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# Class JSci.maths.IntegerTridiagonalMatrix

    java.lang.Object
       |
       +----JSci.maths.Matrix
               |
               +----JSci.maths.IntegerMatrix
                       |
                       +----JSci.maths.IntegerSquareMatrix
                               |
                               +----JSci.maths.IntegerTridiagonalMatrix

public class IntegerTridiagonalMatrix
extends IntegerSquareMatrix

The IntegerTridiagonalMatrix class provides an object for encapsulating tridiagonal matrices containing integers. Uses compressed diagonal storage.

##

storageFormat
TRIDIAGONAL
  Storage format identifier.

##

IntegerTridiagonalMatrix()
  Constructs a matrix.
IntegerTridiagonalMatrix(int)
  Constructs an empty matrix.
IntegerTridiagonalMatrix(int[][])
  Constructs a matrix from an array.

##

add(IntegerMatrix)
  Returns the addition of this matrix and another.
add(IntegerSquareMatrix)
  Returns the addition of this matrix and another.
add(IntegerTridiagonalMatrix)
  Returns the addition of this matrix and another.
choleskyDecompose()
  Returns the Cholesky decomposition of this matrix.
columns()
  Returns the number of columns.
equals(Object)
  Compares two integer tridiagonal matrices for equality.
frobeniusNorm()
  Returns the Frobenius norm.
getElement(int, int)
  Returns an element of the matrix.
infNorm()
  Returns the l(infinity)-norm.
isSymmetric()
  Returns true if this matrix is symmetric.
luDecompose()
  Returns the LU decomposition of this matrix.
multiply(IntegerMatrix)
  Returns the multiplication of this matrix and another.
multiply(IntegerSquareMatrix)
  Returns the multiplication of this matrix and another.
multiply(IntegerTridiagonalMatrix)
  Returns the multiplication of this matrix and another.
multiply(IntegerVector)
  Returns the multiplication of a vector by this matrix.
rows()
  Returns the number of rows.
scalarMultiply(int)
  Returns the multiplication of this matrix by a scalar.
setElement(int, int, int)
  Sets the value of an element of the matrix.
subtract(IntegerMatrix)
  Returns the subtraction of this matrix and another.
subtract(IntegerSquareMatrix)
  Returns the subtraction of this matrix by another.
subtract(IntegerTridiagonalMatrix)
  Returns the subtraction of this matrix by another.
toComplexMatrix()
  Converts this matrix to a complex matrix.
toDoubleMatrix()
  Converts this matrix to a double matrix.
toString()
  Returns a string representing this matrix.
trace()
  Returns the trace.
transpose()
  Returns the transpose of this matrix.

##

TRIDIAGONAL

     protected static final int TRIDIAGONAL

  Storage format identifier.

storageFormat

     protected static final int storageFormat

##

IntegerTridiagonalMatrix

     protected IntegerTridiagonalMatrix()

  Constructs a matrix.

IntegerTridiagonalMatrix

     public IntegerTridiagonalMatrix(int size)

  Constructs an empty matrix.

  Parameters:
    size - the number of rows/columns

IntegerTridiagonalMatrix

     public IntegerTridiagonalMatrix(int array[][])

  Constructs a matrix from an array. Any non-tridiagonal elements in the array are ignored.

  Parameters:
    array - an assigned value
  Throws: MatrixDimensionException
    If the array is not square.

##

equals

     public boolean equals(Object m)

  Compares two integer tridiagonal matrices for equality.

  Parameters:
    m - a integer tridiagonal matrix
  Overrides:
    equals in class IntegerMatrix

toString

     public String toString()

  Returns a string representing this matrix.

  Overrides:
    toString in class IntegerMatrix

toDoubleMatrix

     public DoubleMatrix toDoubleMatrix()

  Converts this matrix to a double matrix.

  Returns:
    a double tridiagonal matrix
  Overrides:
    toDoubleMatrix in class IntegerMatrix

toComplexMatrix

     public ComplexMatrix toComplexMatrix()

  Converts this matrix to a complex matrix.

  Returns:
    a complex tridiagonal matrix
  Overrides:
    toComplexMatrix in class IntegerMatrix

getElement

     public int getElement(int i,
                           int j)

  Returns an element of the matrix.

