com.imsl.math
Class ComplexSparseMatrix

java.lang.Object
  com.imsl.math.ComplexSparseMatrix

All Implemented Interfaces:

Serializable

public class ComplexSparseMatrix
extends Object
implements Serializable

Sparse matrix of type Complex. The class represents a general complex sparse matrix. It is intended to be efficiently and easily updated.

A ComplexSparseMatrix can be constructed from a set of arrays, or it can be abstractly created as an empty array and then incrementally built into final form. It is usually easier to create an empty ComplexSparseMatrix of set size and then use the set method to set the elements of the array. When setting the elements of the sparse array, their positions should be thought of as their positions in the dense array. Elements can be set in any order, but only the elements set are stored.

This class includes methods to update the sparse matrix. There are also methods to multiply a sparse matrix and a vector or to multiply two sparse matrices. To solve a sparse linear system use ComplexSparseCholesky or ComplexSuperLU.

See Also:

ComplexSparseCholesky, ComplexSuperLU, Example: Create from Arrays, Serialized Form

Nested Class Summary

static class

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

Constructor Summary

ComplexSparseMatrix(ComplexSparseMatrix.SparseArray sparseArray)
Constructs a complex sparse matrix from a SparseArray object.

ComplexSparseMatrix(ComplexSparseMatrix A)
Creates a new instance of ComplexSparseMatrix which is a copy of another ComplexSparseMatrix.

ComplexSparseMatrix(int nRows, int nColumns)
Creates a new instance of ComplexSparseMatrix.

ComplexSparseMatrix(int nRows, int nColumns, int[][] index, Complex[][] values)
Constructs a sparse matrix from SparseArray (Java Sparse Array) data.

Method Summary

static ComplexSparseMatrix	add(Complex alpha, Complex beta, ComplexSparseMatrix A, ComplexSparseMatrix B) Performs element-wise addition of two complex sparse matrices A, B of type ComplexSparseMatrix,
void	checkSquareMatrix() Check that the matrix is square.
ComplexSparseMatrix	conjugateTranspose() Returns the conjugate transpose of the matrix.
double	frobeniusNorm() Returns the Frobenius norm of the matrix.
Complex	get(int iRow, int jColumn) Returns the value of an element in the matrix.
int	getNumberOfColumns() Returns the number of columns in the matrix.
long	getNumberOfNonZeros() Returns the number of nonzeros in the matrix.
int	getNumberOfRows() Returns the number of rows in the matrix.
double	infinityNorm() Returns the infinity norm of the matrix.
Complex[]	multiply(Complex[] x) Multiply the matrix by a vector.
static Complex[]	multiply(Complex[] x, ComplexSparseMatrix A) Multiply row array x and sparse matrix A, .
static Complex[]	multiply(ComplexSparseMatrix A, Complex[] x) Multiply sparse matrix A and column array x, .
static ComplexSparseMatrix	multiply(ComplexSparseMatrix A, ComplexSparseMatrix B) Multiply two sparse complex matrices A and B, .
static Complex[]	multiplyHermitian(ComplexSparseMatrix A, Complex[] x) Multiply sparse Hermitian matrix A and column vector x.
double	oneNorm() Returns the matrix one norm of the sparse matrix.
Complex	plusEquals(int iRow, int jColumn, Complex x) Adds a value to an element in the matrix.
void	set(int iRow, int jColumn, Complex x) Sets the value of an element in the matrix.
Complex[][]	toDenseMatrix() Returns the sparse matrix as a dense matrix.
ComplexSparseMatrix.SparseArray	toSparseArray() Returns the sparse matrix in the SparseArray form.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ComplexSparseMatrix

public ComplexSparseMatrix(ComplexSparseMatrix.SparseArray sparseArray)

Constructs a complex sparse matrix from a SparseArray object.

Parameters:

sparseArray - is a SparseArray used to initialize the sparse matrix. The field numberOfNonZeros in SparseArray is not used for initialization, so it does not have to be set.

ComplexSparseMatrix

public ComplexSparseMatrix(ComplexSparseMatrix A)

Creates a new instance of ComplexSparseMatrix which is a copy of another ComplexSparseMatrix.

Parameters:

A - is the ComplexSparseMatrix to be copied.

ComplexSparseMatrix

public ComplexSparseMatrix(int nRows,
                           int nColumns)

Creates a new instance of ComplexSparseMatrix. Initially this is the zero matrix.

Parameters:

nRows - an int containing the number of rows in the sparse matrix.

nColumns - an int containing the number of columns in the sparse matrix.

ComplexSparseMatrix

public ComplexSparseMatrix(int nRows,
                           int nColumns,
                           int[][] index,
                           Complex[][] values)

Constructs a sparse matrix from SparseArray (Java Sparse Array) data.

Parameters:

nRows - an int containing the number of rows in the sparse matrix.

nColumns - an int containing the number of columns in the sparse matrix.

index - an int jagged array containing the column indices of all nonzero elements corresponding to the compressed representation of the sparse matrix in values. The size of index must be identical to the size of values. The i-th row contains the column indices of all nonzero elements of row i of the sparse matrix. The j-th element of row i is the column index of the value located at the same position in values.

values - a Complex jagged array containing the compressed representation of a complex sparse matrix of size nRows by nColumns. The number of rows in values must be nRows. The i-th row contains all nonzero elements of row i of the full sparse matrix.

