Class AtA

java.lang.Object

smile.tensor.AtA

All Implemented Interfaces:

Matrix, Tensor

public class AtA
extends Object
implements Matrix

The square matrix of A' * A or A * A', whichever is smaller. For SVD, we compute eigenvalue decomposition of A' * A when m >= n, or that of A * A' when m < n.

Constructor Summary

Constructors

Constructor	Description
AtA(Matrix A)	Constructor.

Method Summary

Modifier and Type	Method	Description
void	add(int i, int j, double x)	Sets A[i,j] += x.
Matrix	copy()	Returns a deep copy of matrix.
void	div(int i, int j, double x)	Sets A[i,j] /= x.
double	get(int i, int j)	Returns A[i,j].
long	length()	Returns the number of tensor elements.
void	mul(int i, int j, double x)	Sets A[i,j] *= x.
void	mv(Transpose trans, double alpha, Vector x, double beta, Vector y)	Matrix-vector multiplication.
void	mv(Vector work, int inputOffset, int outputOffset)	Matrix-vector multiplication A * x.
int	ncol()	Returns the number of columns.
int	nrow()	Returns the number of rows.
ScalarType	scalarType()	Returns the element data type.
Matrix	scale(double alpha)	A *= alpha
void	set(int i, int j, double x)	Sets A[i,j] = x.
void	sub(int i, int j, double x)	Sets A[i,j] -= x.
Matrix	transpose()	Returns the transpose of matrix.
void	tv(Vector work, int inputOffset, int outputOffset)	Matrix-vector multiplication A' * x.

Methods inherited from class Object

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

Methods inherited from interface Matrix

apply, diagonal, dim, get, mv, mv, mv, mv, reshape, set, shape, size, toArray, toArray, toString, toString, trace, tv, tv, tv, tv, update, vector, vector, vector, xAx

Constructor Details

AtA

public AtA(Matrix A)

Constructor.

Parameters:

A - the base matrix.

Method Details

scalarType

public ScalarType scalarType()

Description copied from interface: Tensor

Returns the element data type.

Specified by:

scalarType in interface Tensor

Returns:

the element data type.

nrow

public int nrow()

Description copied from interface: Matrix

Returns the number of rows.

Specified by:

nrow in interface Matrix

Returns:

the number of rows.

ncol

public int ncol()

Description copied from interface: Matrix

Returns the number of columns.

Specified by:

ncol in interface Matrix

Returns:

the number of columns.

length

public long length()

Description copied from interface: Tensor

Returns the number of tensor elements. For tensors with packed storage (e.g., BandMatrix, SparseMatrix, SymmMatrix), it returns the number of non-zero elements.

Specified by:

length in interface Matrix

Specified by:

length in interface Tensor

Returns:

the number of tensor elements.

get

public double get(int i,
 int j)

Description copied from interface: Matrix

Returns A[i,j].

Specified by:

get in interface Matrix

Parameters:

i - the row index.

j - the column index.

Returns:

the matrix element value.

set

public void set(int i,
 int j,
 double x)

Description copied from interface: Matrix

Sets A[i,j] = x.

Specified by:

set in interface Matrix

Parameters:

i - the row index.

j - the column index.

x - the matrix element value.

add

public void add(int i,
 int j,
 double x)

Description copied from interface: Matrix

Sets A[i,j] += x.

Specified by:

add in interface Matrix

Parameters:

i - the row index.

j - the column index.

x - the operand.

sub

public void sub(int i,
 int j,
 double x)

Description copied from interface: Matrix

Sets A[i,j] -= x.

Specified by:

sub in interface Matrix

Parameters:

i - the row index.

j - the column index.

x - the operand.

mul

public void mul(int i,
 int j,
 double x)

Description copied from interface: Matrix

Sets A[i,j] *= x.

Specified by:

mul in interface Matrix

Parameters:

i - the row index.

j - the column index.

x - the operand.

div

public void div(int i,
 int j,
 double x)

Description copied from interface: Matrix

Sets A[i,j] /= x.

Specified by:

div in interface Matrix

Parameters:

i - the row index.

j - the column index.

x - the operand.

scale

public Matrix scale(double alpha)

Description copied from interface: Matrix

A *= alpha

Specified by:

scale in interface Matrix

Parameters:

alpha - the scaling factor.

Returns:

this matrix.

copy

public Matrix copy()

Description copied from interface: Matrix

Returns a deep copy of matrix.

Specified by:

copy in interface Matrix

Returns:

a deep copy of matrix.

transpose

public Matrix transpose()

Description copied from interface: Matrix

Returns the transpose of matrix. The transpose may share the storage with this matrix.

Specified by:

transpose in interface Matrix

Returns:

the transpose of matrix.

mv

public void mv(Transpose trans,
 double alpha,
 Vector x,
 double beta,
 Vector y)

Description copied from interface: Matrix

Matrix-vector multiplication.

    y = alpha * A * x + beta * y

Specified by:

mv in interface Matrix

Parameters:

trans - normal, transpose, or conjugate transpose operation on the matrix.

alpha - the scalar alpha.

x - the input vector.

beta - the scalar beta. When beta is supplied as zero, y need not be set on input.

y - the input and output vector.

mv

public void mv(Vector work,
 int inputOffset,
 int outputOffset)

Description copied from interface: Matrix

Matrix-vector multiplication A * x.

Specified by:

mv in interface Matrix

Parameters:

work - the workspace for both input and output vector.

inputOffset - the offset of input vector in workspace.

outputOffset - the offset of output vector in workspace.

tv

public void tv(Vector work,
 int inputOffset,
 int outputOffset)

Description copied from interface: Matrix

Matrix-vector multiplication A' * x.

Specified by:

tv in interface Matrix

Parameters:

work - the workspace for both input and output vector.

inputOffset - the offset of input vector in workspace.

outputOffset - the offset of output vector in workspace.