All Superinterfaces:

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

All Known Implementing Classes:

JMatrix
```
public interface DenseMatrix
extends Matrix, MatrixMultiplication<DenseMatrix,DenseMatrix>
```
An abstract interface of dense matrix.

Author:

Haifeng Li

Method Summary

All Methods Instance Methods Abstract Methods Default Methods
Modifier and Type	Method	Description
`DenseMatrix`	`aat()`	Returns A * A'
`default DenseMatrix`	`add(double x)`	In place element-wise addition A = A + x
`default DenseMatrix`	`add(double x, DenseMatrix c)`	Element-wise addition C = A + x
`double`	`add(int i, int j, double x)`	A[i][j] += x
`default DenseMatrix`	`add(DenseMatrix b)`	In place addition A = A + B
`default DenseMatrix`	`add(DenseMatrix b, DenseMatrix c)`	C = A + B
`default double[][]`	`array()`	Return the two-dimensional array of matrix.
`DenseMatrix`	`ata()`	Returns A' * A
`Cholesky`	`cholesky()`	Returns the Cholesky decomposition.
`default Cholesky`	`cholesky(boolean inPlace)`	Returns the Cholesky decomposition.
`default double[]`	`colMeans()`	Returns the mean of each column for a matrix.
`default double[]`	`colSums()`	Returns the sum of each column for a matrix.
`DenseMatrix`	`copy()`	Returns a copy of this matrix.
`double[]`	`data()`	Returns the array of storing the matrix.
`default DenseMatrix`	`div(double x)`	In place element-wise division A = A / x
`default DenseMatrix`	`div(double x, DenseMatrix c)`	Element-wise addition C = A / x
`double`	`div(int i, int j, double x)`	A[i][j] /= x
`default DenseMatrix`	`div(DenseMatrix b)`	In place element-wise division A = A / B A = A - B
`default DenseMatrix`	`div(DenseMatrix b, DenseMatrix c)`	C = A / B
`double[]`	`eig()`	Returns the eigen values in an array of size 2N.
`default double[]`	`eig(boolean inPlace)`	Returns the eigen values in an array of size 2N.
`EVD`	`eigen()`	Returns the eigen value decomposition.
`default EVD`	`eigen(boolean inPlace)`	Returns the eigen value decomposition.
`default DenseMatrix`	`inverse()`	Returns the inverse matrix.
`default DenseMatrix`	`inverse(boolean inPlace)`	Returns the inverse matrix.
`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()`	Returns the LU decomposition.
`default LU`	`lu(boolean inPlace)`	Returns the LU decomposition.
`default DenseMatrix`	`mul(double x)`	In place element-wise multiplication A = A * x
`default DenseMatrix`	`mul(double x, DenseMatrix c)`	Element-wise addition C = A * x
`double`	`mul(int i, int j, double x)`	A[i][j] *= x
`default DenseMatrix`	`mul(DenseMatrix b)`	In place element-wise multiplication A = A * B
`default DenseMatrix`	`mul(DenseMatrix b, DenseMatrix c)`	C = A * B
`default double`	`norm()`	L2 matrix norm.
`default double`	`norm1()`	L1 matrix norm.
`default double`	`norm2()`	L2 matrix norm.
`default double`	`normFro()`	Frobenius matrix norm.
`default double`	`normInf()`	Infinity matrix norm.
`QR`	`qr()`	Returns the QR decomposition.
`default QR`	`qr(boolean inPlace)`	Returns the QR decomposition.
`default DenseMatrix`	`replaceNaN(double x)`	Replaces NaN's with given value.
`default double[]`	`rowMeans()`	Returns the mean of each row for a matrix.
`default double[]`	`rowSums()`	Returns the sum of each row for a matrix.
`double`	`set(int i, int j, double x)`	Set the entry value at row i and column j.
`default DenseMatrix`	`sub(double x)`	In place element-wise subtraction A = A - x
`default DenseMatrix`	`sub(double x, DenseMatrix c)`	Element-wise addition C = A - x
`double`	`sub(int i, int j, double x)`	A[i][j] -= x
`default DenseMatrix`	`sub(DenseMatrix b)`	In place subtraction A = A - B
`default DenseMatrix`	`sub(DenseMatrix b, DenseMatrix c)`	C = A - B
`default double`	`sum()`	Returns the sum of all elements in the matrix.
`SVD`	`svd()`	Returns the singular value decomposition.
`default SVD`	`svd(boolean inPlace)`	Returns the singular value decomposition.
`DenseMatrix`	`transpose()`	Returns the matrix transpose.
`default double`	`update(int i, int j, double x)`	Set the entry value at row i and column j.
`default double`	`xax(double[] x)`	Returns x' * A * x.

