124961184427 / x 31 -^* + 168999009501184879609302220805 / x 41 -^* + 20043180691 - 1374389534720 / x 51 -^* +

x y5 16.8999999712686 - 141163330339690036408888888889 / x 21 -^* + 29365105014603800977343669134225 / - (x 31 -^* + 1862572696508830175921860444161 / x 41 -^* + 225766387279462140737488355329 / - (x 51 -^* + 592865169286965269559816964 / x 61 -^* +