maspack.matrix
Class MatrixNd

java.lang.Object
  maspack.matrix.MatrixObject
      maspack.matrix.MatrixNd

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

SubMatrixNd

public class MatrixNd

extends MatrixObject

implements java.io.Serializable

Implements general m x n matrices, along with most the commonly used operations associated with such matrices.

Normally, these matrices can be resized, either explicitly through a call to setSize, or implicitly through operations that require the matrix size to be modified. The exception is when this matrix is either a submatrix, or is being referenced by a submatrix (see SubMatrixNd).

See Also:

Serialized Form

Constructor Summary

MatrixNd(double[][] values)
Creates a matrix from a two dimensional array of doubles.

MatrixNd(int numRows, int numCols)
Creates a matrix of a specific size, and initializes its elements to 0.

MatrixNd(int numRows, int numCols, double[] values)
Creates a matrix of specific size and initializes its elements from an array of values.

MatrixNd(MatrixObject M)
Creates a matrix whose size and elements are the same as an existing MatrixObject.

Method Summary

void	absolute() Sets the elements of this matrix to their absolute values.
void	add(MatrixNd M1) Adds this matrix to M1 and places the result in this matrix.
void	add(MatrixNd M1, MatrixNd M2) Adds matrix M1 to M2 and places the result in this matrix.
int	colSize() Returns the number of columns in this matrix.
void	copySubMatrix(int baseRowSrc, int baseColSrc, int numRows, int numCols, MatrixNd Msrc, int baseRowDest, int baseColDest) Copies a sub matrix from a specified source matrix Msrc to a region of this matrix.
boolean	epsilonEquals(MatrixNd M1, double epsilon) Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.
boolean	equals(MatrixNd M1) Returns true if the elements of this matrix exactly equal those of matrix M1.
double	frobeniusNorm() Returns the Frobenius norm of this matrix.
void	get(double[] values) Copies the elements of this matrix into an array of doubles.
double	get(int i, int j) Gets a single element of this matrix.
double[]	getBuffer() Returns the internal buffer used to store the elements in this matrix.
int	getBufferBase() Returns the internal buffer base index of this matrix, used for computing the index necessary to reference a particular element.
int	getBufferWidth() Returns the internal buffer width of this matrix, used for computing the index necessary to reference a particular element.
void	getColumn(int j, double[] values) Copies a column of this matrix into an array of doubles.
void	getColumn(int j, VectorObject v) Copies a column of this matrix into a VectorObject.
void	getRow(int i, double[] values) Copies a row of this matrix into an array of doubles.
void	getRow(int i, VectorObject v) Copies a row of this matrix into a VectorObject.
void	getSubMatrix(int[] rows, int[] cols, MatrixNd Mdest) Gets a submatrix of this matrix.
void	getSubMatrix(int baseRow, int baseCol, MatrixNd Mdest) Gets a submatrix of this matrix.
double	infinityNorm() Returns the infinity norm of this matrix.
boolean	invert() Inverts this matrix in place, returning false if the matrix is detected to be singular.
boolean	invert(MatrixNd M1) Inverts the matrix M1 and places the result in this matrix, returning false if the matrix is detected to be singular.
boolean	isFixedSize() Returns true if this matrix is of fixed size.
boolean	isSubMatrix() Returns true if the this matrix is a submatrix; i.e., is a member of the subclass SubMatrixNd.
static void	main(java.lang.String[] args)
double	maxElement() Returns the maximum element value of this matrix.
double	minElement() Returns the minimum element value of this matrix.
void	mul(MatrixNd M1) Multiplies this matrix by M1 and places the result in this matrix.
void	mul(MatrixNd M1, MatrixNd M2) Multiplies matrix M1 by M2 and places the result in this matrix.
void	mul(VectorNd vr, VectorNd v1) Multiplies this matrix by the column vector v1 and places the result in the vector vr.
void	mulDiagonalLeft(double[] diag) Pre-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by the leading elements of an array of doubles.
void	mulDiagonalLeft(VectorNd diag) Pre-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by a vector.
