Linear Equations in Visual Basic QuickStart Sample
Illustrates how to solve systems of simultaneous linear equations in Visual Basic.
View this sample in: C# F# IronPython
Option Infer On
' The DenseMatrix and LUDecomposition classes reside in the
' Extreme.Mathematics.LinearAlgebra namespace.
Imports Extreme.Mathematics
Imports Extreme.Mathematics.LinearAlgebra
' Illustrates solving systems of simultaneous linear
' equations using the DenseMatrix and LUDecomposition classes
' in the Extreme.Mathematics.LinearAlgebra namespace of Extreme Numerics.NET.
Module LinearEquations
Sub Main()
' The license is verified at runtime. We're using
' a demo license here. For more information, see
' https://numerics.net/trial-key
Extreme.License.Verify("Demo license")
' A system of simultaneous linear equations is
' defined by a square matrix A and a right-hand
' side B, which can be a vector or a matrix.
'
' You can use any matrix type for the matrix A.
' The optimal algorithm is automatically selected.
' Let's start with a general matrix:
Dim m = Matrix.Create(4, 4, New Double() _
{1, 1, 1, 1,
1, 2, 3, 4,
1, 4, 9, 16,
1, 2, 1, 2}, MatrixElementOrder.ColumnMajor)
Dim b1 = Vector.Create(New Double() {1, 3, 6, 3})
Dim b2 = Matrix.Create(4, 2, New Double() _
{1, 3, 6, 3,
2, 3, 5, 8}, MatrixElementOrder.ColumnMajor)
Console.WriteLine("m = {0:F4}", m)
'
' The Solve method
'
' The following solves m x = b1. The second
' parameter specifies whether to overwrite the
' right-hand side with the result.
Dim x1 = m.Solve(b1, False)
Console.WriteLine("x1 = {0:F4}", x1)
' If the overwrite parameter is omitted, the
' right-hand-side is overwritten with the solution:
m.Solve(b1)
Console.WriteLine("b1 = {0:F4}", b1)
' You can solve for multiple right hand side
' vectors by passing them in a DenseMatrix:
Dim x2 = m.Solve(b2, False)
Console.WriteLine("x2 = {0:F4}", x2)
'
' Related Methods
'
' You can verify whether a matrix is singular
' using the IsSingular method:
Console.WriteLine("IsSingular(m) = {0:F4}",
m.IsSingular())
' The inverse matrix is returned by the GetInverse
' method:
Console.WriteLine("GetInverse(m) = {0:F4}", m.GetInverse())
' The determinant is also available:
Console.WriteLine("Det(m) = {0:F4}", m.GetDeterminant())
' The condition number is an estimate for the
' loss of precision in solving the equations
Console.WriteLine("Cond(m) = {0:F4}", m.EstimateConditionNumber())
Console.WriteLine()
'
' The LUDecomposition class
'
' If multiple operations need to be performed
' on the same matrix, it is more efficient to use
' the LUDecomposition class. This class does the
' bulk of the calculations only once.
Console.WriteLine("Using LU Decomposition:")
' The constructor takes an optional second argument
' indicating whether to overwrite the original
' matrix with its decomposition:
Dim lu = m.GetLUDecomposition(False)
' All methods mentioned earlier are still available:
x2 = lu.Solve(b2, False)
Console.WriteLine("x2 = {0:F4}", x2)
Console.WriteLine("IsSingular(m) = {0:F4}",
lu.IsSingular())
Console.WriteLine("GetInverse(m) = {0:F4}", lu.GetInverse())
Console.WriteLine("Det(m) = {0:F4}", lu.GetDeterminant())
Console.WriteLine("Cond(m) = {0:F4}", lu.EstimateConditionNumber())
' In addition, you have access to the
' components, L and U of the decomposition.
' L is lower unit-triangular:
Console.WriteLine(" L = {0:F4}", lu.LowerTriangularFactor)
' U is upper triangular:
Console.WriteLine(" U = {0:F4}", lu.UpperTriangularFactor)
Console.Write("Press Enter key to exit...")
Console.ReadLine()
End Sub
End Module