**18.2****
****Value Operations on Matrices** (.NET, C#, CSharp, VB, Visual Basic, F#)

The **NMath**
structured sparse matrix classes have read-only properties for all shape
parameters, and for the underlying data vector:

On square matrix types, the Rows and Cols properties simply return the order. On banded types, the Bandwidth property returns the total bandwidth. For general banded matrices, the total bandwidth is LowerBandwidth + UpperBandwidth + 1; for symmetric and Hermitian banded types, the total bandwidth is 2 * HalfBandwidth + 1.

For example, if A is a
**FloatHermitianBandMatrix** instance:

Code Example – C# matrix

int order = A.Order;

int cols = A.Cols; // cols == order

int rows = A.Rows; // rows == order

int halfband = A.HalfBandwidth

int band = A.Bandwidth // band = 2 * halfband + 1

FloatComplexVector data = A.DataVector;

Code Example – VB matrix

Dim Order As Integer = A.Order

Dim Cols As Integer = A.Cols ' cols == order

Dim Rows As Integer = A.Rows ' rows == order

Dim HalfBand As Integer = A.HalfBandwidth

Dim band As Integer = A.Bandwidth ' band = 2 * halfband + 1

Dim Data As FloatComplexVector = A.DataVector

**Accessing and Modifying Matrix Values**

The matrix classes provide standard
indexers for getting and setting element value at a specified row and
column position in a matrix. Thus, A[i,j]
always returns the element in the *i*th
row and* j*th column of matrix A's view of the data.

**NOTE—****Indexing
starts at 0.**

Attempts to set zero elements outside the stored region
to nonzero values raise a **NonModifiableElementException**.
For instance:

Code Example – C# matrix

var A = new FloatComplexTriDiagMatrix( 8, 8 );

try

{

A[7,0] = new FloatComplex( 1, -1 );

}

catch ( NonModifiableElementException )

{

// Do something here

}

Code Example – VB matrix

Dim A As New FloatComplexTriDiagMatrix(8, 8)

Try

A(7, 0) = New FloatComplex(1.0F, -1.0F)

Catch NonModifiableElementException

' Do something here

End Try

Symmetric matrices are in a different category than the other structured sparse matrix types, because unstored values are not constrained to be zero. Thus, even though only the upper triangular region is stored, you can "set" values in the lower triangular region. The corresponding value in the upper triangular region is changed. Thus:

Code Example – C# matrix

var A = new DoubleSymmetricMatrix( 12 );

Console.WriteLine( A[7,2] ); // "0"

Console.WriteLine( A[2,7] ); // "0"

A[7,2] = 1;

Console.WriteLine( A[7,2] ); // "1"

Console.WriteLine( A[2,7] ); // "1"

Code Example – VB matrix

Dim A As New DoubleSymmetricMatrix(12)

Console.WriteLine(A(7, 2)) ' "0"

Console.WriteLine(A(2, 7)) ' "0"

A(7, 2) = 1

Console.WriteLine(A(7, 2)) ' "1"

Console.WriteLine(A(2, 7)) ' "1"

The matrix classes provide Resize() methods for changing the size of a matrix after it has been created. Zeros are added or values are truncated as necessary. For instance:

Code Example – C# matrix

int order = 7;

var data =

new DoubleComplexVector( ( order * ( order + 1 )) / 2,

new RandGenMTwist() );

var A = new DoubleHermitianMatrix( data );

DoubleHermitianMatrix B2 = (DoubleHermitianMatrix)B.Clone();

B2.Resize( B.Order + 2 );

Code Example – VB matrix

Dim Order As Integer = 7

Dim Data As New DoubleComplexVector((Order * (Order + 1)) / 2,

New RandGenMTwist())

Dim A As New DoubleHermitianMatrix(Data)

Dim B2 As DoubleHermitianMatrix = CType(B.Clone(),

DoubleHermitianMatrix)

B.Resize(B.Order + 2)