{"id":10343,"date":"2025-07-10T02:33:59","date_gmt":"2025-07-10T02:33:59","guid":{"rendered":"https:\/\/voyawave.com\/%e5%ae%9e%e9%aa%8c%e9%a1%b5%e9%9d%a2\/"},"modified":"2025-07-10T02:59:10","modified_gmt":"2025-07-10T02:59:10","slug":"%e5%ae%9e%e9%aa%8c%e9%a1%b5%e9%9d%a2","status":"publish","type":"page","link":"https:\/\/voyawave.com\/zh-hans\/%e5%ae%9e%e9%aa%8c%e9%a1%b5%e9%9d%a2\/","title":{"rendered":"\u5b9e\u9a8c\u9875\u9762"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"10343\" class=\"elementor elementor-10343 elementor-10338\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3175bde elementor-section-boxed elementor-section-height-default elementor-section-height-default wd-section-disabled\" data-id=\"3175bde\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d165b1e\" data-id=\"d165b1e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8f1dd2e elementor-widget elementor-widget-wd_title\" data-id=\"8f1dd2e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"wd_title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"title-wrapper set-mb-s reset-last-child wd-title-color-default wd-title-style-default wd-title-size-default text-center\">\n\n\t\t\t\t\t\t\t<div class=\"title-subtitle subtitle-color-default subtitle-style-default wd-fontsize-xs\">\n\t\t\t\t\t\u5b57\u5e55\u6587\u672c\u793a\u4f8b\t\t\t\t<\/div>\n\t\t\t\n\t\t\t<div class=\"liner-continer\">\n\t\t\t\t<h4 class=\"woodmart-title-container title wd-fontsize-l\">\u6807\u9898\u6587\u672c\u793a\u4f8b<\/h4> \n\t\t\t\t\t\t\t<\/div>\n\n\t\t\t\t\t\t\t<div class=\"title-after_title set-cont-mb-s reset-last-child wd-fontsize-xs\">\n\t\t\t\t\t<p>\u6807\u9898\u540e\u6587\u672c\u793a\u4f8b<\/p>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6a2d4d2 elementor-widget elementor-widget-wd_title\" data-id=\"6a2d4d2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"wd_title.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"title-wrapper set-mb-s reset-last-child wd-title-color-default wd-title-style-default wd-title-size-default text-center\">\n\n\t\t\t\t\t\t\t<div class=\"title-subtitle subtitle-color-default subtitle-style-default wd-fontsize-xs\">\n\t\t\t\t\t\u5b57\u5e55\u6587\u672c\u793a\u4f8b\t\t\t\t<\/div>\n\t\t\t\n\t\t\t<div class=\"liner-continer\">\n\t\t\t\t<h4 class=\"woodmart-title-container title wd-fontsize-l\">\u6807\u9898\u6587\u672c\u793a\u4f8b<\/h4> \n\t\t\t\t\t\t\t<\/div>\n\n\t\t\t\t\t\t\t<div class=\"title-after_title set-cont-mb-s reset-last-child wd-fontsize-xs\">\n\t\t\t\t\tText after title text example\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-622c26b elementor-widget elementor-widget-wd_text_block\" data-id=\"622c26b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"wd_text_block.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"wd-text-block reset-last-child text-left\">\n\t\t\t\n\t\t\t<p><span style=\"font-size: 36pt;\">Lorem ipsum dolor sit amet, consectetur adipiscing elit.\u5728\u8fd9\u91cc\uff0c\u4f60\u4f1a\u53d1\u73b0\uff0c\u4f60\u7684\u8eab\u4f53\u6ca1\u6709\u4efb\u4f55\u53d8\u5316\uff0c\u4f60\u7684\u76ae\u80a4\u4e5f\u6ca1\u6709\u4efb\u4f55\u53d8\u5316\u3002 <\/span><\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-67b204d elementor-widget elementor-widget-html\" data-id=\"67b204d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div>\r\n\r\n\r\n    <meta charset=\"UTF-8\">\r\n    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\r\n    <title>\u4e8c\u6b21\u591a\u9879\u5f0f\u62df\u5408\u5de5\u5177<\/title>\r\n    <!