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script.js
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script.js
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/**
* Gisele Silva Gomes. 16/07/2024, João Pessoa, Paraíba, Brasil.
*/
// Function to handle method selection change
document
.getElementById("method-select")
.addEventListener("change", function () {
var selectedMethod = this.value;
var tableHeaders = document
.getElementById("result-table")
.querySelectorAll("th");
var rangeAInput = document.getElementById("range-a");
var rangeBInput = document.getElementById("range-b");
var aLabel = document.querySelector('label[for="range-a"]');
var bLabel = document.querySelector('label[for="range-b"]');
// Reset table headers to default
tableHeaders[0].textContent = "Iteração";
tableHeaders[1].textContent = "a";
tableHeaders[2].textContent = "b";
tableHeaders[3].textContent = "x";
tableHeaders[4].textContent = "f(a)";
tableHeaders[5].textContent = "f(b)";
tableHeaders[6].textContent = "f(x)";
tableHeaders[7].textContent = "|b - a|";
// Adjust table headers and input visibility based on selected method
if (selectedMethod === "newton" || selectedMethod === "secant") {
tableHeaders[1].textContent = "x"; // Change 'a' to 'x'
tableHeaders[2].textContent = "f(x)"; // Change 'b' to 'f(x)'
tableHeaders[3].textContent = "|x_k+1 - x|"; // Change 'x' to '|x_k+1 - x|'
// Hide a and b inputs and labels
rangeAInput.style.display = "none";
rangeBInput.style.display = "none";
aLabel.style.display = "none";
bLabel.style.display = "none";
} else {
// Show a and b inputs and labels for other methods
rangeAInput.style.display = "";
rangeBInput.style.display = "";
aLabel.style.display = "";
bLabel.style.display = "";
// Show 'a' and 'b' in table headers
tableHeaders[1].textContent = "a";
tableHeaders[2].textContent = "b";
}
});
// Function to handle method selection change
document
.getElementById("method-select")
.addEventListener("change", function () {
var selectedMethod = this.value;
var tableHeaders = document
.getElementById("result-table")
.querySelectorAll("th");
// Reset table headers to default
tableHeaders[0].textContent = "Iteração";
tableHeaders[1].textContent = "a";
tableHeaders[2].textContent = "b";
tableHeaders[3].textContent = "x";
tableHeaders[4].textContent = "f(a)";
tableHeaders[5].textContent = "f(b)";
tableHeaders[6].textContent = "f(x)";
tableHeaders[7].textContent = "|b - a|";
// Adjust table headers based on selected method
if (selectedMethod === "newton") {
tableHeaders[1].textContent = "x"; // Change 'a' to 'x'
tableHeaders[2].textContent = "f(x)"; // Change 'b' to 'f(x)'
tableHeaders[3].textContent = "|x_k+1 - x|"; // Change 'x' to '|x_k+1 - x|'
tableHeaders[4].style.display = "none"; // Hide 'f(a)' column
tableHeaders[5].style.display = "none"; // Hide 'f(b)' column
tableHeaders[6].style.display = "none"; // Hide 'f(x)' column
tableHeaders[7].style.display = "none"; // Hide '|b - a|' column
} else {
tableHeaders[4].style.display = ""; // Show 'f(a)' column
tableHeaders[5].style.display = ""; // Show 'f(b)' column
tableHeaders[6].style.display = ""; // Show 'f(x)' column
tableHeaders[7].style.display = ""; // Show '|b - a|' column'
}
});
// Function to evaluate the user input function, including derivatives
function evaluateFunction(expression, x) {
// expression str and x is a number
const scope = {
x: x,
e: Math.exp(1),
pi: Math.PI,
};
// Replace derivative notation with evaluated derivative
expression = expression.replace(/d\/dx\(([^)]+)\)/g, (_, innerExpr) => {
return math.derivative(innerExpr, "x").toString();
});
return math.evaluate(expression, scope);
}
// Plot the function