Methods inherited from interface smile.math.matrix.Matrix
apply, atx, atxpy, atxpy, ax, axpy, axpy, diag, eigen, eigen, get, isSymmetric, ncols, nrows, setSymmetric, svd, svd, toString, trace

Methods inherited from interface smile.math.matrix.MatrixMultiplication
abmm, abtmm, atbmm

- Method Detail
  - data
```
double[] data()
```
    Returns the array of storing the matrix.
  - ld
```
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. 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).
    
    Returns:
    
    the leading dimension
  - set
```
double set(int i,
           int j,
           double x)
```
    Set the entry value at row i and column j.
  - update
```
default double update(int i,
                      int j,
                      double x)
```
    Set the entry value at row i and column j. For Scala users.
  - lu
```
LU lu()
```
    Returns the LU decomposition. This input matrix will be overwritten with the decomposition.
  - lu
```
default LU lu(boolean inPlace)
```
    Returns the LU decomposition.
    
    Parameters:
    
    inPlace - if true, this matrix will be used for matrix decomposition.
  - cholesky
```
Cholesky cholesky()
```
    Returns the Cholesky decomposition. This input matrix will be overwritten with the decomposition.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the matrix is not positive definite.
  - cholesky
```
default Cholesky cholesky(boolean inPlace)
```
    Returns the Cholesky decomposition.
    
    Parameters:
    
    inPlace - if true, this matrix will be used for matrix decomposition.
    
    Throws:
    
    java.lang.IllegalArgumentException - if the matrix is not positive definite.
  - qr
```
QR qr()
```
    Returns the QR decomposition. This input matrix will be overwritten with the decomposition.
  - qr
```
default QR qr(boolean inPlace)
```
    Returns the QR decomposition.
    
    Parameters:
    
    inPlace - if true, this matrix will be used for matrix decomposition.
  - svd
```
SVD svd()
```
    Returns the singular value decomposition. Note that the input matrix will hold U on output.
  - svd
```
default SVD svd(boolean inPlace)
```
    Returns the singular value decomposition.
    
    Parameters:
    
    inPlace - if true, this matrix will hold U on output.
  - eigen
```
EVD eigen()
```
    Returns the eigen value decomposition. Note that the input matrix will be overwritten on output.
  - eigen
```
default EVD eigen(boolean inPlace)
```
    Returns the eigen value decomposition.
    
    Parameters:
    
    inPlace - if true, this matrix will be overwritten U on output.
  - eig
```
double[] eig()
```
    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.
  - eig
```
default double[] eig(boolean inPlace)
```
    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.
    
    Parameters:
    
    inPlace - if true, this matrix will be overwritten U on output.
  - transpose
```
DenseMatrix transpose()
```
    Returns the matrix transpose.
    
    Specified by:
    
    transpose in interface Matrix
  - inverse
```
default DenseMatrix inverse()
```
    Returns the inverse matrix.
  - inverse
```
default DenseMatrix inverse(boolean inPlace)
```
    Returns the inverse matrix.
    
    Parameters:
    
    inPlace - if true, this matrix will be used for matrix decomposition.
  - norm1
```
default double norm1()
```
    L1 matrix norm. Maximum column sum.
  - norm2
```
default double norm2()
```
    L2 matrix norm. Maximum singular value.
  - norm
```
default double norm()
```
    L2 matrix norm. Maximum singular value.
  - normInf
```
default double normInf()
```
    Infinity matrix norm. Maximum row sum.
  - normFro
```
default double normFro()
```
    Frobenius matrix norm. Sqrt of sum of squares of all elements.
  - xax
```
default double xax(double[] x)
```
    Returns x' * A * x. The left upper submatrix of A is used in the computation based on the size of x.
  - rowSums
```
default double[] rowSums()
```
    Returns the sum of each row for a matrix.
