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jat.matvec.data
Class Matrix

java.lang.Object
  jat.matvec.data.Matrix

All Implemented Interfaces:: java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:: RandomMatrix, RotationMatrix

public class Matrix
extends java.lang.Object
implements java.lang.Cloneable, java.io.Serializable
extends java.lang.Object
implements java.lang.Cloneable, java.io.Serializable

The Matrix Class provides the fundamental operations of numerical linear algebra (from the package JAMA), basic manipulations, and visualization tools. All the operations in this version of the Matrix Class involve only real matrices. This Matrix Class is an extension of JMAT's Matrix Class, which was an extension of JAMA's Matrix Class.

Version:: 1.0
Author:: Dave Gaylor
See Also:: Serialized Form

Field Summary
`double[][]`	`A` Array for internal storage of elements.
`int`	`m` Row and column dimensions.
`int`	`n` Row and column dimensions.

Constructor Summary
`Matrix(double[][] B)` Construct a matrix from a 2D-array.
`Matrix(double[][] B, int m, int n)` Construct a matrix from a 2D-array.
`Matrix(double[] vals, int m)` Construct a matrix from a one-dimensional packed array
`Matrix(int n)` Construct an n-by-n identity matrix.
`Matrix(int m, int n)` Construct an m-by-n matrix of zeros.
`Matrix(int m, int n, double s)` Construct an m-by-n constant matrix.
`Matrix(Matrix in)` Construct a matrix from a Matrix.
`Matrix(VectorN X)` Construct a square matrix from a vector.

