Class Matrix

java.lang.Object
   |
   +----Matrix

class Matrix

extends Object

implements Serializable

DEBUG

Set DEBUG to true to print out debugging info

INDEX_OF_S

INDEX_OF_U

If this matrix happens to be a 3 X 3 matrix, this method will compute the SVD of it, using Jacobi method This is based on code that was generously provided by cvl.

INDEX_OF_V

m_rgrgElt

The matrix Note that we assume the matrix to be rectangular.

Matrix()

Default constructor So we don't cause problems with constructor chaining

Matrix(double[][])

Build an array from a multidimensional array Convenient b/c we can now create a 2D array, initialize it,then turn it into a Matrix

Matrix(int, int)

So we can create a matrix with given dimensions

Matrix(Matrix)

Copy constructor

Add(Matrix)

A helper version of the above add that will handle memory allocation for the user

Add(Matrix, Matrix)

Adds from this matrix the corresponding entry in the matrix add, and writes the resulting matrix into out.

AlignZ(Matrix)

Align the cross porduct of U and V with the Z axis (R1), then Transform U V accordingly into U1 and V1, then Align the bisector of U1 and V1 with the x axis (R2)

Compare(Matrix)

returns true if all of the elements of the "this" matrix, and the "M" matrix are equal, returns false otherwise

Det3()

Computes the determinant of the 3 by 3 matrix, returning a scalar

DivideEltsBy(double)

DivideEltsBy Divide every element in the Matrix by divisor, overwriting the current matrix with the result

DivideEltsBy(double, Matrix)

DivideEltsBy Divide every element in the Matrix by divisor, writing the result into the matrix named out (which must have been allocated previously by the caller.

eye()

eye If the matrix is square, it'll overwrite the contents with an identity matrix

FrobeniusNorm()

Returns the Frobenius Norm of the matrix -- square each element, sum the squares, take the square root of the summation, the result is the 2norm

FrobeniusNormOffDiagonal()

Returns the Frobenius Norm of every element in the matrix, EXCEPT for those elements on the main diagonal.

GetArray()

GetArray returns the n X m matrix as an array of size [n][m].

GetElement(int, int)

Returns an individual element.

Givens(double, double)

Computes the Givens rotation of a matrix, where returnedArray[0] == c returnedArray[1] == s

isColumnVector()

Returns true iff the matrix is actually a column vector

isRowVector()

Returns true iff the matrix is actually a row vector

isScalar()

isScalar Returns true iff the matrix has only 1 row and 1 column (thus, 1 element)

isSymmetric()

isSymmetric returns true iff the matrix is symmetric

isVector()

isVector returns true if the matrix is not a scalar, but does have a single dimension

MultEltByElt(Matrix)

A helper version of the above MultEltByElt that will handle memory allocation for the user

MultEltByElt(Matrix, Matrix)

multiply this matrix and mul matrix entry by entry, and writes the resulting matrix into out.

Multiply(double)

Helper function to multiply the matrix by a constant, but will allocate teh out matrix for the user

Multiply(double, Matrix)

Multiplies each element of the matrix by a scalar value

Multiply(Matrix)

Multiply the "this" matrix by the matrix M, as in retValue = this * M This helper method automatically allocates the new Matrix for you.

Multiply(Matrix, Matrix)

If the matrix stored in the this object is A, and the matrix returned from this method is B, then this method computes B = AM

NumCols()

This works because the array is rectangular

NumRows()

Print()

Helper util to pretty-print hte matrix Probably looks bad when matrix greater than width of screen

readObject(ObjectInputStream)

SetArray(double[][])

SetBlock(int, int, double[][])

A basic mass-copy, only this time for a 2D array

SetBlock(int, int, Matrix)

SetBlock is a covenience, so we can copy a smaller Matrix over part of the current one

SetBlock(int[], int[], Matrix)

SetBlock to take a smaller matrix, rearrange the rows & columns, and copy them over some of the current matrix.

SetElement(int, int, double)

Used to set M[i][j] to 'value'.

Submatrix(int, int, int, int)

Helper function - auto-allocates a matrix to put the submatrix into

Submatrix(int, int, int, int, Matrix)

Submatrix returns the matrix constructed by copying all elements out of the matrix, whose upper left corner is (offRow, offCol), and whose lower right corner is (offRow+cRows-1, offCol+cCol-1) (inclusive for both).

Submatrix(int[], int[])

Much like the last version of SetBlock, which allows for rearranging of the matrix, this edition of Submatrix takes two arrays to indicate which columns and rows the user wants.

Subtract(Matrix)

A helper version of the above subtract that will handle memory allocation for the user

Subtract(Matrix, Matrix)

Subtracts from this matrix the corresponding entry in the matrix sub, and writes the resulting matrix into out.

