c687b382-3f4e-413f-93a2-904284f1d465 18 4 5 fraction

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If the argument is scalar and completely defined, you can plot only the argument, but it does NOT plot mixed, i.e: algo + the scalar function. In this example, ICDFnormal is Smath built-in.

p 10 - 15 9.9 - range 25 pdf.Normal :

q 10 - 15 9.9 - range 23 pdf.Normal :

r 10 - 15 9.9 - range 52 pdf.Normal :

f 0.01 1 0.01 0.02 + range 25 ICDF.Normal :

Plot defined/assigned algo

Plot the scalar function

x 2 5 ICDF.Normal

Plot algo ranged

p q r 3 1 sys

α 2 :

β 5 :

To the contrary of a function that can be plotted algo style ranged, the derivative plots in either of the two styles below: 1. Native derivative wild scalar. 2. Derivative assigned as function also wild scalar.

x α β D x α β pdf.Normal x diff :

x 23 pdf.Normal x diff

Plot derivatives in the two unique "wild scalar x style"

x α β D x 2 3 D x 2 2 D x 2 2.5 pdf.Normal x diff 4 1 sys

Note that the wild scalar plots span unconstrained in the ± X direction of the canvas.

deriv t 10 - 15 9.9 - range : i 1 t rows range vx i el t i el : vy i el t i el α β D : 21 line for vx vy augment 31 line :

You can range discrete plot

deriv

Derivative of spline interpolate

The Smath derivative derived from the built-in al_convr1d(y,f) has not be retained as not being visible and exportable to end user [typical Edu.] In the assignment F(var):=cinterp(X,Y,var) 'var' is just a carrier for the discrete object, but for the plot it has to be F(x). algo:=F(0,0.1..30) will not plot. In F(x), 'x' is not scalar. In this example, ainterp(X,Y,var) is pure disaster , try the 2nd derivative.

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 :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 21 line 31 line :

X Data 1 col :

Data 1 2.61173 2 8.48228 3 16.15875 4 26.15419 5 39.09752 6 55.73891 7 76.9396 8 103.63542 9 136.7611 10 177.12511 11 225.23407 12 281.08655 13 343.98411 14 412.43203 15 484.20056 16 556.57528 17 626.74962 18 692.24603 19 751.23737 20 802.68943 21 846.32288 22 882.45309 23 911.78366 24 935.21381 25 953.69087 26 968.11438 27 979.28442 28 987.8817 29 994.46746 30 999.494 302 mat :

Y Data 2 col :

L 0 :

H 30 :

N 100 :

U L H N xd :

var F X Y var cinterp :

M i 1 U rows range u i el i : F i el U i el F : 21 line for U F augment 21 line :

algo 030 0.5 range F :

Observations: 1. The repeated end point in 'M' is not something to try. 2. Deriv(Dy) takes quite a while 3. Deriv(D1y) takes no time even if it has ~ twice pts.

data Deriv data Derivative BackSubstitution X data 1 col : Y data 2 col : n X rows : D 1 el 0 : D n el 0 : i 2 n 1 - range D i el 0.5 Y i 1 - el Y i el - X i 1 - el X i el - / Y i el Y i 1 - el - X i el X i 1 - el - / + (* : for D 1 el D 2 el : D n el D D rows 1 - el : X D augment 101 line :

Dy M Deriv :

pts X Y . 12 blue plotG :

pts x F Dy 3 1 sys Dy Dy Deriv

The 2nd derivative deserves truncation for export.

span H L - :

m 251 :

dx span m 1 - / :

i 0 m 1 - range y i 1 + el dx i * F : for

Combined derivatives

f 101 - 13 mat transpose :

Adapted from Martin Kraska: 1d convolution [*] of 'y' over 'f'

n f length :

dy 12 dx * / y f al_convr1d * :

y*fi y i 1 + el y i 1 - el - ≡

Fnct dx 0 m 1 - range (* y augment :

y f al_convr1d Smath built-in ≡

P dx 1 - m n + 3 - range (* dy augment :

Die zugehörige x-Differenz ist 2 dx

Le pas correspondant à x est 2 dx

the corresponding x step is 2 dx dy approximates the first derivative of y using divided central differences

D1y P 3 m 1 - 12 submatrix :

D2y D1y Deriv :

D2y D2y 15 D2y rows 10 - 12 submatrix :

1rst derivative

D1y

Truncated [*] 2nd derivative

D2y