smile.math.matrix

Class JMatrix

java.lang.Object

smile.math.matrix.Matrix

smile.math.matrix.DenseMatrix

smile.math.matrix.JMatrix

All Implemented Interfaces:

java.io.Serializable, MatrixMultiplication<DenseMatrix,DenseMatrix>

public class JMatrix
extends DenseMatrix

A pure Java implementation of DenseMatrix whose data is stored in a single 1D array of doubles in column major order.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
JMatrix(double[] A) Constructor of a column vector/matrix with given array as the internal storage.
JMatrix(double[][] A) Constructor.
JMatrix(int rows, int cols) Constructor of all-zero matrix.
JMatrix(int rows, int cols, double value) Constructor.
JMatrix(int rows, int cols, double[] value) Constructor.

Method Summary

Modifier and Type	Method and Description
JMatrix	aat() Returns A * A'
JMatrix	abmm(DenseMatrix B) Returns the result of matrix multiplication A * B.
JMatrix	abtmm(DenseMatrix B) Returns the result of matrix multiplication A * B'.
JMatrix	add(DenseMatrix b) In place addition A = A + B
DenseMatrix	add(DenseMatrix b, DenseMatrix c) C = A + B
JMatrix	add(double x) In place element-wise addition A = A + x
DenseMatrix	add(double x, DenseMatrix c) Element-wise addition C = A + x
JMatrix	add(double x, JMatrix c)
double	add(int i, int j, double x) A[i][j] += x
JMatrix	add(JMatrix b)
JMatrix	add(JMatrix b, JMatrix c)
JMatrix	ata() Returns A' * A
JMatrix	atbmm(DenseMatrix B) Returns the result of matrix multiplication A' * B.
double[]	atx(double[] x, double[] y) y = A' * x
double[]	atxpy(double[] x, double[] y) y = A' * x + y
double[]	atxpy(double[] x, double[] y, double b) y = A' * x + b * y
double[]	ax(double[] x, double[] y) y = A * x
double[]	axpy(double[] x, double[] y) y = A * x + y
double[]	axpy(double[] x, double[] y, double b) y = A * x + b * y
Cholesky	cholesky() Cholesky decomposition for symmetric and positive definite matrix.
JMatrix	copy() Returns a copy of this matrix.
double[]	data() Returns the array of storing the matrix.
JMatrix	div(DenseMatrix b) In place element-wise division A = A / B A = A - B
DenseMatrix	div(DenseMatrix b, DenseMatrix c) C = A / B
JMatrix	div(double x) In place element-wise division A = A / x
DenseMatrix	div(double x, DenseMatrix c) Element-wise addition C = A / x
JMatrix	div(double x, JMatrix c)
double	div(int i, int j, double x) A[i][j] /= x
JMatrix	div(JMatrix b)
JMatrix	div(JMatrix b, JMatrix c)
double[]	eig() Returns the eigen values in an array of size 2N.
EVD	eigen() Returns the eigen value decomposition.
double	get(int i, int j) Returns the entry value at row i and column j.
int	ld() The LDA (and LDB, LDC, etc.) parameter in BLAS is effectively the stride of the matrix as it is laid out in linear memory.
LU	lu() LU decomposition is computed by a "left-looking", dot-product, Crout/Doolittle algorithm.
JMatrix	mul(DenseMatrix b) In place element-wise multiplication A = A * B
DenseMatrix	mul(DenseMatrix b, DenseMatrix c) C = A * B
JMatrix	mul(double x) In place element-wise multiplication A = A * x
DenseMatrix	mul(double x, DenseMatrix c) Element-wise addition C = A * x
JMatrix	mul(double x, JMatrix c)
double	mul(int i, int j, double x) A[i][j] *= x
JMatrix	mul(JMatrix b)
JMatrix	mul(JMatrix b, JMatrix c)
int	ncols() Returns the number of columns.
int	nrows() Returns the number of rows.
QR	qr() QR Decomposition is computed by Householder reflections.
JMatrix	replaceNaN(double x) Replaces NaN's with given value.
double	set(int i, int j, double x) Set the entry value at row i and column j.
JMatrix	sub(DenseMatrix b) In place subtraction A = A - B
DenseMatrix	sub(DenseMatrix b, DenseMatrix c) C = A - B
JMatrix	sub(double x) In place element-wise subtraction A = A - x
DenseMatrix	sub(double x, DenseMatrix c) Element-wise addition C = A - x
JMatrix	sub(double x, JMatrix c)
double	sub(int i, int j, double x) A[i][j] -= x
JMatrix	sub(JMatrix b)
JMatrix	sub(JMatrix b, JMatrix c)
double	sum() Returns the sum of all elements in the matrix.
SVD	svd() Returns the singular value decomposition.
JMatrix	transpose() Returns the matrix transpose.

