MatrixInt (ph-matrix 9.5.5 API)

java.lang.Object
- com.helger.matrix.MatrixInt

All Implemented Interfaces:

com.helger.commons.lang.ICloneable<MatrixInt>, Serializable
```
public class MatrixInt
extends Object
implements Serializable, com.helger.commons.lang.ICloneable<MatrixInt>
```
Jama = Java Matrix class.
The Java Matrix Class provides the fundamental operations of numerical linear algebra. Various constructors create Matrices from two dimensional arrays of double precision floating point numbers. Various "gets" and "sets" provide access to submatrices and matrix elements. Several methods implement basic matrix arithmetic, including matrix addition and multiplication, matrix norms, and element-by-element array operations. Methods for reading and printing matrices are also included. All the operations in this version of the Matrix Class involve real matrices. Complex matrices may be handled in a future version.

Five fundamental matrix decompositions, which consist of pairs or triples of matrices, permutation vectors, and the like, produce results in five decomposition classes. These decompositions are accessed by the Matrix class to compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions. The five decompositions are:
- Cholesky Decomposition of symmetric, positive definite matrices.
- LU Decomposition of rectangular matrices.
- QR Decomposition of rectangular matrices.
- Singular Value Decomposition of rectangular matrices.
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices.
Example of use:
Solve a linear system A x = b and compute the residual norm, ||b - A x||.
```
 double [] [] vals = { { 1., 2., 3 }, { 4., 5., 6. }, { 7., 8., 10. } };
 Matrix A = new Matrix (vals);
 Matrix b = Matrix.random (3, 1);
 Matrix x = A.solve (b);
 Matrix r = A.times (x).minus (b);
 double rnorm = r.normInf ();
 
```
Version:

5 August 1998

Author:

The MathWorks, Inc. and the National Institute of Standards and Technology.