Method Summary
`void`	`checkColumnDimension(int column)` Check if number of Columns(A) == column.
`void`	`checkColumnDimension(Matrix B)` Check if number of Columns(A) == number of Columns(B).
`static void`	`checkIndicesDimensions(int[][] i, int[][] j)` Check if indices have the same length.
`static void`	`checkIndicesLengths(int[] i, int[] j)` Check if indices have the same length.
`void`	`checkMatrixDimensions(int m2, int n2)` Check if size(A) == m2*n2.
`void`	`checkMatrixDimensions(Matrix B)` Check if size(A) == size(B).
`void`	`checkRowDimension(int row)` Check if number of Rows(A) == row.
`void`	`checkRowDimension(Matrix B)` Check if number of Rows(A) == number of Rows(B).
`CholeskyDecomposition`	`chol()` Cholesky Decomposition
`java.lang.Object`	`clone()` Clone the Matrix object.
`double`	`cond()` Matrix condition (2 norm)
`Matrix`	`copy()` Make a deep copy of a matrix
`double`	`det()` Matrix determinant
`Matrix`	`diag()` Matrix diagonal extraction.
`Matrix`	`diag(int num)` Matrix diagonal extraction.
`VectorN`	`diagonal()` Return the diagonals of a square matrix in a VectorN
`Matrix`	`dist(Matrix B)` Generate a matrix, each column contents the Euclidian distance between the columns.
`Matrix`	`distColumns(Matrix B)` Generate a matrix, each line contents the Euclidian distance between the lines.
`Matrix`	`distRows(Matrix B)` Generate a matrix, each column contents the Euclidian distance between the columns.
`Matrix`	`divide(double s)` Divide a matrix by a scalar, C = A/s
`Matrix`	`divide(Matrix B)` Linear algebraic matrix division, A / B
`Matrix`	`ebeAbs()` Element-by-element inverse
`Matrix`	`ebeCos()` Element-by-element cosinus
`Matrix`	`ebeDivide(double s)` Divide a matrix by a scalar, C = A/s
`Matrix`	`ebeDivide(Matrix B)` Element-by-element right division, C = A./B
`Matrix`	`ebeExp()` Element-by-element exponential
`Matrix`	`ebeFun(DoubleFunction fun)` Element-by-element function evaluation
`Matrix`	`ebeIndFun(DoubleFunction fun)` Element-by-element indicial function evaluation
`Matrix`	`ebeInv()` Element-by-element inverse
`Matrix`	`ebeLog()` Element-by-element neperian logarithm
`Matrix`	`ebeMinus(double s)` Sub a scalar to each element of a matrix, C = A .- B
`Matrix`	`ebePlus(double s)` Add a scalar to each element of a matrix, C = A .+ s
`Matrix`	`ebePow(double p)` Element-by-element power
`Matrix`	`ebePow(Matrix B)` Element-by-element power
`Matrix`	`ebeSin()` Element-by-element sinus
`Matrix`	`ebeSqrt()` Element-by-element inverse
`Matrix`	`ebeTimes(double s)` Multiply a matrix by a scalar, C = s*A
`Matrix`	`ebeTimes(Matrix B)` Element-by-element multiplication, C = A.*B
`EigenvalueDecomposition`	`eig()` Eigenvalue Decomposition
`int[][]`	`find(double e)` Find an element
`int[][]`	`find(java.lang.String test, double e)` Find elements verifying a boolean test
`Matrix`	`findMatrix(double e)` Find an element
`Matrix`	`findMatrix(java.lang.String test, double e)` Find elements verifying a boolean test
`static Matrix`	`fromFile(java.io.File file)` Load the Matrix from a file
`static Matrix`	`fromFile(java.lang.String fileName)` Load the Matrix from a file.
`static Matrix`	`fromString(java.lang.String s)` Load the Matrix from a String
`Matrix`	`get(int[][] I, int[][] J)` Get a several elements.
`Matrix`	`get(int[] I, int[] J)` Get a several elements in Column.
`double`	`get(int i, int j)` Get a single element.
`double[][]`	`getArray()` Access the internal two-dimensional array.
`double[][]`	`getArrayCopy()` Copy the internal two-dimensional array.
`Matrix`	`getColumn(int c)` Copy an internal one-dimensional array from a column.
`double[]`	`getColumnArrayCopy(int c)` Copy an internal one-dimensional array from a column.
`int`	`getColumnDimension()` Get column dimension.
`double[]`	`getColumnPackedCopy()` Make a one-dimensional column packed copy of the internal array.
`VectorN`	`getColumnPackedVector()` Make a one-dimensional column packed copy of the internal array.
`Matrix`	`getColumns(int[] c)` Copy an internal one-dimensional array from a column.
`VectorN`	`getColumnVector(int c)` Copy a column into a VectorN.
`Matrix`	`getMatrix(int i0, int i1, int j0, int j1)` Get a submatrix.
`Matrix`	`getRow(int l)` Copy an internal one-dimensional array from a row.
`double[]`	`getRowArrayCopy(int l)` Copy an internal one-dimensional array from a row.
`int`	`getRowDimension()` Get row dimension.
`double[]`	`getRowPackedCopy()` Make a one-dimensional row packed copy of the internal array.
`VectorN`	`getRowPackedVector()` Make a one-dimensional row packed copy of the internal array.
`Matrix`	`getRows(int[] l)` Copy an internal one-dimensional array from many rows.
`VectorN`	`getRowVector(int c)` Copy a row into a VectorN.
`static Matrix`	`identity(int m, int n)` Generate identity matrix
`static Matrix`	`increment(int m, int n, double begin, double pitch)` Generate a matrix with a constant pitch beetwen each row
`static Matrix`	`incrementColumns(int m, int n, double begin, double pitch)` Generate a matrix with a constant pitch beetwen each column
`static Matrix`	`incrementRows(int m, int n, double begin, double pitch)` Generate a matrix with a constant pitch beetwen each row
`Matrix`	`inverse()` Matrix inverse or pseudoinverse
`Matrix`	`invert()` Invert a matrix.
`LUDecomposition`	`lu()` LU Decomposition
`Matrix`	`max()` Generate a row matrix, each column contents the maximum value of the columns.
`Matrix`	`maxColumns()` Generate a column matrix, each line contents the maximum value of the lines.
`Matrix`	`maxRows()` Generate a row matrix, each column contents the maximum value of the columns.
`Matrix`	`merge(Matrix B)` Matrix merge.
`static Matrix`	`merge(Matrix[] Xs)` Generate a matrix from other matrix.
`Matrix`	`mergeColumns(Matrix B)` Matrix merge.
`static Matrix`	`mergeColumns(Matrix[] Xs)` Generate a matrix from other matrix.
`Matrix`	`mergeRows(Matrix B)` Matrix merge.
`static Matrix`	`mergeRows(Matrix[] Xs)` Generate a matrix from other matrix.
`Matrix`	`min()` Generate a row matrix, each column contents the minimum value of the columns.
`Matrix`	`minColumns()` Generate a column matrix, each line contents the minimum value of the lines.
`Matrix`	`minRows()` Generate a row matrix, each column contents the minimum value of the columns.
`Matrix`	`minus(Matrix B)` C = A - B
`double`	`norm1()` One norm
`double`	`norm2()` Two norm
`double`	`normF()` Frobenius norm
`double`	`normInf()` Infinity norm
`Matrix`	`plus(Matrix B)` C = A + B
`void`	`print()` Print the Matrix to System.out
`void`	`print(java.io.PrintWriter pw)` Print the Matrix to a PrintWriter
`void`	`print(java.lang.String title)` Print the Matrix to System.out
`void`	`printrows(java.lang.String title, int rows)` Print the first n rows of Matrix to System.out
`Matrix`	`prod()` Generate a row matrix, each column contents the product value of the columns.
`Matrix`	`prodColumns()` Generate a column matrix, each line contents the product value of the lines.
`Matrix`	`prodRows()` Generate a row matrix, each column contents the product value of the columns.
`QRDecomposition`	`qr()` QR Decomposition
`static Matrix`	`random(int m, int n)` Generate matrix with random elements
`int`	`rank()` Matrix rank
`Matrix`	`reshape(int m2, int n2)` Matrix reshape by Row.
`Matrix`	`reshapeColumns(int m2, int n2)` Matrix reshape by Column.
`Matrix`	`reshapeRows(int m2, int n2)` Matrix reshape by Row.
`Matrix`	`resize(int m2, int n2)` Matrix resize.
`void`	`set(int[] I, int[] J, double s)` Set several elements.
`void`	`set(int i, int j, double s)` Set a single element.
`void`	`setColumn(int c, Matrix B)` Set a column to an internal one-dimensional Column.
`void`	`setColumn(int c, VectorN B)` Set a column to an internal one-dimensional Column.
`void`	`setColumns(int[] c, Matrix B)` Copy an internal one-dimensional array from a column.
`void`	`setMatrix(int[] I0, int[] J0, Matrix X)` Set a submatrix.
`void`	`setMatrix(int i0, int i1, int j0, int j1, double v)` Set a submatrix.
`void`	`setMatrix(int i0, int i1, int j0, int j1, Matrix X)` Set a submatrix.
`void`	`setMatrix(int i0, int j0, Matrix X)` Set a submatrix.
`void`	`setRow(int l, Matrix B)` Copy an internal one-dimensional array from a row.
`void`	`setRow(int l, VectorN B)` Copy an internal one-dimensional array from a row.
`void`	`setRows(int[] l, Matrix B)` Copy an internal one-dimensional array from many rows.
`Matrix`	`solve(Matrix B)` Solve A*X = B
`int[]`	`sort(int c)` Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'
`int[]`	`sortColumns(int l)` Generate a row-permuted matrix, columns are permuted in order to sort the row 'l'
`Matrix`	`sortedColumnsMatrix(int l)` Generate a row-permuted matrix, columns are permuted in order to sort the row 'l'
`Matrix`	`sortedMatrix(int c)` Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'
`Matrix`	`sortedRowsMatrix(int c)` Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'
`int[]`	`sortRows(int c)` Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'
`Matrix`	`sum()` Generate a row matrix, each column contents the sum value of the columns.
`Matrix`	`sumColumns()` Generate a column matrix, each line contents the sum value of the lines.
`Matrix`	`sumRows()` Generate a row matrix, each column contents the sum value of the columns.
`SingularValueDecomposition`	`svd()` Singular Value Decomposition
`Matrix`	`times(double s)` Multiply a matrix by a scalar, C = s*A
`double[]`	`times(double[] B)` Matrix multiplied by a column array
`Matrix`	`times(Matrix B)` Linear algebraic matrix multiplication, A * B
`VectorN`	`times(VectorN B)` Matrix multiplied by a column vector
`void`	`toCommandLine(java.lang.String title)` Print the Matrix in the Command Line.
`void`	`toFile(java.io.File file)` Save the Matrix in a file.
`void`	`toFile(java.lang.String fileName)` Save the Matrix in a file.
`MatrixPlot2D`	`toFramePlot2D(java.lang.String title)` Plot the Matrix in a JFrame
`MatrixPlot2D`	`toFramePlot2D(java.lang.String title, Matrix X)` Plot the Matrix in a JFrame
`MatrixPlot3D`	`toFramePlot3D(java.lang.String title)` Plot the Matrix in a JFrame
`MatrixPlot3D`	`toFramePlot3D(java.lang.String title, Matrix X, Matrix Y)` Plot the Matrix in a Window in a JFrame
`void`	`toFrameTable(java.lang.String title)` Print the Matrix data in a Table in a JFrame
`MatrixPlot2D`	`toPanelPlot2D()` Plot the Matrix in a JPanel
`MatrixPlot2D`	`toPanelPlot2D(Matrix X)` Plot the Matrix in a JPanel
`MatrixPlot3D`	`toPanelPlot3D()` Plot the Matrix in a JPanel
`MatrixPlot3D`	`toPanelPlot3D(Matrix X, Matrix Y)` Plot the Matrix in a JFrame
`MatrixTable`	`toPanelTable()` Print the Matrix in a JTable
`java.lang.String`	`toString()` Convert the Matrix into a String
`double`	`trace()` Matrix trace.
`Matrix`	`transpose()` Matrix transpose.
`Matrix`	`uminus()` Unary minus

