3764a438-bbc1-4486-b915-80ecce3a8d46 35 4 5 decimal

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

kPa @ altitude(m) h NASA 101.29 288.14 0.00649 h * - 288.08 / (5.256^* 1000 - h ≤ (h 11000 ≤ (& 22.65 1.73 0.000157 h * - exp * 11000 h ≤ (h 25000 ≤ (& 2.488 141.89 0.00299 h * + 216.6 / (11.388 -^* cases :

altitude(m)@ kPa λ 1 el 101.4009 : λ 2 el 22.7074 : λ 3 el 2.52227 : 13 mat p NASA_alt 20001440714404100 p * 10129 / ln 5.256 / exp * - (* 649 / λ 2 el p ≤ (p λ 1 el ≤ (& 1000017310020 p * 453 / ln * - (* 157 / λ 3 el p ≤ (p λ 2 el ≤ (& 100014189 - 21660125 p * 311 / ln 11.388 / - exp * + (* 299 / cases : 21 sys

x c 1 0.027912 x ≤ (x 101.4009 ≤ (& cases :

kPa 1 :

m 1 :

kPa kPa NASA_alt 8000 - kPa 1648 solve : kPa 35.69

m m NASA kPa - m 500010000 solve : m 8000

altitude(m) from measured kPa

x NASA_alt x c *

kPa from altitude(m)

x NASA

x f 0 x π 2 / ≤ 0 x π ≥ (x 3 π * 2 / ≤ (& x sin cases :

x f

u f u 04 π * int 0.039

data x 02 π * (0.05 range : i 1 x rows range u i el x i el : F i el u i el f eval : 21 line for u F augment 31 line :

data Σ Finite differences Cumul Integration vx data 1 col : vy data 2 col : Y 1 el 0 : i 2 vx rows range Δx i el vx i el vx i 1 - el - : Y i el Y i 1 - el 12 / vy i 1 - el vy i el + (Δx i el * (* + eval : 21 line for vx Y augment 61 line :

Discontinuous functions must be specified completely. The Smath numerical integrator supports "if/otherwise" as well the finite differences integrator.

Finite differences Cumulative Integral

data Σ data 2 1 sys

Bolean scalar plot

x f x 3^:

x plot 0.1 x f x U / * 0.1 x f x V / * 0.1 x f x W / * 31 sys :

x U 10 - x ≤ (x 10 ≤ (* : x V 30 - x ≤ (x 40 ≤ (* : x W 50 - x ≤ (x 50 ≤ (* : 31 sys

x y axes x y / - : scale 0.005 : x U 5 - x ≤ (x 5 ≤ (* : 31 sys

x plot x plot scale x f * x U * axes 2 1 sys

pilot X_Y lo 5 - : hi 4 : 12 mat scale 0.0075 : 21 sys

x U lo x ≤ (x hi ≤ (* :

data x lo hi lo 0.1 + range : i 1 x rows range Y i el scale x i el f x i el U / * eval : for x Y augment 31 line :

data data eval :

data axes 2 1 sys

Bolean otherwise

ε 0.25 :

t f 1 t / : u ε x ≤ (x e ≤ (* : v e x ≤ (x 2 π * ≤ (* : w 2 π * x ≤ (x 16 ≤ (* : 41 sys

plot x f u / x f v / x f w / 31 sys :

j 31 range :

plot

plot j el $u ε e ε 0.1 + range : v e 2 π * (e 0.1 + range : w 2 π * (162 π * 0.1 + range : 31 sys$ $XY u u f vectorize augment v v f vectorize augment w w f vectorize augment 31 sys :$ XY XY 1 el XY 3 el 2 1 sys

QuickPlot Bolean Exclusive

x f x 3^x erf 1 x 2 + / 1 - 13 mat transpose :

range exclusive Lo 1.5 - : Hi 1.5 : 12 mat

select f(x) j 3 :

x fnct break a trace 0 x Lo ≤ 0 Hi x ≤ x f j el cases 21 line :