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor and Description
`MatrixInt(int[] aVals, int nRows)` Construct a matrix from a one-dimensional packed array
`MatrixInt(int nRows, int nCols)` Construct an nRows-by-nCols matrix of zeros.
`MatrixInt(int nRows, int nCols, int nValue)` Construct an nRows-by-nCols constant matrix.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`MatrixInt`	`arrayLeftDivide(MatrixInt aMatrix)` Element-by-element left division, C = B.
`MatrixInt`	`arrayLeftDivideEquals(MatrixInt aMatrix)` Element-by-element left division in place, A = B.
`MatrixInt`	`arrayRightDivide(MatrixInt aMatrix)` Element-by-element right division, C = A.
`MatrixInt`	`arrayRightDivideEquals(MatrixInt aMatrix)` Element-by-element right division in place, A = A.
`MatrixInt`	`arrayTimes(MatrixInt aMatrix)` Element-by-element multiplication, C = A.
`MatrixInt`	`arrayTimesEquals(MatrixInt aMatrix)` Element-by-element multiplication in place, A = A.
`static MatrixInt`	`constructWithCopy(int[][] aArray)` Construct a matrix from a copy of a 2-D array.
`boolean`	`equals(Object o)`
`int`	`get(int nRow, int nCol)` Get a single element.
`int[][]`	`getArrayCopy()` Copy the internal two-dimensional array.
`MatrixInt`	`getClone()`
`int`	`getColumnDimension()` Get column dimension.
`int[]`	`getColumnPackedCopy()` Make a one-dimensional column packed copy of the internal array.
`MatrixInt`	`getMatrix(int[] aRows, int[] aCols)` Get a submatrix.
`MatrixInt`	`getMatrix(int[] aRows, int nStartColumnIndex, int nEndColumnIndex)` Get a submatrix.
`MatrixInt`	`getMatrix(int nStartRowIndex, int nEndRowIndex, int[] aCols)` Get a submatrix.
`MatrixInt`	`getMatrix(int nStartRowIndex, int nEndRowIndex, int nStartColumnIndex, int nEndColumnIndex)` Get a submatrix.
`int`	`getRowDimension()` Get row dimension.
`int[]`	`getRowPackedCopy()` Make a one-dimensional row packed copy of the internal array.
`int`	`hashCode()`
`static MatrixInt`	`identity(int nRows, int nCols)` Generate identity matrix
`int[][]`	`internalGetArray()` Access the internal two-dimensional array.
`boolean`	`isSymmetrical()`
`MatrixInt`	`minus(MatrixInt aMatrix)` C = A - B
`MatrixInt`	`minusEquals(MatrixInt aMatrix)` A = A - B
`int`	`norm1()` One norm
`double`	`normF()` Frobenius norm
`int`	`normInf()` Infinity norm
`MatrixInt`	`plus(MatrixInt aMatrix)` C = A + B
`MatrixInt`	`plusEquals(MatrixInt aMatrix)` A = A + B
`void`	`print(PrintWriter aPW, int nWidth, int nFractionDigits)` Print the matrix to the output stream.
`void`	`print(PrintWriter aPW, NumberFormat aFormat, int nWidth)` Print the matrix to the output stream.
`static MatrixInt`	`random(int nRows, int nCols)` Generate matrix with random elements
`static MatrixInt`	`read(Reader aReader)` Read a matrix from a stream.
`void`	`set(int nRow, int nCol, int nValue)` Set a single element.
`void`	`setMatrix(int[] aRows, int[] aCols, MatrixInt aMatrix)` Set a submatrix.
`void`	`setMatrix(int[] aRows, int nStartColumnIndex, int nEndColumnIndex, MatrixInt aMatrix)` Set a submatrix.
`void`	`setMatrix(int nStartRowIndex, int nEndRowIndex, int[] aCols, MatrixInt aMatrix)` Set a submatrix.
`void`	`setMatrix(int nStartRowIndex, int nEndRowIndex, int nStartColumnIndex, int nEndColumnIndex, MatrixInt aMatrix)` Set a submatrix.
`MatrixInt`	`times(int s)` Multiply a matrix by a scalar, C = s*A
`MatrixInt`	`times(MatrixInt aMatrix)` Linear algebraic matrix multiplication, A * B
`MatrixInt`	`timesEquals(double s)` Multiply a matrix by a scalar in place, A = s*A
`int`	`trace()` Matrix trace.
`MatrixInt`	`transpose()` Matrix transpose.
`MatrixInt`	`uminus()` Unary minus

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MatrixInt

public MatrixInt(@Nonnegative
                 int nRows,
                 @Nonnegative
                 int nCols)

Construct an nRows-by-nCols matrix of zeros.

Parameters:: nRows - Number of rows.; nCols - Number of columns.

MatrixInt

public MatrixInt(@Nonnegative
                 int nRows,
                 @Nonnegative
                 int nCols,
                 int nValue)

Construct an nRows-by-nCols constant matrix.

Parameters:: nRows - Number of rows.; nCols - Number of columns.; nValue - Fill the matrix with this scalar value.

MatrixInt
```
public MatrixInt(@Nonnull
                 int[] aVals,
                 @Nonnegative
                 int nRows)
```
Construct a matrix from a one-dimensional packed array

Parameters:

aVals - One-dimensional array of doubles, packed by columns (ala Fortran).

nRows - Number of rows.

Throws:

IllegalArgumentException - Array length must be a multiple of nRows.

Method Detail

constructWithCopy
```
@Nonnull
public static MatrixInt constructWithCopy(@Nonnull
                                                    int[][] aArray)
```
Construct a matrix from a copy of a 2-D array.

Parameters:

aArray - Two-dimensional array of doubles.

Returns:

The new matrix

Throws:

IllegalArgumentException - All rows must have the same length

getClone
```
@Nonnull
 @ReturnsMutableCopy
public MatrixInt getClone()
```
Specified by:

getClone in interface com.helger.commons.lang.ICloneable<MatrixInt>

Returns:

a deep copy of a matrix

internalGetArray
```
@Nonnull
public int[][] internalGetArray()
```
Access the internal two-dimensional array.

