Matrix (LCSim 3.1.7 API)

java.lang.Object
- Jama.Matrix

All Implemented Interfaces:

Serializable, Cloneable
```
public class Matrix
extends Object
implements Cloneable, Serializable
```
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 $Id: Matrix.java,v 1.1.1.1 2010/11/30 21:31:59 jeremy Exp $

Author:

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

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`private double[][]`	`A` Array for internal storage of elements.
`private int`	`m` Row and column dimensions.
`private int`	`n` Row and column dimensions.

Constructor Summary

Constructors
Constructor and Description
`Matrix(double[][] A)` Construct a matrix from a 2-D array.
`Matrix(double[][] A, int m, int n)` Construct a matrix quickly without checking arguments.
`Matrix(double[] vals, int m)` Construct a matrix from a one-dimensional packed array
`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.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`amax()` Matrix absolute maximum element.
`double`	`amin()` Matrix absolute minimum element.
`Matrix`	`arrayLeftDivide(Matrix B)` Element-by-element left division, C = A.\B
`Matrix`	`arrayLeftDivideEquals(Matrix B)` Element-by-element left division in place, A = A.\B
`Matrix`	`arrayRightDivide(Matrix B)` Element-by-element right division, C = A./B
`Matrix`	`arrayRightDivideEquals(Matrix B)` Element-by-element right division in place, A = A./B
`Matrix`	`arrayTimes(Matrix B)` Element-by-element multiplication, C = A.*B
`Matrix`	`arrayTimesEquals(Matrix B)` Element-by-element multiplication in place, A = A.*B
`private void`	`checkMatrixDimensions(Matrix B)` Check if size(A) == size(B)
`CholeskyDecomposition`	`chol()` Cholesky Decomposition
`Object`	`clone()` Clone the Matrix object.
`double`	`cond()` Matrix condition (2 norm)
`static Matrix`	`constructWithCopy(double[][] A)` Construct a matrix from a copy of a 2-D array.
`Matrix`	`copy()` Make a deep copy of a matrix
`double`	`det()` Matrix determinant
`EigenvalueDecomposition`	`eig()` Eigenvalue Decomposition
`double`	`get(int i, int j)`
`double[][]`	`getArray()` Access the internal two-dimensional array.
`double[][]`	`getArrayCopy()` Copy the internal two-dimensional array.
`int`	`getColumnDimension()`
`double[]`	`getColumnPackedCopy()` Make a one-dimensional column packed copy of the internal array.
`Matrix`	`getMatrix(int[] r, int[] c)` Returns a submatrix.
`Matrix`	`getMatrix(int[] r, int j0, int j1)` Returns a submatrix.
`Matrix`	`getMatrix(int i0, int i1, int[] c)` Returns a submatrix.
`Matrix`	`getMatrix(int i0, int i1, int j0, int j1)` Returns a submatrix.
`int`	`getRowDimension()`
`double[]`	`getRowPackedCopy()` Make a one-dimensional row packed copy of the internal array.
`static Matrix`	`identity(int m, int n)` Generate identity matrix
`Matrix`	`inverse()` Matrix inverse or pseudoinverse
`LUDecomposition`	`lu()` LU Decomposition
`double`	`max()` Matrix maximum element.
`double`	`min()` Matrix minimum element.
`Matrix`	`minus(Matrix B)` C = A - B
`Matrix`	`minusEquals(Matrix B)` A = 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
`Matrix`	`plusEquals(Matrix B)` A = A + B
`void`	`print(int w, int d)` Print the matrix to stdout.
`void`	`print(NumberFormat format, int width)` Print the matrix to stdout.
`void`	`print(PrintWriter output, int w, int d)` Print the matrix to the output stream.
`void`	`print(PrintWriter output, NumberFormat format, int width)` Print the matrix to the output stream.
`QRDecomposition`	`qr()` QR Decomposition
`static Matrix`	`random(int m, int n)` Generate matrix with random elements
`int`	`rank()` Matrix rank
`static Matrix`	`read(BufferedReader input)` Read a matrix from a stream.
`void`	`set(int i, int j, double s)` Sets a single element.
`void`	`setMatrix(int[] r, int[] c, Matrix X)` Sets a submatrix.
`void`	`setMatrix(int[] r, int j0, int j1, Matrix X)` Sets a submatrix.
`void`	`setMatrix(int i0, int i1, int[] c, Matrix X)` Sets a submatrix.
`void`	`setMatrix(int i0, int i1, int j0, int j1, Matrix X)` Sets a submatrix.
`Matrix`	`solve(Matrix B)` Solve A*X = B
`Matrix`	`solveTranspose(Matrix B)` Solve XA = B, which is also A'X' = B'
`SingularValueDecomposition`	`svd()` Singular Value Decomposition
`Matrix`	`times(double s)` Multiply a matrix by a scalar, C = s*A
`double[]`	`times(double[] x)` Calculates the vector y = A.x
`Matrix`	`times(Matrix B)` Linear algebraic matrix multiplication, A * B
`Matrix`	`timesEquals(double s)` Multiply a matrix by a scalar in place, A = s*A
`String`	`toString()` String representation for this Object.
`double`	`trace()` Matrix trace.
`Matrix`	`transpose()` Returns the transpose of the matrix.
`Matrix`	`uminus()` Unary minus

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

- Field Detail
  - A
```
private double[][] A
```
    Array for internal storage of elements.
  - m
```
private int m
```
    Row and column dimensions.
  - n
```
private 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 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(double[][] A)
```
    Construct a matrix from a 2-D array.
    