void	mulDiagonalRight(double[] diag) Post-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by the leading elements of an array of doubles.
void	mulDiagonalRight(VectorNd diag) Post-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by a vector.
void	mulTranspose(MatrixNd M1) Multiplies this matrix by the transpose of M1 and places the result in this matrix.
void	mulTranspose(VectorNd vr, VectorNd v1) Multiplies the transpose of this matrix by the vector v1 and places the result in vr.
void	mulTransposeBoth(MatrixNd M1, MatrixNd M2) Multiplies the transpose of matrix M1 by the transpose of M2 and places the result in this matrix.
void	mulTransposeLeft(MatrixNd M1, MatrixNd M2) Multiplies the transpose of matrix M1 by M2 and places the result in this matrix.
void	mulTransposeRight(MatrixNd M1, MatrixNd M2) Multiplies matrix M1 by the transpose of M2 and places the result in this matrix.
void	negate() Negates this matrix in place.
void	negate(MatrixNd M1) Sets this matrix to the negative of M1.
double	oneNorm() Returns the 1 norm of this matrix.
void	permuteColumns(int[] permutation) Rearrange the columns of this matrix according to the specified permutation, such that each column j is replaced by column permutation[j].
void	permuteRows(int[] permutation) Rearrange the rows of this matrix according to the specified permutation, such that each row i is replaced by row permutation[i].
int	rowSize() Returns the number of rows in this matrix.
void	scale(double s) Scales the elements of this matrix by s.
void	scale(double s, MatrixNd M1) Scales the elements of matrix M1 by s and places the results in this matrix.
void	set(double[] values) Sets the elements of this matrix from an array of doubles.
void	set(int i, int j, double value) Sets a single element of this matrix.
void	set(MatrixNd M1) Sets the size and values of this matrix to those of matrix M1.
void	setBuffer(int numRows, int numCols, double[] buffer, int bufWidth) Explicitly sets the size and internal buffer associated with this matrix.
void	setColumn(int j, double[] values) Sets a column of this matrix from an array of doubles.
void	setColumn(int j, VectorObject v) Sets a column of this matrix from a VectorObject.
void	setDiagonal(double[] diag) Sets this matrix to a diagonal matrix whose diagonal elements are specified by the leading elements of an array of doubles
void	setDiagonal(VectorNd diag) Sets this matrix to a diagonal matrix whose diagonal elements are specified by a vector.
void	setIdentity() Sets this matrix to the identity matrix.
void	setRandom() Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).
void	setRandom(double lower, double upper) Sets the elements of this matrix to uniformly distributed random values in a specified range.
void	setRandom(double lower, double upper, java.util.Random generator) Sets the elements of this matrix to uniformly distributed random values in a specified range, using a supplied random number generator.
void	setRandomOrthogonal() Sets this matrix to a random orthogonal matrix.
void	setRandomOrthogonal(java.util.Random generator) Sets this matrix to a random orthogonal matrix, using a supplied random number generator.
void	setRandomSvd(double[] singularValues) Sets this matrix to a random matrix with specified singular values.
void	setRandomSvd(double[] singularValues, java.util.Random generator) Sets this matrix to a random matrix with specified singular values, using a supplied random number generator.
void	setRow(int i, double[] values) Set a row of this matrix from an array of doubles.
void	setRow(int i, VectorObject v) Sets a row of this matrix from a VectorObject.
void	setSize(int numRows, int numCols) Sets the size of this matrix.
void	setSubMatrix(int[] rows, int[] cols, MatrixNd Msrc) Sets a submatrix of this matrix.
void	setSubMatrix(int baseRow, int baseCol, MatrixNd Msrc) Sets a submatrix of this matrix.
void	setZero() Sets the elements of this matrix to zero.
void	sub(MatrixNd M1) Subtracts this matrix from M1 and places the result in this matrix.
void	sub(MatrixNd M1, MatrixNd M2) Subtracts matrix M1 from M2 and places the result in this matrix.
void	transpose() Replaces this matrix by its tranpose.
void	transpose(MatrixNd M1) Takes the transpose of matrix M1 and places the result in this matrix.
void	unsetBuffer() Removes an explicit buffer provided for this matrix and replaces it with a default implicit buffer.