Returns:

Pointer to the two-dimensional array of matrix elements.

getArrayCopy
```
@Nonnull
 @ReturnsMutableCopy
public int[][] getArrayCopy()
```
Copy the internal two-dimensional array.

Returns:

Two-dimensional array copy of matrix elements.

getColumnPackedCopy
```
@Nonnull
public int[] getColumnPackedCopy()
```
Make a one-dimensional column packed copy of the internal array.

Returns:

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

getRowPackedCopy
```
@Nonnull
public int[] getRowPackedCopy()
```
Make a one-dimensional row packed copy of the internal array.

Returns:

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

getRowDimension
```
@Nonnegative
public int getRowDimension()
```
Get row dimension.

Returns:

nRows, the number of rows.

getColumnDimension
```
@Nonnegative
public int getColumnDimension()
```
Get column dimension.

Returns:

nCols, the number of columns.

isSymmetrical
```
public boolean isSymmetrical()
```
Returns:

true if the matrix is symmetrical, meaning number of rows and columns is identical.

get

public int get(@Nonnegative
               int nRow,
               @Nonnegative
               int nCol)

Get a single element.

Parameters:: nRow - Row index.; nCol - Column index.
Returns:: A(nRow,nCol)

getMatrix

@Nonnull
 @ReturnsMutableCopy
public MatrixInt getMatrix(@Nonnegative
                                                           int nStartRowIndex,
                                                           @Nonnegative
                                                           int nEndRowIndex,
                                                           @Nonnegative
                                                           int nStartColumnIndex,
                                                           @Nonnegative
                                                           int nEndColumnIndex)

Get a submatrix.

Parameters:: nStartRowIndex - Initial row index; nEndRowIndex - Final row index; nStartColumnIndex - Initial column index; nEndColumnIndex - Final column index
Returns:: Matrix(nStartRowIndex:nEndRowIndex,nStartColumnIndex: nEndColumnIndex )
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

@Nonnull
 @ReturnsMutableCopy
public MatrixInt getMatrix(@Nonnull
                                                           int[] aRows,
                                                           @Nonnull
                                                           int[] aCols)

Get a submatrix.

Parameters:: aRows - Array of row indices.; aCols - Array of column indices.
Returns:: Matrix(aRows(:),aCols(:))
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

@Nonnull
 @ReturnsMutableCopy
public MatrixInt getMatrix(@Nonnegative
                                                           int nStartRowIndex,
                                                           @Nonnegative
                                                           int nEndRowIndex,
                                                           @Nonnull
                                                           int[] aCols)

Get a submatrix.

Parameters:: nStartRowIndex - Initial row index; nEndRowIndex - Final row index; aCols - Array of column indices.
Returns:: Matrix(nStartRowIndex:nEndRowIndex,aCols(:))
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

@Nonnull
 @ReturnsMutableCopy
public MatrixInt getMatrix(@Nonnull
                                                           int[] aRows,
                                                           @Nonnegative
                                                           int nStartColumnIndex,
                                                           @Nonnegative
                                                           int nEndColumnIndex)

Get a submatrix.

Parameters:: aRows - Array of row indices.; nStartColumnIndex - Initial column index; nEndColumnIndex - Final column index
Returns:: Matrix(aRows(:),nStartColumnIndex:nEndColumnIndex)
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

set

public void set(@Nonnegative
                int nRow,
                @Nonnegative
                int nCol,
                int nValue)

Set a single element.

Parameters:: nRow - Row index.; nCol - Column index.; nValue - A(nRow,nCol).

setMatrix

public void setMatrix(@Nonnegative
                      int nStartRowIndex,
                      @Nonnegative
                      int nEndRowIndex,
                      @Nonnegative
                      int nStartColumnIndex,
                      @Nonnegative
                      int nEndColumnIndex,
                      @Nonnull
                      MatrixInt aMatrix)

Set a submatrix.