Methods inherited from class smile.math.matrix.DenseMatrix

array, cholesky, colMeans, colSums, eig, eigen, inverse, inverse, lu, norm, norm1, norm2, normFro, normInf, qr, rowMeans, rowSums, svd, update, xax

Methods inherited from class smile.math.matrix.Matrix

apply, diag, diag, eigen, eigen, eye, eye, isSymmetric, newInstance, newInstance, newInstance, ones, randn, randn, setSymmetric, svd, svd, toString, toString, trace, zeros

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

JMatrix

public JMatrix(double[][] A)

Constructor.

Parameters:

A - the array of matrix.

JMatrix

public JMatrix(double[] A)

Constructor of a column vector/matrix with given array as the internal storage.

Parameters:

A - the array of column vector.

JMatrix

public JMatrix(int rows,
               int cols)

Constructor of all-zero matrix.

JMatrix

public JMatrix(int rows,
               int cols,
               double value)

Constructor. Fill the matrix with given value.

JMatrix

public JMatrix(int rows,
               int cols,
               double[] value)

Constructor.

Parameters:

value - the array of matrix values arranged in column major format

Method Detail

copy

public JMatrix copy()

Description copied from class: DenseMatrix

Returns a copy of this matrix.

Specified by:

copy in class DenseMatrix

data

public double[] data()

Description copied from class: DenseMatrix

Returns the array of storing the matrix.

Specified by:

data in class DenseMatrix

transpose

public JMatrix transpose()

Description copied from class: DenseMatrix

Returns the matrix transpose.

Specified by:

transpose in class DenseMatrix

nrows

public int nrows()

Description copied from class: Matrix

Returns the number of rows.

Specified by:

nrows in class Matrix

ncols

public int ncols()

Description copied from class: Matrix

Returns the number of columns.

Specified by:

ncols in class Matrix

ld

public int ld()

Description copied from class: DenseMatrix

The LDA (and LDB, LDC, etc.) parameter in BLAS is effectively the stride of the matrix as it is laid out in linear memory. It is perfectly valid to have an LDA value which is larger than the leading dimension of the matrix which is being operated on. Typical cases where it is either useful or necessary to use a larger LDA value are when you are operating on a sub matrix from a larger dense matrix, and when hardware or algorithms offer performance advantages when storage is padded to round multiples of some optimal size (cache lines or GPU memory transaction size, or load balance in multiprocessor implementations, for example).

Specified by:

ld in class DenseMatrix

Returns:

the leading dimension

get

public double get(int i,
                  int j)

Description copied from class: Matrix

Returns the entry value at row i and column j.

Specified by:

get in class Matrix

set

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

Description copied from class: DenseMatrix

Set the entry value at row i and column j.

Specified by:

set in class DenseMatrix

add

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

Description copied from class: DenseMatrix

A[i][j] += x

Specified by:

add in class DenseMatrix

sub

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

Description copied from class: DenseMatrix

A[i][j] -= x

Specified by:

sub in class DenseMatrix

mul

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

Description copied from class: DenseMatrix

A[i][j] *= x

Specified by:

mul in class DenseMatrix

div

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

Description copied from class: DenseMatrix

A[i][j] /= x

Specified by:

div in class DenseMatrix

add

public JMatrix add(DenseMatrix b)

Description copied from class: DenseMatrix

In place addition A = A + B

Overrides:

add in class DenseMatrix

Returns:

this matrix

add

public JMatrix add(JMatrix b)

add

public DenseMatrix add(DenseMatrix b,
                       DenseMatrix c)

Description copied from class: DenseMatrix

C = A + B

Overrides:

add in class DenseMatrix

Returns:

the result matrix

add

public JMatrix add(JMatrix b,
                   JMatrix c)

sub

public JMatrix sub(DenseMatrix b)

Description copied from class: DenseMatrix

In place subtraction A = A - B

Overrides:

sub in class DenseMatrix

Returns:

this matrix

sub

public JMatrix sub(JMatrix b)

sub

public DenseMatrix sub(DenseMatrix b,
                       DenseMatrix c)

Description copied from class: DenseMatrix

C = A - B

Overrides:

sub in class DenseMatrix

Returns:

the result matrix

sub

public JMatrix sub(JMatrix b,
                   JMatrix c)

mul

public JMatrix mul(DenseMatrix b)

Description copied from class: DenseMatrix

In place element-wise multiplication A = A * B

Overrides:

mul in class DenseMatrix

Returns:

this matrix

mul

public JMatrix mul(JMatrix b)

mul

public DenseMatrix mul(DenseMatrix b,
                       DenseMatrix c)

Description copied from class: DenseMatrix

C = A * B

Overrides:

mul in class DenseMatrix

Returns:

the result matrix

mul

public JMatrix mul(JMatrix b,
                   JMatrix c)

div

public JMatrix div(DenseMatrix b)

Description copied from class: DenseMatrix

In place element-wise division A = A / B A = A - B

Overrides:

div in class DenseMatrix

Returns:

this matrix

div

public JMatrix div(JMatrix b)

div

public DenseMatrix div(DenseMatrix b,
                       DenseMatrix c)

Description copied from class: DenseMatrix

C = A / B

Overrides:

div in class DenseMatrix

Returns:

the result matrix

div

public JMatrix div(JMatrix b,
                   JMatrix c)

add

public JMatrix add(double x)

