<p> Disabled EERNITY </p>

5efbe309-53c5-4be8-88fd-8a935bb8eba0 49 4 5 decimal

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

Optimiz Advanced Maths . . .

Option 0: Brute force . . . eternity .

Option 1: Simply recast inner integrand .

Option 2: Recode the double integrator . . . faster .

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This document is a demo. It does not revisit miscellaneous tips/techniques already explored. Simply optimizing the double ∫∫ expected usable for more projects.

Option 1: Recast the inner integrand ... 24 min

β 0.125 :

x q 11 x abs β^+ / :

Fourier transform of position wave function into 
momentum representation to get diffraction pattern 
@ the detection screen ... recast Φ(px,py) . px py Φ i px x * y py * + (* - exp y r 2^x 2^- sqrt - r 2^x 2^- sqrt int x r - r int ≡

The mapping function

x q 0.275 0.625 0.275 0.25 2 2 mat 2 1 sys

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - / (* lo + :

Recast inner integrand wrt the dependents Φ(px,py) ... acc 50.... SYMBOLIC .... px py Φ i i px x * r 2^x 2^- sqrt py * + (* - exp - i px x * r 2^x 2^- sqrt py * - (* - exp + (* py / - vectorize x r - r int :

r 0.275 : (pin hole radius ≡ Δ 51 : (size momentum ≡ N 51 : (canvas size ≡ N Δ ≥ (N<Δ not diffraction ≡ px py 12 mat position momentum ≡ N odd escape divide zero j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 12 mat 81 line

t0 1 time :

..... NUMERIC ..... CoC m 1 N range n 1 N range Fo m 1 - n 1 - el px m el py n el Φ abs (2^: for for fmap Fo q vectorize : fmap - 0255 Scale 31 line :

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1 time t0 - min 26.6

Option 2: Recode the integrator ... 8 min

Fourier transform of position wave function into 
momentum representation to get diffraction pattern 
@ the detection screen ... recast Φ(px,py) . px py Φ i px x * y py * + (* - exp y r 2^x 2^- sqrt - r 2^x 2^- sqrt int x r - r int ≡

β 0.125 :

x q 11 x abs β^+ / :

The mapping function

x q 0.275 0.625 0.275 0.25 2 2 mat 2 1 sys

Optimized CoC . . .

For the double integration, this Simpson is 'n' dependent,

perfectly symmetric vs the built-in integrator.

]]>

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - / (* lo + :

inner integrand borrowed/extracted from  ...  Maple Φ(px,py) x px py f i i px x * r 2^x 2^- sqrt py * + (* - exp - i px x * r 2^x 2^- sqrt py * - (* - exp + (* py / - :

Numeric

recast ▼ Simpson

f a b n ∫∫ h b a - n / : 13 / h 2 / a px py f b px py f + (* h a k h * + px py f k 1 n 1 - sum * + (* 23 / h * a h 2 / - k h * + px py f k 1 n sum * + eval 21 line :

[n,24]  convenient display a r - : b r : n 20 : 13 mat

recast Simpson double integral px py Φ f a b n ∫∫ :

r 0.275 : (pin hole radius ≡ Δ 51 : (size momentum ≡ N 51 : (canvas size ≡ N Δ ≥ (N<Δ not diffraction ≡ px py 12 mat position momentum ≡ N odd escape divide zero j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 12 mat 81 line

..... NUMERIC ..... Ω m 1 N range n 1 N range Fo m 1 - n 1 - el px m el py n el Φ abs (2^: for for fmap Fo q vectorize : fmap - 0255 Scale 31 line :

t0 1 time :

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 Ω

1 time t0 - min 9.4

DONOT vectorize px,py

'fmap' does not vectorize over bolean q(x). Transit algorithm via dual for loop. Example: zoom Cosmos [luminosity algorithm].

Option 0: Naive brute force.

<p> Disabled EERNITY </p>

β 0.125 :

x q 11 x abs β^+ / :

The mapping function

x q 0.275 0.625 0.275 0.25 2 2 mat 2 1 sys

px py Φ i px x * y py * + (* - exp y r 2^x 2^- sqrt - r 2^x 2^- sqrt int x r - r int :

r 0.275 : (pin hole radius ≡ Δ 51 : (size momentum ≡ N 51 : (canvas size ≡ N Δ ≥ (N<Δ not diffraction ≡ px py 12 mat position momentum ≡ N odd escape divide zero j 0 N range : px Δ - 2 Δ * j * N / + : py Δ - 2 Δ * j * N / + : 12 mat 81 line

..... NUMERIC ..... Ω m 1 N range n 1 N range Fo m 1 - n 1 - el px m el py n el Φ abs (2^: for for fmap Fo q vectorize : fmap - 0255 Scale 31 line :

jmG: 20230131