DotNetMatrix.GeneralMatrix Class Reference

.NET GeneralMatrix class. More...

Inheritance diagram for DotNetMatrix.GeneralMatrix:

Collaboration diagram for DotNetMatrix.GeneralMatrix:

Public Member Functions
	GeneralMatrix (int m, int n)
	Construct an m-by-n matrix of zeros. More...
	GeneralMatrix (int m, int n, double s)
	Construct an m-by-n constant matrix. More...
	GeneralMatrix (double[][] A)
	Construct a matrix from a 2-D array. More...
	GeneralMatrix (double[][] A, int m, int n)
	Construct a matrix quickly without checking arguments. More...
	GeneralMatrix (double[] vals, int m)
	Construct a matrix from a one-dimensional packed array More...
virtual GeneralMatrix	Copy ()
	Make a deep copy of a matrix More...
virtual double	GetElement (int i, int j)
	Get a single element. More...
virtual GeneralMatrix	GetMatrix (int i0, int i1, int j0, int j1)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int[] r, int[] c)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int i0, int i1, int[] c)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int[] r, int j0, int j1)
	Get a submatrix. More...
virtual void	SetElement (int i, int j, double s)
	Set a single element. More...
virtual void	SetMatrix (int i0, int i1, int j0, int j1, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int[] r, int[] c, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int[] r, int j0, int j1, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int i0, int i1, int[] c, GeneralMatrix X)
	Set a submatrix. More...
virtual GeneralMatrix	Transpose ()
	Matrix transpose. More...
virtual double	Norm1 ()
	One norm More...
virtual double	Norm2 ()
	Two norm More...
virtual double	NormInf ()
	Infinity norm More...
virtual double	NormF ()
	Frobenius norm More...
virtual GeneralMatrix	UnaryMinus ()
	Unary minus More...
virtual GeneralMatrix	Add (GeneralMatrix B)
	C = A + B More...
virtual GeneralMatrix	AddEquals (GeneralMatrix B)
	A = A + B More...
virtual GeneralMatrix	Subtract (GeneralMatrix B)
	C = A - B More...
virtual GeneralMatrix	SubtractEquals (GeneralMatrix B)
	A = A - B More...
virtual GeneralMatrix	ArrayMultiply (GeneralMatrix B)
	Element-by-element multiplication, C = A.*B More...
virtual GeneralMatrix	ArrayMultiplyEquals (GeneralMatrix B)
	Element-by-element multiplication in place, A = A.*B More...
virtual GeneralMatrix	ArrayRightDivide (GeneralMatrix B)
	Element-by-element right division, C = A./B More...
virtual GeneralMatrix	ArrayRightDivideEquals (GeneralMatrix B)
	Element-by-element right division in place, A = A./B More...
virtual GeneralMatrix	ArrayLeftDivide (GeneralMatrix B)
	Element-by-element left division, C = A. More...
virtual GeneralMatrix	ArrayLeftDivideEquals (GeneralMatrix B)
	Element-by-element left division in place, A = A. More...
virtual GeneralMatrix	Multiply (double s)
	Multiply a matrix by a scalar, C = s*A More...
virtual GeneralMatrix	MultiplyEquals (double s)
	Multiply a matrix by a scalar in place, A = s*A More...
virtual GeneralMatrix	Multiply (GeneralMatrix B)
	Linear algebraic matrix multiplication, A * B More...
virtual LUDecomposition	LUD ()
	LU Decomposition More...
virtual QRDecomposition	QRD ()
	QR Decomposition More...
virtual CholeskyDecomposition	chol ()
	Cholesky Decomposition More...
virtual SingularValueDecomposition	SVD ()
	Singular Value Decomposition More...
virtual EigenvalueDecomposition	Eigen ()
	Eigenvalue Decomposition More...
virtual GeneralMatrix	Solve (GeneralMatrix B)
	Solve A*X = B More...
virtual GeneralMatrix	SolveTranspose (GeneralMatrix B)
	Solve X*A = B, which is also A'*X' = B' More...
virtual GeneralMatrix	Inverse ()
	Matrix inverse or pseudoinverse More...
virtual double	Determinant ()
	GeneralMatrix determinant More...
virtual int	Rank ()
	GeneralMatrix rank More...
virtual double	Condition ()
	Matrix condition (2 norm) More...
virtual double	Trace ()
	Matrix trace. More...
void	Dispose ()
	Do not make this method virtual. A derived class should not be able to override this method. More...
System.Object	Clone ()
	Clone the GeneralMatrix object. More...
	GeneralMatrix (int m, int n)
	Construct an m-by-n matrix of zeros. More...
	GeneralMatrix (int m, int n, double s)
	Construct an m-by-n constant matrix. More...
	GeneralMatrix (double[][] A)
	Construct a matrix from a 2-D array. More...
	GeneralMatrix (double[][] A, int m, int n)
	Construct a matrix quickly without checking arguments. More...
	GeneralMatrix (double[] vals, int m)
	Construct a matrix from a one-dimensional packed array More...
virtual GeneralMatrix	Copy ()
	Make a deep copy of a matrix More...
virtual double	GetElement (int i, int j)
	Get a single element. More...
virtual GeneralMatrix	GetMatrix (int i0, int i1, int j0, int j1)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int[] r, int[] c)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int i0, int i1, int[] c)
	Get a submatrix. More...
virtual GeneralMatrix	GetMatrix (int[] r, int j0, int j1)
	Get a submatrix. More...
virtual void	SetElement (int i, int j, double s)
	Set a single element. More...
virtual void	SetMatrix (int i0, int i1, int j0, int j1, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int[] r, int[] c, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int[] r, int j0, int j1, GeneralMatrix X)
	Set a submatrix. More...
virtual void	SetMatrix (int i0, int i1, int[] c, GeneralMatrix X)
	Set a submatrix. More...
virtual GeneralMatrix	Transpose ()
	Matrix transpose. More...
virtual double	Norm1 ()
	One norm More...
virtual double	Norm2 ()
	Two norm More...
virtual double	NormInf ()
	Infinity norm More...
virtual double	NormF ()
	Frobenius norm More...
virtual GeneralMatrix	UnaryMinus ()
	Unary minus More...
virtual GeneralMatrix	Add (GeneralMatrix B)
	C = A + B More...
virtual GeneralMatrix	AddEquals (GeneralMatrix B)
	A = A + B More...
virtual GeneralMatrix	Subtract (GeneralMatrix B)
	C = A - B More...
virtual GeneralMatrix	SubtractEquals (GeneralMatrix B)
	A = A - B More...
virtual GeneralMatrix	ArrayMultiply (GeneralMatrix B)
	Element-by-element multiplication, C = A.*B More...
virtual GeneralMatrix	ArrayMultiplyEquals (GeneralMatrix B)
	Element-by-element multiplication in place, A = A.*B More...
virtual GeneralMatrix	ArrayRightDivide (GeneralMatrix B)
	Element-by-element right division, C = A./B More...
virtual GeneralMatrix	ArrayRightDivideEquals (GeneralMatrix B)
	Element-by-element right division in place, A = A./B More...
virtual GeneralMatrix	ArrayLeftDivide (GeneralMatrix B)
	Element-by-element left division, C = A. More...
virtual GeneralMatrix	ArrayLeftDivideEquals (GeneralMatrix B)
	Element-by-element left division in place, A = A. More...
virtual GeneralMatrix	Multiply (double s)
	Multiply a matrix by a scalar, C = s*A More...
virtual GeneralMatrix	MultiplyEquals (double s)
	Multiply a matrix by a scalar in place, A = s*A More...
virtual GeneralMatrix	Multiply (GeneralMatrix B)
	Linear algebraic matrix multiplication, A * B More...
virtual LUDecomposition	LUD ()
	LU Decomposition More...
virtual QRDecomposition	QRD ()
	QR Decomposition More...
virtual CholeskyDecomposition	chol ()
	Cholesky Decomposition More...
virtual SingularValueDecomposition	SVD ()
	Singular Value Decomposition More...
virtual EigenvalueDecomposition	Eigen ()
	Eigenvalue Decomposition More...
virtual GeneralMatrix	Solve (GeneralMatrix B)
	Solve A*X = B More...
virtual GeneralMatrix	SolveTranspose (GeneralMatrix B)
	Solve X*A = B, which is also A'*X' = B' More...
virtual GeneralMatrix	Inverse ()
	Matrix inverse or pseudoinverse More...
virtual double	Determinant ()
	GeneralMatrix determinant More...
virtual int	Rank ()
	GeneralMatrix rank More...
virtual double	Condition ()
	Matrix condition (2 norm) More...
virtual double	Trace ()
	Matrix trace. More...
void	Dispose ()
	Do not make this method virtual. A derived class should not be able to override this method. More...
System.Object	Clone ()
	Clone the GeneralMatrix object. More...