Methods inherited from class maspack.matrix.MatrixObject

determinant, epsilonEquals, equals, equals, get, scan, set, set, toString, toString, toString

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

MatrixNd

public MatrixNd(int numRows,
                int numCols)

Creates a matrix of a specific size, and initializes its elements to 0. It is legal to create a matrix with zero rows and columns.

Parameters:

numRows - number of rows

numCols - number of columns

Throws:

ImproperSizeException - if numRows or numCols are negative

MatrixNd

public MatrixNd(double[][] values)

Creates a matrix from a two dimensional array of doubles. The matrix size will be determined by the size of this array.

Parameters:

values - element values for the new matrix

MatrixNd

public MatrixNd(int numRows,
                int numCols,
                double[] values)

Creates a matrix of specific size and initializes its elements from an array of values.

Parameters:

numRows - number of rows

numCols - number of columns

values - element values for the matrix, with element (i,j) stored at location i*numCols+j

MatrixNd

public MatrixNd(MatrixObject M)

Creates a matrix whose size and elements are the same as an existing MatrixObject.

Parameters:

M - matrix object to be copied.

Method Detail

isFixedSize

public boolean isFixedSize()

Returns true if this matrix is of fixed size. This will be true if the matrix is either a submatrix or is being referenced by a submatrix (see SubMatrixNd). If the matrix is not of fixed size, then it can be resized dynamically, either explicitly using setSize, or implicitly when being used as a result for various matrix operations.

Overrides:

isFixedSize in class MatrixObject

Returns:

true if this matrix is of fixed size

See Also:

setSize(int, int)

isSubMatrix

public boolean isSubMatrix()

Returns true if the this matrix is a submatrix; i.e., is a member of the subclass SubMatrixNd.

Returns:

true if this matrix is a submatrix

getBuffer

public double[] getBuffer()

Returns the internal buffer used to store the elements in this matrix. When possible, applications should access the matrix elements using the various set and get methods. However, if efficiency requires it, this buffer can be used directly.

Roughly speaking, elements are stored in the buffer in row-column order. However, the buffer may be larger than the matrix, and there may be extra space at the beginning of the buffer. The buffer index which access the element (i,j) is computed as i*w + j + b, where w and b are the width and base values returned by getBufferWidth and getBufferBase, respectively.

Note also that if this matrix is a submatrix, the buffer will actually belong to the root matrix, and so modifying values in the buffer (including those outside the nominal range of this matrix) will change the root matrix as well.

If this matrix is resized, then the internal buffer may change and the buffer previously returned by this routine may no longer be valid.

Returns:

internal buffer for this matrix

See Also:

getBufferWidth(), getBufferBase(), setBuffer(int, int, double[], int)

getBufferWidth

public int getBufferWidth()

Returns the internal buffer width of this matrix, used for computing the index necessary to reference a particular element.

Returns:

internal buffer width

See Also:

getBuffer()

getBufferBase

public int getBufferBase()

Returns the internal buffer base index of this matrix, used for computing the index necessary to reference a particular element.

Returns:

internal buffer base index

See Also:

getBuffer()

setSize

public void setSize(int numRows,
                    int numCols)

Sets the size of this matrix. This operation is only supported if isFixedSize returns false. If necessary, this operation will enlarge the internal buffer associated with this matrix, invalidating buffers previously returned by getBuffer.

If a matrix is resized, then any previous element values which are still within the new matrix dimensions are preserved. Other (new) element values are undefined.

Overrides:

setSize in class MatrixObject

Parameters:

numRows - new row size

numCols - new column size

Throws:

ImproperSizeException - if this matrix has an explicit internal buffer and that buffer is too small to support the requested size

java.lang.UnsupportedOperationException - if this matrix has fixed size

See Also:

isFixedSize()

rowSize

public final int rowSize()

Returns the number of rows in this matrix.

