Class Matrix

A matrix is represented by a nested list of double point numbers.
So, you would write simply [[1,0],[0,1]] to create a 2x2 identity matrix.

Inheritance

System.Object

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>

Matrix

Inherited Members

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.get_Item(System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.set_Item(System.Int32, System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Add(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.AddRange(System.Collections.Generic.IEnumerable<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.AsReadOnly()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.BinarySearch(System.Int32, System.Int32, System.Collections.Generic.List<System.Double>, System.Collections.Generic.IComparer<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.BinarySearch(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.BinarySearch(System.Collections.Generic.List<System.Double>, System.Collections.Generic.IComparer<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Clear()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Contains(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.ConvertAll<TOutput>(System.Converter<System.Collections.Generic.List<System.Double>, TOutput>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.CopyTo(System.Int32, System.Collections.Generic.List<System.Double>[], System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.CopyTo(System.Collections.Generic.List<System.Double>[])

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.CopyTo(System.Collections.Generic.List<System.Double>[], System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Exists(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Find(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindAll(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindIndex(System.Int32, System.Int32, System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindIndex(System.Int32, System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindIndex(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindLast(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindLastIndex(System.Int32, System.Int32, System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindLastIndex(System.Int32, System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.FindLastIndex(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.ForEach(System.Action<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.GetEnumerator()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.GetRange(System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.IndexOf(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.IndexOf(System.Collections.Generic.List<System.Double>, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.IndexOf(System.Collections.Generic.List<System.Double>, System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Insert(System.Int32, System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.InsertRange(System.Int32, System.Collections.Generic.IEnumerable<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.LastIndexOf(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.LastIndexOf(System.Collections.Generic.List<System.Double>, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.LastIndexOf(System.Collections.Generic.List<System.Double>, System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Remove(System.Collections.Generic.List<System.Double>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.RemoveAll(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.RemoveAt(System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.RemoveRange(System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Reverse()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Reverse(System.Int32, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Sort()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Sort(System.Collections.Generic.IComparer<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Sort(System.Comparison<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Sort(System.Int32, System.Int32, System.Collections.Generic.IComparer<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.Generic.IEnumerable<System.Collections.Generic.List<System.Double>>.GetEnumerator()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.ICollection.CopyTo(System.Array, System.Int32)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IEnumerable.GetEnumerator()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.Add(System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.Contains(System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.IndexOf(System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.Insert(System.Int32, System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.Remove(System.Object)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.ToArray()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.TrimExcess()

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.TrueForAll(System.Predicate<System.Collections.Generic.List<System.Double>>)

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Capacity

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Count

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.Item[System.Int32]

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.Generic.ICollection<System.Collections.Generic.List<System.Double>>.IsReadOnly

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.ICollection.IsSynchronized

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.ICollection.SyncRoot

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.IsFixedSize

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.IsReadOnly

System.Collections.Generic.List<System.Collections.Generic.List<System.Double>>.System.Collections.IList.Item[System.Int32]

System.Object.Equals(System.Object)

System.Object.Equals(System.Object, System.Object)

System.Object.GetHashCode()

System.Object.GetType()

System.Object.MemberwiseClone()

System.Object.ReferenceEquals(System.Object, System.Object)

Syntax

public class Matrix : List<List<double>>, IList<List<double>>, ICollection<List<double>>, IReadOnlyList<List<double>>, IReadOnlyCollection<List<double>>, IEnumerable<List<double>>, IList, ICollection, IEnumerable

Constructors

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Matrix()

Initializes an empty matrix.

Declaration

public Matrix()

Methods

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Construct(Int32, Int32)

Constructs a matrix by given number of rows and columns.
All the parameters are set to zero.

Declaration

public static Matrix Construct(int rows, int columns)

Parameters

Type	Name	Description
System.Int32	rows	A positive integer, for the number of rows.
System.Int32	columns	A positive integer, for the number of columns.

Returns

Type	Description
Matrix	A matrix reflecting the number of rows and columns provided.

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Decompose(Matrix, out Int32[])

This routine uses Doolittle's method with partial pivoting to decompose the n x n matrix A,
into a unit lower triangular matrix L and an upper triangular matrix U and P is a permutation array
such that PA = LU. With this method you can always have a LU decomposition, rather than LU factorization.
The LU decomposition with pivoting always exists, even if the matrix is singular, so the constructor will never fail.
The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations.
The LUP decomposition provides a more robust method of solving linear systems than LU decomposition without pivoting, and it is approximately the same cost.
This will fail if non singular.

Declaration

public static Matrix Decompose(Matrix m, out int[] permutation)

Parameters

Type	Name	Description
Matrix	m	Matrix has to be decomposed.
System.Int32[]	permutation	The row pivot information is in one-dimensional array.

