Utilities

fced449d-5611-4c73-af64-e6a0832d329e 41 6 12 decimal

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Utilities

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 :

Error 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 :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 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 :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat 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 β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

Otherwise Pearson independent of f(x,ParameterName) x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit.Y ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

data

data 03 - 0.2 2.951 - 0.4 2.589 - 0.6 1.581 - 0.8 0.054 1 1.5 1.2 2.112 1.4 2.111 1.6 1.879 1.8 1.608 2 1.364 2.2 1.159 2.4 0.992 2.6 0.855 2.8 0.744 3 0.652 3.2 0.575 3.4 0.511 3.6 0.457 3.8 0.411 4 0.372 212 mat :

X 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4211 mat :

Y 3 - 2.951 - 2.589 - 1.581 - 0.054 1.5 2.112 2.111 1.879 1.608 1.364 1.159 0.992 0.855 0.744 0.652 0.575 0.511 0.457 0.411 0.372 211 mat :

t 10 - 3 - 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 10241 mat :

data rows 21

Lagrange Quadratic System

The vector of the control points 't' must be in ascending order

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Lagrange piecewise Quadratic [order 2] k x B1 k 4 el x - (2^k 4 el k 2 el - (k 4 el k 3 el - (* / : k x B2 k 4 el k 1 el - (k 3 el x - (2^* - k 4 el k 3 el - (k 3 el k 2 el - (* k 3 el k 1 el - (* / : k x B3 k 4 el k 1 el - (k 2 el x - (2^* k 4 el k 2 el - (k 3 el k 2 el - (* k 2 el k 1 el - (* / : 31 sys

Lagrange Quadratic Generatrix k x b k 1 el x ≤ (x k 2 el ≤ (& k x B1 k x B2 + k x B3 + k 2 el x ≤ (x k 3 el ≤ (& k x B1 k x B2 + k 3 el x ≤ (x k 4 el ≤ (& k x B1 0 if if if 11 line :

x t 1 el t t rows el t 1 el 0.01 + (range :

Lagrange poly from Quad knots. n x Bp t n el t n 1 + el t n 2 + el t n 3 + el 41 mat x b :

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 6 1 sys

1 x Bp 2 x Bp 3 x Bp 4 x Bp 5 x Bp 6 x Bp 61 sys

Tridiag of QuadCoeff r 1 X rows range : ii r j r M ii j el j X ii el Bp : for for 31 line

XY data . 10 black plot : 11 line

s M 1 -^Y * : 3.0907 - 2.9887 - 2.6746 - 1.6757 - 0.081 1.6215 2.1897 2.136 1.882 1.6038 1.359 1.1541 0.9884 0.8517 0.7417 0.6502 0.5733 0.5098 0.456 0.4103 0.37 211 mat

Scalar spline Lagrange x L s j el j x Bp * (j 1 s rows sum :

x 1 - 5 0.975 - range :

Spline i 1 x rows range vy i el x i el L eval : for x vy augment 21 line :

Spline Spline :

XY Spline 2 1 sys

x c 10 x ≤ (x 6 ≤ (& cases :

h 0.001 :

x f x L :

classical infinitesimal 1rst derivative x deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* :

less noisy ... 10 decimals x h D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / :

piecewise linear of quadratic segments

x h D1 x c * 0.7 10 0.7 2 - 2 2 mat 2 1 sys

Absolute  residuals observer δ j 1 XY rows range Δ j el Y j el X j el L - eval eval : for X Δ augment 21 line :

rescue integrator vx Spline 1 col : vy Spline 2 col : x f vx vy x ainterp : 31 line

x f x 04 int 1.71

x c 1 0.5 x ≤ (x 1 ≤ (& cases :

J 0.7 :

Spline Lagrange Quadratic . . .

1. Passes through the support points exactly,

residuals are 0's through all data.

2. Being quadratic, the spline does not joint

smooth wrt 1rst derivative ... piecewise linear.

3. Alternately: decimate Spline, cinterp, D1(x,h)

]]> x h D1 x c * J 10 J 2 - 2 2 mat 2 1 sys