Interpolation linear f(x0,x¹x²), quadratic f(x0, x¹x²x³), cubic f(x0,x¹x²x³x⁴), etc.

06062020, 08:44 PM
(This post was last modified: 01132023 12:31 PM by Gil.)
Post: #1




Interpolation linear f(x0,x¹x²), quadratic f(x0, x¹x²x³), cubic f(x0,x¹x²x³x⁴), etc.
For HP49HP50
Small interpolation program. Valid for 2 points (linear solution) and for 3 points (quadratic function). Valid also for 4 points (cubic function). Valid also for 5 points, 6, 7, 8,...,68, 69, 70, 71... points. It is not a linear regression program : the function calculated here goes really exactly through all the given points. Once you have introduced the points in the calculator (stared / stored in matrix XY), you get the requested result in one single step (numbers 3 and4 below). Observation 1 The program works in RPN mode. Suppose you have the two points A(1;10), B(2;20). Find a function that goes exactly through them. Find f(x=1.7) = 17 Solution 1) Write Matrix XY: [[1 10] [2 20]] ENTER[/b] 2) Save/store it in XY: 'XY' STO 3)Press 1.7 INTERPOL 4) New values of xo, for example f(1.9) : skip steps 1 and 2 Press 1.9 INTERPOL Suppose now that you have the 3 points A(1;10), B(2;20), C(3;35). Find a function that goes exactly through them. Find f(x=1.7) = 16.475 Solution 1) Write Matrix XY: [[1 10] [2 20] [3 35]] ENTER 2) Save/store it again in XY: 'XY' STO 3)Press 1.7 INTERPOL 4) New values of xo, for example f(1.9) : skip steps 1 and 2 Press 1.7 INTERPOL Suppose now that you have n points A(1;10), B(2;20), C(3;35)... ZZn(n; f(n)). Find a function that goes exactly through them. Find f(x=1.7) Solution 1) Write Matrix XY: [[1 10] [2 20] [3 30] [... ....] [n f(n)]] ENTER 2) Save/store it again in XY: 'XY' STO 3)Press 1.7 INTERPOL 4) New values of xo, for example f(1.9) : skip steps 1 and 2 Press 1.7 INTERPOL Observation 2 You can have already the first coordinate xi of all the points saved in matrix X. All the second coordinates yi of all the points already in matrix Y. To build the requested matrix XY: 1) X ENTER 2) Y ENTER 3) 2 COL+ 4) 'XY' STO Then 1.7 INTERPOL Hope that it is useful. Regards, Gil 

07112020, 01:20 AM
(This post was last modified: 01122023 02:13 PM by Gil.)
Post: #2




RE: HP 49G/ HP50G : Interpolation linear, quadratic, cubic, etc.
New version 1.2 with slight changes : explanations for the arguments given at the beginning of the program and explanations given how to build once for all the matrix XY with the n given points.
Two separate files in the directory called interp.1.2doc:  the "npoints" Matrix XY  and the program itself. Just copy / transfer the directory called interp.1.2.doc in your calculator or phone EMU48 Android application. Code for the program itself: \<< "1) Create once Mat XY w/ the n given points [[x1 y1] [x2 y2] [ ] [xn yn]] 'XY' STO 2)Arg:value xo INTERP 3)Repeat step 2) for other values xo " DROP XY \> xo XY \<< XY SIZE OBJ\> 1 == IF THEN DROP XY OBJ\> 1 SWAP + \>ARRY 'XY' STO ELSE DROP2 END XY SIZE 1 GET 1 == IF THEN XY DUP 2 * 2 ROW+ 'XY' STO END XY 1 COL DUP SIZE OBJ\> DROP 1  \> x size \<< 1 size 1 + FOR i 0 size FOR j x i GET j ^ NEXT NEXT size 1 + DUP 2 \>LIST \>ARRY / "a0\183x^0" IF size 1 > THEN "+" + END "+a" + size \>STR DUP SIZE 1  1 SWAP SUB + "\183x^" + size \>STR DUP SIZE 1  1 SWAP SUB + \>TAG DUP TRN 0 size FOR i xo i ^ NEXT size 1 + 1 2 \>LIST \>ARRY * OBJ\> DROP "y(" xo + ")" + \>TAG \>> \>> \>> Remarks welcome. Regards, Gil 

01122023, 02:14 PM
(This post was last modified: 01122023 02:14 PM by Gil.)
Post: #3




RE: HP 49G/ HP50G : Interpolation linear, quadratic, cubic, etc.
File with .hp ending.


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