Description copied from class: DenseMatrix

In place element-wise addition A = A + x

Overrides:

add in class DenseMatrix

add

public DenseMatrix add(double x,
                       DenseMatrix c)

Description copied from class: DenseMatrix

Element-wise addition C = A + x

Overrides:

add in class DenseMatrix

add

public JMatrix add(double x,
                   JMatrix c)

sub

public JMatrix sub(double x)

Description copied from class: DenseMatrix

In place element-wise subtraction A = A - x

Overrides:

sub in class DenseMatrix

sub

public DenseMatrix sub(double x,
                       DenseMatrix c)

Description copied from class: DenseMatrix

Element-wise addition C = A - x

Overrides:

sub in class DenseMatrix

sub

public JMatrix sub(double x,
                   JMatrix c)

mul

public JMatrix mul(double x)

Description copied from class: DenseMatrix

In place element-wise multiplication A = A * x

Overrides:

mul in class DenseMatrix

mul

public DenseMatrix mul(double x,
                       DenseMatrix c)

Description copied from class: DenseMatrix

Element-wise addition C = A * x

Overrides:

mul in class DenseMatrix

mul

public JMatrix mul(double x,
                   JMatrix c)

div

public JMatrix div(double x)

Description copied from class: DenseMatrix

In place element-wise division A = A / x

Overrides:

div in class DenseMatrix

div

public DenseMatrix div(double x,
                       DenseMatrix c)

Description copied from class: DenseMatrix

Element-wise addition C = A / x

Overrides:

div in class DenseMatrix

div

public JMatrix div(double x,
                   JMatrix c)

replaceNaN

public JMatrix replaceNaN(double x)

Description copied from class: DenseMatrix

Replaces NaN's with given value.

Overrides:

replaceNaN in class DenseMatrix

sum

public double sum()

Description copied from class: DenseMatrix

Returns the sum of all elements in the matrix.

Overrides:

sum in class DenseMatrix

Returns:

the sum of all elements.

ata

public JMatrix ata()

Description copied from class: Matrix

Returns A' * A

Specified by:

ata in class DenseMatrix

aat

public JMatrix aat()

Description copied from class: Matrix

Returns A * A'

Specified by:

aat in class DenseMatrix

ax

public double[] ax(double[] x,
                   double[] y)

Description copied from class: Matrix

y = A * x

Specified by:

ax in class Matrix

Returns:

y

axpy

public double[] axpy(double[] x,
                     double[] y)

Description copied from class: Matrix

y = A * x + y

Specified by:

axpy in class Matrix

Returns:

y

axpy

public double[] axpy(double[] x,
                     double[] y,
                     double b)

Description copied from class: Matrix

y = A * x + b * y

Specified by:

axpy in class Matrix

Returns:

y

atx

public double[] atx(double[] x,
                    double[] y)

Description copied from class: Matrix

y = A' * x

Specified by:

atx in class Matrix

Returns:

y

atxpy

public double[] atxpy(double[] x,
                      double[] y)

Description copied from class: Matrix

y = A' * x + y

Specified by:

atxpy in class Matrix

Returns:

y

atxpy

public double[] atxpy(double[] x,
                      double[] y,
                      double b)

Description copied from class: Matrix

y = A' * x + b * y

Specified by:

atxpy in class Matrix

Returns:

y

abmm

public JMatrix abmm(DenseMatrix B)

Description copied from interface: MatrixMultiplication

Returns the result of matrix multiplication A * B.

abtmm

public JMatrix abtmm(DenseMatrix B)

Description copied from interface: MatrixMultiplication

Returns the result of matrix multiplication A * B'.

atbmm

public JMatrix atbmm(DenseMatrix B)

Description copied from interface: MatrixMultiplication

Returns the result of matrix multiplication A' * B.

lu

public LU lu()

LU decomposition is computed by a "left-looking", dot-product, Crout/Doolittle algorithm.

Specified by:

lu in class DenseMatrix

cholesky

public Cholesky cholesky()

Cholesky decomposition for symmetric and positive definite matrix. Only the lower triangular part will be used in the decomposition.

Specified by:

cholesky in class DenseMatrix

Throws:

java.lang.IllegalArgumentException - if the matrix is not positive definite.

qr

public QR qr()

QR Decomposition is computed by Householder reflections.

Specified by:

qr in class DenseMatrix

svd

public SVD svd()

Description copied from class: DenseMatrix

Returns the singular value decomposition. Note that the input matrix will hold U on output.

Specified by:

svd in class DenseMatrix

eig

public double[] eig()

Description copied from class: DenseMatrix

Returns the eigen values in an array of size 2N. The first half and second half of returned array contain the real and imaginary parts, respectively, of the computed eigenvalues.

Specified by:

eig in class DenseMatrix

eigen

public EVD eigen()

Description copied from class: DenseMatrix

Returns the eigen value decomposition. Note that the input matrix will be overwritten on output.

Specified by:

eigen in class DenseMatrix