-- \u4f7f\u7528 defer \u786e\u4fdd\u811a\u672c\u6309\u987a\u5e8f\u52a0\u8f7d -->\r\n    <script src=\"https:\/\/cdn.jsdelivr.net\/npm\/chart.js@3.7.1\/dist\/chart.min.js\" defer><\/script>\r\n    <script src=\"https:\/\/cdn.jsdelivr.net\/npm\/mathjs@11.6.0\/lib\/browser\/math.min.js\" defer><\/script>\r\n    <style>\r\n        body {\r\n            font-family: Arial, sans-serif;\r\n            max-width: 900px;\r\n            margin: 0 auto;\r\n            padding: 20px;\r\n        }\r\n        .container {\r\n            display: flex;\r\n            flex-wrap: wrap;\r\n            gap: 20px;\r\n        }\r\n        .data-input {\r\n            flex: 1;\r\n            min-width: 300px;\r\n        }\r\n        .chart-container {\r\n            flex: 2;\r\n            min-width: 500px;\r\n        }\r\n        textarea {\r\n            width: 100%;\r\n            height: 150px;\r\n            margin-bottom: 10px;\r\n        }\r\n        button {\r\n            padding: 8px 16px;\r\n            background-color: #4CAF50;\r\n            color: white;\r\n            border: none;\r\n            cursor: pointer;\r\n            margin-right: 10px;\r\n        }\r\n        button:hover {\r\n            background-color: #45a049;\r\n        }\r\n        table {\r\n            width: 100%;\r\n            border-collapse: collapse;\r\n            margin-top: 20px;\r\n        }\r\n        th, td {\r\n            border: 1px solid #ddd;\r\n            padding: 8px;\r\n            text-align: left;\r\n        }\r\n        th {\r\n            background-color: #f2f2f2;\r\n        }\r\n        .equation {\r\n            font-size: 18px;\r\n            margin: 15px 0;\r\n            padding: 10px;\r\n            background-color: #f8f8f8;\r\n            border-radius: 5px;\r\n        }\r\n        .error {\r\n            color: red;\r\n            margin: 10px 0;\r\n        }\r\n    <\/style>\r\n\r\n\r\n    <h1>\u4e8c\u6b21\u591a\u9879\u5f0f\u62df\u5408\u5de5\u5177<\/h1>\r\n    <div id=\"error-message\" class=\"error\"><\/div>\r\n    <div class=\"container\">\r\n        <div class=\"data-input\">\r\n            <h2>\u8f93\u5165\u6570\u636e<\/h2>\r\n            <div>\r\n                <label for=\"xData\">x\u503c\uff08\u7528\u9017\u53f7\u3001\u7a7a\u683c\u6216\u6362\u884c\u5206\u9694\uff09\uff1a<\/label><br>                <textarea id=\"xData\" placeholder=\"\u4f8b\u5982\uff1a1, 2, 3, 4, 5\"><\/textarea>\r\n            <\/div>\r\n            <div>\r\n                <label for=\"yData\">y\u503c\uff08\u7528\u9017\u53f7\u3001\u7a7a\u683c\u6216\u6362\u884c\u5206\u9694\uff09\uff1a<\/label><br>                <textarea id=\"yData\" placeholder=\"\u4f8b\u5982\uff1a 2, 3, 5, 7, 11\"><\/textarea>\r\n            <\/div>\r\n            <button onclick=\"fitData()\">\u8fdb\u884c\u62df\u5408<\/button>\r\n            <button onclick=\"clearData()\">\u6e05\u9664\u6570\u636e<\/button>\r\n            \r\n            <h3>\u62df\u5408\u7ed3\u679c<\/h3>\r\n            <div id=\"equation\" class=\"equation\"><\/div>\r\n            \r\n            <h3>\u6570\u636e\u8868<\/h3>\r\n            <table id=\"dataTable\">\r\n                <thead>\r\n                    <tr>\r\n                        <th>X<\/th>\r\n                        <th>Y<\/th>\r\n                    <\/tr>\r\n                <\/thead>\r\n                <tbody><\/tbody>\r\n            <\/table>\r\n        <\/div>\r\n        \r\n        <div class=\"chart-container\">\r\n            <canvas id=\"fitChart\"><\/canvas>\r\n        <\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n        \/\/ \u68c0\u67e5\u6240\u9700\u5e93\u662f\u5426\u5df2\u52a0\u8f7d\r\n        function checkLibraries() {\r\n            if (typeof Chart === 'undefined') {\r\n                document.getElementById('error-message').textContent = \r\n                    '\u9519\u8bef: Chart.js \u5e93\u672a\u6b63\u786e\u52a0\u8f7d\u3002\u8bf7\u68c0\u67e5\u7f51\u7edc\u8fde\u63a5\u6216\u5237\u65b0\u9875\u9762\u3002';\r\n                return false;\r\n            }\r\n            if (typeof math === 'undefined') {\r\n                document.getElementById('error-message').textContent = \r\n                    '\u9519\u8bef: math.js \u5e93\u672a\u6b63\u786e\u52a0\u8f7d\u3002\u8bf7\u68c0\u67e5\u7f51\u7edc\u8fde\u63a5\u6216\u5237\u65b0\u9875\u9762\u3002';\r\n                return false;\r\n            }\r\n            return true;\r\n        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borderColor: 'rgba(255, 99, 132, 1)',\r\n                                backgroundColor: 'rgba(255, 99, 132, 0.2)',\r\n                                borderWidth: 2,\r\n                                pointRadius: 0,\r\n                                fill: false\r\n                            }\r\n                        ]\r\n                    },\r\n                    options: {\r\n                        responsive: true,\r\n                        scales: {\r\n                            x: {\r\n                                title: {\r\n                                    display: true,\r\n                                    text: 'X'\r\n                                }\r\n                            },\r\n                            y: {\r\n                                title: {\r\n                                    display: true,\r\n                                    text: 'Y'\r\n                                }\r\n                            }\r\n                     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let sumY = 0, sumXY = 0, sumX2Y = 0;\r\n            \r\n            for (let i = 0; i < n; i++) {\r\n                const xi = x[i];\r\n                const xi2 = xi * xi;\r\n                const xi3 = xi2 * xi;\r\n                const xi4 = xi3 * xi;\r\n                \r\n                sumX += xi;\r\n                sumX2 += xi2;\r\n                sumX3 += xi3;\r\n                sumX4 += xi4;\r\n                \r\n                sumY += y[i];\r\n                sumXY += xi * y[i];\r\n                sumX2Y += xi2 * y[i];\r\n            }\r\n            \r\n            \/\/ \u6784\u5efa\u77e9\u9635 [[n, sumX, sumX2], [sumX, sumX2, sumX3], [sumX2, sumX3, sumX4]]\r\n            const A = math.matrix([\r\n                [n, sumX, sumX2],\r\n                [sumX, sumX2, sumX3],\r\n                [sumX2, sumX3, sumX4]\r\n            ]);\r\n            \r\n            \/\/ \u6784\u5efa\u5411\u91cf [sumY, sumXY, sumX2Y]\r\n            const b = math.matrix([sumY, sumXY, sumX2Y]);\r\n            \r\n            \/\/ \u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4 A * c = b\r\n            const coefficients = math.lusolve(A, b);\r\n            \r\n            return {\r\n                a: coefficients.get([2, 0]),  \/\/ x\u00b2\u7cfb\u6570\r\n                b: coefficients.get([1, 0]),  \/\/ x\u7cfb\u6570\r\n                c: coefficients.get([0, 0])   \/\/ \u5e38\u6570\u9879\r\n            };\r\n        }\r\n        \r\n        \/\/ \u62df\u5408\u6570\u636e\u5e76\u7ed8\u5236\u56fe\u8868\r\n        function fitData() {\r\n            if (!checkLibraries()) return;\r\n            \r\n            try {\r\n                const xInput = document.getElementById('xData').value;\r\n                const yInput = document.getElementById('yData').value;\r\n                \r\n                const x = parseInput(xInput);\r\n                const y = parseInput(yInput);\r\n                \r\n                if (x.length === 0 || y.length === 0) {\r\n                    alert('\u8bf7\u8f93\u5165\u6709\u6548\u7684X\u548cY\u6570\u636e\uff01');\r\n                    return;\r\n                }\r\n                \r\n                if (x.length !== y.length) {\r\n                    alert('X\u548cY\u6570\u636e\u7684\u6570\u91cf\u5fc5\u987b\u76f8\u540c\uff01');\r\n                    return;\r\n                }\r\n                \r\n                \/\/ \u66f4\u65b0\u6570\u636e\u8868\r\n                updateDataTable(x, y);\r\n                \r\n                \/\/ \u8fdb\u884c\u4e8c\u6b21\u591a\u9879\u5f0f\u62df\u5408\r\n                const coefficients = quadraticFit(x, y);\r\n                const a = coefficients.a;\r\n                const b = coefficients.b;\r\n                const c = coefficients.c;\r\n                \r\n                \/\/ \u663e\u793a\u62df\u5408\u65b9\u7a0b\r\n                document.getElementById('equation').innerHTML = \r\n                    `\u62df\u5408\u65b9\u7a0b: y = ${a.toFixed(4)}x\u00b2 + ${b.toFixed(4)}x + ${c.toFixed(4)}`;\r\n                \r\n                \/\/ \u751f\u6210\u62df\u5408\u66f2\u7ebf\u6570\u636e\u70b9\r\n                const minX = Math.min(...x);\r\n                const maxX = Math.max(...x);\r\n                const step = (maxX - minX) \/ 100;\r\n                \r\n                const fitData = [];\r\n                for (let xi = minX - 1; xi <= maxX + 1; xi += step) {\r\n                    fitData.push({\r\n                        x: xi,\r\n                        y: a * xi * xi + b * xi + c\r\n                    });\r\n                }\r\n                \r\n                \/\/ \u51c6\u5907\u539f\u59cb\u6570\u636e\u70b9\r\n                const originalData = x.map((xi, i) => ({ x: xi, y: y[i] }));\r\n                \r\n                \/\/ \u66f4\u65b0\u56fe\u8868\r\n                myChart.data.datasets[0].data = originalData;\r\n                myChart.data.datasets[1].data = fitData;\r\n                myChart.update();\r\n       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document.getElementById('equation').innerHTML = '';\r\n            document.querySelector('#dataTable tbody').innerHTML = '';\r\n            document.getElementById('error-message').textContent = '';\r\n            \r\n            if (myChart) {\r\n                myChart.data.datasets[0].data = [];\r\n                myChart.data.datasets[1].data = [];\r\n                myChart.update();\r\n            }\r\n        }\r\n        \r\n        \/\/ \u9875\u9762\u52a0\u8f7d\u5b8c\u6210\u540e\u521d\u59cb\u5316\u56fe\u8868\r\n        document.addEventListener('DOMContentLoaded', function() {\r\n            \/\/ \u6dfb\u52a0\u5ef6\u8fdf\u786e\u4fdd\u6240\u6709\u5e93\u5df2\u52a0\u8f7d\r\n            setTimeout(initChart, 100);\r\n        });\r\n    <\/script>\r\n\r\n<\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ec27a5a 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