# Band Matrices in C# QuickStart Sample

Illustrates how to work with the BandMatrix class in C#.

View this sample in: Visual Basic F# IronPython

``````using System;

using Numerics.NET;
// The BandMatrix class resides in the Numerics.NET.LinearAlgebra
// namespace.
using Numerics.NET.LinearAlgebra;

namespace Numerics.NET.QuickStart.CSharp
{
/// <summary>
/// Illustrates the use of the BandMatrix class in the
/// Numerics.NET.LinearAlgebra namespace of Numerics.NET.
/// </summary>
class BandMatrices
{
static void Main(string[] args)
{
// The license is verified at runtime. We're using
// a 30 day trial key here. For more information, see
//     https://numerics.net/trial-key

// Band matrices are matrices whose elements
// are nonzero only in a diagonal band around
// the main diagonal.
//
// General band matrices, upper and lower band
// matrices, and symmetric band matrices are all
// represented by a single class: BandMatrix.

//
// Constructing band matrices
//

// Constructing band matrices is similar to
// constructing general matrices. It is done by
// calling a factory method on the Matrix class.
// See theBasicMatrices QuickStart samples
// for a more complete discussion.

// The following creates a 7x5 band matrix with
// upper bandwidth 1 and lower bandwidth 2:
var b1 = Matrix.CreateBanded<double>(7, 5, 2, 1);

// Once the upper and lower bandwidth are set,
// it cannot be changed. Elements that are outside
// the band cannot be set.

// A second factory method lets you create upper
// or lower band matrices. The following constructs
// an 11x11 upper band matrix with unit diagonal
// and three non-zero upper diagonals.
var b2 = Matrix.CreateUpperBanded<double>(11, 11, 3, MatrixDiagonal.UnitDiagonal);

// To create a symmetric band matrix, you only need
// the size and the bandwith. The following creates
// a 6x6 symmetric tri-diagonal matrix:
var b3 = Matrix.CreateSymmetricBanded<double>(7, 1);

// We can assign values to the components by using
// the GetDiagonal method.
b3.GetDiagonal(0).SetValue(2);
b3.GetDiagonal(1).SetValue(-1);

// Extracting band matrices

// Another way to construct a band matrix is by
// extracting them from an existing matrix.
var m = Matrix.CreateFromArray(3, 4, new double[]
{
1, 2, 3,
2, 3, 4,
3, 4, 5,
4, 5, 7
}, MatrixElementOrder.ColumnMajor);
// To get the lower band part of m with bandwidth 2:
var b4 = BandMatrix<double>.Extract(m, 2, 0);

//
// BandMatrix properties
//

// A number of properties are available to determine
// whether a BandMatrix has a special structure:
Console.WriteLine(\$"b2 is upper? {b2.IsUpperTriangular}");
Console.WriteLine(\$"b2 is lower? {b2.IsUpperTriangular}");
Console.WriteLine(\$"b2 is unit diagonal? {b2.IsUnitDiagonal}");
Console.WriteLine(\$"b2 is symmetrical? {b2.IsSymmetrical}");

//
// BandMatrix methods
//

// You can get and set matrix elements:
b3[2, 3] = 55;
Console.WriteLine("b3[2, 3] = {0:F0}", b3[2, 3]);
// And the change will automatically be reflected
// in the symmetric element:
Console.WriteLine("b3[3, 2] = {0:F0}", b3[3, 2]);

//
// Row and column views
//

// The GetRow and GetColumn methods are
// available.
var row = b2.GetRow(1);
Console.WriteLine(\$"row 1 of b2 = {row:F0}");
var column = b2.GetColumn(2, 3, 4);
Console.WriteLine("column 3 of b2 from row 4 to ");
Console.WriteLine(\$"  row 5 = {column:F0}");

//
// Band matrix decompositions
//

// Specialized classes exist to represent the
// LU decomposition of a general band matrix
// and the Cholesky decomposition of a
// symmetric band matrix.

// Because of pivoting, the upper band matrix of
// the LU decomposition has larger bandwidth.
// You need to allocate extra space to be able to
// overwrite a matrix with its LU decomposition.

// The following creates a 7x5 band matrix with
// upper bandwidth 1 and lower bandwidth 2.
var b5 = Matrix.CreateBanded<double>(7, 7, 2, 1, true);
b5.GetDiagonal(0).SetValue(2.0);
b5.GetDiagonal(-2).SetValue(-1.0);
b5.GetDiagonal(1).SetValue(-1.0);

// Other than that, the API is the same as
// other decomposition classes.
var blu = b5.GetLUDecomposition(true);
var solution = blu.Solve(Vector.CreateConstant(b5.ColumnCount, 1.0));
Console.WriteLine(\$"  solution of b5*x = ones: {solution:F4}");

Console.Write("Press Enter key to exit...");