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Field Detail

A

public double[][] A

Array for internal storage of elements.

m

public int m

Row and column dimensions.

n

public int n

Row and column dimensions.

Constructor Detail

Matrix

public Matrix(int m,
              int n)

Construct an m-by-n matrix of zeros.

Parameters:: m - Number of rows.; n - Number of colums.

Matrix

public Matrix(int n)

Construct an n-by-n identity matrix.

Parameters:: n - Number of rows and colums.

Matrix

public Matrix(Matrix in)

Construct a matrix from a Matrix.

Parameters:: in - Matrix to create a copy of.

Matrix

public Matrix(int m,
              int n,
              double s)

Construct an m-by-n constant matrix.

Parameters:: m - Number of rows.; n - Number of colums.; s - Fill the matrix with this scalar value.

Matrix

public Matrix(VectorN X)

Construct a square matrix from a vector.

Parameters:: X - Put the elements of x on the diagonal.

Matrix

public Matrix(double[][] B)

Construct a matrix from a 2D-array.

Parameters:: B - Two-dimensional array of doubles.
Throws:: java.lang.IllegalArgumentException - All rows must have the same length
See Also:: #constructWithCopy

Matrix

public Matrix(double[][] B,
              int m,
              int n)

Construct a matrix from a 2D-array.

Parameters:: B - Two-dimensional array of doubles.; m - Number of rows.; n - Number of columns.
Throws:: java.lang.IllegalArgumentException - All rows must have the same length
See Also:: #constructWithCopy

Matrix

public Matrix(double[] vals,
              int m)

Construct a matrix from a one-dimensional packed array

Parameters:: vals - One-dimensional array of doubles, packed by columns (ala Fortran).; m - Number of rows.
Throws:: java.lang.IllegalArgumentException - Array length must be a multiple of m.

