// 4.13.js
// created on 2024-09-06
// $Id: 4.13.js 1.1 2024/11/02 08:42:59 s Exp $

'use strict'
const math = require("./math.js"); // see below.

//# input
const s_percent = [7.67, 8.27, 8.81, 9.31, 9.75, 10.16, 10.52, 10.85];
const x  =        [ 500,  900,  600,  500,  100,   100,   100,    50];
const p1 =  65.95;
const d1 =   7.07;
const p2 = 101.66;
const d2 =   3.80;

// calculation
const s = s_percent.map(x => x / 100);
const n = x.length;
const t     =  x.map((_, i) => i + 1);
const a     =  x.map((_, i) => (1 + s[i]) ** t[i]);
const df    =  a.map((x)    => 1 / x);
const a2    =  s.map((_, i) => (1 + s[i]) ** (t[i] + 1));
const df2   = a2.map((x)    => 1 / x);
const dfx   = df.map((_, i) => df[i] * x[i]);
const txdf2 =  t.map((_, i) => t[i] * x[i] * df2[i]);
const sumtxdf2 = txdf2.reduce((x, y) => x + y);
const pv       =   dfx.reduce((x, y) => x + y);
const duration = sumtxdf2 / pv;
const A = [[p1, p2], [ p1 * d1, p2 * d2]];
const b = [pv, pv * duration];
// x1, x2 = A \ b
;const [x1, x2] = math.lusolve(A, b); // see below.
const xx = math.lusolve(A, b); // see below.

// output
console.log("4.13.js");
console.log('t'.padStart(7),
            's'.padStart(7),
           'df'.padStart(7),
            'x'.padStart(7),
          'dfx'.padStart(7),
        'txdf2'.padStart(7));
console.log("-".repeat(7*6+5));
for(let i = 0; i < n; i++){
    console.log(t[i].toFixed(0).padStart(7),
                s[i].toFixed(3).padStart(7),
               df[i].toFixed(3).padStart(7),
                x[i].toFixed(0).padStart(7), 
              dfx[i].toFixed(0).padStart(7), 
            txdf2[i].toFixed(0).padStart(7));
};
console.log("-".repeat(7*6+5));
console.log('PV= ',      Math.round(pv));
console.log('sumtxdf2=', Math.round(sumtxdf2));
console.log('D=',        duration.toFixed(2));

console.log('p1= ', p1);
console.log('p2= ', p2);
console.log('d1= ', d1);
console.log('d2= ', d2);

console.log("Ax = b");
console.log("A ");
console.log(A[0]);
console.log(A[1]);
console.log("b ");
console.log(b)
console.log("x")
console.log(xx.flat());

// end
// references
// David Flanagan著,村上列(訳)『JavaScript 第7版』オライリー・ジャパン,2021.
// ** : p.80.
// => : p.202.
// console.log() : p.630.
// const : p.57.
// length : p.176.
// let : p.57.
// map() : p.182.
// padStart() : p.39.
// reduce() : p.184.
// repeat() : p.39.
// toFixed() : p.51.
// use strict : p.134.
//
// math.js : https://mathjs.org/
// Math.js is an extensive math library for JavaScript and Node.js. 
// lusolve() : Solves the linear system A * x = b 
//             where A is an [n x n] matrix and b is a [n] column vector.
// eof