# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.algebra.linear.matrix.doubles.matrixtype.dense.diagonal

## Class TridiagonalMatrix

• java.lang.Object
• com.numericalmethod.suanshu.algebra.linear.matrix.doubles.matrixtype.dense.diagonal.TridiagonalMatrix
• ### Constructor Summary

Constructors
Constructor and Description
TridiagonalMatrix(double[][] data)
Constructs a tri-diagonal matrix from a 3-row 2D double[][] array such that: the first row is the super diagonal with (dim - 1) entries; the second row is the main diagonal with dim entries; the third row is the sub diagonal with (dim - 1) entries. For example,
TridiagonalMatrix(int dim)
Constructs a 0 tri-diagonal matrix of dimension dim * dim.
TridiagonalMatrix(Matrix A)
Casts a matrix to tridiagonal by copying the 3 diagonals (ignoring all other entries).
TridiagonalMatrix(TridiagonalMatrix that)
Copy constructor performing a deep copy.
• ### Method Summary

All Methods
Modifier and Type Method and Description
Matrix add(Matrix that)
this + that
TridiagonalMatrix deepCopy()
The implementation returns an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.
boolean equals(Object obj)
double get(int i, int j)
Get the matrix entry at [i,j].
Vector getColumn(int j)
Get the specified column in the matrix as a vector.
DenseVector getDiagonal()
Gets the main diagonal of the matrix.
Vector getRow(int i)
Get the specified row in the matrix as a vector.
DenseVector getSubDiagonal()
Gets the sub-diagonal of the matrix.
DenseVector getSuperDiagonal()
Gets the super-diagonal of the matrix.
int hashCode()
Matrix minus(Matrix that)
this - that
Matrix multiply(Matrix that)
this * that
Vector multiply(Vector v)
Right multiply this matrix, A, by a vector.
int nCols()
Gets the number of columns.
int nRows()
Gets the number of rows.
TridiagonalMatrix ONE()
Get an identity matrix that has the same dimension as this matrix.
TridiagonalMatrix opposite()
For each a in G, there exists an element b in G such that a + b = b + a = 0.
TridiagonalMatrix scaled(double scalar)
Scale this matrix, A, by a constant.
void set(int i, int j, double value)
Set the matrix entry at [i,j] to a value.
TridiagonalMatrix t()
Get the transpose of this matrix.
DenseMatrix toDense()
Densify a matrix, i.e., convert a matrix implementation to the standard dense matrix, DenseMatrix.
String toString()
TridiagonalMatrix ZERO()
The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
• ### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait
• ### Constructor Detail

• #### TridiagonalMatrix

public TridiagonalMatrix(int dim)
Constructs a 0 tri-diagonal matrix of dimension dim * dim.
Parameters:
dim - the dimension of the matrix
• #### TridiagonalMatrix

public TridiagonalMatrix(double[][] data)
Constructs a tri-diagonal matrix from a 3-row 2D double[][] array such that:
1. the first row is the super diagonal with (dim - 1) entries;
2. the second row is the main diagonal with dim entries;
3. the third row is the sub diagonal with (dim - 1) entries.
For example,

new double[][]{
{2, 5, 8, 11},
{1, 4, 7, 10, 13},
{3, 6, 9, 12}
}

gives $\begin{bmatrix} 1 & 2 & 0 & 0 & 0\\ 3 & 4 & 5 & 0 & 0\\ 0 & 6 & 7 & 8 & 0\\ 0 & 0 & 9 & 10 & 11\\ 0 & 0 & 0 & 12 & 13 \end{bmatrix}$ We allow null input when a diagonal is 0s. For example,

new double[][]{
{2, 5, 8, 11},
{1, 4, 7, 10, 13},
null
}

gives $\begin{bmatrix} 1 & 2 & 0 & 0 & 0\\ 0 & 4 & 5 & 0 & 0\\ 0 & 0 & 7 & 8 & 0\\ 0 & 0 & 0 & 10 & 11\\ 0 & 0 & 0 & 0 & 13 \end{bmatrix}$ The following is not allowed because the dimension cannot be determined.

new double[][]{
null,
null,
null
}

Parameters:
data - the 2D array input
• #### TridiagonalMatrix

public TridiagonalMatrix(Matrix A)
Casts a matrix to tridiagonal by copying the 3 diagonals (ignoring all other entries).
Parameters:
A - the matrix
• #### TridiagonalMatrix

public TridiagonalMatrix(TridiagonalMatrix that)
Copy constructor performing a deep copy.
Parameters:
that - a tri-diagonal matrix
• ### Method Detail