Method Detail

random

public static Matrix random(int m,
                            int n)

Generate matrix with random elements

Parameters:: m - Number of rows.; n - Number of colums.
Returns:: An m-by-n matrix with uniformly distributed random elements.

identity

public static Matrix identity(int m,
                              int n)

Generate identity matrix

Parameters:: m - Number of rows.; n - Number of colums.
Returns:: An m-by-n matrix with ones on the diagonal and zeros elsewhere.

increment

public static Matrix increment(int m,
                               int n,
                               double begin,
                               double pitch)

Generate a matrix with a constant pitch beetwen each row

Parameters:: m - Number of rows.; n - Number of colums.; begin - begining value to increment.; pitch - pitch to add.
Returns:: An m-by-n matrix.

incrementRows

public static Matrix incrementRows(int m,
                                   int n,
                                   double begin,
                                   double pitch)

Generate a matrix with a constant pitch beetwen each row

Parameters:: m - Number of rows.; n - Number of colums.; begin - begining value to increment.; pitch - pitch to add.
Returns:: An m-by-n matrix.

incrementColumns

public static Matrix incrementColumns(int m,
                                      int n,
                                      double begin,
                                      double pitch)

Generate a matrix with a constant pitch beetwen each column

Parameters:: m - Number of rows.; n - Number of colums.; begin - begining value to increment.; pitch - pitch to add.
Returns:: An m-by-n matrix.

merge

public static Matrix merge(Matrix[] Xs)

Generate a matrix from other matrix.

Parameters:: Xs - Matrix to merge.
Returns:: An m1+m2+...-by-n matrix.

mergeRows

public static Matrix mergeRows(Matrix[] Xs)

Generate a matrix from other matrix.

Parameters:: Xs - Matrix to merge.
Returns:: An m1+m2+...-by-n matrix.

mergeColumns

public static Matrix mergeColumns(Matrix[] Xs)

Generate a matrix from other matrix.

Parameters:: Xs - Matrix to merge.
Returns:: An m-by-n1+n2+... matrix.

copy

public Matrix copy()

Make a deep copy of a matrix

Returns:: A matrix.

clone

public java.lang.Object clone()

Clone the Matrix object.

Overrides:: clone in class java.lang.Object

Returns:: A matrix Object.

getArray

public double[][] getArray()

Access the internal two-dimensional array.

Returns:: Pointer to the two-dimensional array of matrix elements.

getArrayCopy

public double[][] getArrayCopy()

Copy the internal two-dimensional array.

Returns:: Two-dimensional array copy of matrix elements.

get

public double get(int i,
                  int j)

Get a single element.

Parameters:: i - Row index.; j - Column index.
Returns:: A(i,j)
Throws:: java.lang.ArrayIndexOutOfBoundsException

get

public Matrix get(int[] I,
                  int[] J)

Get a several elements in Column.

Parameters:: I - Row index.; J - Column index.
Returns:: A(I(:),J(:))
Throws:: java.lang.ArrayIndexOutOfBoundsException

get

public Matrix get(int[][] I,
                  int[][] J)

Get a several elements.

Parameters:: I - Row index.; J - Column index.
Returns:: A(I(:,:),J(:,:))
Throws:: java.lang.ArrayIndexOutOfBoundsException

getMatrix

public Matrix getMatrix(int i0,
                        int i1,
                        int j0,
                        int j1)

Get a submatrix.

Parameters:: i0 - Initial row index; i1 - Final row index; j0 - Initial column index; j1 - Final column index
Returns:: A(i0:i1,j0:j1)
Throws:: java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getRowArrayCopy

public double[] getRowArrayCopy(int l)

Copy an internal one-dimensional array from a row.

Parameters:: l - Row index
Returns:: one-dimensional array copy of matrix elements.

getRowVector

public VectorN getRowVector(int c)

Copy a row into a VectorN.

Parameters:: c - Row index
Returns:: VectorN copy of matrix elements.

getRow

public Matrix getRow(int l)

Copy an internal one-dimensional array from a row.

Parameters:: l - Row index
Returns:: one-dimensional array copy of matrix elements.

getRows

public Matrix getRows(int[] l)

Copy an internal one-dimensional array from many rows.

Parameters:: l - Rows indexes
Returns:: one-dimensional array copy of matrix elements.

getColumnArrayCopy

public double[] getColumnArrayCopy(int c)

Copy an internal one-dimensional array from a column.

Parameters:: c - Column index
Returns:: one-dimensional array copy of matrix elements.

getColumn

public Matrix getColumn(int c)

Copy an internal one-dimensional array from a column.

Parameters:: c - Column index
Returns:: one-dimensional array copy of matrix elements.

getColumnVector

public VectorN getColumnVector(int c)

Copy a column into a VectorN.

Parameters:: c - Column index
Returns:: VectorN copy of matrix elements.

getColumns

public Matrix getColumns(int[] c)

Copy an internal one-dimensional array from a column.

