DApp基于区块链的底层开发平台，18I链上合约-259l开发系统3365能够理解为App的升级版。用白话说明一下:DAPP和底层链（Ethereum、EOS、星云链等）的瓜葛，就像App和iOS以及安卓系统之间的差别同样。以是现阶段不少做法都是复制现有的APP，扔在区块链，加之一顶“去中心化”的帽子，成为Dapp。
using System;
namespace NumNet { ///
#region 公有属性
/// <summary>
/// 矩阵行数
/// </summary>
public int RowCount => _data.GetLength(0);
/// <summary>
/// 矩阵列数
/// </summary>
public int ColumnCount => _data.GetLength(1);
#endregion
#region 构造方法
/// <summary>
/// 构造一个空矩阵
/// </summary>
public Matrix()
{
_data = new double[0, 0];
}
/// <summary>
/// 构造rowCount行的方阵，默认元素均为0；
/// fillOne为true时，元素均为1
/// </summary>
/// <param name="rowCount"></param>
/// <param name="fillOne"></param>
public Matrix(int rowCount, bool fillOne = false)
: this(rowCount, rowCount, fillOne)
{
}
/// <summary>
/// 构造rowCount行、colCount列的矩阵，默认元素均为0；
/// fillOne为true时，元素均为1
/// </summary>
/// <param name="rowCount"></param>
/// <param name="colCount"></param>
/// <param name="fillOne"></param>
public Matrix(int rowCount, int colCount, bool fillOne = false)
{
_data = new double[rowCount, colCount];
if (fillOne)
{
for (int i = 0; i < rowCount; i++)
{
for (int j = 0; j < colCount; j++)
{
_data[i, j] = 1;
}
}
}
}
/// <summary>
/// 根据二维数组构造矩阵
/// </summary>
/// <param name="data"></param>
public Matrix(double[,] data)
{
_data = new double[data.GetLength(0), data.GetLength(1)];
Array.Copy(data, _data, data.Length);
}
/// <summary>
/// 根据一系列行向量构造新矩阵，这些向量具有相同的长度；
/// 若要作为列向量构造，请对得到的矩阵进行转置
/// </summary>
/// <param name="rows"></param>
/// <exception cref="Exception"></exception>
public Matrix(params Vector[] rows)
{
int rowCount = rows.Length;
if (rowCount == 0)
{
_data = new double[0, 0];
return;
}
int colCount = rows[0].Length;
for (int i = 1; i < rowCount; i++)
{
if (rows[i].Length != colCount)
throw new Exception("各行向量的长度不同，无法组成矩阵！");
}
_data = new double[rowCount, colCount];
for (int i = 0; i < rowCount; i++)
{
rows[i].CopyTo(_data, i * colCount);
}
}
#endregion
#region 公共方法
/// <summary>
/// 返回size行size列的单位矩阵
/// </summary>
/// <param name="size"></param>
/// <returns></returns>
public static Matrix Identity(int size)
{
Matrix m = new Matrix(size, size);
for (int i = 0; i < size; i++)
{
m[i, i] = 1;
}
return m;
}
/// <summary>
/// 返回size行size列的Hilbert矩阵
/// </summary>
/// <param name="size"></param>
/// <returns></returns>
public static Matrix Hilbert(int size)
{
Matrix m = new Matrix(size);
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
m[i, j] = 1.0 / (i + j + 1);
}
}
return m;
}
/// <summary>
/// 根据对角线元素构造对角方阵
/// </summary>
/// <param name="diag"></param>
/// <returns></returns>
public static Matrix Diagonal(Vector diag)
{
Matrix m = new Matrix(diag.Length, diag.Length);
for (int i = 0; i < diag.Length; i++)
{
m[i, i] = diag[i];
}
return m;
}
/// <summary>
/// 获取矩阵中第rowDex行，第colDex列的元素
/// </summary>
/// <param name="rowDex"></param>
/// <param name="colDex"></param>
/// <returns></returns>
public double this[int rowDex, int colDex]
{
get => _data[rowDex, colDex];
set => _data[rowDex, colDex] = value;
}
/// <summary>
/// 获取矩阵中的第rowDex行，作为向量返回；
/// 对向量元素的修改不会反映到矩阵中
/// </summary>
/// <param name="rowDex"></param>
/// <returns></returns>
public Vector GetRow(int rowDex)
{
double[] data = new double[ColumnCount];
Buffer.BlockCopy(_data, rowDex * ColumnCount * sizeof(double),
data, 0, ColumnCount * sizeof(double));
