SimplySoft.Matrix 1.0.0

Matrix-Library

Matrix-Library is .NET 5.0 based reusable library designed perform manipulate matrix properties and common matrix operations. Any .NET 5.0 or above application can utilize the functionalities of Matrix-Library by referring it in the project dependencies.

Prerequisites

Matrix-Library requires .NET 5.0 (v5.#.#) or .NET 6.0 (v6.#.#).

Get Started

Add MatrixLibrary.dll to project dependencies.
Refer the content from the code by adding using MatrixLibrary; at the top.

Implementation Overview

Following tables indicate the implementation structure of MatrixLibray.

Properties

Constructors

Methods

Operators

Usage

Following section describe the general usage of MatrixLibrary to perform matrix operations.

Initialize New Matrix

Define order of 3x3 matrix m

Matrix m = new(3, 3);

After defined a matrix, there are two ways to set element to the matrix.
To set elements to the above matrix m, pass the value set as a double[] array. Here in the value set array, the element count must match matrix order. Therefore, the element array must contain 9 elements to match with 3x3 order. Otherwise the function throws MatrixDimesionNotMatchException.

m.SetMatrix(new double[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 });

The value set can be passed as a multi-dimensional array double[,] as well. Here also the element count must match with matrix order.

m.SetMatrix(new double[3, 3] {
  { 1, 2, 3 },
  { 4, 5, 6 },
  { 7, 8, 9 }
});

Set and Get Values

Matrix elements can be changed at a specific location of the matrix even after it is defined. Set or change value at i = 2, and j = 3 with new value -10.

m.SetValueAt(2, 3, -10);

Get the value at i = 1 and j = 3.

double value = m.GetValueAt(1, 3);

To get all values as a multi-dimensional array, the matrix can be converted to an array double[,].

double[,] values = m.ToArray();

All elements of the matrix can be returned as a string formatted with matrix tubular format.

string matrix = m.Print()

In here, the decimal precision, left-padding offset and padding character can be applied when returning it using Print function. These settings are optional. Print the matrix with 5 decimal precision, 8 left-padding offset, * padding character.

string matrix = m.Print(precision: 5, paddingLeft: 8, paddingChar: '*');

Matrix Transpose

Transpose of a matrix will flip the values over its diagonal from rows to columns.

Matrix transposedMatrix = m.Transpose();

Matrix Determinant

The determinant of the matrix can be computed with Determinant function. To perform this operation, the matrix must be a square matrix, otherwise the function throws InvalidOperationException. The IsSquare function can be used to verify whether the matrix order square or not.

double value = m.Determinant();

Minors and Cofactors

The minor and cofactor values of a specific element in the matrix can be read by providing the location indexes of the element using GetMinorAt and GetCoFactorAt functions. To perform these operations, the matrix must be a square matrix, otherwise the function throws InvalidOperationException. If the indexes are out of reach from matrix dimension, the function throws IndexOutOfRangeException.
To get minor value and cofactor value of the element located at i = 2 and j = 3 in matrix m.

double minorValue = m.GetMinorAt(2, 3);
double cofactorValue = m.GetCoFactorAt(2, 3);

The entire minor matrix and cofactor matrix for any square matrix can also be constructed.

Matrix minorMatrix = m.MinorMatrix();
Matrix cofactorMatrix = m.CoFactorMatrix();

Adjoint (Adjugate) and Inverse

The adjoint and inverse matrix can be constructed for a square matrix. To perform these operations, the matrix must be a square matrix, otherwise the function throws InvalidOperationException. In InverseMatrix function, if the determinant is 0, the function throws MatrixNotInvertibleException.

Matrix adjointMatrix = m.AdjointMatrix();
Matrix inverseMatrix = m.InverseMatrix();

Identity

For any square matrix can construct its identity matrix. To perform this operation, the matrix must be a square matrix, otherwise the function throws InvalidOperationException. The resultant matrix will have the same dimension as the original matrix.

Matrix identity = m.IdentityMatrix();

Matrix Operations

Matrix object can perform following binary operations.

Addition

Add two same-dimensional matrices a and b. The function throws MatrixNotInitializedException if matrix a or b is null and throws InvalidMatrixOrderException if the order of both matrices do not match.

Matrix a = new(2, 2);
Matrix b = new(2, 2);
a.SetMatrix(new double[] { 1, 2, 3, 4 });
b.SetMatrix(new double[] { 5, 6, 7, 8 });

Matrix result = a + b;

Subtraction

Subtract two same-dimensional matrices a and b. The function throws MatrixNotInitializedException if matrix a or b is null and throws InvalidMatrixOrderException if the order of both matrices do not match.

Matrix a = new(2, 2);
Matrix b = new(2, 2);
a.SetMatrix(new double[] { 1, 2, 3, 4 });
b.SetMatrix(new double[] { 5, 6, 7, 8 });

Matrix result = a - b;

Multiply by Scalar

Multiply matrix m by scalar value. The function throws MatrixNotInitializedException if matrix m is null.

Matrix m = new(2, 2);
double k = 3;
m.SetMatrix(new double[] { 1, 2, 3, 4 });

Matrix result = k * m;

Multiply by Matrix

Multiply matrix a with matrix b. The function throws MatrixNotInitializedException if matrix a or b is null and throws InvalidMatrixOrderException if the order of both matrices do not match for the multiplication. The number of columns of first operand a must be same for the number of rows in operand b in order to perform matrix multiplication.

Matrix a = new(2, 2);
Matrix b = new(2, 2);
a.SetMatrix(new double[] { 1, 2, 3, 4 });
b.SetMatrix(new double[] { 5, 6, 7, 8 });

Matrix result = a * b;

Matrix Comparison

If the number of rows, columns and the elements are same for another matrix, then the matrix are equals to each other.

Matrix m = new(2, 2);
m.SetMatrix(new double[] { 1, 2, 3, 4 });
Matrix i = m.IdentityMatrix(); // Construct identity matrix of m
Matrix v = m.InverseMatrix(); // Construct inverse matrix of m

// Verifying whether the product of matrix and its inverse is equals to identity
Console.WriteLine((m * v) == i); // This results as True because this is the law of matrix invertibility

// Verifying matrix m is not equals to its identity
Console.WriteLine(m != i); // This results as True