L H N Φ i 1 N range x i el L i N / H L - (* + : A i 1 el x i el : A i 2 el x i el fnct eval : 31 line for A 21 line :

data 3 - 3100 Φ : plot data 1 col data 2 col augment : 21 sys

Discrete outer exclusive outer u plot 1 col : v plot 2 col : k 0 : i 1 plot rows 1 - (range v i 1 + el v i el ≤ (v i 1 + el v i el ≥ (¤ P k k 1 + : el u i 1 + el v i 1 + el 12 mat : 11 line out search region if 11 line for 21 line v P 1 el : j 2 P rows 1 - (range v v P j el stack : for v 61 line :

Exclusive QuickPlot

outer

scalar inner exclusive x f 1 r x 2^+ / : r 0.75 : d 2 : 13 mat datum d - r f d r f 22 mat : x c 1 x r - x ≤ (r x ≥ (& (¤ cases : 31 sys

x plot x f x c * r 1 r 0.25 - 22 mat datum 31 sys :

x plot

2 x f x 4 - r - int * 1.4869

scalar outer exclusive x f 11 x 2^+ / : r 1 : d 2 : 13 mat datum d - r f d r f 22 mat : x c 1 x x r ≥ (¤ (x x r - ≤ (¤ (& cases : 31 sys

x plot x f x c * x f datum 31 sys :

x plot

alternate bolean ... x x r ≥ (¤ (x x r - ≤ (¤ (& x x r ≥ (¤ (x x r - ≤ (¤ (* 21 sys

x plot x f x c * datum r 1 r 0.25 - 22 mat 31 sys :

x plot

∫ x f x r - r int 2 r * r f * (- : 0.5708

Delimitate and fill critical domain

'N' random in critical region N 500 :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

size/define critical region.
Plot first before filling xmin r - : xmax r : ymin r f : ymax 1 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

x critical x f x c * :

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x f ≤ (x xmax ≤ (* :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

a b c spec . 5 #808080 13 mat : fill Pts a b c spec pts : 21 line

fill x critical datum 3 1 sys

∫ 0.5708

View ON/OFF control saw tooth simplified

α 100 :

Δt 0.005 :

Qhi 1 :

Qlo 0.25 :

d 0.125 : differential ≡

SP 0.75 : SetPoint ≡

x f Qhi 1 Δt α * (x * - exp - (* :

Tlo SP d 2 / - :

Thi SP d 2 / + :

N 1000 :

Saw tooth ON/OFF control algorithm ON_OFF i 1 N range t i el i α / : for t Q 1 el Qhi : T 1 el 0 : i 2 N range T i el Q i 1 - el (Δt * T i 1 - el 1 Δt - (* + : T i el Tlo ≤ Q i el Qhi : T i 1 - el T i el ≤ (Thi T i el ≥ Tlo ≥ (& Q i el Qhi : T i 1 - el T i el ≥ (Thi T i el ≥ Tlo ≥ (& Q i el Qlo : Q i el 0 : if if if 21 line for t T augment 61 line :

Experiment Sp = [0.4, 0.8] to see the ramp up/down shape reverse direction. f(x) is a simplified XFR for demo. The main idea is the "for/if" algorithm.

sp 0.5 SP 0.033 + (SP 14 black 15 mat :

Thi SP Tlo 31 mat 0.8125 0.75 0.6875 31 mat

f t 010 0.01 range : i 1 t rows range xfr i el t i el f eval : for t xfr augment 31 line :

Collect plotting arguments collect ON_OFF SP Thi Tlo f sp 61 sys :

collect

Analyse => Arrive

1. The given function ...

t T t diff t T Q t T - ≡

2... in finite differences...

t Δt - T t T - Δt / t T Q t T - ≡

t Δt - T t T Q Δt * t T 1 Δt - (* + ≡

3... in indexed continuity...

T i el Q i 1 - el (Δt * T i 1 - el 1 Δt - (* + ≡

4... additional constrain

Q 0 ≡

for

T Thi ≥