<p> Range Algo </p>

01bade81-fe6a-4f93-a5fb-983fd7e27ba4 19 6 5 decimal

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

Comprehensive 2D matrix algo

t0 1 time :

x y f L H N Sym U 0 : dx H L - N / : 12 mat i 1 N range U i el L dx i * dx - (+ : for r 1 : i 1 U rows range c 1 : j 1 U rows range M r c el U i el U j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for 21 line M 41 line :

either direction

L 1 - :

H 1 :

N 64 :

εxy 2 :

x y f 255 x 2^εxy y * (2^+ (- 0.25 / exp * : N x y f L H N Sym : 21 sys

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 N

1 time t0 - 11 s *

L 3 π * - :

H 3 π * :

N 64 :

x y f 255 x sin y cos + (* : N x y f L H N Sym : 21 sys

x y f x cos y cos * :

iVBORw0KGgoAAAANSUhEUgAAAEAAAABACAIAAAAlC+aJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA6NSURBVGhD1dn3z4/XH8fxy6gVo0atGi1BjLtuVBB71ApSe1T1FjMoitKSEBJ7z9ASq/YMYtYm2lg3t5FWUKV3rdaMPb4POX/Et5cfrlz3ud7n9Xpe57zP+5zrI0qTJk3WrFnLlSv31VdfLV68+ObNmxUqVPjuu++2bdv2xx9/vHjx4vXr13fu3Dl69OjUqVObNm0aRdH27dsHDx5cvXr1Dz74IF26dBkyZPjoo4+aNWs2YcKE06dP58+fv2vXrkuXLj137tzjx4/fvn3r6l6Ldk/FiBSvl74U6FCjSZk+F14c+XLHgAQPKmwIcaLFjDzasWPHoUOH/vzzTypt27ZdtGiRiE8++aRPnz7z5s3bvHnz1q1beY8YMaJ+/fqBvl+/fqVLl37w4MHx48d37dr1888/X7hwIW3atLVq1Ro7diy+fPnytW/fftKkSWvWrGHs6l6Ldk/FiBSvl74U6FCjSTm8Ay+OfLljQIIHFTaEONFiRh4NGTJk1KhR3unMmTM5c+bs1KnTihUrvHrJkiVbt25NceDAgV9++WWVKlXo7t271zhx+uuvvzZu3Dh+/Phvv/32+++/nzVr1v79+1++fFm3bt0pU6YY7zx58jRs2LBnz57ffPONq3st2j0VI1K8XvpSoEONJmX6XHhx5MsdAxI8qLAhxIkWM/KoRo0ajRo16tWr1w8//PD7778XK1bs66+/Nmz379//8MMPP/3006pVq+pM8ddffzV45tpo8Rs6dOjnn39uLAERBXH48OEsWbK0adPGIF2+fDl79uzGrFq1aq7utWj3VIxI8XrpS4EONZqU6XPhxZEvdwxI8KDChhAnWszIo7x583788ceEvLr5evXqlVYpSOLJkyeMc+XKRUuf5cuXyzxzZ8bZczVgsiK8p/zGd/36dbhoZOatW7cyZcqUO3duV/datHsqRqT4QEaBDjWalOlz4cWRL3cMSPCgwoYQJ1rMyKP06dPnyJGjfPnyYeXdvn2brvzjd+PGDWuIyr///vvLL7/MmDGjefPm1pysNe9Gjvd7772XOXNmo9KiRYvJkyeb2UKFCnXv3v2nn366ePHi06dPFQlX91q0eypGpHi99KVAhxpNyvS58OLIlzsGJHhQYUMY6gFm5FHGjBm9ZcWKFXv06CHD/vnnH7Mmt/bs2fP333/rT/Hhw4cnTpyYM2eOcVI3rDy5awCMHwKlwFy3atVq2rRp58+fL1q0aO/evVevXm0IFRAD5Opei3ZPxYgUr5e+FOhQo0mZPhdeHPlyx4AEDypsCHGixfwuO8yCeqSojRw5ct++fd6nZcuW8+fPt+D0LFCggDGTtVbYhg0blAK1T/Ww/mSw8TCKOGrXrt23b99Vq1YZM0k/evTogwcPqp7yp0iRIq7utWj3VIxI8XrpS4EONZqU6XPhxZEvdwxI8KDChhAnWszII/PVoUMHJXbt2rWWeaVKlTw7cuSIPh5/9tlnTZo0URDef/99o6ic6aYCqiFS1jzKBGOJJrxzwYIFjY3liNJgQ1TUXd1r0e6pmECjl74U6FCjSZk+F14c+XLH8A40ilBhQ4gTLWbk0cSJE82XBW6aSpUqNWDAgN27d4tWncy4MVMTrBi6ltfZs2ftQfJVHVRJrEXZLB+MKCaWin1YSNblF198IWvHjRvn6l5LSF8xIsXrpS8FOtRoUqbPhRdHvtwxIMGDChtCnGgxI4+Sk5MvXbqkc0JCgiIV9hFle8yYMZs2bbKS5KK1NXv2bBBhHyUqZc2vemJFymmja1yRQbHXWF7q97Jly2w0J0+edHWvRXvYiUSK10tfCnSo0aQc9nJeHPlyx4AEDypsCHGixYw8IlSiRAnTZEZ27twpwqTPnDmT8fPnz6WvOmshXrlyZeXKld26dQvvYD9S0dVEOSo9ZLbcMLr47PbDhw83VFZbtmzZVBhX91q0h7OASPF66UuBDjWagZ4LL458uWNAggdVOMvgRIsZeSS6f//+pvLAgQOeNW7c2Kv/9ttvJrFevXpGQlW2Tqy2e/furVu3Tr5ikgAGUl1XGUOmyW8ZYoxRygfVo3Llyvb8pKQkV/datHsqRqT4kBsU6FCjSZk+F14c+XLHgAQPKmwIcaLFjDyyZdA6deqU1jp16kjBlJQUC79du3Zm7ccff7Rj20EcBxhbPSGJnQvsrGqz6q4+qjDyQZbLEyON1WFGXZ87d+6SJUtc3WvR7qkYkeL10pcCHWo0wxLiwosjX+4YkOBBhQ0hTrSYkUcq17Vr1/ytrA4aNEi5tbNYQOKsEkFyVH1YsGCBsVETjZOTmXS0Qdpf7VAqhiopGQyVXJctxhsxOOnL0tW9Fu2eihEpXi99KdChRpMyfS68OPLljgEJHlTYEOJEi/kduV3aHTkVTSW2LCSW8xNLWsbJ+eTq1avWkxlXJbg6XRoeieuMYJe1T0lTtVK1sV5lvJwx6ril+6NHj1zda9HuqRiR4vXSlwIdajQp0+fCiyNf7hiQ4EGFDSFOtJiRv/unApQpU8bRTyKmpqYmJiYOGzbMeUN/q8fZQ8qqwRaZqux8bzycMS1BBE4Klpoxs7xUTEtNHst7mWPs0b9588bVvRbtnooRKV4vfSnQoUaTMn0uvDjy5Y4BCR5U2BDiRIsZefxnIPZrIPZVKPb7QOx34tifhWJ/Go3990Dsv8hi/03MIN6/SsT+d6HY/zIX+99GzayNJsa/Tsf+/wcIGRspaJwsNRFe3Zv5EPHF0KBBA3nmKGa9qySqW3gHs2wgqagYMjhMlx00nGScxnjbAYy0ncjVvRbt4TQlMgyqvuHERi1kDn0uvDjy5Y4BCR5U2BDiRIsZeTR9+nQLwhZ99+5d72RJyE6lTaY668lOJU+mKttWEl1jE3LJOlMr1Dt+9h0Ly0A6MjiHOUuGumznkvSu7rVo91SMSPF66UuBTli1lOlz4cWRL3cMSPCgwoYQJ1rMyKNjx44ZD1tG8eLFDc/69evVrJo1a+rMTAfvLQslMUWjYmYNQ1jTIMJpz/qz85tMJzCnSAvOwvVFIr/t/67utWj3VIxI8XqFsxodajQp0+fCiyNf7hiQ4EGFDSFOtJiRRza2Z8+eWV7mWh9NhQsXFiHPApn5MiS0SJhTmSCb1Qc0XO01hFRG9pIYq51RVhhIxr4J7Tuu7rVo91SMSPF66Rt2K2o0KdPnwosjX+7hPfGgwoYQJ1rMyCOLzHaoAnTu3HnhwoX2PHOttG3ZssVo2USVPCpGwmzKSKtKZVDdVOiwx1mF9leK8piTnTHUA5VObbHvuIaqp91TMSLF66UvBTrUaFKmz4UXR77cMSDBgwobQpxoMSOPGCgFBsDJzmnJV2bZsmV9dCrMZlYB0d8YGEK5aD2pCcZGvbO/2J74IXDecmaU6/LB1ivLfQf65DO6vkVc3WvR7qkYkeLDKY0CHWo0KdPnwosjX+4YkOBBhQ0hTrSYkUeqqSxSj5wN7QuWhPHo2LGjD1nnRz29vTGThVaSaqCiKSB2FutMRhqPcOazsJzVfHkg9gXo+0PhUz3lj6t7Ldo9FSNSvF76UqBDjSZl+lx4ceTLHQMSPKiwIcSJFjPyd0XdY6/lmaVjnFJTUwONPt7b3Jl9SakOqGVQlD9vb29XOuyDzokQ0TiVoPQJpsj4BlfsnUBlhat7Ldo9FRO+TvTSlwIdajQp0+fCiyNf7hiQhHfGhhAnWszII9+pMtIWbcWE9FViyYn2xmZN5lk9KoAqJi/tJnZES42TdaluGA9zGr6BHBl8ufr6lh5KjawYNmyYq3st2j0NX4bi9dKXAh1qNCnT58KLI1/uGJDgQYUtLCS0mJFHPnBsNF26dFGPLbWwE4nzrt5Szlk31r5ZlpRhH7EX6uxcZbWF057vDF8Y4VvUTqRQpqSkgPDRnZiY6Opei/awD4oUr1c4q9GhRjOcA7jw4siXOwYkeFBhQ4gTLWbkkZX+6NEja8vA+H4NZwFvaaZkm2mSoyqX6msHCfROI05UToUKgCopEX0VGQhfq+Es0LhxYzkjPXx0M3Z1ryX8IiJGpHi99KVAhxrNcBLjwosjX+4YkOBBhQ0hTrSYkUdLliyxwztOqQZmzTPvZ47kWcgNNUvd9eom0dvKS2cp50FrK5zzjJxvPAngW9tAht9m6tSpY+qdNzG5ug+/RnkqRqR4vfSlQIcaTcr0ufDiyJd7yDQ8qLAhxIkWM/IoKSnJ56m66yii1ZuZHRlm1qx01UrFVbPtfHbvkILWIiHbuP3IGcHXnXzwla2kJCQkSOLwG5lPPq62J9fwS6B2T8WIFK+XvhToUKNJOSxCXhz5cseABA8qbAhxosWMPCInEQX52zuZF7llYEycOqUy2C/sebZMiev8ZGxUXuPke0KtkKPgrFFkFqJ9R4H3yRt+q/QFrCa6utei3VMxIsXrpS8FOtRoUqbPhRdHvtwxIMGDChtCnGgxI4+yZcsmsdx5GzMiq6wMq1uFkqB2CrudHVs6GiSnP1qqhDm18nzRObcYG67knMykuyWriqt9LHE7L7i616LdUzEixeulLwU61GhSps+FF0e+3DEgwYMKG0KcaDEjj3xYeAfzEH7Ul3+Wl9pqqRkPy8tZQ3/LyLnVmPl+ULktMrVcUjrbWIsInHMmTpyYnJxcsGBB6euA6XtFJUHv6l6Ldk/FiBSvl74U6FCjSZk+F14c+XLHgAQPKmwIw381YEYe/xmI/RqIfRWK/T4gWlaZF2/mWfx2YkJWhtwyO95PhFc3ibE5C8X+NGpCVSjT5C3lmZnyrqJj8z2gcklEdcpKNx6yzTNvrI/H1tZ//YvMArJTeHvVypx6LTln1ry3njH4Jo79rxJmwY5tz6Oo7qpc1r7Vw4+TMaBixRgbSflf/F1ISmkiZOcTofrKSBWAhCxkbCRo6WPpOLf8536Zi/1vowbD6c/5SYk1X2Ef8d5qmWpgPclIc2pU6PILO5GjiDyW07Li//nrdPv2/wOO8ERaDXLzxQAAAABJRU5ErkJggg== N f <p> Range Algo </p>