    Parameters:
    A - Two-dimensional array of doubles.
    
    Throws:
    
    IllegalArgumentException - All rows must have the same length
    See Also:
    constructWithCopy(double[][])
  - Matrix
```
public Matrix(double[][] A,
      int m,
      int n)
```
    Construct a matrix quickly without checking arguments.
    
    Parameters:
    A - Two-dimensional array of doubles.
    m - Number of rows.
    n - Number of colums.
  - 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:
    
    IllegalArgumentException - Array length must be a multiple of m.
- Method Detail
  - constructWithCopy
```
public static Matrix constructWithCopy(double[][] A)
```
    Construct a matrix from a copy of a 2-D array.
    
    Parameters:
    A - Two-dimensional array of doubles.
    
    Throws:
    
    IllegalArgumentException - All rows must have the same length
  - copy
```
public Matrix copy()
```
    Make a deep copy of a matrix
  - clone
```
public Object clone()
```
    Clone the Matrix object.
    
    Overrides:
    
    clone in class 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.
  - 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.
  - 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.
  - getRowDimension
```
public int getRowDimension()
```
    Returns:
    the number of rows.
  - getColumnDimension
```
public int getColumnDimension()
```
    Returns:
    the number of columns.
  - get
```
public double get(int i,
         int j)
```
    Parameters:
    i - Row index.
    j - Column index.
    
    Returns:
    A(i,j)
    
    Throws:
    
    ArrayIndexOutOfBoundsException
  - getMatrix
```
public Matrix getMatrix(int i0,
               int i1,
               int j0,
               int j1)
```
    Returns 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:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - getMatrix
```
public Matrix getMatrix(int[] r,
               int[] c)
```
    Returns a submatrix.
    
    Parameters:
    r - Array of row indices.
    c - Array of column indices.
    
    Returns:
    A(r(:),c(:))
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - getMatrix
```
public Matrix getMatrix(int i0,
               int i1,
               int[] c)
```
    Returns a submatrix.
    
    Parameters:
    i0 - Initial row index
    i1 - Final row index
    c - Array of column indices.
    
    Returns:
    A(i0:i1,c(:))
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - getMatrix
```
public Matrix getMatrix(int[] r,
               int j0,
               int j1)
```
    Returns a submatrix.
    
    Parameters:
    r - Array of row indices.
    j0 - Initial column index
    j1 - Final column index
    
    Returns:
    A(r(:),j0:j1)
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - set
```
public void set(int i,
       int j,
       double s)
```
    Sets a single element.
    
    Parameters:
    i - Row index.
    j - Column index.
    s - A(i,j).
    
    Throws:
    
    ArrayIndexOutOfBoundsException
  - setMatrix
```
public void setMatrix(int i0,
             int i1,
             int j0,
             int j1,
             Matrix X)
```
    Sets 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:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - setMatrix
```
public void setMatrix(int[] r,
             int[] c,
             Matrix X)
```
    Sets a submatrix.
    
    Parameters:
    r - Array of row indices.
    c - Array of column indices.
    X - A(r(:),c(:))
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - setMatrix
```
public void setMatrix(int[] r,
             int j0,
             int j1,
             Matrix X)
```
    Sets a submatrix.
    
    Parameters:
    r - Array of row indices.
    j0 - Initial column index
    j1 - Final column index
    X - A(r(:),j0:j1)
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - setMatrix
```
public void setMatrix(int i0,
             int i1,
             int[] c,
             Matrix X)
```
    Sets a submatrix.
    
    Parameters:
    i0 - Initial row index
    i1 - Final row index
    c - Array of column indices.
    X - A(i0:i1,c(:))
    
    Throws:
    
    ArrayIndexOutOfBoundsException - Submatrix indices
  - transpose
```
public Matrix transpose()
```
    Returns the transpose of the matrix. The elements of this matrix remain unchanged.
    