Parameters:: c - Columns indexes
Returns:: one-dimensional array copy of matrix elements.

getRowPackedCopy

public double[] getRowPackedCopy()

Make a one-dimensional row packed copy of the internal array.

Returns:: Matrix elements packed in a one-dimensional array by rows.

getRowPackedVector

public VectorN getRowPackedVector()

Make a one-dimensional row packed copy of the internal array.

Returns:: Matrix elements packed in a vector by rows.

getColumnPackedCopy

public double[] getColumnPackedCopy()

Make a one-dimensional column packed copy of the internal array.

Returns:: Matrix elements packed in a one-dimensional array by columns.

getColumnPackedVector

public VectorN getColumnPackedVector()

Make a one-dimensional column packed copy of the internal array.

Returns:: Matrix elements packed in a vector by column.

getRowDimension

public int getRowDimension()

Get row dimension.

Returns:: m, the number of rows.

getColumnDimension

public int getColumnDimension()

Get column dimension.

Returns:: n, the number of columns.

diag

public Matrix diag()

Matrix diagonal extraction.

Returns:: An d*1 Matrix of diagonal elements, d = min(m,n).

diag

public Matrix diag(int num)

Matrix diagonal extraction.

Parameters:: num - diagonal number.
Returns:: Matrix of the n-th diagonal elements.

diagonal

public VectorN diagonal()

Return the diagonals of a square matrix in a VectorN

Returns:: VectorN containing the diagonal elements

set

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

Set a single element.

Parameters:: i - Row index.; j - Column index.; s - A(i,j).
Throws:: java.lang.ArrayIndexOutOfBoundsException

set

public void set(int[] I,
                int[] J,
                double s)

Set several elements.

Parameters:: I - Row index.; J - Column index.; s - A(I(:),J(:)).
Throws:: java.lang.ArrayIndexOutOfBoundsException

setMatrix

public void setMatrix(int i0,
                      int j0,
                      Matrix X)

Set a submatrix.

Parameters:: i0 - Initial row index; j0 - Initial column index; X - subMatrix to set
Throws:: java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int[] I0,
                      int[] J0,
                      Matrix X)

Set a submatrix.

Parameters:: I0 - Initial row indexes; J0 - Initial column indexes; X - subMatrix to set
Throws:: java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int i0,
                      int i1,
                      int j0,
                      int j1,
                      double v)

Set a submatrix.

Parameters:: i0 - Initial row index; i1 - Final row index; j0 - Initial column index; j1 - Final column index; v - Value to set in the submatrix
Throws:: java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int i0,
                      int i1,
                      int j0,
                      int j1,
                      Matrix X)

Set a submatrix.

Parameters:: i0 - Initial row index; i1 - Final row index; j0 - Initial column index; j1 - Final column index; X - A(i0:i1,j0:j1)
Throws:: java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setRow

public void setRow(int l,
                   Matrix B)

Copy an internal one-dimensional array from a row.

Parameters:: l - Row index; B - Row-matrix

setRow

public void setRow(int l,
                   VectorN B)

Copy an internal one-dimensional array from a row.

Parameters:: l - Row index; B - VectorN

setRows

public void setRows(int[] l,
                    Matrix B)

Copy an internal one-dimensional array from many rows.

Parameters:: l - Rows indexes; B - Rows-matrix

setColumn

public void setColumn(int c,
                      Matrix B)

Set a column to an internal one-dimensional Column.

Parameters:: c - Column index; B - Column-matrix

setColumn

public void setColumn(int c,
                      VectorN B)

Set a column to an internal one-dimensional Column.

Parameters:: c - Column index; B - VectorN

setColumns

public void setColumns(int[] c,
                       Matrix B)

Copy an internal one-dimensional array from a column.

Parameters:: c - Columns indexes; B - Columns-matrix

resize

public Matrix resize(int m2,
                     int n2)

Matrix resize.

Parameters:: m2 - number of rows; n2 - number of columns
Returns:: resized matrix

reshape

public Matrix reshape(int m2,
                      int n2)

Matrix reshape by Row.

Parameters:: m2 - number of rows; n2 - number of columns
Returns:: reshaped matrix

reshapeRows

public Matrix reshapeRows(int m2,
                          int n2)

Matrix reshape by Row.

Parameters:: m2 - number of rows; n2 - number of columns
Returns:: reshaped matrix

reshapeColumns

public Matrix reshapeColumns(int m2,
                             int n2)

Matrix reshape by Column.

Parameters:: m2 - number of rows; n2 - number of columns
Returns:: reshaped matrix

transpose

public Matrix transpose()

Matrix transpose.

Returns:: A'

merge

public Matrix merge(Matrix B)

Matrix merge.

Parameters:: B - matrix to merge
Returns:: An m.B.m-by-n matrix

mergeRows

public Matrix mergeRows(Matrix B)

Matrix merge.

Parameters:: B - matrix to merge
Returns:: An m.B+m-by-n matrix

mergeColumns

public Matrix mergeColumns(Matrix B)

Matrix merge.