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

Low High N # f Npts U Low High N xd : i 1 U rows range f i el U i el f eval : for U f augment 31 line :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 41 line :

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 :

t0 1 time :

x F 0.1 1 x 2^+ / :

x q 0.125 x sin * :

x S 0.05 x sqrt * :

Plot_1 5 - 5 4.95 - x F inc :

Plot_2 π - π π - 0.05 + (x q inc :

Plot_3 05 0.05 x S inc :

P Plot_1 Plot_2 Plot_3 31 sys :

1 time t0 - 0.8 s *

Plot range, collect global

Plot range/mesh in canvas

3 - 3 2.95 - x F inc

Plot_1 rows Plot_2 rows Plot_3 rows 31 mat 20112610131 mat

x F 11 x 2^+ / :

F 5 - 550 x F Npts :

x int 11 x 2^+ / x int maple : x atan

a b c spec . 8 black 13 mat :

pts F a b c spec pts :

Function, Derivative, Integral curve. If you want the area under the function, you must use the "Cumulative Integral".

x F x F x diff x int 3 1 sys 0 pts 2 1 sys

Finite Differences Derivative/Cumulative Integral

data Σ Finite Diff's 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 * (* + : 21 line for vx Y augment 61 line :

data Deriv Finite Diff's Derivative X data 1 col : Y data 2 col : n X rows : deriv 1 el 0 : deriv n el 0 : i 2 n 1 - range deriv 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 deriv 1 el deriv 2 el : deriv n el deriv deriv rows el : X deriv augment 101 line :

Remenber: no matter the shape and the position of the function in the Cartesian quadrant, Cumulative Integral always starts valued = 0.

Σ F Σ :

Deriv F Deriv :

<= Assign: Deriv/CumulInt

Assign points trace: size/color

a b c spec o 5 red 13 mat :

Σ Σ a b c spec pts :

a b c spec . 10 green 13 mat :

Deriv Deriv a b c spec pts :

Disambiguation:

a b c spec . 10 black 13 mat :

F F a b c spec pts :

In this work, the function is analytic i.e: it can be derived/Integrated. The real life is a much different story. Sampled data are necessarily noisy from at least two sources: instantaneous hysteresis & quantisation. Whether high or low noise, the finite Diff's Cumulative Integral will be "almost exact" providing the sampled collection is reasonable. At very low noise, the finite Diff's Deriv will only reveal the "allure" of the deriv. This is so because the derivative is a violent noise amplifier, while the integrate is a very powerful noise reducer. What to do ? 1. On low noise, you can attempt to smooth via the gaussian "Ksmooth" 2. If "Kmooth" is still unsatisfactory, NO alternative: find the best analytic function via "Smath Genfit". If you don't feel comfortable, pass to a "guru fitter".

Collect 0 F Σ Deriv 41 sys :

Datum Function Cumulative integral Derivative 41 sys

Collect

3D-solid CreateMesh < 1 min

r 1 b 2^- :

b 0.4 :

w r sqrt :

u v d b w b u * cosh (2^* b w v * sin * (2^+ (* :

u v f u - 2 r * b u * cosh * b u * sinh * u v d / + 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / 31 mat :

M u v f 13.2 - 13.2 37.4 - 37.4 3030 CreateMesh :