Parameters:: nStartRowIndex - Initial row index; nEndRowIndex - Final row index; nStartColumnIndex - Initial column index; nEndColumnIndex - Final column index; aMatrix - Matrix(nStartRowIndex:nEndRowIndex,nStartColumnIndex:nEndColumnIndex )
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(@Nonnull
                      int[] aRows,
                      @Nonnull
                      int[] aCols,
                      @Nonnull
                      MatrixInt aMatrix)

Set a submatrix.

Parameters:: aRows - Array of row indices.; aCols - Array of column indices.; aMatrix - Matrix(aRows(:),aCols(:))
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(@Nonnull
                      int[] aRows,
                      @Nonnegative
                      int nStartColumnIndex,
                      @Nonnegative
                      int nEndColumnIndex,
                      @Nonnull
                      MatrixInt aMatrix)

Set a submatrix.

Parameters:: aRows - Array of row indices.; nStartColumnIndex - Initial column index; nEndColumnIndex - Final column index; aMatrix - Matrix(aRows(:),nStartColumnIndex:nEndColumnIndex
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(@Nonnegative
                      int nStartRowIndex,
                      @Nonnegative
                      int nEndRowIndex,
                      @Nonnull
                      int[] aCols,
                      @Nonnull
                      MatrixInt aMatrix)

Set a submatrix.

Parameters:: nStartRowIndex - Initial row index; nEndRowIndex - Final row index; aCols - Array of column indices.; aMatrix - Matrix(nStartRowIndex:nEndRowIndex,aCols(:))
Throws:: ArrayIndexOutOfBoundsException - Submatrix indices

transpose

@Nonnull
 @ReturnsMutableCopy
 @CheckReturnValue
public MatrixInt transpose()

Matrix transpose.

Returns:: A'

norm1
```
public int norm1()
```
One norm

Returns:

maximum column sum.

normInf
```
public int normInf()
```
Infinity norm

Returns:

maximum row sum.

normF
```
public double normF()
```
Frobenius norm

Returns:

sqrt of sum of squares of all elements.

uminus

@Nonnull
 @ReturnsMutableCopy
public MatrixInt uminus()

Unary minus

Returns:: -A

plus

@Nonnull
 @ReturnsMutableCopy
public MatrixInt plus(@Nonnull
                                                      MatrixInt aMatrix)

C = A + B

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

plusEquals

@Nonnull
public MatrixInt plusEquals(@Nonnull
                                      MatrixInt aMatrix)

A = A + B

Parameters:: aMatrix - another matrix
Returns:: this

minus

@Nonnull
 @ReturnsMutableCopy
public MatrixInt minus(@Nonnull
                                                       MatrixInt aMatrix)

C = A - B

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

minusEquals

@Nonnull
public MatrixInt minusEquals(@Nonnull
                                       MatrixInt aMatrix)

A = A - B

Parameters:: aMatrix - another matrix
Returns:: this

arrayTimes

@Nonnull
 @ReturnsMutableCopy
public MatrixInt arrayTimes(@Nonnull
                                                            MatrixInt aMatrix)

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

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

arrayTimesEquals

@Nonnull
public MatrixInt arrayTimesEquals(@Nonnull
                                            MatrixInt aMatrix)

Element-by-element multiplication in place, A = A.*B

Parameters:: aMatrix - another matrix
Returns:: this

arrayRightDivide

@Nonnull
 @ReturnsMutableCopy
public MatrixInt arrayRightDivide(@Nonnull
                                                                  MatrixInt aMatrix)

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

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

arrayRightDivideEquals

@Nonnull
public MatrixInt arrayRightDivideEquals(@Nonnull
                                                  MatrixInt aMatrix)

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

Parameters:: aMatrix - another matrix
Returns:: this

arrayLeftDivide

@Nonnull
 @ReturnsMutableCopy
public MatrixInt arrayLeftDivide(@Nonnull
                                                                 MatrixInt aMatrix)