Parameters:: B - matrix to merge
Returns:: An m-by-n+B.n matrix

norm1

public double norm1()

One norm

Returns:: maximum column sum.

norm2

public double norm2()

Two norm

Returns:: maximum singular value.

normInf

public double normInf()

Infinity norm

Returns:: maximum row sum.

normF

public double normF()

Frobenius norm

Returns:: sqrt of sum of squares of all elements.

det

public double det()

Matrix determinant

Returns:: determinant

rank

public int rank()

Matrix rank

Returns:: effective numerical rank, obtained from SVD.

cond

public double cond()

Matrix condition (2 norm)

Returns:: ratio of largest to smallest singular value.

trace

public double trace()

Matrix trace.

Returns:: sum of the diagonal elements.

min

public Matrix min()

Generate a row matrix, each column contents the minimum value of the columns.

Returns:: An 1-by-n matrix.

minRows

public Matrix minRows()

Generate a row matrix, each column contents the minimum value of the columns.

Returns:: An 1-by-n matrix.

minColumns

public Matrix minColumns()

Generate a column matrix, each line contents the minimum value of the lines.

Returns:: An m-by-1 matrix.

max

public Matrix max()

Generate a row matrix, each column contents the maximum value of the columns.

Returns:: An 1-by-n matrix.

maxRows

public Matrix maxRows()

Generate a row matrix, each column contents the maximum value of the columns.

Returns:: An 1-by-n matrix.

maxColumns

public Matrix maxColumns()

Generate a column matrix, each line contents the maximum value of the lines.

Returns:: An m-by-1 matrix.

sum

public Matrix sum()

Generate a row matrix, each column contents the sum value of the columns.

Returns:: An 1-by-n matrix.

sumRows

public Matrix sumRows()

Generate a row matrix, each column contents the sum value of the columns.

Returns:: An 1-by-n matrix.

sumColumns

public Matrix sumColumns()

Generate a column matrix, each line contents the sum value of the lines.

Returns:: An m-by-1 matrix.

prod

public Matrix prod()

Generate a row matrix, each column contents the product value of the columns.

Returns:: An 1-by-n matrix.

prodRows

public Matrix prodRows()

Generate a row matrix, each column contents the product value of the columns.

Returns:: An 1-by-n matrix.

prodColumns

public Matrix prodColumns()

Generate a column matrix, each line contents the product value of the lines.

Returns:: An m-by-1 matrix.

dist

public Matrix dist(Matrix B)

Generate a matrix, each column contents the Euclidian distance between the columns.

Parameters:: B - Matrix
Returns:: An m-by-B.m matrix.

distRows

public Matrix distRows(Matrix B)

Generate a matrix, each column contents the Euclidian distance between the columns.

Parameters:: B - Matrix
Returns:: An m-by-B.m matrix.

distColumns

public Matrix distColumns(Matrix B)

Generate a matrix, each line contents the Euclidian distance between the lines.

Parameters:: B - Matrix
Returns:: An B.n-by-n matrix.

uminus

public Matrix uminus()

Unary minus

Returns:: -A

plus

public Matrix plus(Matrix B)

C = A + B

Parameters:: B - another matrix
Returns:: A + B

minus

public Matrix minus(Matrix B)

C = A - B

Parameters:: B - another matrix
Returns:: A - B

times

public Matrix times(double s)

Multiply a matrix by a scalar, C = s*A

Parameters:: s - scalar
Returns:: s*A

times

public Matrix times(Matrix B)

Linear algebraic matrix multiplication, A * B

Parameters:: B - another matrix
Returns:: Matrix product, A * B
Throws:: java.lang.IllegalArgumentException - Matrix inner dimensions must agree.

divide

public Matrix divide(double s)

Divide a matrix by a scalar, C = A/s

Parameters:: s - scalar
Returns:: A/s

divide

public Matrix divide(Matrix B)

Linear algebraic matrix division, A / B

Parameters:: B - another matrix
Returns:: Matrix division, A / B
Throws:: java.lang.IllegalArgumentException - Matrix inner dimensions must agree.; java.lang.IllegalArgumentException - Matrix inner dimensions must agree.

solve

public Matrix solve(Matrix B)

Solve A*X = B

Parameters:: B - right hand side
Returns:: solution if A is square, least squares solution otherwise

inverse

public Matrix inverse()

Matrix inverse or pseudoinverse

Returns:: inverse(A) if A is square, pseudoinverse otherwise.

times

public double[] times(double[] B)

Matrix multiplied by a column array

Parameters:: B - array to be post-multiplied
Returns:: A*B

times

public VectorN times(VectorN B)

Matrix multiplied by a column vector

Parameters:: B - vector to be post-multiplied
Returns:: A*B

ebePlus

public Matrix ebePlus(double s)

Add a scalar to each element of a matrix, C = A .+ s

Parameters:: s - double
Returns:: A .+ s

ebeMinus

public Matrix ebeMinus(double s)

Sub a scalar to each element of a matrix, C = A .- B

Parameters:: s - double
Returns:: A .- s

ebeTimes

public Matrix ebeTimes(double s)

Multiply a matrix by a scalar, C = s*A

Parameters:: s - scalar
Returns:: s*A

ebeTimes

public Matrix ebeTimes(Matrix B)

Element-by-element multiplication, C = A.*B

Parameters:: B - another matrix
Returns:: A.*B

ebeDivide

public Matrix ebeDivide(double s)

