LU分解，Javascript代码
///A 为矩阵，这里写成一维数组，如 【1】，【1，2，3，4】
function GetLU(a)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var L = new Array(n);
var U = new Array(n);
if (GetDet(a) != 0)
{
var allOrderNotEqulesZero = true;
for (var i = 0; i < s; i++)
{
if (GetDet(GetOrderMatrix(a, i)) == 0)
{
allOrderNotEqulesZero = false;
break;
}
}
if (allOrderNotEqulesZero)
{
for (var i = 0; i < s; i++)
{
for (var j = 0; j < s; j++)
{
if (i == j)
{
L[i*s + j] = 1;
}
else if (i < j)
{
L[i*s+j] = 0;
}
if (i > j)
U[i*s+j] = 0;
U[0*s+j] = a[0*s+j];
L[i*s+0] = a[i*s+0] / U[0*s+0];
}
}
for (var k = 1; k < s; k++)
{
for (var j = k; j < s; j++)
{
tmp = 0;
for (var m = 0; m < k; m++)
{
tmp += L[k*s+m] * U[m*s+j];
}
U[k*s+j] = a[k*s+j] - tmp;
}
for (var i = k+1; i < s; i++)
{
tmp = 0;
for (var m = 0; m < k; m++)
{
tmp += L[i*s+m] * U[m*s+k];
}
L[i*s+k] = ( a[i*s+k] - tmp ) / U[k*s+k];
}
}
}
else
{
alert('该矩阵的顺序主子式中有零！')
console.log(GetLastMatrix(a));
for (var i = 0; i < s; i++)
{
for (var j = 0; j < s; j++)
{
if (j > i)
{
U[i * s + j] = a[i * s + j];
L[i * s + j] = 0;
}
else if (j == i)
{
U[i * s + j] = a[i * s + j];
L[i * s + j] = 1;
}
else
{
L[i * s + j] = a[i * s + j];
U[i * s + j] = 0;
}
}
}
}
console.log(L);
console.log(U);
}
else
{
alert('该矩阵为奇异矩阵，无法进行LU分解！');
}
}
function GetDet(a)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var sum = 0;
if (n == 1)
{
return a[0];
}
for (var i = 0; i < s; i++)
{
if (i % 2 == 0)
{
sum += a[i] * GetDet(GetSubMatrix(a, i))
}
else
{
sum -= a[i] * GetDet(GetSubMatrix(a, i))
}
}
return sum;
}
///获取比较第n列之后的矩阵
function GetLastMatrix(a)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var p = [];
for (var i = 0; i < s; i++)
{
for (var j = 0; j < s; j++)
{
if (i == j)
{
p.push(1);
}
else {
p.push(0);
}
}
}
for (var i = 0; i < s -1; i++)
{
a = GetNewMatrix(a, i, p);
}
console.log(p);
return a;
}
function GetNewMatrix(a, k, p)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var result = [];
var maxRowNum = 0;
var MAXValue = Math.abs(a[ k * s + k]);
for (var i = 1; i < s; i++)
{
if ( i >= k && Math.abs(a[i * s + k]) > MAXValue )
{
maxRowNum = i;
MAXValue = Math.abs(a[i * s + k]);
}
}
//console.log('maxRowNum:' + maxRowNum);
//console.log('MAXValue:' + MAXValue);
if (maxRowNum != k)
{
for (var i = 0; i < s; i++)
{
var temp = a[k * s + i];
a[k * s + i] = a[maxRowNum * s + i]
a[maxRowNum * s + i] = temp;
var tmp1 = p[k * s + i];
p[k * s + i] = p[maxRowNum * s + i]
p[maxRowNum * s + i] = tmp1;
}
//console.log(a);
//console.log(p);
if (MAXValue != 0)
{
for (var i = k + 1; i < s; i++)
{
if (a[i * s + k] != 0)
{
a[i * s + k] = parseFloat(a[i * s + k] / a[k * s + k])
for (var j = k + 1; j< s; j++)
{
a[i * s + j] = parseFloat(a[i * s + j]- a[i * s + k] * a[k * s + j])
}
}
}
}
}else
{
if (MAXValue != 0)
{
for (var i = k + 1; i < s; i++)
{
if (a[i * s + k] != 0)
{
a[i * s + k] = parseFloat(a[i * s + k] / a[k * s + k])
for (var j = k + 1; j< s; j++)
{
a[i * s + j] = parseFloat(a[k * s + j] - a[i * s + k] * a[i * s + j])
}
}
}
}
}
//console.log(a);
return a;
}
///a为原始矩阵，k为所在的列数
function GetSubMatrix(a, k)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var result = [];
for (var i = 1; i < s; i++)
{
for (var j = 0; j < s; j++)
{
if (k != j)
{
result.push(a[i*s +j]);
}
}
}
return result;
}
///获取顺序主子式的矩阵, k为阶数
function GetOrderMatrix(a, k)
{
var n = a.length;//矩阵的总数据数目
var s = Math.sqrt(n);//矩阵的阶数
var result = [];
for (var i = 0; i < s; i++)
{
for (var j = 0; j < s; j++)
{
if (i <= k && j <= k)
{
result.push(a[i*s +j]);
}
}
}
return result;
}