1b67ca4a-e5de-4b47-9171-9d6d829a3c0a 21 6 9 decimal

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

Linear interpolation/extrapolation data x Linterp vx data 1 col : vy data 2 col : x vx 1 el ≤ k 1 : x vx vx rows el ≥ k vx rows 1 - : k 1 : x vx k 1 + el ≥ k k 1 + : while 21 line if if vy k el vy k 1 + el vy k el - vx k 1 + el vx k el - / x vx k el - (* + 41 line :

XY 0.175 301.5 0.319 212.419 0.525 132.948 0.7 70.127 0.875 37.642 1.05 48.892 1.225 93.052 1.4 143.028 1.575 168.217 1.75 152.09 1.925 104.526 2.1 54.35 2.275 31.11 2.45 53.392 2.625 123.308 2.8 221.034 2.975 307.124 3.15 340.85 3.325 304.367 3.5 215.563 3.675 118.199 3.85 48.228 4.025 10.832 4.2 7.717 - 242 mat :

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 :

a b c spec o 8 black 13 mat :

pts XY a b c spec pts :

pts

Sanity check ...

XY 0.175 Linterp 301.5

XY 1.4 Linterp 143.028

XY 3.5 Linterp 215.563

XY 4.2 Linterp 7.717 -

Spline_interpolate in data table

The matrix may be square or rectangular. In this demo, we must prepare the data set by bordering the right and upper sides with ascending numbers. We leave these scales in integer to avoid confusion. The program is a dummy function that carries the 3 variates (x,y,M). Smath offers three interpolation options: 1. linterp [linear], 2. ainterp [Akima cubic spline], 3. cinterp [the more univsersal cubic spline].

x y M Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x ainterp 51 line :

data 0.01 0.03 0.05 0.03 0.02 0.05 - 0.02 - 0.01 - 0.06 - 0.01 - 0.02 0.06 0.1 0.06 0.04 0.01 - 0.04 - 0.02 - 0.12 - 0.02 - 0.09 0.08 0.07 0.05 0.02 0.04 - 0.06 - 0.03 0.08 0.01 0.05 0.02 - 0.03 0.01 - 0.06 0.08 0.02 0.02 - 0.05 - 0.08 - 410 mat :

Prepare the data set ------------------------------------------------

data C j 1 data cols range C j el j : for C transpose 21 line :

data R i 1 data rows 1 + range R i el i 1 - : for R 21 line :

data C 12345678910110 mat

data R 0123451 mat

data R data C data stack augment

New data R data C data stack augment :

New 11 el x/y :

<= this position may be any alpha/numeric char.

New x/y 123456789101 0.01 0.03 0.05 0.03 0.02 0.05 - 0.02 - 0.01 - 0.06 - 0.01 - 2 0.02 0.06 0.1 0.06 0.04 0.01 - 0.04 - 0.02 - 0.12 - 0.02 - 3 0.09 0.08 0.07 0.05 0.02 0.04 - 0.06 - 0.03 0.08 0.01 4 0.05 0.02 - 0.03 0.01 - 0.06 0.08 0.02 0.02 - 0.05 - 0.08 - 511 mat

3.5 8.5 New Spline 0.24906 -

If we have done it right ? Answer is YES

Times Table n M i 1 n range j 1 n range M i j el i j * : for for M 21 line :

data 5 M :

data 1234524681036912154812162051015202555 mat

data C j 1 data cols range C j el j : for C transpose 21 line :

data R i 1 data rows 1 + range R i el i 1 - : for R 21 line :

data C 1234515 mat

data R 01234561 mat

data R data C data stack augment

New data R data C data stack augment :

New 11 el x/y :

<= this position may be any alpha/numeric char.

New x/y 12345112345224681033691215448121620551015202566 mat

Sanity check

2.5 2.5 New Spline 1.5 1.5 New Spline 10 sqrt 10 sqrt New Spline 31 mat 6.25 2.25 1031 mat

col row # Spline