SVDThreeByThree(double)

SVDTwoByTwo(double, double, double, double, double[])

based on code graciously provided by cvl.

toString()

toString formats a String, suitable for printing, that expresses the Matrix

Trace()

Computes the trace of a matrix, where trace = sum of the elements along the main diagonal (ie, summation from n = 1 to i of m_rgrgElt[n][n]) We need a square matrix, and we'll throw MatrixDimensionException if it isn't

Transpose()

returns the tranpose of the matrix, A', This helper function automatically allocates a new Matrix to hold the result Note that A = (A')'

Transpose(Matrix)

returns the tranpose of the matrix, A' Note that A = (A')'

UnitVectorize()

UnitVectorize Assumes that each row will be treated as a vector, and that we want to find the unit vector between row[i] and row[i+1] For for row[0], we find the unit vector between it and the origin.

writeObject(ObjectOutputStream)

zero()

 public boolean DEBUG

Set DEBUG to true to print out debugging info

 protected double m_rgrgElt[][]

The matrix Note that we assume the matrix to be rectangular. [row][col]

 public static final int INDEX_OF_U

If this matrix happens to be a 3 X 3 matrix, this method will compute the SVD of it, using Jacobi method This is based on code that was generously provided by cvl. The inlined Matlab code should provide guidance to the algorithm.

 public static final int INDEX_OF_S

 public static final int INDEX_OF_V

 public Matrix()

Default constructor So we don't cause problems with constructor chaining

 public Matrix(int cRows,
               int cCols)

So we can create a matrix with given dimensions

 public Matrix(double MrgrgElt[][])

Build an array from a multidimensional array Convenient b/c we can now create a 2D array, initialize it,then turn it into a Matrix

 public Matrix(Matrix M) throws MatrixDimensionException

Copy constructor

 public final double[][] GetArray()

GetArray returns the n X m matrix as an array of size [n][m]. Kind of an accessor. Nice for doing ops like multiplication, where we don't want the overhead of a function call on every access.

 public void SetArray(double d[][])

 public int NumRows()

 public int NumCols()

This works because the array is rectangular

 public final double GetElement(int i,
                                int j)

Returns an individual element.

 public void zero() throws MatrixDimensionException

 public boolean isSymmetric() throws MatrixDimensionException

isSymmetric returns true iff the matrix is symmetric

 public boolean isScalar()

isScalar Returns true iff the matrix has only 1 row and 1 column (thus, 1 element)

 public boolean isVector()

isVector returns true if the matrix is not a scalar, but does have a single dimension

 public boolean isColumnVector()

Returns true iff the matrix is actually a column vector

 public boolean isRowVector()

Returns true iff the matrix is actually a row vector

 public void SetElement(int i,
                        int j,
                        double value)

Used to set M[i][j] to 'value'.

 public void SetBlock(int offRow,
                      int offCol,
                      Matrix m) throws MatrixDimensionException

SetBlock is a covenience, so we can copy a smaller Matrix over part of the current one

 public void SetBlock(int offRow,
                      int offCol,
                      double NewRgrgElt[][]) throws MatrixDimensionException

A basic mass-copy, only this time for a 2D array

 public void SetBlock(int rgRow[],
                      int rgCol[],
                      Matrix m) throws MatrixDimensionException

SetBlock to take a smaller matrix, rearrange the rows & columns, and copy them over some of the current matrix. Matlab has similar functionality in its matrixNew = bigMatrix[ 1:3, 2:4] This does the same thing, only this time in Java!

 public Matrix Submatrix(int offRow,
                         int offCol,
                         int cRow,
                         int cCol,
                         Matrix AM) throws MatrixDimensionException

Submatrix returns the matrix constructed by copying all elements out of the matrix, whose upper left corner is (offRow, offCol), and whose lower right corner is (offRow+cRows-1, offCol+cCol-1) (inclusive for both).

 public Matrix Submatrix(int offRow,
                         int offCol,
                         int cRow,
                         int cCol) throws MatrixDimensionException

Helper function - auto-allocates a matrix to put the submatrix into

 public Matrix Submatrix(int rgRow[],
                         int rgCol[]) throws MatrixDimensionException

Much like the last version of SetBlock, which allows for rearranging of the matrix, this edition of Submatrix takes two arrays to indicate which columns and rows the user wants. The zeroth row of the output matrix contains the entries of the row given in rgRow, the first row from the 1st entry in rgRow, etc,etc

 public String toString()

toString formats a String, suitable for printing, that expresses the Matrix

Overrides:

toString in class Object

 public double Trace() throws MatrixDimensionException

Computes the trace of a matrix, where trace = sum of the elements along the main diagonal (ie, summation from n = 1 to i of m_rgrgElt[n][n]) We need a square matrix, and we'll throw MatrixDimensionException if it isn't

 public double Det3() throws MatrixDimensionException

Computes the determinant of the 3 by 3 matrix, returning a scalar

 public void DivideEltsBy(double divisor) throws MatrixDimensionException

DivideEltsBy Divide every element in the Matrix by divisor, overwriting the current matrix with the result

 public void DivideEltsBy(double divisor,
                          Matrix out) throws MatrixDimensionException