return new Vector(data);
}
/// <summary>
/// 设置矩阵的第rowDex行，其中row的长度与矩阵列数相同
/// </summary>
/// <param name="rowDex"></param>
/// <param name="row"></param>
/// <exception cref="Exception"></exception>
public void SetRow(int rowDex, Vector row)
{
if (row.Length != ColumnCount)
throw new Exception("行向量长度与矩阵列数不同，不能设置！");
row.CopyTo(_data, rowDex * ColumnCount);
}
/// <summary>
/// 获取矩阵中的第colDex列，作为向量返回；
/// 对向量元素的修改不会反映到矩阵中
/// </summary>
/// <param name="colDex"></param>
/// <returns></returns>
public Vector GetColumn(int colDex)
{
Vector v = new Vector(RowCount);
for (int i = 0; i < RowCount; i++)
{
v[i] = this[i, colDex];
}
return v;
}
/// <summary>
/// 设置矩阵的第colDex列，其中col的长度与矩阵行数相同
/// </summary>
/// <param name="colDex"></param>
/// <param name="col"></param>
/// <exception cref="Exception"></exception>
public void SetColumn(int colDex, Vector col)
{
if (col.Length != RowCount)
throw new Exception("列向量长度与矩阵行数不同，不能设置！");
for (int i = 0; i < RowCount; i++)
{
this[i, colDex] = col[i];
}
}
/// <summary>
/// 获取矩阵对角线元素组成的向量；
/// 返回向量的长度为行数与列数的较小值
/// </summary>
/// <returns></returns>
public Vector GetDiagonal()
{
Vector v = new Vector(Math.Min(RowCount, ColumnCount));
for (int i = 0; i < v.Length; i++)
{
v[i] = this[i, i];
}
return v;
}
/// <summary>
/// 正号，返回m1的拷贝
/// </summary>
/// <param name="m1"></param>
/// <returns></returns>
public static Matrix operator +(Matrix m1)
{
return m1.Copy();
}
/// <summary>
/// 负号，返回m1的相反矩阵
/// </summary>
/// <param name="m1"></param>
/// <returns></returns>
public static Matrix operator -(Matrix m1)
{
Matrix m = new Matrix(m1.RowCount, m1.ColumnCount);
for (int i = 0; i < m1.RowCount; i++)
{
for (int j = 0; j < m1.ColumnCount; j++)
{
m[i, j] = -m1[i, j];
}
}
return m;
}
/// <summary>
/// 矩阵加法
/// </summary>
/// <param name="m1"></param>
/// <param name="m2"></param>
/// <returns></returns>
/// <exception cref="Exception"></exception>
public static Matrix operator +(Matrix m1, Matrix m2)
{
if (m1.RowCount != m2.RowCount || m1.ColumnCount != m2.ColumnCount)
throw new Exception("两矩阵形状不同，不能相加！");
Matrix m = new Matrix(m1.RowCount, m1.ColumnCount);
for (int i = 0; i < m1.RowCount; i++)
{
for (int j = 0; j < m1.ColumnCount; j++)
{
m[i, j] = m1[i, j] + m2[i, j];
}
}
return m;
}
/// <summary>
/// 矩阵减法
/// </summary>
/// <param name="m1"></param>
/// <param name="m2"></param>
/// <returns></returns>
/// <exception cref="Exception"></exception>
public static Matrix operator -(Matrix m1, Matrix m2)
{
if (m1.RowCount != m2.RowCount || m1.ColumnCount != m2.ColumnCount)
throw new Exception("两矩阵形状不同，不能相减！");
Matrix m = new Matrix(m1.RowCount, m1.ColumnCount);
for (int i = 0; i < m1.RowCount; i++)
{
for (int j = 0; j < m1.ColumnCount; j++)
{
m[i, j] = m1[i, j] - m2[i, j];
}
}
return m;
}
/// <summary>
/// 矩阵乘法
/// </summary>
/// <param name="m1"></param>
/// <param name="m2"></param>
/// <returns></returns>
/// <exception cref="Exception"></exception>
public static Matrix operator *(Matrix m1, Matrix m2)
{
if (m1.ColumnCount != m2.RowCount)
throw new Exception("左矩阵列数与右矩阵行数不同，不能相乘！");
Matrix m = new Matrix(m1.RowCount, m2.ColumnCount);
for (int i = 0; i < m.RowCount; i++)
{
for (int j = 0; j < m.ColumnCount; j++)
{
for (int k = 0; k < m1.ColumnCount; k++)
{
m[i, j] += m1[i, k] * m2[k, j];
}
}
}
return m;
}