Specified by:

rowSize in class MatrixObject

Returns:

number of rows

colSize

public final int colSize()

Returns the number of columns in this matrix.

Specified by:

colSize in class MatrixObject

Returns:

number of columns

setBuffer

public void setBuffer(int numRows,
                      int numCols,
                      double[] buffer,
                      int bufWidth)

Explicitly sets the size and internal buffer associated with this matrix. Any previous values will be discarded, and the matrix will assume new values with each element (i,j) given by the buffer contents at index [i*bufWidth+j]. In particular, bufWidth must satisfy bufWidth >= numCols, and the length of buffer must satisfy buffer.length >= numRows*bufWidth. The matrix can continue to be resized as long as requested sizes stay do not violate these bounds. The value of bufWidth will become the value returned by getBufferWidth, while the value returned by getBufferBase will be 0.

Parameters:

numRows - new row size

numCols - new column size

buffer - explicit buffer for this matrix

bufWidth - width for the explicit buffer

Throws:

java.lang.IllegalStateException - if this matrix has referring submatrices or is itself a submatrix

ImproperSizeException - if the specified buffer and/or width is too small for the requested size

See Also:

getBufferWidth(), getBufferBase(), unsetBuffer()

unsetBuffer

public void unsetBuffer()

Removes an explicit buffer provided for this matrix and replaces it with a default implicit buffer. The matrix retains its present size but all values are replaced with zero.

Throws:

java.lang.IllegalStateException - if this matrix does not have an explicit buffer given by setBuffer

java.lang.IllegalStateException - if this matrix has referring submatrices

See Also:

setBuffer(int, int, double[], int)

copySubMatrix

public void copySubMatrix(int baseRowSrc,
                          int baseColSrc,
                          int numRows,
                          int numCols,
                          MatrixNd Msrc,
                          int baseRowDest,
                          int baseColDest)
                   throws ImproperSizeException

Copies a sub matrix from a specified source matrix Msrc to a region of this matrix. The base row and column of the source and destination may be different.

Parameters:

baseRowSrc - starting submatrix row in the source matrix

baseColSrc - starting submatrix column in the source matrix

numRows - number of rows in the submatrix

numCols - number of columns in the submatrix

Msrc - source matrix

baseRowDest - starting submatrix row in this matrix

baseColDest - starting submatrix column in this matrix

Throws:

ImproperSizeException - if the specified submatrix dimensions are infeasible

See Also:

getSubMatrix(int,int,MatrixNd), setSubMatrix(int,int,MatrixNd)

get

public final double get(int i,
                        int j)

Gets a single element of this matrix.

Specified by:

get in class MatrixObject

Parameters:

i - element row index

j - element column index

Returns:

element value

get

public final void get(double[] values)

Copies the elements of this matrix into an array of doubles. The elements are stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Overrides:

get in class MatrixObject

Parameters:

values - array into which values are copied

getColumn

public final void getColumn(int j,
                            double[] values)

Copies a column of this matrix into an array of doubles.

Overrides:

getColumn in class MatrixObject

Parameters:

j - column index

values - array into which the column is copied

getRow

public final void getRow(int i,
                         double[] values)

Copies a row of this matrix into an array of doubles.

Overrides:

getRow in class MatrixObject

Parameters:

i - row index

values - array into which the row is copied

getColumn

public final void getColumn(int j,
                            VectorObject v)

Copies a column of this matrix into a VectorObject.

Overrides:

getColumn in class MatrixObject

Parameters:

j - column index

v - vector into which the column is copied

Throws:

ImproperSizeException - vector's size not equal to the number of matrix rows and the vector cannot be resized

getRow

public final void getRow(int i,
                         VectorObject v)

Copies a row of this matrix into a VectorObject.