Static Public Member Functions
static GeneralMatrix	Create (double[][] A)
	Construct a matrix from a copy of a 2-D array. More...
static GeneralMatrix	operator+ (GeneralMatrix m1, GeneralMatrix m2)
	Addition of matrices More...
static GeneralMatrix	operator- (GeneralMatrix m1, GeneralMatrix m2)
	Subtraction of matrices More...
static GeneralMatrix	operator* (GeneralMatrix m1, GeneralMatrix m2)
	Multiplication of matrices More...
static GeneralMatrix	Random (int m, int n)
	Generate matrix with random elements More...
static GeneralMatrix	Identity (int m, int n)
	Generate identity matrix More...
static GeneralMatrix	Create (double[][] A)
	Construct a matrix from a copy of a 2-D array. More...
static GeneralMatrix	operator+ (GeneralMatrix m1, GeneralMatrix m2)
	Addition of matrices More...
static GeneralMatrix	operator- (GeneralMatrix m1, GeneralMatrix m2)
	Subtraction of matrices More...
static GeneralMatrix	operator* (GeneralMatrix m1, GeneralMatrix m2)
	Multiplication of matrices More...
static GeneralMatrix	Random (int m, int n)
	Generate matrix with random elements More...
static GeneralMatrix	Identity (int m, int n)
	Generate identity matrix More...

