My matrix class java

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.

Solve a linear system A x = b and compute the residual norm, ||b — A x||.

double[][] vals = ,,>; 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();

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.\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
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) 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	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) 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	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
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
double	trace () Matrix trace.
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

Matrix

Parameters: m — Number of rows. n — Number of colums.

Matrix

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

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

Matrix

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)

Parameters: A — Two-dimensional array of doubles. m — Number of rows. n — Number of colums.

Matrix

public Matrix(double[] vals, int m)

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)

Parameters: A — Two-dimensional array of doubles. Throws: IllegalArgumentException — All rows must have the same length

copy

clone

getArray

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

getArrayCopy

public double[][] getArrayCopy()

Returns: Two-dimensional array copy of matrix elements.

getColumnPackedCopy

public double[] getColumnPackedCopy()

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

getRowPackedCopy

public double[] getRowPackedCopy()

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

getRowDimension

public int getRowDimension()

Returns: m, the number of rows.

getColumnDimension

public int getColumnDimension()

Returns: n, 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)

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

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)

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)

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)

Parameters: i — Row index. j — Column index. s — A(i,j). Throws: ArrayIndexOutOfBoundsException

setMatrix

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

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

setMatrix

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

setMatrix

Parameters: i0 — Initial row index i1 — Final row index c — Array of column indices. X — A(i0:i1,c(:)) Throws: ArrayIndexOutOfBoundsException — Submatrix indices

transpose

norm1

Returns: maximum column sum.

norm2

Returns: maximum singular value.

normInf

normF

Returns: sqrt of sum of squares of all elements.

uminus

plus

Parameters: B — another matrix Returns: A + B

plusEquals

Parameters: B — another matrix Returns: A + B

minus

Parameters: B — another matrix Returns: A — B

minusEquals

Parameters: B — another matrix Returns: A — B

arrayTimes

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

arrayTimesEquals

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

arrayRightDivide

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

arrayRightDivideEquals

public Matrix arrayRightDivideEquals(Matrix B)

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

arrayLeftDivide

Parameters: B — another matrix Returns: A.\B

arrayLeftDivideEquals

public Matrix arrayLeftDivideEquals(Matrix B)

Parameters: B — another matrix Returns: A.\B

times

Parameters: s — scalar Returns: s*A

timesEquals

Parameters: s — scalar Returns: replace A by s*A

times

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

lu

Returns: LUDecomposition See Also: LUDecomposition

qr

Returns: QRDecomposition See Also: QRDecomposition

chol

Returns: CholeskyDecomposition See Also: CholeskyDecomposition

svd

Returns: SingularValueDecomposition See Also: SingularValueDecomposition

eig

Returns: EigenvalueDecomposition See Also: EigenvalueDecomposition

solve

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

solveTranspose

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

inverse

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

det

rank

Returns: effective numerical rank, obtained from SVD.

cond

Returns: ratio of largest to smallest singular value.

trace

Returns: sum of the diagonal elements.

random

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

identity

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)

Parameters: w — Column width. d — Number of digits after the decimal.

print

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

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)

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

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