From 61d3b7a2a3411ab4aa6d69ef29d8a9d5d43a1d84 Mon Sep 17 00:00:00 2001 From: dm1sh Date: Wed, 24 Nov 2021 03:20:08 +0300 Subject: [PATCH] Added more detaled description in readme with example screenshots --- README.md | 88 ++++++++++++++++++++++++++++++++++++++++++++++- img/console.png | Bin 0 -> 36287 bytes img/console2.png | Bin 0 -> 53907 bytes img/console3.png | Bin 0 -> 51994 bytes img/plot.png | Bin 0 -> 80388 bytes img/plot2.png | Bin 0 -> 210626 bytes img/wolfram.png | Bin 0 -> 84582 bytes img/wolfram2.png | Bin 0 -> 148240 bytes 8 files changed, 87 insertions(+), 1 deletion(-) create mode 100644 img/console.png create mode 100644 img/console2.png create mode 100644 img/console3.png create mode 100644 img/plot.png create mode 100644 img/plot2.png create mode 100644 img/wolfram.png create mode 100644 img/wolfram2.png diff --git a/README.md b/README.md index d78d042..a6f9b06 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,89 @@ # Polynomial Interpolation -ANSI C program which composes polynomial of n - 1 degree that passes through n dots. +ANSI C program which composes polynomial of n - 1 degree that passes through n dots. It presents it in Newton interpolation polynomial and monic form. + +## Interface + +Application accepts as standart input decimal below 2147483647 `n` as number of dots, followed by n dots in format: ` (space) ` on each line, where `x` is an abscisse and `y` is an ordinate of single dot. Dot coordinates must fit [2.22507e-308;1.79769e+308] range by modulo. + +Result will be printed to standart output in the following format: + +Newton polynomial form: + +f_0 - f_1*(x-x_0) + ... + f_n(x-x_0)*(x-x_1)*...*(x-x_{n-1}) + +Simplified coefficients array (starting from 0 upto n-1 power): + +a_0 a_1 ... a_{n-1} a_n + +Polynomial in monic form: + +a_0 - a_1*x + ... + a_{n-1}*x^(n-2) + a_n*x^(n-1) + +Where f_i is a divided difference of y_1,...,y_i, a_i are coefficients of resulting monic polynomial + +## Data structure + +- `n` is an `unsigned int` variable, that is used to input and store number of dots + +- `x` is a pointer to array of `n` `double`s, that is used to store abscisses of dots + +- `y` is a pointer to array of `n` `double`s, that is used to store ordinates of dots + +- `coefficients` is a pointer to array of `n` `double`s, that is used to store coefficients of monic interpolation polynomial + +- `i`, `j` are `int` variables, those are used in loops as iterators + +- `tmp_polynomial` is a pointer to array of `n` `double`s, that is used to store coefficients of polynomial, resulting during simplification of interpolation polynomial summands. + +## Example + +Build and run application: + +```bash +gcc main.c +./a.out +``` + +### Input/output + +For input n = 3 and the following dots + +```plain +1 5 +2 3 +4 8 +``` + +Output is + +```plain +Newton polynomial form: +5 - 2*(x-1) + 1.5*(x-1)*(x-2) +Simplified coefficients array (starting from 0 upto n-1 power): +10 -6.5 1.5 +Polynomial in standart form: +10 - 6.5*x + 1.5*x^2 +``` + +### Illustrations + +#### Example 1 + + + + + + + +#### Example 2 + + + +or + + + + + + \ No newline at end of file diff --git a/img/console.png b/img/console.png new file mode 100644 index 0000000000000000000000000000000000000000..68e2fd7977e4ffbb67f66f3b8f1a42d4f9f8814a GIT binary patch literal 36287 zcmYg%Rajh2(=7=QT!I9*;1=9n2X~jj-Q6MR;2MHMaJS&@?(UGm-JJn`-tXL;i`_T< 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