C # basic matrix Math Library tutorial,

C # basic matrix Math Library tutorial,

First, start SimpleMatrix. cs and define the total number of rows, total number of columns, and all data (double type)

using System;using System.IO;namespace NeuralDefs.Matrix{    public class SimpleMatrix : IMatrix    {        public int Row { get; set; }        public int Column { get; set; }        public double[,] Data { get; set; }

The IMatrix matrix is used for organization, because I also wrote a sparse matrix. This interface can be written again when introducing the sparse matrix.

1. First, implement the basic functions of a simple matrix-assignment and Output

I often use csv files to store and view matrices in a natural way.

public SimpleMatrix(int row, int col)        {            // init matrix            Row = row;            Column = col;            Data = new double[row, col];            for (var i = 0; i < row; i++)            {                for (var j = 0; j < col; j++)                {                    Data[i, j] = 0;                }            }        }        public SimpleMatrix(string fileName)        {            //var splitUnit = '\t';            var splitUnit = ',';            // count columns            var srCol = new StreamReader(fileName);            var firstLine = srCol.ReadLine();            if (firstLine != null)            {                var firstArray = firstLine.Split(splitUnit);                Column = firstArray.Length;            }            srCol.Close();            // count rows            Row = 0;            var srRow = new StreamReader(fileName);            while (srRow.ReadLine() != null)            {                Row++;            }            srRow.Close();            // init matrix            Data = new double[Row, Column];            // fill matrix            var srData = new StreamReader(fileName);            var curRow = 0;            string line;            while ((line = srData.ReadLine()) != null)            {                var lineArray = line.Split(splitUnit);                for (var i = 0; i < lineArray.Length; i++)                {                    Data[curRow, i] = double.Parse(lineArray[i]);                }                curRow++;            }            srData.Close();        }        public void WriteTo(string path)        {            var fs = new FileStream(path, FileMode.Create);            var sw = new StreamWriter(fs);            for (var i = 0; i < Row; i++)            {                sw.WriteLine(this.RowVector(i).ToSingleLineRow());            }            sw.Close();            fs.Close();        }

2. Use the index tool to retrieve the subscript

public double this[int row, int column]        {            get { return Data[row, column]; }            set { Data[row, column] = value; }        }

3. randomization (used for Neural Network Initial Value assignment and other purposes)

public void Randomize()        {            var rm = new Random();            for (var i = 0; i < Row; i++)            {                for (var j = 0; j < Column; j++)                {                    Data[i, j] = rm.Next(-100, 100) / 1000.0;                }            }        }

4. Fetch a row

public SimpleMatrix RowVector(int row)        {            var result = new SimpleMatrix(1, Column);            for (var i = 0; i < Column; i++)            {                result[0, i] = Data[row, i];            }            return result;        }

5. Subtraction

public static SimpleMatrix operator -(SimpleMatrix a, SimpleMatrix b)        {            var minus = new SimpleMatrix(a.Row, a.Column);            for (var i = 0; i < minus.Row; i++)            {                for (var j = 0; j < minus.Column; j++)                {                    minus[i, j] = a[i, j] - b[i, j];                }            }            return minus;        }

6. Norm

public static double Norm2(SimpleMatrix a)        {            var norm = 0.0;            for (var i = 0; i < a.Row; i++)            {                for (var j = 0; j < a.Column; j++)                {                    norm += a[i, j] * a[i, j];                }            }            return Math.Sqrt(norm);        }

7. connect two vectors

public static SimpleMatrix Link(SimpleMatrix vector1, SimpleMatrix vector2)        {            // check is vector            if (vector1.Column != 1 || vector2.Column != 1)                return null;            var newRow = vector1.Row + vector2.Row;            var result = new SimpleMatrix(newRow, 1);            for (var i = 0; i < vector1.Row; i++)            {                result[i, 0] = vector1[i, 0];            }            for (var i = 0; i < vector2.Row; i++)            {                result[vector1.Row + i, 0] = vector2[i, 0];            }            return result;        }

8. Single Element Matrix

 public static SimpleMatrix SingleValueMatrix(double val)        {            return new SimpleMatrix(1, 1) { Data = { [0, 0] = val } };        }

9. Maximum absolute value

public static double MaxAbsMember(SimpleMatrix a)        {            var max = -1.0;            foreach (var d in a.Data)            {                if (Math.Abs(d) > max)                    max = Math.Abs(d);            }            return max;        }

10. Matrix transpose

public static SimpleMatrix Transpose(SimpleMatrix a)        {            var result = new SimpleMatrix(a.Column, a.Row);            for (var i = 0; i < result.Row; i++)            {                for (var j = 0; j < result.Column; j++)                {                    result[i, j] = a[j, i];                }            }            return result;        }