SparseMatrix.SparseArray Class

SparseMatrixSparseArray Class

The SparseArray class uses public fields to hold the data for a sparse matrix in the Sparse Array format.

Inheritance Hierarchy

SystemObject
Imsl.MathSparseMatrixSparseArray

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class SparseArray

<SerializableAttribute>
Public Class SparseArray

[SerializableAttribute]
public ref class SparseArray

[<SerializableAttribute>]
type SparseArray =  class end

The SparseMatrixSparseArray type exposes the following members.

Constructors

	Name	Description
	SparseMatrixSparseArray	Initializes a new instance of the SparseMatrixSparseArray class

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Fields

	Name	Description
	Index	Jagged array containing column indices. The length of this array equals numberOfRows. The length of each row equals the number of nonzeros in that row of the sparse matrix.
	NumberOfColumns	Number of columns in the matrix.
	NumberOfNonZeros	Number of nonzeros in the matrix.
	NumberOfRows	Number of rows in the matrix.
	Values	Jagged array containing sparse array values. This array must have the same shape as Index.

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Remarks

This format came about as a means for storing sparse matrices. In this format, a sparse matrix is represented by two arrays of arrays. One array contains the references to the nonzero value arrays for each row of the sparse matrix. The other contains the references to the associated column index arrays.

As an example, consider the following real sparse matrix:

$A=\begin{pmatrix} 10.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\ 0.0 & 10.0 & -3.0 & -1.0 & 0.0 & 0.0 \\ 0.0 & 0.0 & 15.0 & 0.0 & 0.0 & 0.0 \\ -2.0 & 0.0 & 0.0 & 10.0 & -1.0 & 0.0 \\ -1.0 & 0.0 & 0.0 & -5.0 & 1.0 & -3.0 \\ -1.0 & -2.0 & 0.0 & 0.0 & 0.0 & 6.0 \end{pmatrix}$

In SparseArray, this matrix can be represented by the two jagged arrays, values and index, where values refers to the nonzero entries in A and index to the column indices:

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double values[][] = {{10.0},
                     {10.0, -3.0, -1.0},
                     {15.0},
                     {-2.0, 10.0, -1.0}, 
                     {-1.0, -5.0, 1.0, -3.0},
                     {-1.0, -2.0, 6.0}
                    };

int index[][] = {{0}, 
                 {1, 2, 3},
                 {2},
                 {0, 3, 4},
                 {0, 3, 4, 5},
                 {0, 1, 5}
                };

Reference

Imsl.Math Namespace