Returns

Type	Description
Matrix	The matrix representing the lower matrix and upper matrix together.

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Duplicate(Matrix)

Creates a copy.

Declaration

public static Matrix Duplicate(Matrix matrix)

Parameters

Type	Name	Description
Matrix	matrix	Matrix has to be duplicated.

Returns

Type	Description
Matrix	Copied matrix.

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FillDiagonal(Int32, Int32, Double)

Fills the diagonal determined by the row and column position of a matrix.

Declaration

public Matrix FillDiagonal(int row, int column, double valueToFill)

Parameters

Type	Name	Description
System.Int32	row	The value row where the diagonal begin.
System.Int32	column	The column value where the diagonal begin.
System.Double	valueToFill	The value to fill on the diagonal.

Returns

Type	Description
Matrix	A matrix with the identified diagonal filled.

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Identity(Int32, Double)

Creates an identity matrix of a given size.

Declaration

public static Matrix Identity(int size, double diagonalValue = 1)

Parameters

Type	Name	Description
System.Int32	size	The size of the matrix.
System.Double	diagonalValue	The value which will be filled the diagonal.

Returns

Type	Description
Matrix	Identity matrix of the given size.

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Inverse(Matrix)

Computes the inverse of a Matrix.

Declaration

public static Matrix Inverse(Matrix matrix)

Parameters

Type	Name	Description
Matrix	matrix	The matrix to invert.

Returns

Type	Description
Matrix	The inverted matrix.

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IsValid()

Gets a value indicating whether this matrix is valid.
Matrix is valid when has at least one column and one row and rows have at least 2 elements.

Declaration

public bool IsValid()

Returns

Type	Description
System.Boolean	True if it is a valid matrix.

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Solve(Matrix, Int32[], Vector)

This routine uses Doolittle's method to solve the linear equation Ax = B.
This routine is called after the matrix A has been decomposed.
The solution proceeds by solving the linear equation Ly = B for y and,
subsequently solving the linear equation Ux = y for x.

Declaration

public static Vector Solve(Matrix LuMatrix, int[] permutation, Vector b)

Parameters

Type	Name	Description
Matrix	LuMatrix	Decomposed matrix in lower and upper triangle.
System.Int32[]	permutation	The permutation row, or pivot row interchanged with row i.
Vector	b	Column vector.

Returns

Type	Description
Vector	The solution of the equation Ax = B is a vector.

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ToString()

Constructs the string representation the matrix.

Declaration

public override string ToString()

Returns

Type	Description
System.String	Text string.

Overrides

System.Object.ToString()

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Transpose()

Transposes a matrix.
This is like swapping rows with columns.

Declaration

public Matrix Transpose()

Returns

Type	Description
Matrix	The matrix transposed.

Operators

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Addition(Matrix, Matrix)

Adds two matrices.

Declaration

public static Matrix operator +(Matrix a, Matrix b)

Parameters

Type	Name	Description
Matrix	a	First matrix.
Matrix	b	Second matrix.

Returns

Type	Description
Matrix	The result sum matrix.

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Division(Matrix, Double)

Divides a matrix by a constant.

Declaration

public static Matrix operator /(Matrix m, double a)

Parameters

Type	Name	Description
Matrix	m	Matrix has to be multiply.
System.Double	a	Value to operate the division.

Returns

Type	Description
Matrix	Matrix divided by a constant.

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Multiply(Matrix, Matrix)

Multiplies two matrices assuming they are of compatible dimensions.

Declaration

public static Matrix operator *(Matrix a, Matrix b)

Parameters

Type	Name	Description
Matrix	a	First matrix.
Matrix	b	Second matrix.

Returns

Type	Description
Matrix	The product matrix.

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Multiply(Matrix, Double)

Multiplies a matrix by a constant.

Declaration

public static Matrix operator *(Matrix m, double a)

Parameters

Type	Name	Description
Matrix	m	Matrix has to be multiply.
System.Double	a	Value to operate the multiplication.

Returns

Type	Description
Matrix	Matrix multiply by a constant.

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Subtraction(Matrix, Matrix)

Subtracts two matrices.

Declaration

public static Matrix operator -(Matrix a, Matrix b)

Parameters

Type	Name	Description
Matrix	a	First matrix.
Matrix	b	Second matrix.

Returns

Type	Description
Matrix	The subtraction matrix.

Implements

System.Collections.Generic.IList<T>

System.Collections.Generic.ICollection<T>

System.Collections.Generic.IReadOnlyList<T>

System.Collections.Generic.IReadOnlyCollection<T>

System.Collections.Generic.IEnumerable<T>

System.Collections.IList

System.Collections.ICollection

System.Collections.IEnumerable

Extension Methods

ExtendedEnumerable.Unique<T>(IEnumerable<T>, Func<T, T, Boolean>)