• #### deepCopy

public TridiagonalMatrix deepCopy()
Description copied from interface: DeepCopyable
The implementation returns an instance created from this by the copy constructor of the class, or just this if the instance itself is immutable.
Returns:
an independent (deep) copy of the instance

public Matrix add(Matrix that)
Description copied from interface: MatrixRing
this + that
Specified by:
add in interface MatrixRing
Specified by:
add in interface AbelianGroup<Matrix>
Parameters:
that - a matrix
Returns:
the sum of this and that
• #### minus

public Matrix minus(Matrix that)
Description copied from interface: MatrixRing
this - that
Specified by:
minus in interface MatrixRing
Specified by:
minus in interface AbelianGroup<Matrix>
Parameters:
that - a matrix
Returns:
the difference between this and that
• #### scaled

public TridiagonalMatrix scaled(double scalar)
Description copied from interface: Matrix
Scale this matrix, A, by a constant.
Parameters:
scalar - a double
Returns:
cA
• #### opposite

public TridiagonalMatrix opposite()
Description copied from interface: AbelianGroup
For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
this.add(this.opposite()) == this.ZERO
Returns:
• #### t

public TridiagonalMatrix t()
Description copied from interface: MatrixRing
Get the transpose of this matrix. This is the involution on the matrix ring.
Returns:
the transpose of this matrix
• #### ZERO

public TridiagonalMatrix ZERO()
Description copied from interface: AbelianGroup
The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
Returns:
• #### ONE

public TridiagonalMatrix ONE()
Description copied from interface: MatrixRing
Get an identity matrix that has the same dimension as this matrix. For a non-square matrix, it zeros out the rows (columns) with index > nCols (nRows).
Returns:
an identity matrix
• #### toDense

public DenseMatrix toDense()
Description copied from interface: Densifiable
Densify a matrix, i.e., convert a matrix implementation to the standard dense matrix, DenseMatrix.
Specified by:
toDense in interface Densifiable
Returns:
a matrix representation in DenseMatrix
• #### getDiagonal

public DenseVector getDiagonal()
Gets the main diagonal of the matrix.
Returns:
the main diagonal
• #### getSuperDiagonal

public DenseVector getSuperDiagonal()
Gets the super-diagonal of the matrix.
Returns:
the super-diagonal
• #### getSubDiagonal

public DenseVector getSubDiagonal()
Gets the sub-diagonal of the matrix.
Returns:
the sub-diagonal
• #### nRows

public int nRows()
Description copied from interface: Table
Gets the number of rows. Rows count from 1.
Specified by:
nRows in interface Table
Returns:
the number of rows
• #### nCols

public int nCols()
Description copied from interface: Table
Gets the number of columns. Columns count from 1.
Specified by:
nCols in interface Table
Returns:
the number of columns
• #### set

public void set(int i,
int j,
double value)
throws MatrixAccessException
Description copied from interface: MatrixAccess
Set the matrix entry at [i,j] to a value. This is the only method that may change a matrix.
Specified by:
set in interface MatrixAccess
Parameters:
i - the row index
j - the column index
value - the value to set A[i,j] to
Throws:
MatrixAccessException - if i or j is out of range
• #### get

public double get(int i,
int j)
throws MatrixAccessException
Description copied from interface: MatrixAccess
Get the matrix entry at [i,j].
Specified by:
get in interface MatrixAccess
Parameters:
i - the row index
j - the column index
Returns:
A[i,j]
Throws:
MatrixAccessException - if i or j is out of range
• #### getRow

public Vector getRow(int i)
Description copied from interface: Matrix
Get the specified row in the matrix as a vector.
Specified by:
getRow in interface Matrix
Parameters:
i - the row index
Returns:
the vector A[i, ]
• #### getColumn

public Vector getColumn(int j)
Description copied from interface: Matrix
Get the specified column in the matrix as a vector.
Specified by:
getColumn in interface Matrix
Parameters:
j - the column index
Returns:
a vector A[, j]
• #### multiply

public Matrix multiply(Matrix that)
Description copied from interface: MatrixRing
this * that
Specified by:
multiply in interface MatrixRing
Specified by:
multiply in interface Monoid<Matrix>
Parameters:
that - a matrix
Returns:
the product ofthis and that
• #### multiply

public Vector multiply(Vector v)
Description copied from interface: Matrix
Right multiply this matrix, A, by a vector.
Specified by:
multiply in interface Matrix
Parameters:
v - a vector
Returns:
Av, a vector
• #### toString

public String toString()
Overrides:
toString in class Object
• #### equals

public boolean equals(Object obj)
Overrides:
equals in class Object
• #### hashCode

public int hashCode()
Overrides:
hashCode in class Object