Method Detail

add

public static ComplexSparseMatrix add(Complex alpha,
                                      Complex beta,
                                      ComplexSparseMatrix A,
                                      ComplexSparseMatrix B)

Performs element-wise addition of two complex sparse matrices A, B of type ComplexSparseMatrix,

Parameters:

alpha - a Complex scalar.

beta - a Complex scalar.

A - a ComplexSparseMatrix matrix.

B - a ComplexSparseMatrix matrix.

Returns:

a ComplexSparseMatrix matrix representing the computed sum.

Throws:

IllegalArgumentException - This exception is thrown if the matrices are not of the same size.

checkSquareMatrix

public void checkSquareMatrix()

Check that the matrix is square.

Throws:

IllegalArgumentException - is thrown if the matrix is not square.

conjugateTranspose

public ComplexSparseMatrix conjugateTranspose()

Returns the conjugate transpose of the matrix.

Returns:

a ComplexSparseMatrix object which is the conjugate transpose of the constructed ComplexSparseMatrix object.

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius norm of the matrix.

Returns:

a double scalar value equal to the Frobenius norm of the matrix.

get

public Complex get(int iRow,
                   int jColumn)

Returns the value of an element in the matrix.

Parameters:

iRow - an int containing the row index of the element.

jColumn - an int containing the column index of the element.

Returns:

a Complex containing the value of the iRow-th and jColumn-th element. If the element was never set, its value is zero.

getNumberOfColumns

public int getNumberOfColumns()

Returns the number of columns in the matrix.

Returns:

an int containing the number of columns in the matrix.

getNumberOfNonZeros

public long getNumberOfNonZeros()

Returns the number of nonzeros in the matrix.

Returns:

a long containing the number of nonzeros in the matrix.

getNumberOfRows

public int getNumberOfRows()

Returns the number of rows in the matrix.

Returns:

an int containing the number of rows in the matrix.

infinityNorm

public double infinityNorm()

Returns the infinity norm of the matrix.

Returns:

a double scalar value equal to the maximum of the row sums of the absolute values of the array elements of the sparse matrix.

multiply

public Complex[] multiply(Complex[] x)

Multiply the matrix by a vector.

Parameters:

x - a Complex column array.

Returns:

a Complex vector representing the product of this matrix times x.

Throws:

IllegalArgumentException - This exception is thrown if the number of columns in the ComplexSparseMatrix object is not equal to the number of elements in the input column vector.

multiply

public static Complex[] multiply(Complex[] x,
                                 ComplexSparseMatrix A)

Multiply row array x and sparse matrix A, .

Parameters:

x - a Complex row array.

A - a ComplexSparseMatrix matrix.

Returns:

a Complex vector representing the product of the arguments, .

Throws:

IllegalArgumentException - This exception is thrown when the number of elements in the input vector is not equal to the number of rows of the matrix.

multiply

public static Complex[] multiply(ComplexSparseMatrix A,
                                 Complex[] x)

Multiply sparse matrix A and column array x, .

Parameters:

A - a ComplexSparseMatrix matrix.

x - a Complex column array.

Returns:

a Complex vector representing the product of the arguments, .

Throws:

IllegalArgumentException - This exception is thrown when the number of columns in the input matrix is not equal to the number of elements in the input column vector.

multiply

public static ComplexSparseMatrix multiply(ComplexSparseMatrix A,
                                           ComplexSparseMatrix B)

Multiply two sparse complex matrices A and B, .

Parameters:

A - a ComplexSparseMatrix sparse matrix.

B - a ComplexSparseMatrix sparse matrix.

Returns:

the ComplexSparseMatrix product AB of A and B.

Throws:

IllegalArgumentException - This exception is thrown when the column number of matrix A is not equal to the row number of matrix B.

multiplyHermitian

public static Complex[] multiplyHermitian(ComplexSparseMatrix A,
                                          Complex[] x)

Multiply sparse Hermitian matrix A and column vector x.

Parameters:

A - a ComplexSparseMatrix sparse Hermitian matrix, where only the lower triangular part of the matrix is to be used.

x - A Complex vector.

Returns:

a Complex vector representing the product of the arguments, .

Throws:

IllegalArgumentException - This exception is thrown when the input matrix is not square or the number of columns in the input matrix is not equal to the number of elements in the input column vector.

oneNorm

public double oneNorm()

Returns the matrix one norm of the sparse matrix.

Returns:

a double value equal to the maximum of the column sums of the absolute values of the array elements.

plusEquals

public Complex plusEquals(int iRow,
                          int jColumn,
                          Complex x)

Adds a value to an element in the matrix.

Parameters:

iRow - an int containing the row index of the element.

jColumn - an int containing the column index of the element.

x - a Complex containing the value to be added.

Returns:

a Complex containing the updated value of the element, which equals its old value plus x.

set

public void set(int iRow,
                int jColumn,
                Complex x)

Sets the value of an element in the matrix.

Parameters:

iRow - an int containing the row index of the element.

jColumn - an int containing the column index of the element.

x - a Complex containing the value of the iRow-th and jColumn-th element.

toDenseMatrix

public Complex[][] toDenseMatrix()

Returns the sparse matrix as a dense matrix.

Returns:

a rectangular Java array of type Complex containing this matrix with all of the zeros explicitly present. The number of rows and columns in the returned matrix is the same as in the sparse matrix.

toSparseArray

public ComplexSparseMatrix.SparseArray toSparseArray()

Returns the sparse matrix in the SparseArray form.