Divide a matrix by a scalar, C = A/s

Parameters:: s - scalar
Returns:: A/s

ebeDivide

public Matrix ebeDivide(Matrix B)

Element-by-element right division, C = A./B

Parameters:: B - another matrix
Returns:: A./B

ebeCos

public Matrix ebeCos()

Element-by-element cosinus

Returns:: cos.(A)

ebeSin

public Matrix ebeSin()

Element-by-element sinus

Returns:: sin.(A)

ebeExp

public Matrix ebeExp()

Element-by-element exponential

Returns:: exp.(A)

ebePow

public Matrix ebePow(double p)

Element-by-element power

Parameters:: p - double
Returns:: A.^p

ebePow

public Matrix ebePow(Matrix B)

Element-by-element power

Parameters:: B - another matrix
Returns:: A.^B

ebeLog

public Matrix ebeLog()

Element-by-element neperian logarithm

Returns:: log.(A)

ebeInv

public Matrix ebeInv()

Element-by-element inverse

Returns:: A.^-1

ebeSqrt

public Matrix ebeSqrt()

Element-by-element inverse

Returns:: A.^-1

ebeAbs

public Matrix ebeAbs()

Element-by-element inverse

Returns:: A.^-1

ebeFun

public Matrix ebeFun(DoubleFunction fun)

Element-by-element function evaluation

Parameters:: fun - function to apply
Returns:: f.(A)

ebeIndFun

public Matrix ebeIndFun(DoubleFunction fun)

Element-by-element indicial function evaluation

Parameters:: fun - function to apply
Returns:: f.(A)

lu

public LUDecomposition lu()

LU Decomposition

Returns:: LUDecomposition
See Also:: LUDecomposition

qr

public QRDecomposition qr()

QR Decomposition

Returns:: QRDecomposition
See Also:: QRDecomposition

chol

public CholeskyDecomposition chol()

Cholesky Decomposition

Returns:: CholeskyDecomposition
See Also:: CholeskyDecomposition

svd

public SingularValueDecomposition svd()

Singular Value Decomposition

Returns:: SingularValueDecomposition
See Also:: SingularValueDecomposition

eig

public EigenvalueDecomposition eig()

Eigenvalue Decomposition

Returns:: EigenvalueDecomposition
See Also:: EigenvalueDecomposition

sort

public int[] sort(int c)

Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'

Parameters:: c - Number of the colum which leads the permuation
Returns:: An Integer Array.

sortRows

public int[] sortRows(int c)

Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'

Parameters:: c - Number of the colum which leads the permuation
Returns:: An m-by-n matrix.

sortColumns

public int[] sortColumns(int l)

Generate a row-permuted matrix, columns are permuted in order to sort the row 'l'

Parameters:: l - Number of the row which leads the permuation
Returns:: An Integer Array.

sortedMatrix

public Matrix sortedMatrix(int c)

Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'

Parameters:: c - Number of the colum which leads the permuation
Returns:: An m-by-n matrix.

sortedRowsMatrix

public Matrix sortedRowsMatrix(int c)

Generate a column-permuted matrix, rows are permuted in order to sort the column 'c'

Parameters:: c - Number of the colum which leads the permuation
Returns:: An m-by-n matrix.

sortedColumnsMatrix

public Matrix sortedColumnsMatrix(int l)

Generate a row-permuted matrix, columns are permuted in order to sort the row 'l'

Parameters:: l - Number of the row which leads the permuation
Returns:: An m-by-n matrix.

find

public int[][] find(double e)

Find an element

Parameters:: e - Element (value) to find
Returns:: A list of indices where this element is found.

find

public int[][] find(java.lang.String test,
                    double e)

Find elements verifying a boolean test

Parameters:: test - Test to apply: < > =...; e - Element (value) to compare
Returns:: A list of indices where this element is found.

findMatrix

public Matrix findMatrix(double e)

Find an element

Parameters:: e - Element (value) to find
Returns:: A list of indices where this element is found.

findMatrix

public Matrix findMatrix(java.lang.String test,
                         double e)

Find elements verifying a boolean test

Parameters:: test - Test to apply: < > =...; e - Element (value) to compare
Returns:: A list of indices where this element is found.

toCommandLine

public void toCommandLine(java.lang.String title)

Print the Matrix in the Command Line.

Parameters:: title - title to display in the command line.

toFile

public void toFile(java.lang.String fileName)

Save the Matrix in a file.

Parameters:: fileName - filename to save in.

toFile

public void toFile(java.io.File file)

Save the Matrix in a file.

Parameters:: file - file to save in.

fromFile

public static Matrix fromFile(java.lang.String fileName)

Load the Matrix from a file.