DivideEltsBy Divide every element in the Matrix by divisor, writing the result into the matrix named out (which must have been allocated previously by the caller.

 public void eye() throws MatrixDimensionException

eye If the matrix is square, it'll overwrite the contents with an identity matrix

 public double FrobeniusNorm() throws MatrixDimensionException

Returns the Frobenius Norm of the matrix -- square each element, sum the squares, take the square root of the summation, the result is the 2norm

 public double FrobeniusNormOffDiagonal() throws MatrixDimensionException

Returns the Frobenius Norm of every element in the matrix, EXCEPT for those elements on the main diagonal. square each element that isn't on the main diagonal, sum the squares, take the square root of the summation, the result is the 2norm

 public static double[] Givens(double a,
                               double b)

Computes the Givens rotation of a matrix, where returnedArray[0] == c returnedArray[1] == s

 public Matrix Multiply(Matrix M,
                        Matrix out) throws MatrixDimensionException

If the matrix stored in the this object is A, and the matrix returned from this method is B, then this method computes B = AM

Throws: MatrixDimensionException

If the number of columns in this matrix does not equal the number of rows in matrix M

 public Matrix Multiply(Matrix M) throws MatrixDimensionException

Multiply the "this" matrix by the matrix M, as in retValue = this * M This helper method automatically allocates the new Matrix for you.

 public Matrix Multiply(double scalar,
                        Matrix out) throws MatrixDimensionException

Multiplies each element of the matrix by a scalar value

 public Matrix Multiply(double scalar) throws MatrixDimensionException

Helper function to multiply the matrix by a constant, but will allocate teh out matrix for the user

 public Matrix Subtract(Matrix sub,
                        Matrix out) throws MatrixDimensionException

Subtracts from this matrix the corresponding entry in the matrix sub, and writes the resulting matrix into out. Thus, we get out = this[i][j] - sub[i][j] for all i,j

 public Matrix Subtract(Matrix sub) throws MatrixDimensionException

A helper version of the above subtract that will handle memory allocation for the user

 public Matrix Add(Matrix add,
                   Matrix out) throws MatrixDimensionException

Adds from this matrix the corresponding entry in the matrix add, and writes the resulting matrix into out. Thus, we get out = this[i][j] + add[i][j] for all i,j

 public Matrix Add(Matrix add) throws MatrixDimensionException

A helper version of the above add that will handle memory allocation for the user

 public Matrix MultEltByElt(Matrix mul,
                            Matrix out) throws MatrixDimensionException

multiply this matrix and mul matrix entry by entry, and writes the resulting matrix into out. Thus, we get out = this[i][j] * mul[i][j] for all i,j

 public Matrix MultEltByElt(Matrix mul) throws MatrixDimensionException

A helper version of the above MultEltByElt that will handle memory allocation for the user

 public Matrix[] SVDThreeByThree(double Tolerance) throws MatrixDimensionException

 protected static void SVDTwoByTwo(double w,
                                   double x,
                                   double y,
                                   double z,
                                   double SVD2Output[])

based on code graciously provided by cvl. The array returned by this function contains the following values in the following locations: SVD2Output[0] == c1 SVD2Output[1] == s1 SVD2Output[2] == c2 SVD2Output[3] == s2

 public Matrix Transpose(Matrix out) throws MatrixDimensionException

returns the tranpose of the matrix, A' Note that A = (A')'

 public Matrix Transpose() throws MatrixDimensionException

returns the tranpose of the matrix, A', This helper function automatically allocates a new Matrix to hold the result Note that A = (A')'

 public Matrix UnitVectorize()

UnitVectorize Assumes that each row will be treated as a vector, and that we want to find the unit vector between row[i] and row[i+1] For for row[0], we find the unit vector between it and the origin.

 public boolean Compare(Matrix M) throws MatrixDimensionException

returns true if all of the elements of the "this" matrix, and the "M" matrix are equal, returns false otherwise

Throws: MatrixDimensionException

if the number of rows or columns differ between matrices

 public Matrix AlignZ(Matrix V) throws MatrixDimensionException

Align the cross porduct of U and V with the Z axis (R1), then Transform U V accordingly into U1 and V1, then Align the bisector of U1 and V1 with the x axis (R2)

 public void Print()

Helper util to pretty-print hte matrix Probably looks bad when matrix greater than width of screen

 private void writeObject(ObjectOutputStream out) throws IOException

 private void readObject(ObjectInputStream in) throws IOException, ClassNotFoundException