【原创程序】行列式计算器_JavaScript吧

1樓巨大八爪鱼 2015-12-14 20:18

2樓巨大八爪鱼 2015-12-14 20:19

【HTML代码】
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Determinant</title>
<style>
body {
    font-family: Arial;
}
table {
    margin-top: 6px;
}
td {
    text-align: center;
}
td > span {
    color: red;
}
</style>
<script>
function createDeterminant() {
    var size = Number(document.getElementById("number").value);
    var i, j, name;
    var html = '<table border="1"><tbody>';
    html += '<tr><th colspan="' + size + '" style="padding:3px">Determinant</th></tr>';
    for (i = 1; i <= size; i++) {
        html += '<tr>';
        for (j = 1; j <= size; j++) {
            name = "A" + i + "_" + j;
            html += '<td><input title="' + name.replace("_", ",") + '" name="' + name + '" type="number" style="width:40px" value="1"></td>';
        }
        html += '</tr>';
    }
    html += '<tr><td colspan="' + size + '" style="padding:5px"><input type="submit" value="Calculate" onClick="calculate();return false"></td></tr>';
    html += '<tr><td colspan="' + size + '" style="padding:3px;text-align:left"><b>Result: </b><span>0</span></td></tr>';
    html += '</tbody></table>';
    document.getElementById("calculator").innerHTML = html;
}
function calculate() {
    var det = getDeterminant();
    var value = calculateDeterinant(det);
    document.getElementsByTagName("table").item(0).firstChild.lastChild.getElementsByTagName("span").item(0).innerHTML = value;
}

/* row and column begin at 1 */
function getMinor(det, row, column) {
    var minor = [];
    var size = det.length;
    var r, c;
    var r2 = 0;
    var c2 = 0;
    for (r = 0; r < size; r++) {
        if (r == row - 1) {
            continue;
        }
        minor[r2] = [];
        c2 = 0;
        for (c = 0; c < size; c++) {
            if (c == column - 1) {
                continue;
            }
            minor[r2][c2] = det[r][c];
            c2++;
        }
        r2++;
    }
    return minor;
}

function splitDeterminant(det) {
    var size = det.length;
    var result = [];
    var i;
    for (i = 0; i < size; i++) {
        result[i] = {};
        result[i].coefficient = det[0][i];
        if (i % 2 == 1) {
            result[i].coefficient = -result[i].coefficient;
        }
        result[i].determinant = getMinor(det, 1, i + 1);
    }
    return result;
}

function calculateDeterinant(det) {
    if (det.length == 1) {
        return det[0][0];
    }
    var result = splitDeterminant(det);
    var size = result.length;
    var sum = 0;
    var i;
    for (i = 0; i < size; i++) {
        sum += result[i].coefficient * calculateDeterinant(result[i].determinant);
    }
    return sum;
}

/* Get the input determinant on the generated form */
function getDeterminant() {
    var det = [];
    var size = document.getElementsByTagName("table").item(0).firstChild.childNodes.item(1).childNodes.length;
    var i, j, name;
    for (i = 0; i < size; i++) {
        det[i] = [];
        for (j = 0; j < size; j++) {
            name = "A" + (i + 1) + "_" + (j + 1);
            det[i][j] = Number(document.getElementsByName(name).item(0).value);
            if (isNaN(det[i][j])) {
                det[i][j] = 0;
            }
        }
    }
    return det;
}
</script>
</head>

<body onLoad="createDeterminant()">
<form id="creator" name="creator" method="get" onSubmit="createDeterminant();return false">
<label for="number">Size:</label>
<input name="number" type="number" autofocus required id="number" style="width:40px" min="1" value="3">
<input type="submit" id="create" value="Create">
</form>
<form id="calculator" name="calculator" method="get"></form>
</body>
</html>

3樓巨大八爪鱼 2015-12-14 20:23

4樓巨大八爪鱼 2015-12-14 20:24

5樓巨大八爪鱼 2015-12-14 20:26

除了1~2阶以外，其余阶按顺序输入数字得出的结果都是0

6樓巨大八爪鱼 2015-12-14 22:19

对于10维来说，计算机也要算好几秒钟了。

7樓巨大八爪鱼 2015-12-15 23:13

8樓巨大八爪鱼 2015-12-15 23:13

9樓巨大八爪鱼 2015-12-15 23:15

附PHP程序：
【行列式化简器】
<?php
function printDet($det, $newline = true, $color = NULL) {
    $size = count($det);
    if (!is_null($color)) {
        $color = sprintf(' style="color:#%06X;border-color:#%06X"', $color, $color);
    }
    echo "<div class=\"determinant\"$color>";
    for ($i = 0; $i < $size; $i++) {
        for ($j = 0; $j < $size; $j++) {
            if ($j == $size - 1) {
                echo $det[$i][$j];
            } else {
                echo str_replace(' ', ' ', sprintf('%-5d', $det[$i][$j]));
            }
        }
        echo '<br>';
    }
    echo '</div>';
    if ($newline) {
        echo '<br>';
    }
}
?>
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Determinant</title>
<style>
.determinant {
    border-left: 1px solid black;
    border-right: 1px solid black;
    padding: 0px 3px 0px 3px;
    display: inline-block;
    margin: 0px 10px 4px 2px;
}
</style>
</head>

<body>
<?php
$det = array();
/*$det[0] = array(6, 8, 5);
$det[1] = array(5, 19, 6);
$det[2] = array(3, 1, 7);*/

$det[0] = array(1, 7, 4, 6, 8);
$det[1] = array(4, 3, 5, 7, 1);
$det[2] = array(2, 3, 5, 9, 2);
$det[3] = array(8, 6, 4, 5, 3);
$det[4] = array(8, 2, 9, 1, 7);

/*$det[0] = array(1, 2, 3, 4, 5);
$det[1] = array(6, 7, 8, 9, 10);
$det[2] = array(11, 12, 13, 14, 15);
$det[3] = array(16, 17, 18, 19, 20);
$det[4] = array(21, 22, 23, 24, 25);*/

printDet($det);

$size = count($det);
$divideBy = 1;
for ($i = 0; $i < $size - 1; $i++) {
    for ($j = $i + 1; $j < $size; $j++) {
        $value1 = $det[$i][$i];
        $value2 = $det[$j][$i];
        $row = $det[$i];
        foreach ($row as $k => $v) {
            $row[$k] = $v * $value2;
        }
        foreach ($det[$j] as $k => $v) {
            $det[$j][$k] = $v * $value1 - $row[$k];
        }
        if ($value1 != 0) {
            $divideBy *= $value1;
        }
        if ($i + 1 == $size - 1 && $j + 1 == $size) {
            echo '<br>';
        } else {
            if ($divideBy != 1) {
                echo "(1/$divideBy)";
            }
            printDet($det, false, 0xff1122);
        }
    }
}
if ($divideBy != 1) {
    echo "(1/$divideBy)";
}
printDet($det);
$result = 1;
for ($i = 0; $i < $size; $i++) {
    $result *= $det[$i][$i];
}
if ($divideBy == 0) {
    $result = 0;
} else {
    $result /= $divideBy;
}
echo "<b>Result:</b> $result";
?>
</body>
</html>

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