function plotFunction() {
const funcInput = document.getElementById("function-input").value;
if (!funcInput) {
alert("Por favor, insira uma função.");
return;
}
const xValues = [];
const yValues = [];
for (let x = -4; x <= 4; x += 0.01) {
xValues.push(x);
yValues.push(evaluateFunction(funcInput, x));
}
const trace = {
x: xValues,
y: yValues,
type: "scatter",
mode: "lines",
name: "f(x)",
line: { shape: "spline" },
};
const data = [trace];
const layout = {
title: `Graph of f(x) = ${funcInput}`,
xaxis: { title: "x" },
yaxis: { title: "f(x)" },
};
Plotly.newPlot("graph", data, layout);
// Clear previous results
document.getElementById("solution").textContent = "";
document.getElementById("iterations").textContent = "";
const tableBody = document
.getElementById("result-table")
.getElementsByTagName("tbody")[0];
while (tableBody.rows.length) {
tableBody.deleteRow(0);
}
}
// Use default function
function useDefaultFunction() {
document.getElementById("function-input").value = "x*log10(x)-1";
plotFunction();
}
// Generate a random function
function generateRandomFunction() {
const terms = [
"x",
"x^2",
"x^3",
"cos(x)",
"sin(x)",
"tan(x)",
"exp(x)",
"log10(x)",
];
let func = "";
const numTerms = Math.floor(Math.random() * 5) + 1;
for (let i = 0; i < numTerms; i++) {
const coeff = (Math.random() * 10 - 5).toFixed(2);
const term = terms[Math.floor(Math.random() * terms.length)];
func += `${coeff}*${term} + `;
}
return func.slice(0, -3); // Remove last ' + '
}
// Use random function
function useRandomFunction() {
const randomFunc = generateRandomFunction();
document.getElementById("function-input").value = randomFunc;
plotFunction();
}
// Bisection method implementation
function bisection(a, b, f, epsilon) {
let iterations = 0;
const table = document
.getElementById("result-table")
.getElementsByTagName("tbody")[0];
while (true) {
if (iterations > 100) {
alert("Iterações acima de 100.");
return;
}
const x = (a + b) / 2; // the middle between a and b (bisection method works like that)
const fa = f(a);
const fb = f(b);
const fx = f(x);
const row = table.insertRow();
row.insertCell(0).textContent = iterations + 1;
row.insertCell(1).textContent = a.toFixed(6);
row.insertCell(2).textContent = b.toFixed(6);
row.insertCell(3).textContent = x.toFixed(6);
try {
row.insertCell(4).textContent = fa.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de a não existe no domínio da função");
return;
}
throw e;
}
try {
row.insertCell(5).textContent = fb.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de b não existe no domínio da função");
return;
}
throw e;
}
row.insertCell(6).textContent = fx.toFixed(6);
row.insertCell(7).textContent = Math.abs(b - a).toFixed(6);
if (fa * fx < 0) {
// TVM
b = x;
} else {
a = x;
}
iterations++;
if (Math.abs(fx) < epsilon || Math.abs(b - a) < epsilon) {
row.cells[3].style.backgroundColor = "#78fa9f";
return { raiz: x, iterations: iterations };
}
}
}
// False Position method implementation
function false_pos(a, b, f, epsilon) {
let iterations = 0;
const table = document
.getElementById("result-table")
.getElementsByTagName("tbody")[0];
while (true) {
if (iterations > 100) {
alert("Iterações acima de 100.");
return;
}
const fa = f(a);
const fb = f(b);
const x =
(a * Math.abs(fb) + b * Math.abs(fa)) / (Math.abs(fb) + Math.abs(fa));
const fx = f(x);
const row = table.insertRow();
row.insertCell(0).textContent = iterations + 1;
row.insertCell(1).textContent = a.toFixed(6);
row.insertCell(2).textContent = b.toFixed(6);
row.insertCell(3).textContent = x.toFixed(6);
try {
row.insertCell(4).textContent = fa.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de a não existe no domínio da função");
return;
}
throw e;
}
try {