    Returns:
    a new matrix A^T
  - 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.
  - uminus
```
public Matrix uminus()
```
    Unary minus
    
    Returns:
    -A
  - plus
```
public Matrix plus(Matrix B)
```
    C = A + B
    
    Parameters:
    B - another matrix
    
    Returns:
    A + B
  - plusEquals
```
public Matrix plusEquals(Matrix B)
```
    A = 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
  - minusEquals
```
public Matrix minusEquals(Matrix B)
```
    A = A - B
    
    Parameters:
    B - another matrix
    
    Returns:
    A - B
  - arrayTimes
```
public Matrix arrayTimes(Matrix B)
```
    Element-by-element multiplication, C = A.*B
    
    Parameters:
    B - another matrix
    
    Returns:
    A.*B
  - arrayTimesEquals
```
public Matrix arrayTimesEquals(Matrix B)
```
    Element-by-element multiplication in place, A = A.*B
    
    Parameters:
    B - another matrix
    
    Returns:
    A.*B
  - arrayRightDivide
```
public Matrix arrayRightDivide(Matrix B)
```
    Element-by-element right division, C = A./B
    
    Parameters:
    B - another matrix
    
    Returns:
    A./B
  - arrayRightDivideEquals
```
public Matrix arrayRightDivideEquals(Matrix B)
```
    Element-by-element right division in place, A = A./B
    
    Parameters:
    B - another matrix
    
    Returns:
    A./B
  - arrayLeftDivide
```
public Matrix arrayLeftDivide(Matrix B)
```
    Element-by-element left division, C = A.\B
    
    Parameters:
    B - another matrix
    
    Returns:
    A.\B
  - arrayLeftDivideEquals
```
public Matrix arrayLeftDivideEquals(Matrix B)
```
    Element-by-element left division in place, A = 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
  - timesEquals
```
public Matrix timesEquals(double s)
```
    Multiply a matrix by a scalar in place, A = s*A
    
    Parameters:
    s - scalar
    
    Returns:
    replace A by s*A
  - times
```
public Matrix times(Matrix B)
```
    Linear algebraic matrix multiplication, A * B
    
    Parameters:
    B - another matrix
    
    Returns:
    Matrix product, A * B
    
    Throws:
    
    IllegalArgumentException - Matrix inner dimensions must agree.
  - times
```
public double[] times(double[] x)
```
    Calculates the vector y = A.x
    
    Parameters:
    x -
    
    Returns:
    a new vector y
  - 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
  - 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
  - solveTranspose
```
public Matrix solveTranspose(Matrix B)
```
    Solve X*A = B, which is also 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.
  - 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.
  - amax
```
public double amax()
```
    Matrix absolute maximum element.
    
    Returns:
    absolute value of largest element.
  - amin
```
public double amin()
```
    Matrix absolute minimum element.
    
    Returns:
    absolute value of smallest element.
  - max
```
public double max()
```
    Matrix maximum element.
    
    Returns:
    value of largest element.
  - min
```
public double min()
```
    Matrix minimum element.
    
    Returns:
    value of smallest element.
  - 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.
  - print
```
public void print(int w,
         int d)
```
    Print the matrix to stdout. Line the elements up in columns with a Fortran-like 'Fw.d' style format.
    
    Parameters:
    w - Column width.
    d - Number of digits after the decimal.
  - print
```
public void print(PrintWriter output,
         int w,
         int d)
```
    Print the matrix to the output stream. Line the elements up in columns with a Fortran-like 'Fw.d' style format.
    
    Parameters:
    output - Output stream.
    w - Column width.
    d - Number of digits after the decimal.
  - print
```
public void print(NumberFormat format,
         int width)
```
    Print the matrix to stdout. 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:
    format - A Formatting object for individual elements.
    width - Field width for each column.
    See Also:
    DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)
  - print
```
public void print(PrintWriter output,
         NumberFormat format,
         int width)
```
    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:
    output - the output stream.
    format - A formatting object to format the matrix elements
    width - Column width.
    See Also:
    DecimalFormat.setDecimalFormatSymbols(java.text.DecimalFormatSymbols)
  - toString
```
public String toString()
```
    String representation for this Object.
    
    Overrides:
    
    toString in class Object
    
    Returns:
    string representation of this object.
  - read
```
public static Matrix read(BufferedReader input)
                   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:
    input - the input stream.
    
    Throws:
    
    IOException
  - checkMatrixDimensions
```
private void checkMatrixDimensions(Matrix B)
```
    Check if size(A) == size(B)

Class Matrix

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

A

m

n

Constructor Detail

Matrix

Matrix

Matrix

Matrix

Matrix

Method Detail

constructWithCopy

copy

clone

getArray

getArrayCopy

getColumnPackedCopy

getRowPackedCopy

getRowDimension

getColumnDimension

get

getMatrix

getMatrix

getMatrix

getMatrix

set

setMatrix

setMatrix

setMatrix

setMatrix

transpose

norm1

norm2

normInf

normF

uminus

plus

plusEquals

minus

minusEquals

arrayTimes

arrayTimesEquals

arrayRightDivide

arrayRightDivideEquals

arrayLeftDivide

arrayLeftDivideEquals

times

timesEquals

times

times

lu

qr

chol

svd

eig

solve

solveTranspose

inverse

det

rank

cond

trace

amax

amin

max

min

random

identity

print

print

print

print

toString

read

checkMatrixDimensions