Jama
Class Matrix

java.lang.Object
  extended byJama.Matrix
All Implemented Interfaces:
java.lang.Cloneable, java.io.Serializable

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

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

Field Summary
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
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
 Matrix arrayLeftDivide(Matrix B)
          Element-by-element left division, C = A.
 Matrix arrayLeftDivideEquals(Matrix B)
          Element-by-element left division in place, A = A.
 Matrix arrayRightDivide(Matrix B)
          Element-by-element right division, C = A.
 Matrix arrayRightDivideEquals(Matrix B)
          Element-by-element right division in place, A = A.
 Matrix arrayTimes(Matrix B)
          Element-by-element multiplication, C = A.
 Matrix arrayTimesEquals(Matrix B)
          Element-by-element multiplication in place, A = A.
private  void checkMatrixDimensions(Matrix B)
          Check if size(A) == size(B)
 java.lang.Object clone()
          Clone the Matrix object.
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
 EigenvalueDecomposition eig()
          Eigenvalue Decomposition
 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.
 int getColumnDimension()
          Get column dimension.
 double[] getColumnPackedCopy()
          Make a one-dimensional column packed copy of the internal array.
 Matrix getMatrix(int[] r, int[] c)
          Get a submatrix.
 Matrix getMatrix(int[] r, int j0, int j1)
          Get a submatrix.
 Matrix getMatrix(int i0, int i1, int[] c)
          Get a submatrix.
 Matrix getMatrix(int i0, int i1, int j0, int j1)
          Get a submatrix.
 int getRowDimension()
          Get row dimension.
 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
 Matrix minus(Matrix B)
          C = A - B
 Matrix minusEquals(Matrix B)
          A = A - B
 double norm1()
          One 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(java.text.NumberFormat format, int width)
          Print the matrix to stdout.
 void print(java.io.PrintWriter output, int w, int d)
          Print the matrix to the output stream.
 void print(java.io.PrintWriter output, java.text.NumberFormat format, int width)
          Print the matrix to the output stream.
 void set(int i, int j, double s)
          Set a single element.
 void setMatrix(int[] r, int[] c, Matrix X)
          Set a submatrix.
 void setMatrix(int[] r, int j0, int j1, Matrix X)
          Set a submatrix.
 void setMatrix(int i0, int i1, int[] c, Matrix X)
          Set a submatrix.
 void setMatrix(int i0, int i1, int j0, int j1, Matrix X)
          Set a submatrix.
 Matrix solve(Matrix B)
          Solve A*X = B
 Matrix times(double s)
          Multiply a matrix by a scalar, C = s*A
 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
 Matrix transpose()
          Matrix transpose.
 Matrix uminus()
          Unary minus
 
Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, 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(double[][] A)
Construct a matrix from a 2-D array.

Parameters:
A - Two-dimensional array of doubles.
Throws:
java.lang.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:
java.lang.IllegalArgumentException - Array length must be a multiple of m.

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.
Method Detail

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

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

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

checkMatrixDimensions

private void checkMatrixDimensions(Matrix B)
Check if size(A) == size(B)


clone

public java.lang.Object clone()
Clone the Matrix object.


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:
java.lang.IllegalArgumentException - All rows must have the same length

copy

public Matrix copy()
Make a deep copy of a matrix


eig

public EigenvalueDecomposition eig()
Eigenvalue Decomposition

Returns:
EigenvalueDecomposition
See Also:
EigenvalueDecomposition

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

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.

getColumnDimension

public int getColumnDimension()
Get column dimension.

Returns:
n, the number of columns.

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.

getMatrix

public Matrix getMatrix(int[] r,
                        int[] c)
Get a submatrix.

Parameters:
r - Array of row indices.
c - Array of column indices.
Returns:
A(r(:),c(:))
Throws:
java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

public Matrix getMatrix(int[] r,
                        int j0,
                        int j1)
Get a submatrix.

Parameters:
r - Array of row indices.
Returns:
A(r(:),j0:j1)
Throws:
java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

getMatrix

public Matrix getMatrix(int i0,
                        int i1,
                        int[] c)
Get a submatrix.

Parameters:
i0 - Initial row index
i1 - Final row index
c - Array of column indices.
Returns:
A(i0:i1,c(:))
Throws:
java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

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

getRowDimension

public int getRowDimension()
Get row dimension.

Returns:
m, the number of rows.

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.

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.

inverse

public Matrix inverse()
Matrix inverse or pseudoinverse

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

lu

public LUDecomposition lu()
LU Decomposition

Returns:
LUDecomposition
See Also:
LUDecomposition

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

norm1

public double norm1()
One norm

Returns:
maximum column sum.

normF

public double normF()
Frobenius norm

Returns:
sqrt of sum of squares of all elements.

normInf

public double normInf()
Infinity norm

Returns:
maximum row sum.

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

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(java.text.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(java.io.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(java.io.PrintWriter output,
                  java.text.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)

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

setMatrix

public void setMatrix(int[] r,
                      int[] c,
                      Matrix X)
Set a submatrix.

Parameters:
r - Array of row indices.
c - Array of column indices.
X - A(r(:),c(:))
Throws:
java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int[] r,
                      int j0,
                      int j1,
                      Matrix X)
Set a submatrix.

Parameters:
r - Array of row indices.
j0 - Initial column index
j1 - Final column index
X - A(r(:),j0:j1)
Throws:
java.lang.ArrayIndexOutOfBoundsException - Submatrix indices

setMatrix

public void setMatrix(int i0,
                      int i1,
                      int[] c,
                      Matrix X)
Set a submatrix.

Parameters:
i0 - Initial row index
i1 - Final row index
c - Array of column indices.
X - A(i0:i1,c(:))
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

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

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.

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

transpose

public Matrix transpose()
Matrix transpose.

Returns:
A'

uminus

public Matrix uminus()
Unary minus

Returns:
-A