plot, mesh discrete,Scale(M,Low,High)

01135cb0-a13f-48f1-ae07-2fba495b8fbe 36 3 12 decimal

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

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 :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

A robust construct of the Scale function M Low High Scale min M Min : max M Max : 12 mat maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 51 line :

Stem ... Bar

Spectrum stem plot for QuickPlot unicolor data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

j v Bar data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line : ----------------------------------------------- L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx - (dx i * + : for U 41 line : --------------------------- N X j el : U N size - N size + fill xd : 21 line p i 1 U rows range Y i el v : for U Y augment 21 line : Bar p Stem : 71 line :

High order polyfit

High order polynomials are numerically unstable @ high range of the variate 'x'. In this example order 7 and range 0..19 fails to fit. We scale the samples 'x' in the range x => 0..1

XY 0 2113.3 0.05 2111.7 0.11 2109.2 0.16 2105.2 0.21 2099.4 0.26 2092.1 0.32 2084.7 0.37 2078.6 0.42 2075.1 0.47 2073.9 0.53 2074.1 0.58 2074.4 0.63 2074 0.68 2072.5 0.74 2070.1 0.79 2067.2 0.84 2064.4 0.89 2062 0.95 2060.5 1 2059.6 202 mat :

x φ 1 x x 2^x 3^x 4^x 5^x 6^x 7^x 8^19 mat transpose :

samples 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 :

X XY 1 col : Y XY 2 col : Data XY . 12 black plot : 31 line

Cholesky companion solver degree x φ rows : j 1 degree range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : b Φ 1 -^eval d * : 51 line

b 2113.374 75.206 - 1213.734 11272.305 - 37378.177 57874.151 - 43559.133 13791.896 - 808.378 91 mat

2113.244 637.7119 - 84.21096 5.026034 - 0.1213578 0.3012873 - 0.03988496 0.002389478 - 0.00005800783 91 mat

β 1 el β 2 el x * + β 3 el x 2^* + β 4 el x 3^* + β 5 el x 4^* + 1 β 6 el x * + β 7 el x 2^* + β 8 el x 3^* + β 9 el x 4^* + /

Mathcad 11 GenfitMatrix delivers a sensibly better rational fit on the native 0..19 range... better @ the extrapolated ends.

x fit b x φ * :

<= recast the scalar model

Δr i 1 Y rows range resd i el Y i el X i el fit - : for X resd augment 21 line :

poly 01 0.005 x fit inc :

Discrete polyfit on reduced 'x'

Data poly 2 1 sys

Absolute residuals

Δr 0.01 BarSize 0 2 1 sys

b 2113.374173 75.206157 - 1213.734114 11272.305446 - 37378.176678 57874.150984 - 43559.133482 13791.896436 - 808.378334 91 mat

Δr 0.25 BarSize

χ X Mean : μ Y Mean : n XY rows : 31 line

χ μ n 31 mat 0.5 2081.1 2031 mat

Pearson’s correlation coefficient corr X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el fit eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el fit eval μ - (2^(i 1 n sum * sqrt / / : 0.99901

correlation between [X,Y]

correlation of the model

correlation between [X,fitted model]

sx samples 1 col : sy samples 2 col : 21 line

vx poly 1 col : vy poly 2 col : data sx sy augment . 12 black plot : Origin vx 019 Scale vy augment : 41 line

data Origin 2 1 sys