Parameters:: fileName - filename of the file to load.
Returns:: A matrix.

fromFile

public static Matrix fromFile(java.io.File file)

Load the Matrix from a file

Parameters:: file - file to load
Returns:: A matrix

toString

public java.lang.String toString()

Convert the Matrix into a String

Overrides:: toString in class java.lang.Object

Returns:: A String

fromString

public static Matrix fromString(java.lang.String s)

Load the Matrix from a String

Parameters:: s - String to load
Returns:: A matrix

toPanelTable

public MatrixTable toPanelTable()

Print the Matrix in a JTable

Returns:: A Swing JTable in a JPanel

toFrameTable

public void toFrameTable(java.lang.String title)

Print the Matrix data in a Table in a JFrame

Parameters:: title - Title of the JFrame.

toPanelPlot2D

public MatrixPlot2D toPanelPlot2D()

Plot the Matrix in a JPanel

Returns:: A MatrixPlot2D (extends a JPanel)

toFramePlot2D

public MatrixPlot2D toFramePlot2D(java.lang.String title)

Plot the Matrix in a JFrame

Parameters:: title - Title of the JFrame.
Returns:: A MatrixPlot2D (extends a Swing JPanel)

toPanelPlot2D

public MatrixPlot2D toPanelPlot2D(Matrix X)

Plot the Matrix in a JPanel

Parameters:: X - Matrix
Returns:: A MatrixPlot2D (extends a Swing JPanel)

toFramePlot2D

public MatrixPlot2D toFramePlot2D(java.lang.String title,
                                  Matrix X)

Plot the Matrix in a JFrame

Parameters:: title - Title of the JFrame.; X - Matrix
Returns:: A MatrixPlot2D (extends a Swing JPanel)

toPanelPlot3D

public MatrixPlot3D toPanelPlot3D()

Plot the Matrix in a JPanel

Returns:: A MatrixPlot3D (extends a Swing JPanel)

toFramePlot3D

public MatrixPlot3D toFramePlot3D(java.lang.String title)

Plot the Matrix in a JFrame

Parameters:: title - Title of the JFrame.
Returns:: A MatrixPlot3D (extends a Swing JPanel)

toPanelPlot3D

public MatrixPlot3D toPanelPlot3D(Matrix X,
                                  Matrix Y)

Plot the Matrix in a JFrame

Parameters:: X - Matrix; Y - Matrix
Returns:: A MatrixPlot3D (extends a Swing JPanel)

toFramePlot3D

public MatrixPlot3D toFramePlot3D(java.lang.String title,
                                  Matrix X,
                                  Matrix Y)

Plot the Matrix in a Window in a JFrame

Parameters:: title - Title of the JFrame.; X - Matrix; Y - Matrix
Returns:: A MatrixPlot3D (extends a Swing JPanel)

print

public void print()

Print the Matrix to System.out

print

public void print(java.io.PrintWriter pw)

Print the Matrix to a PrintWriter

Parameters:: pw - PrintWriter to print to.

print

public void print(java.lang.String title)

Print the Matrix to System.out

Parameters:: title - A title or label for the matrix

printrows

public void printrows(java.lang.String title,
                      int rows)

Print the first n rows of Matrix to System.out

Parameters:: title - A title or label for the matrix; rows - Number of rows to print

checkMatrixDimensions

public void checkMatrixDimensions(Matrix B)

Check if size(A) == size(B).

Parameters:: B - Matrix to test.

checkMatrixDimensions

public void checkMatrixDimensions(int m2,
                                  int n2)

Check if size(A) == m2*n2.

Parameters:: m2 - Number of rows.; n2 - Number of columns.

checkIndicesLengths

public static void checkIndicesLengths(int[] i,
                                       int[] j)

Check if indices have the same length.

Parameters:: i - Indices.; j - Indices.

checkIndicesDimensions

public static void checkIndicesDimensions(int[][] i,
                                          int[][] j)

Check if indices have the same length.

Parameters:: i - Indices.; j - Indices.

checkRowDimension

public void checkRowDimension(Matrix B)

Check if number of Rows(A) == number of Rows(B).

Parameters:: B - Matrix to test.

checkRowDimension

public void checkRowDimension(int row)

Check if number of Rows(A) == row.

Parameters:: row - number of rows.

checkColumnDimension

public void checkColumnDimension(Matrix B)

Check if number of Columns(A) == number of Columns(B).

Parameters:: B - Matrix to test.

checkColumnDimension

public void checkColumnDimension(int column)

Check if number of Columns(A) == column.

Parameters:: column - number of columns.

invert

public Matrix invert()

Invert a matrix.

Returns:: the inverse.

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jat.matvec.data Class Matrix

A

m

n

Matrix

Matrix

Matrix

Matrix

Matrix

Matrix

Matrix

Matrix

random

identity

increment

incrementRows

incrementColumns

merge

mergeRows

mergeColumns

copy

clone

getArray

getArrayCopy

get

get

get

getMatrix

getRowArrayCopy

getRowVector

getRow

getRows

getColumnArrayCopy

getColumn

getColumnVector

getColumns

getRowPackedCopy

getRowPackedVector

getColumnPackedCopy

getColumnPackedVector

getRowDimension

getColumnDimension

diag

diag

diagonal

set

set

setMatrix

setMatrix

setMatrix

setMatrix

setRow

setRow

setRows

setColumn

setColumn

setColumns

resize

reshape

reshapeRows

reshapeColumns

transpose

merge

mergeRows

mergeColumns

norm1

norm2

normInf

normF

det

rank

cond

trace

min

minRows

minColumns

max

maxRows

maxColumns

sum

jat.matvec.data
Class Matrix