Overrides:

getRow in class MatrixObject

Parameters:

i - row index

v - vector into which the row is copied

Throws:

ImproperSizeException - vector's size not equal to the number of matrix columns and the vector cannot be resized

getSubMatrix

public void getSubMatrix(int baseRow,
                         int baseCol,
                         MatrixNd Mdest)
                  throws ImproperSizeException

Gets a submatrix of this matrix. The first row and column of the submatrix are given by baseRow and baseCol, and the values are written into the matrix Mdest. The size of the submatrix is determined by the dimensions of Mdest.

Parameters:

baseRow - first row of the submatrix

baseCol - first column of the submatrix

Mdest - destination for submatrix values

Throws:

ImproperSizeException - if baseRow or baseCol are negative, or if the submatrix exceeds the current matrix bounds.

See Also:

copySubMatrix(int, int, int, int, maspack.matrix.MatrixNd, int, int)

getSubMatrix

public void getSubMatrix(int[] rows,
                         int[] cols,
                         MatrixNd Mdest)
                  throws ImproperSizeException

Gets a submatrix of this matrix. The row and column indices of the submatrix are specified by rows and the cols, respectively, and the values are written into the matrix Mdest. The size of the submatrix is determined by the existing dimensions of Mdest.

Parameters:

rows - row indices of the submatrix

cols - column indices of the submatrix

Mdest - destination for submatrix values

Throws:

ImproperSizeException - if the number of rows or columns exceed the dimensions of Mdest, or if any of the specified indices lie outside the bounds of this matrix.

set

public final void set(int i,
                      int j,
                      double value)

Sets a single element of this matrix.

Specified by:

set in class MatrixObject

Parameters:

i - element row index

j - element column index

value - element value

set

public final void set(double[] values)

Sets the elements of this matrix from an array of doubles. The elements in the array should be stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Overrides:

set in class MatrixObject

Parameters:

values - array from which values are copied

setColumn

public final void setColumn(int j,
                            double[] values)

Sets a column of this matrix from an array of doubles.

Overrides:

setColumn in class MatrixObject

Parameters:

j - column index

values - array from which column values are copied

setRow

public final void setRow(int i,
                         double[] values)

Set a row of this matrix from an array of doubles.

Overrides:

setRow in class MatrixObject

Parameters:

i - row index

values - array from which the row is copied

setColumn

public void setColumn(int j,
                      VectorObject v)

Sets a column of this matrix from a VectorObject.

Overrides:

setColumn in class MatrixObject

Parameters:

j - column index

v - vector from which the column is copied

Throws:

ImproperSizeException - vector's size not equal to the number of matrix rows

setRow

public void setRow(int i,
                   VectorObject v)

Sets a row of this matrix from a VectorObject.

Overrides:

setRow in class MatrixObject

Parameters:

i - row index

v - vector from which the row is copied

Throws:

ImproperSizeException - vector's size not equal to the number of matrix columns

setSubMatrix

public void setSubMatrix(int baseRow,
                         int baseCol,
                         MatrixNd Msrc)
                  throws ImproperSizeException

Sets a submatrix of this matrix. The first row and column of the submatrix are given by baseRow and baseCol, and the new values are given by the matrix Msrc. The size of the submatrix is determined by the dimensions of Msrc.

Parameters:

baseRow - index of the first row of the submatrix

baseCol - index of the first column of the submatrix

Msrc - new values for the submatrix.

Throws:

ImproperSizeException - if baseRow or baseCol are negative, or if the submatrix exceeds the current matrix bounds

See Also:

copySubMatrix(int, int, int, int, maspack.matrix.MatrixNd, int, int)

setSubMatrix

public void setSubMatrix(int[] rows,
                         int[] cols,
                         MatrixNd Msrc)
                  throws ImproperSizeException

Sets a submatrix of this matrix. The row and column indices of the submatrix are specified by rows and the cols, respectively, and the new values are given by the matrix Msrc. The size of the submatrix is determined by the existing dimensions of Msrc.