  - rowMeans
```
default double[] rowMeans()
```
    Returns the mean of each row for a matrix.
  - colSums
```
default double[] colSums()
```
    Returns the sum of each column for a matrix.
  - colMeans
```
default double[] colMeans()
```
    Returns the mean of each column for a matrix.
  - copy
```
DenseMatrix copy()
```
    Returns a copy of this matrix.
  - ata
```
DenseMatrix ata()
```
    Description copied from interface: Matrix
    
    Returns A' * A
    
    Specified by:
    
    ata in interface Matrix
  - aat
```
DenseMatrix aat()
```
    Description copied from interface: Matrix
    
    Returns A * A'
    
    Specified by:
    
    aat in interface Matrix
  - add
```
double add(int i,
           int j,
           double x)
```
    A[i][j] += x
  - sub
```
double sub(int i,
           int j,
           double x)
```
    A[i][j] -= x
  - mul
```
double mul(int i,
           int j,
           double x)
```
    A[i][j] *= x
  - div
```
double div(int i,
           int j,
           double x)
```
    A[i][j] /= x
  - add
```
default DenseMatrix add(DenseMatrix b,
                        DenseMatrix c)
```
    C = A + B
    
    Returns:
    
    the result matrix
  - add
```
default DenseMatrix add(DenseMatrix b)
```
    In place addition A = A + B
    
    Returns:
    
    this matrix
  - sub
```
default DenseMatrix sub(DenseMatrix b,
                        DenseMatrix c)
```
    C = A - B
    
    Returns:
    
    the result matrix
  - sub
```
default DenseMatrix sub(DenseMatrix b)
```
    In place subtraction A = A - B
    
    Returns:
    
    this matrix
  - mul
```
default DenseMatrix mul(DenseMatrix b,
                        DenseMatrix c)
```
    C = A * B
    
    Returns:
    
    the result matrix
  - mul
```
default DenseMatrix mul(DenseMatrix b)
```
    In place element-wise multiplication A = A * B
    
    Returns:
    
    this matrix
  - div
```
default DenseMatrix div(DenseMatrix b,
                        DenseMatrix c)
```
    C = A / B
    
    Returns:
    
    the result matrix
  - div
```
default DenseMatrix div(DenseMatrix b)
```
    In place element-wise division A = A / B A = A - B
    
    Returns:
    
    this matrix
  - add
```
default DenseMatrix add(double x,
                        DenseMatrix c)
```
    Element-wise addition C = A + x
  - add
```
default DenseMatrix add(double x)
```
    In place element-wise addition A = A + x
  - sub
```
default DenseMatrix sub(double x,
                        DenseMatrix c)
```
    Element-wise addition C = A - x
  - sub
```
default DenseMatrix sub(double x)
```
    In place element-wise subtraction A = A - x
  - mul
```
default DenseMatrix mul(double x,
                        DenseMatrix c)
```
    Element-wise addition C = A * x
  - mul
```
default DenseMatrix mul(double x)
```
    In place element-wise multiplication A = A * x
  - div
```
default DenseMatrix div(double x,
                        DenseMatrix c)
```
    Element-wise addition C = A / x
  - div
```
default DenseMatrix div(double x)
```
    In place element-wise division A = A / x
  - replaceNaN
```
default DenseMatrix replaceNaN(double x)
```
    Replaces NaN's with given value.
  - sum
```
default double sum()
```
    Returns the sum of all elements in the matrix.
    
    Returns:
    
    the sum of all elements.
  - array
```
default double[][] array()
```
    Return the two-dimensional array of matrix.
    
    Returns:
    
    the two-dimensional array of matrix.

Interface DenseMatrix

Method Summary

Methods inherited from interface smile.math.matrix.Matrix

Methods inherited from interface smile.math.matrix.MatrixMultiplication

Method Detail

data

ld

set

update

lu

lu

cholesky

cholesky

qr

qr

svd

svd

eigen

eigen

eig

eig

transpose

inverse

inverse

norm1

norm2

norm

normInf

normFro

xax

rowSums

rowMeans

colSums

colMeans

copy

ata

aat

add

sub

mul

div

add

add

sub

sub

mul

mul

div

div

add

add

sub

sub

mul

mul

div

div

replaceNaN

sum

array