<p> Data set </p>

c81e9baf-9ff1-4e4d-aebf-7f46f2e9fc37 12 4 5 decimal

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

Incremental analytical spline derivative

data 0 0.195162 0.05 0.199478 0.1 0.208073 0.15 0.220832 0.2 0.23765 0.25 0.258297 0.3 0.282608 0.35 0.31025 0.4 0.341006 0.45 0.374454 0.5 0.410342 0.55 0.448173 0.6 0.487676 0.65 0.5283 0.7 0.569774 0.75 0.611512 0.8 0.653261 0.85 0.694421 0.9 0.734779 0.95 0.773736 1 0.811136 1.05 0.846402 1.1 0.879447 1.15 0.909728 1.2 0.937241 1.25 0.961489 1.3 0.982557 1.35 1 1.4 1.013997 1.45 1.024155 1.5 1.030749 1.55 1.033436 1.6 1.03258 1.65 1.027885 1.7 1.019796 1.75 1.008054 1.8 0.993176 1.85 0.974929 1.9 0.953886 1.95 0.929829 2 0.903376 2.05 0.874307 2.1 0.843271 2.15 0.810036 2.2 0.775267 2.25 0.738707 2.3 0.701026 2.35 0.661933 2.4 0.622092 2.45 0.581171 2.5 0.53982 2.55 0.497663 2.6 0.455334 2.65 0.412408 2.7 0.369501 2.75 0.326143 2.8 0.282936 2.85 0.239366 2.9 0.196024 2.95 0.152361 3 0.108965 3.05 0.06526 3.1 0.021834 3.15 0.021905 - 3.2 0.065357 - 3.25 0.109124 - 3.3 0.152587 - 3.35 0.196347 - 3.4 0.239758 - 3.45 0.283414 - 3.5 0.326638 - 3.55 0.37001 - 3.6 0.412818 - 3.65 0.455624 - 3.7 0.497683 - 3.75 0.539536 - 3.8 0.580405 - 3.85 0.620813 - 3.9 0.659954 - 3.95 0.698338 - 4 0.735134 - 4.05 0.770845 - 4.1 0.804626 - 4.15 0.836979 - 4.2 0.867054 - 4.25 0.895362 - 4.3 0.921057 - 4.35 0.944666 - 4.4 0.965357 - 4.45 0.983684 - 4.5 0.998839 - 4.55 1.011406 - 4.6 1.020609 - 4.65 1.02707 - 4.7 1.03005 - 4.75 1.030212 - 4.8 1.026857 - 4.85 1.020691 - 4.9 1.011055 - 4.95 0.998695 - 5 0.982994 - 5.05 0.964733 - 5.1 0.943331 - 5.15 0.919598 - 5.2 0.892986 - 5.25 0.864325 - 5.3 0.83309 - 5.35 0.800124 - 5.4 0.764919 - 5.45 0.728319 - 5.5 0.689824 - 5.55 0.650271 - 5.6 0.609159 - 5.65 0.56731 - 5.7 0.524216 - 5.75 0.480676 - 5.8 0.436171 - 5.85 0.39147 - 5.9 0.346041 - 5.95 0.300621 - 6 0.254662 - 6.05 0.208869 - 6.1 0.162682 - 6.15 0.116774 - 6.2 0.070577 - 6.25 0.024736 - 6.3 0.02132 6.35 0.066967 6.4 0.112773 6.45 0.158126 6.5 0.203584 6.55 0.248543 6.6 0.293537 6.65 0.337966 6.7 0.382334 6.75 0.426035 6.8 0.46954 6.85 0.512232 6.9 0.554542 6.95 0.595841 7 0.636519 7.05 0.675936 7.1 0.714439 7.15 0.751381 7.2 0.78707 7.25 0.820858 7.3 0.85302 7.35 0.882914 7.4 0.910793 7.45 0.93603 7.5 0.958868 7.55 0.978707 7.6 0.995789 7.65 1.009557 7.7 1.020264 7.75 1.027408 7.8 1.031263 7.85 1.031398 7.9 1.028119 7.95 1.02107 8 1.0106 8.05 0.99644 8.1 0.978984 8.15 0.958052 8.2 0.934088 8.25 0.907002 8.3 0.877284 8.35 0.84493 8.4 0.810473 8.45 0.773988 8.5 0.736038 8.55 0.696767 8.6 0.656758 8.65 0.616207 8.7 0.575699 8.75 0.53547 8.8 0.496088 8.85 0.457809 8.9 0.421165 8.95 0.386415 9 0.354037 9.05 0.324271 9.1 0.297526 9.15 0.274007 9.2 0.254036 9.25 0.23777 9.3 0.225431 9.35 0.217118 9.4 0.212945 1892 mat :

Recast cspline as a canvas function

X data 1 col : Y data 2 col : 21 line

x φ 0 x ≤ (x 9.4 ≤ (& X Y x cinterp OUT of data range if :

Smath 6179 interpolates on the "canvas values" Smath 5346 could only start interpolate for x > 0.2 and x < 9.2

x φ

0 φ 9.4 φ 21 mat 0.1952 0.2129 21 mat

DOES cspline canvas function works ? ANSWER: Yes ! code it correct.

X data 1 col : Y data 2 col : 21 line

L 0 : H 9.4 : h 0.1 : 31 line

x D1 x 2 h * - φ x 2 h * + φ - 4 h * / - : 1rst spline derivative ≡

x D2 x 2 h * + φ - 16 x h + φ * + 30 x φ * - 16 x h - φ * + x 2 h * - φ - 12 h 2^* / : 2nd spline derivative ≡

Analytical/incremental spline derivative

x φ x D1 x D2 3 1 sys

Derivative operator does not recognise D1(x) as derivable. It does not have an applicable rule vs more traditional math function from the book.

x D1 x diff