Parameters:

rows - row indices of the submatrix

cols - column indices of the submatrix

Msrc - new values for the submatrix

Throws:

ImproperSizeException - if the number of rows or columns exceed the dimensions of Msrc, or if any of the specified indices lie outside the bounds of this matrix.

setRandom

public void setRandom()

Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).

setRandom

public void setRandom(double lower,
                      double upper)

Sets the elements of this matrix to uniformly distributed random values in a specified range.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

setRandom

public void setRandom(double lower,
                      double upper,
                      java.util.Random generator)

Sets the elements of this matrix to uniformly distributed random values in a specified range, using a supplied random number generator.

Parameters:

lower - lower random value (inclusive)

upper - upper random value (exclusive)

generator - random number generator

setRandomOrthogonal

public void setRandomOrthogonal()

Sets this matrix to a random orthogonal matrix. This is a matrix whose rows and columns are randomly selected while still being orthonormal.

setRandomOrthogonal

public void setRandomOrthogonal(java.util.Random generator)

Sets this matrix to a random orthogonal matrix, using a supplied random number generator.

Parameters:

generator - random number generator

See Also:

setRandomOrthogonal()

setRandomSvd

public void setRandomSvd(double[] singularValues)

Sets this matrix to a random matrix with specified singular values. The size of the matrix is unchanged, and the number of supplied singular values must equal the minimum matrix dimension. This routine is useful for creating random matrices with a prescribed degeneracy.

Parameters:

singularValues - singular values for this matrix

Throws:

ImproperSizeException - if the length of singularValues is less than the minimum matrix dimension

setRandomSvd

public void setRandomSvd(double[] singularValues,
                         java.util.Random generator)

Sets this matrix to a random matrix with specified singular values, using a supplied random number generator.

Parameters:

singularValues - singular values for this matrix

generator - random number generator

Throws:

ImproperSizeException - if the length of singularValues is less than the minimum matrix dimension

See Also:

setRandomSvd(double[])

mul

public void mul(MatrixNd M1)

Multiplies this matrix by M1 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - right-hand matrix

Throws:

ImproperSizeException - if this matrix and M1 do not conform, or if this matrix needs resizing but is of fixed size

mul

public void mul(MatrixNd M1,
                MatrixNd M2)
         throws ImproperSizeException

Multiplies matrix M1 by M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if matrices M1 and M2 do not comform, or if this matrix needs resizing but is of fixed size

mulTranspose

public void mulTranspose(MatrixNd M1)

Multiplies this matrix by the transpose of M1 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - right-hand matrix

Throws:

ImproperSizeException - if this matrix and the transpose of M1 do not conform, or if this matrix needs resizing but is of fixed size

mulTransposeRight

public void mulTransposeRight(MatrixNd M1,
                              MatrixNd M2)
                       throws ImproperSizeException

Multiplies matrix M1 by the transpose of M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if M1 and the transpose of M2 do not comform, or if this matrix needs resizing but is of fixed size

mulTransposeLeft

public void mulTransposeLeft(MatrixNd M1,
                             MatrixNd M2)
                      throws ImproperSizeException

Multiplies the transpose of matrix M1 by M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if the transpose of M1 and M2 do not comform, or if this matrix needs resizing but is of fixed size

mulTransposeBoth

public void mulTransposeBoth(MatrixNd M1,
                             MatrixNd M2)
                      throws ImproperSizeException

Multiplies the transpose of matrix M1 by the transpose of M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if the transpose of M1 and the transpose of M2 do not comform, or if this matrix needs resizing but is of fixed size

mulDiagonalLeft

public void mulDiagonalLeft(VectorNd diag)

Pre-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by a vector. This is the same as multiplying the rows of this matrix by the elements of the vector.

Parameters:

diag - specifies the diagonal elements of the implied left-hand matrix

Throws:

ImproperSizeException - if the size of diag does not equal the row size of this matrix

mulDiagonalLeft

public void mulDiagonalLeft(double[] diag)

Pre-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by the leading elements of an array of doubles. This is the same as multiplying the rows of this matrix by the elements of the array.