Element-by-element left division, C = B.\A

Parameters:: aMatrix - another matrix
Returns:: B.\A

arrayLeftDivideEquals

@Nonnull
public MatrixInt arrayLeftDivideEquals(@Nonnull
                                                 MatrixInt aMatrix)

Element-by-element left division in place, A = B.\A

Parameters:: aMatrix - another matrix
Returns:: this

times
```
@Nonnull
 @ReturnsMutableCopy
public MatrixInt times(int s)
```
Multiply a matrix by a scalar, C = s*A

Parameters:

s - scalar

Returns:

s*A

timesEquals
```
@Nonnull
public MatrixInt timesEquals(double s)
```
Multiply a matrix by a scalar in place, A = s*A

Parameters:

s - scalar

Returns:

this

times

@Nonnull
 @ReturnsMutableCopy
public MatrixInt times(@Nonnull
                                                       MatrixInt aMatrix)

Linear algebraic matrix multiplication, A * B

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

trace
```
public int trace()
```
Matrix trace.

Returns:

sum of the diagonal elements.

random

@Nonnull
 @ReturnsMutableCopy
public static MatrixInt random(@Nonnegative
                                                               int nRows,
                                                               @Nonnegative
                                                               int nCols)

Generate matrix with random elements

Parameters:: nRows - Number of rows.; nCols - Number of columns.
Returns:: An nRows-by-nCols matrix with uniformly distributed random elements.

identity

@Nonnull
 @ReturnsMutableCopy
public static MatrixInt identity(@Nonnegative
                                                                 int nRows,
                                                                 @Nonnegative
                                                                 int nCols)

Generate identity matrix

Parameters:: nRows - Number of rows.; nCols - Number of columns.
Returns:: An nRows-by-nCols matrix with ones on the diagonal and zeros elsewhere.

print

public void print(@Nonnull
                  PrintWriter aPW,
                  @Nonnegative
                  int nWidth,
                  @Nonnegative
                  int nFractionDigits)

Print the matrix to the output stream. Line the elements up in columns with a Fortran-like 'Fw.d' style format.

Parameters:: aPW - Output stream.; nWidth - Column width.; nFractionDigits - Number of digits after the decimal.

print
```
public void print(@Nonnull
                  PrintWriter aPW,
                  @Nonnull
                  NumberFormat aFormat,
                  @Nonnegative
                  int nWidth)
```
Print the matrix to the output stream. Line the elements up in columns. Use the format object, and right justify within columns of width characters. Note that is the matrix is to be read back in, you probably will want to use a NumberFormat that is set to US Locale.

Parameters:

aPW - the output stream.

aFormat - A formatting object to format the matrix elements

nWidth - Column width.

See Also:

DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)

equals
```
public boolean equals(Object o)
```
Overrides:

equals in class Object

hashCode
```
public int hashCode()
```
Overrides:

hashCode in class Object

read
```
@Nonnull
public static MatrixInt read(@Nonnull @WillNotClose
                                       Reader aReader)
                                throws IOException
```
Read a matrix from a stream. The format is the same the print method, so printed matrices can be read back in (provided they were printed using US Locale). Elements are separated by whitespace, all the elements for each row appear on a single line, the last row is followed by a blank line.

Parameters:

aReader - the input stream.

Returns:

The read matrix

Throws:

IOException - in case of an I/O error

Class MatrixInt

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MatrixInt

MatrixInt

MatrixInt

Method Detail

constructWithCopy

getClone

internalGetArray

getArrayCopy

getColumnPackedCopy

getRowPackedCopy

getRowDimension

getColumnDimension

isSymmetrical

get

getMatrix

getMatrix

getMatrix

getMatrix

set

setMatrix

setMatrix

setMatrix

setMatrix

transpose

norm1

normInf

normF

uminus

plus

plusEquals

minus

minusEquals

arrayTimes

arrayTimesEquals

arrayRightDivide

arrayRightDivideEquals

arrayLeftDivide

arrayLeftDivideEquals

times

timesEquals

times

trace

random

identity

print

print

equals

hashCode

read