Solve Method (Double[,], Double[], Boolean)

Matrix Solve Method ( Double , Double , Boolean)

Accord.NET Framework

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Returns the solution matrix if the matrix is square or the least squares solution otherwise.

Namespace: Accord.Math
Assembly: Accord.Math (in Accord.Math.dll) Version: 2.9.0.0 (2.9.0.0)

Syntax

C++

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public static double[] Solve(
	this double[,] matrix,
	double[] rightSide,
	bool leastSquares = false
)

public static double[] Solve(
	this double[,] matrix,
	double[] rightSide,
	bool leastSquares = false
)

Parameters

matrix: Type: System Double
The matrix for the linear problem.

rightSide: Type: System Double
The right side b.

leastSquares (Optional): Type: System Boolean
True to produce a solution even if the matrix is singular; false otherwise. Default is false.

Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type . When you use instance method syntax to call this method, omit the first parameter. For more information, see Online

Extension Methods (Visual Basic) or Online

Extension Methods (C# Programming Guide).

Remarks

Please note that this does not check if the matrix is non-singular before attempting to solve. If a least squares solution is desired in case the matrix is singular, pass true to the leastSquares parameter when calling this function.

Examples

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// Create a matrix. Please note that this matrix 
// is singular (i.e. not invertible), so only a  
// least squares solution would be feasible here. 

double[,] matrix = 
{
    { 1, 2, 3 },
    { 4, 5, 6 },
    { 7, 8, 9 },
};

// Define a right side vector b: 
double[] rightSide = { 1, 2, 3 };

// Solve the linear system Ax = b by finding x: 
double[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);

// The answer should be { -1/18, 2/18, 5/18 }.

// Create a matrix. Please note that this matrix 
// is singular (i.e. not invertible), so only a  
// least squares solution would be feasible here. 

double[,] matrix = 
{
    { 1, 2, 3 },
    { 4, 5, 6 },
    { 7, 8, 9 },
};

// Define a right side vector b: 
double[] rightSide = { 1, 2, 3 };

// Solve the linear system Ax = b by finding x: 
double[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);

// The answer should be { -1/18, 2/18, 5/18 }.