row.insertCell(5).textContent = fb.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de b não existe no domínio da função");
return;
}
throw e;
}
row.insertCell(6).textContent = fx.toFixed(6);
row.insertCell(7).textContent = Math.abs(b - a).toFixed(6);
if (fa * fx < 0) {
// TVM
b = x;
} else {
a = x;
}
iterations++;
if (Math.abs(fx) < epsilon || Math.abs(b - a) < epsilon) {
row.cells[3].style.backgroundColor = "#78fa9f";
return { raiz: x, iterations: iterations };
}
}
}
// Newton's method implementation
function newton(x, f_s, f, symbol, epsilon) {
const fi = math.derivative(f_s, symbol).toString(); // only accepts str and the symbol is the var (x)
const table = document
.getElementById("result-table")
.getElementsByTagName("tbody")[0];
let iterations = 0;
while (true) {
if (iterations > 100) {
alert("Iterações acima de 100.");
return;
}
const fx = f(x);
const aux = x - fx / math.evaluate(fi, { x: x });
const row = table.insertRow();
row.insertCell(0).textContent = iterations + 1;
row.insertCell(1).textContent = x.toFixed(6);
row.insertCell(2).textContent = f(x).toFixed(6);
row.insertCell(3).textContent = Math.abs(aux - x).toFixed(6);
iterations++;
if (Math.abs(fx) < epsilon || Math.abs(aux - x) < epsilon) {
row.cells[1].style.backgroundColor = "#78fa9f";
return { raiz: x, iterations: iterations };
}
x = aux;
}
}
// Secant method implementation
function secant(a, b, f, epsilon) {
let iterations = 0;
const table = document
.getElementById("result-table")
.getElementsByTagName("tbody")[0];
while (true) {
if (iterations > 100) {
alert("Não foi possível encontrar a raíz.");
return;
}
const fa = f(a);
const fb = f(b);
const x = b - (fb * (a - b)) / (fa - fb);
const row = table.insertRow();
row.insertCell(0).textContent = iterations + 1;
row.insertCell(1).textContent = a.toFixed(6);
row.insertCell(2).textContent = b.toFixed(6);
row.insertCell(3).textContent = x.toFixed(6);
try {
row.insertCell(4).textContent = fa.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de a não existe no domínio da função");
return;
}
throw e;
}
try {
row.insertCell(5).textContent = fb.toFixed(6);
} catch (e) {
if (e instanceof TypeError) {
alert("O valor de b não existe no domínio da função");
return;
}
throw e;
}
row.insertCell(6).textContent = f(x).toFixed(6);
row.insertCell(7).textContent = Math.abs(b - a).toFixed(6);
iterations++;
if (Math.abs(f(x)) < epsilon) {
row.cells[3].style.backgroundColor = "#78fa9f";
return { raiz: x, iterations: iterations };
}
a = b;
b = x;
}
}
// Function to solve the selected method
function solveMethod() {
const method = document.getElementById("method-select").value;
const funcInput = document.getElementById("function-input").value;
const a = parseFloat(document.getElementById("range-a").value);
const b = parseFloat(document.getElementById("range-b").value);
const epsilon = parseFloat(document.getElementById("epsilon").value);
if (!funcInput) {
alert("Por favor, insira uma função.");
return;
}
plotFunction();
let result;
switch (method) {
case "bisection":
result = bisection(a, b, (x) => evaluateFunction(funcInput, x), epsilon);
break;
case "false_pos":
result = false_pos(a, b, (x) => evaluateFunction(funcInput, x), epsilon);
break;
case "newton":
result = newton(
a,
math.parse(funcInput).toString(),
(x) => evaluateFunction(funcInput, x),
"x",
epsilon
);
break;
case "secant":
result = secant(a, b, (x) => evaluateFunction(funcInput, x), epsilon);
break;
default:
alert("Seleção de método inválida.");
return;
}
if (result) {
document.getElementById(
"solution"
).textContent = `Solução: ${result.raiz.toFixed(6)}`;
document.getElementById(
"iterations"
).textContent = `Iterações: ${result.iterations}`;
}
}