Parameters:

diag - specifies the diagonal elements of the implied left-hand matrix

Throws:

ImproperSizeException - if the length of diag is less than the row size of this matrix

mulDiagonalRight

public void mulDiagonalRight(VectorNd diag)

Post-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by a vector. This is the same as multiplying the columns of this matrix by the elements of the vector.

Parameters:

diag - specifies the diagonal elements of the implied right-hand matrix

Throws:

ImproperSizeException - if the size of diag does not equal the column size of this matrix

mulDiagonalRight

public void mulDiagonalRight(double[] diag)

Post-multiplies, in place, this matrix by a diagonal matrix whose (diagonal) elements are specified by the leading elements of an array of doubles. This is the same as multiplying the columns of this matrix by the elements of the array.

Parameters:

diag - specifies the diagonal elements of the implied right-hand matrix

Throws:

ImproperSizeException - if the length of diag is less than the column size of this matrix

set

public void set(MatrixNd M1)
         throws ImproperSizeException

Sets the size and values of this matrix to those of matrix M1.

Parameters:

M1 - matrix whose size and values are copied

Throws:

ImproperSizeException - if matrices have different sizes and this matrix cannot be resized accordingly

absolute

public void absolute()

Sets the elements of this matrix to their absolute values.

maxElement

public double maxElement()

Returns the maximum element value of this matrix.

Returns:

maximum element value

minElement

public double minElement()

Returns the minimum element value of this matrix.

Returns:

minimum element value

add

public void add(MatrixNd M1)
         throws ImproperSizeException

Adds this matrix to M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

Throws:

ImproperSizeException - if this matrix and M1 have different sizes

add

public void add(MatrixNd M1,
                MatrixNd M2)
         throws ImproperSizeException

Adds matrix M1 to M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if matrices M1 and M2 have different sizes, or if this matrix needs resizing but is of fixed size

sub

public void sub(MatrixNd M1)
         throws ImproperSizeException

Subtracts this matrix from M1 and places the result in this matrix.

Parameters:

M1 - right-hand matrix

Throws:

ImproperSizeException - if this matrix and M1 have different sizes

sub

public void sub(MatrixNd M1,
                MatrixNd M2)
         throws ImproperSizeException

Subtracts matrix M1 from M2 and places the result in this matrix. This matrix is resized if necessary.

Parameters:

M1 - left-hand matrix

M2 - right-hand matrix

Throws:

ImproperSizeException - if matrices M1 and M2 have different sizes, or if this matrix needs resizing but is of fixed size

negate

public void negate(MatrixNd M1)
            throws ImproperSizeException

Sets this matrix to the negative of M1. This matrix is resized if necessary.

Parameters:

M1 - matrix to negate

Throws:

ImproperSizeException - if this matrix needs resizing but is of fixed size

negate

public void negate()

Negates this matrix in place.

scale

public void scale(double s,
                  MatrixNd M1)
           throws ImproperSizeException

Scales the elements of matrix M1 by s and places the results in this matrix. This matrix is resized if necessary.

Parameters:

s - scaling factor

M1 - matrix to be scaled

Throws:

ImproperSizeException - if this matrix needs resizing but is of fixed size

scale

public void scale(double s)

Scales the elements of this matrix by s.

Parameters:

s - scaling factor

transpose

public void transpose()

Replaces this matrix by its tranpose. The matrix is resized if necessary.

Throws:

ImproperSizeException - if this matrix needs resizing but is of fixed size

transpose

public void transpose(MatrixNd M1)
               throws ImproperSizeException

Takes the transpose of matrix M1 and places the result in this matrix. The matrix is resized if necessary.

Parameters:

M1 - matrix to take the transpose of

Throws:

ImproperSizeException - if this matrix needs resizing but is of fixed size

setIdentity

public void setIdentity()

Sets this matrix to the identity matrix. If this matrix matrix is not square, then element (i,j) is set to 1 if i and j are equal, and 0 otherwise.

setZero

public void setZero()

Sets the elements of this matrix to zero.

setDiagonal

public void setDiagonal(VectorNd diag)

Sets this matrix to a diagonal matrix whose diagonal elements are specified by a vector.