  Parameters:
    i - row index of the element
    j - column index of the element
  Throws: MatrixDimensionException
    If attempting to access an invalid element.
  Overrides:
    getElement in class IntegerMatrix

setElement

     public void setElement(int i,
                            int j,
                            int x)

  Sets the value of an element of the matrix.

  Parameters:
    i - row index of the element
    j - column index of the element
    x - a number
  Throws: MatrixDimensionException
    If attempting to access an invalid element.
  Overrides:
    setElement in class IntegerMatrix

isSymmetric

     public boolean isSymmetric()

  Returns true if this matrix is symmetric.

  Overrides:
    isSymmetric in class IntegerSquareMatrix

trace

     public int trace()

  Returns the trace.

  Overrides:
    trace in class IntegerSquareMatrix

infNorm

     public int infNorm()

  Returns the l(infinity)-norm.

  Overrides:
    infNorm in class IntegerMatrix

frobeniusNorm

     public double frobeniusNorm()

  Returns the Frobenius norm.

  Overrides:
    frobeniusNorm in class IntegerMatrix

rows

     public int rows()

  Returns the number of rows.

  Overrides:
    rows in class IntegerMatrix

columns

     public int columns()

  Returns the number of columns.

  Overrides:
    columns in class IntegerMatrix

add

     public IntegerMatrix add(IntegerMatrix m)

  Returns the addition of this matrix and another.

  Parameters:
    m - an integer matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    add in class IntegerSquareMatrix

add

     public IntegerSquareMatrix add(IntegerSquareMatrix m)

  Returns the addition of this matrix and another.

  Parameters:
    m - an integer square matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    add in class IntegerSquareMatrix

add

     public IntegerTridiagonalMatrix add(IntegerTridiagonalMatrix m)

  Returns the addition of this matrix and another.

  Parameters:
    m - an integer tridiagonal matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.

subtract

     public IntegerMatrix subtract(IntegerMatrix m)

  Returns the subtraction of this matrix and another.

  Parameters:
    m - an integer matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    subtract in class IntegerSquareMatrix

subtract

     public IntegerSquareMatrix subtract(IntegerSquareMatrix m)

  Returns the subtraction of this matrix by another.

  Parameters:
    m - an integer square matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    subtract in class IntegerSquareMatrix

subtract

     public IntegerTridiagonalMatrix subtract(IntegerTridiagonalMatrix m)

  Returns the subtraction of this matrix by another.

  Parameters:
    m - an integer tridiagonal matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.

scalarMultiply

     public IntegerMatrix scalarMultiply(int x)

  Returns the multiplication of this matrix by a scalar.

  Parameters:
    x - an integer
  Returns:
    an integer tridiagonal matrix
  Overrides:
    scalarMultiply in class IntegerSquareMatrix

multiply

     public IntegerVector multiply(IntegerVector v)

  Returns the multiplication of a vector by this matrix.

  Parameters:
    v - an integer vector
  Throws: DimensionException
    If the matrix and vector are incompatible.
  Overrides:
    multiply in class IntegerSquareMatrix

multiply

     public IntegerMatrix multiply(IntegerMatrix m)

  Returns the multiplication of this matrix and another.

  Parameters:
    m - an integer matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    multiply in class IntegerSquareMatrix

multiply

     public IntegerSquareMatrix multiply(IntegerSquareMatrix m)

  Returns the multiplication of this matrix and another.

  Parameters:
    m - an integer square matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.
  Overrides:
    multiply in class IntegerSquareMatrix

multiply

     public IntegerSquareMatrix multiply(IntegerTridiagonalMatrix m)

  Returns the multiplication of this matrix and another.

  Parameters:
    m - an integer tridiagonal matrix
  Throws: MatrixDimensionException
    If the matrices are different sizes.

transpose

     public Matrix transpose()

  Returns the transpose of this matrix.

  Returns:
    an integer tridiagonal matrix
  Overrides:
    transpose in class IntegerSquareMatrix

luDecompose

     public DoubleSquareMatrix[] luDecompose()

  Returns the LU decomposition of this matrix.

  Returns:
    an array with [0] containing the L-matrix and [1] containing the U-matrix.
  Overrides:
    luDecompose in class IntegerSquareMatrix

choleskyDecompose

     public DoubleSquareMatrix[] choleskyDecompose()

  Returns the Cholesky decomposition of this matrix. Matrix must be symmetric and positive definite.

  Returns:
    an array with [0] containing the L-matrix and [1] containing the U-matrix.

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