Math.net之矩阵运算

矩阵相乘

var A = new DenseMatrix(3, 5, 2.0);
var B = new DenseMatrix(5, 4, 3);
var y = A * B;
//或
var y = A.Multiply(B) ;
Console.WriteLine("A:\n{0}\nB:\n{1}\ny:\n{2}",A,B,y);

A:

2,2,2,2,2

2,2,2,2,2

2,2,2,2,2

B:

3,3,3,3

3,3,3,3

3,3,3,3

3,3,3,3

3,3,3,3

y:

30,30,30,30

30,30,30,30

30,30,30,30

矩阵相减

var A = new DenseMatrix(3, 3, 2.0);
var B = new DenseMatrix(3, 3, 1.2);
var C = A.Subtract(B);

矩阵相加

var A = new DenseMatrix(3, 3, 2.0);
var B = new DenseMatrix(3, 3, 1.2);
var C = A.Add(B);

矩阵转置

var A = new DenseMatrix(new double[,] {{1,2,3,4},{5,6,7,8},{
9,10,11,12},{13,14,15,16}});
var B = A.Transpose();

矩阵求逆

var A = new DenseMatrix(new double[,]
{
{1,1,2},
{-1,2,0},
{1,1,3}
});
var B = A.Inverse();

A:

1,1,2

-1,2,0

1,1,3

B:

2,-0.3,-1.33

1,0.33,-0.67

-1,0,1

矩阵行列式的值

var A = new DenseMatrix(new double[,]
{
{1,1,2},
{-1,2,0},
{1,1,3}
});
var B = A.Determinant();

矩阵的秩

var A = new DenseMatrix(new double[,] {{1,2,3,4},{5,6,7,8},{
9,10,11,12},{13,14,15,16}});
var B =A.Rank();

矩阵左乘向量：y=b*A

var A = new DenseMatrix(3, 5, 2.0);

var b = new DenseVector(3, 3);
var y = A.LeftMultiply(b);
Console.WriteLine("A:\n{0}\nB:\n{1}\ny:\n{2}",A,b,y);

A:

2,2,2,2,2

2,2,2,2,2

2,2,2,2,2

B:

3,3,3

y:

18,18,18,18,18

矩阵分解

LU分解

var A = new DenseMatrix(3, 3, 2.0);
var l=A.LU().L;
var u = A.LU().U;
Console.WriteLine("A:\n{0}\nl:\n{1}\nu:\n{2}",A,l,u);

A:

2,2,2

2,2,2

2,2,2

l:

1,0,0

1,1,0

1,0,1

u:

2,2,2

0,0,0

0,0,0

类似的还有Cholesky分解，Evd分解，GramSchmidt分解，QR分解，Svd分解。