Parameters:

diag - diagonal elements for this matrix

Throws:

ImproperSizeException - if the size of diag does not equal the minimum matrix dimension

setDiagonal

public void setDiagonal(double[] diag)

Sets this matrix to a diagonal matrix whose diagonal elements are specified by the leading elements of an array of doubles

Parameters:

diag - diagonal elements for this matrix

Throws:

ImproperSizeException - if the length of diag is less than the minimum matrix dimension

epsilonEquals

public boolean epsilonEquals(MatrixNd M1,
                             double epsilon)

Returns true if the elements of this matrix equal those of matrix M1within a prescribed tolerance epsilon.

Parameters:

M1 - matrix to compare with

epsilon - comparison tolerance

Returns:

false if the matrices are not equal within the specified tolerance, or have different sizes

equals

public boolean equals(MatrixNd M1)

Returns true if the elements of this matrix exactly equal those of matrix M1.

Parameters:

M1 - matrix to compare with

Returns:

false if the matrices are not equal or have different sizes

infinityNorm

public double infinityNorm()

Returns the infinity norm of this matrix. This is equal to the maximum of the vector 1-norm of each row.

Overrides:

infinityNorm in class MatrixObject

Returns:

infinity norm of this matrix

oneNorm

public double oneNorm()

Returns the 1 norm of this matrix. This is equal to the maximum of the vector 1-norm of each column.

Overrides:

oneNorm in class MatrixObject

Returns:

1 norm of this matrix

frobeniusNorm

public double frobeniusNorm()

Returns the Frobenius norm of this matrix. This is equal to the square root of the sum of the squares of each element.

Overrides:

frobeniusNorm in class MatrixObject

Returns:

Frobenius norm of this matrix

invert

public boolean invert()
               throws ImproperSizeException

Inverts this matrix in place, returning false if the matrix is detected to be singular. The inverse is computed using LU decomposition with partial pivoting.

Throws:

ImproperSizeException - if this matrix is not square

invert

public boolean invert(MatrixNd M1)
               throws ImproperSizeException

Inverts the matrix M1 and places the result in this matrix, returning false if the matrix is detected to be singular. This matrix is resized if necessary. The inverse is computed using LU decomposition with partial pivoting.

Parameters:

M1 - matrix to take the inverse of

Throws:

ImproperSizeException - if matrix M1 is not square, or if this matrix needs resizing but is of fixed size

permuteColumns

public void permuteColumns(int[] permutation)

Rearrange the columns of this matrix according to the specified permutation, such that each column j is replaced by column permutation[j].

Parameters:

permutation - describes the column exchanges

Throws:

ImproperSizeException - if the length of permutation is less than the column size of this matrix.

permuteRows

public void permuteRows(int[] permutation)

Rearrange the rows of this matrix according to the specified permutation, such that each row i is replaced by row permutation[i].

Parameters:

permutation - describes the row exchanges

Throws:

ImproperSizeException - if the length of permutation is less than the row size of this matrix.

mul

public void mul(VectorNd vr,
                VectorNd v1)

Multiplies this matrix by the column vector v1 and places the result in the vector vr. If M represents this matrix, this is equivalent to computing

  vr = M v1
 

The vector vr is resized if necessary.

Parameters:

vr - result vector

v1 - vector to multiply by

Throws:

ImproperSizeException - if the size of v1 does not equal the number of columns of this matrix, or if vr needs resizing but is of fixed size

mulTranspose

public void mulTranspose(VectorNd vr,
                         VectorNd v1)

Multiplies the transpose of this matrix by the vector v1 and places the result in vr. If M represents this matrix, this is equivalent to computing

  vr = v1 M
 

The vector vr is resized if necessary.

Parameters:

vr - result vector

v1 - vector to multiply by

Throws:

ImproperSizeException - if the size of v1 does not equal the number of rows of this matrix, or if vr needs resizing but is of fixed size

main

public static void main(java.lang.String[] args)