Data Analysis Mathematics Linear Algebra Statistics
New Version 7.0!  QuickStart Samples

# Accessing Matrix Components QuickStart Sample (C#)

Illustrates different ways of iterating through the rows and columns of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace in C#.

```using System;

namespace Extreme.Numerics.QuickStart.CSharp
{
// The var and var classes resides in the
// Extreme.Mathematics namespace.
using Extreme.Mathematics;
using Extreme.Mathematics.LinearAlgebra;

/// <summary>
/// Illustrates accessing matrix components and iterating
/// through the rows and columns of a matrix. Matrix classes
/// reside in the Extreme.Mathematics.LinearAlgebra namespace
/// of the Extreme Optimization Mathematics Library for .NET.
/// </summary>
class AccessingMatrixComponents
{
/// <summary>
/// The main entry point for the application.
/// </summary>
static void Main(string[] args)
{
// We'll work with this matrix:
var m = Matrix.Create(2, 3, new double[] { 1, 2, 3, 4, 5, 6 },
MatrixElementOrder.ColumnMajor);

//
// Individual components
//
// The Matrix class has an indexer property that takes two arguments:
// the row and column index. Both are zero based.
Console.WriteLine("m[1,1] = {0}", m[1, 1]);

//
// Rows and columns
//

// Indexed range access

// The indexer property is overloaded to allow for direct indexed access
// to complete or partial rows or columns.

var row1 = m[0, new Range(1, 2)];
// This prints "[3, 5]":
Console.WriteLine("row1 = {0}", row1);

// The special range Range.All lets you access an entire row
// or column without having to specify any details about the range.
var row2 = m[1, Range.All];
// This prints "[2, 4, 6]":
Console.WriteLine("2nd row = {0}", row2);
var column1 = m[Range.All, 0];
// This prints "[1, 2]":
Console.WriteLine("column1 = {0}", column1);

// We can assign to rows and columns, too:
m[Range.All, 0] = row1;
// This prints "[[3, 3, 5] [5, 4, 6]]"
Console.WriteLine("m = {0}", m);

// GetRow and GetColumn provide an alternate mechanism
// for achieving the same result.

// Passing just one parameter retrieves the specified row or column:
row1 = m.GetRow(1);
// This prints "[2, 4, 6]":
Console.WriteLine("row1 = {0}", row1);
column1 = m.GetColumn(0);
// This prints "[1, 2]":
Console.WriteLine("column1 = {0}", column1);

// You can also pass a start and end index:
row2 = m.GetRow(0, 1, 2);
// This prints "[3, 5]":
Console.WriteLine("row2 = {0}", row2);

// We can assign to rows and columns, too, using CopyTo:
row2.CopyTo(m.GetColumn(0));
// This prints "[[3, 3, 5] [5, 4, 6]]"
Console.WriteLine("m = {0}", m);

// Enumeration

// The Rows and Columns methods allow you to enumerate over
// the rows and columns of a matrix.

// For example: this calculates the sum of the absolute values
// of the components of the matrix m:
double sum = 0;
foreach(Vector<double> column in m.Columns )
sum += column.OneNorm();

//
// Accessing diagonals
//

// Diagonals are retrieved using the GetDiagonal method:
var mainDiagonal = m.GetDiagonal();
// An optional parameter specifies which diagonal:
//   n < 0 means subdiagonal
//   n > 0 means nth superdiagonal:
var superDiagonal = m.GetDiagonal(1);

//
// Accessing submatrices
//

// Indexed range access

// A fourth overload of the indexer property lets you
// extract a part of a matrix. Both parameters are Range
// structures:
var a = Matrix.Create<double>(10, 10);
// Extract the 2nd to the 5th row of m:
var a1 = a[new Range(1, 4), Range.All];
// Extract the odd columns:
var a2 = a[Range.All, new Range(1, 9, 2)];
// Extract the 4x4 leading submatrix of m:
var a3 = a[new Range(0, 3), new Range(0, 3)];

// You can also assign to submatrices:
var identity5 = DenseMatrix<double>.GetIdentity(5);
a[new Range(0, 4), new Range(5, 9)] = identity5;
a[new Range(5, 9), new Range(0, 4)] = identity5;

// The same results can be achieved with the GetSubmatrix method.

// Extract the 2nd to the 5th row of m.
// Start and end columns are supplied manually.
var a4 = a.GetSubmatrix(1, 4, 0, 9);
// Extract the odd columns:
// Here we need to supply the transpose parameter.
var a5 = a.GetSubmatrix(0, 9, 1, 1, 9, 2,
TransposeOperation.None);
// Extract the 4x4 leading submatrix of m.
// And let's get its transpose, just because we can.
// We need to specify the row and column stride:
var a6 = a.GetSubmatrix(0, 3, 1, 0, 3, 1,
TransposeOperation.Transpose);

// You can still assign to submatrices, using the
// CopyTo method:
identity5.CopyTo(a.GetSubmatrix(0, 4, 5, 9));
identity5.CopyTo(a.GetSubmatrix(5, 9, 0, 4));

Console.WriteLine("Press Enter key to continue.");