Properties
virtual double[][]	Array [get]
	Access the internal two-dimensional array. More...
virtual double[][]	ArrayCopy [get]
	Copy the internal two-dimensional array. More...
virtual double[]	ColumnPackedCopy [get]
	Make a one-dimensional column packed copy of the internal array. More...
virtual double[]	RowPackedCopy [get]
	Make a one-dimensional row packed copy of the internal array. More...
virtual int	RowDimension [get]
	Get row dimension. More...
virtual int	ColumnDimension [get]
	Get column dimension. More...

Private Member Functions
void	CheckMatrixDimensions (GeneralMatrix B)
	Check if size(A) == size(B) * More...
void	Dispose (bool disposing)
	Dispose(bool disposing) executes in two distinct scenarios. If disposing equals true, the method has been called directly or indirectly by a user's code. Managed and unmanaged resources can be disposed. If disposing equals false, the method has been called by the runtime from inside the finalizer and you should not reference other objects. Only unmanaged resources can be disposed. More...
	~GeneralMatrix ()
	This destructor will run only if the Dispose method does not get called. It gives your base class the opportunity to finalize. Do not provide destructors in types derived from this class. More...
void ISerializable.	GetObjectData (SerializationInfo info, StreamingContext context)
	A method called when serializing this class More...
void	CheckMatrixDimensions (GeneralMatrix B)
	Check if size(A) == size(B) * More...
void	Dispose (bool disposing)
	Dispose(bool disposing) executes in two distinct scenarios. If disposing equals true, the method has been called directly or indirectly by a user's code. Managed and unmanaged resources can be disposed. If disposing equals false, the method has been called by the runtime from inside the finalizer and you should not reference other objects. Only unmanaged resources can be disposed. More...
	~GeneralMatrix ()
	This destructor will run only if the Dispose method does not get called. It gives your base class the opportunity to finalize. Do not provide destructors in types derived from this class. More...
void ISerializable.	GetObjectData (SerializationInfo info, StreamingContext context)
	A method called when serializing this class More...

Private Attributes
double[][]	A
	Array for internal storage of elements. internal array storage. More...
int	m
	Row and column dimensions. row dimension. column dimension. More...
int	n

Detailed Description

.NET GeneralMatrix class.

The .NET GeneralMatrix 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 GeneralMatrix 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 GeneralMatrix 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.}};
GeneralMatrix A = new GeneralMatrix(vals);
GeneralMatrix b = GeneralMatrix.Random(3,1);
GeneralMatrix x = A.Solve(b);
GeneralMatrix r = A.Multiply(x).Subtract(b);
double rnorm = r.NormInf();

<author> The MathWorks, Inc. and the National Institute of Standards and Technology. </author> <version> 5 August 1998 </version>

Constructor & Destructor Documentation

DotNetMatrix.GeneralMatrix.GeneralMatrix ( int  m, int  n  )

inline

Construct an m-by-n matrix of zeros.

Parameters

m	Number of rows.
n	Number of colums.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.GeneralMatrix.Copy(), DotNetMatrix.GeneralMatrix.Create(), DotNetMatrix.GeneralMatrix.GetMatrix(), DotNetMatrix.GeneralMatrix.Identity(), DotNetMatrix.GeneralMatrix.Multiply(), DotNetMatrix.GeneralMatrix.Random(), DotNetMatrix.GeneralMatrix.Subtract(), DotNetMatrix.GeneralMatrix.Transpose(), and DotNetMatrix.GeneralMatrix.UnaryMinus().

DotNetMatrix.GeneralMatrix.GeneralMatrix ( int  m, int  n, double  s  )

inline

Construct an m-by-n constant matrix.

Parameters

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

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double  A[][] )

inline

Construct a matrix from a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

System.ArgumentException

All rows must have the same length

See also

Create

References DotNetMatrix.GeneralMatrix.A, and DotNetMatrix.GeneralMatrix.m.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double  A[][], int  m, int  n  )

inline

Construct a matrix quickly without checking arguments.

Parameters

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

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double[]  vals, int  m  )

inline

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.

Exceptions

System.ArgumentException

Array length must be a multiple of m.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.~GeneralMatrix ( )

inlineprivate

This destructor will run only if the Dispose method does not get called. It gives your base class the opportunity to finalize. Do not provide destructors in types derived from this class.

References DotNetMatrix.GeneralMatrix.Dispose().

DotNetMatrix.GeneralMatrix.GeneralMatrix ( int  m, int  n  )

inline

Construct an m-by-n matrix of zeros.

Parameters

m	Number of rows.
n	Number of colums.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( int  m, int  n, double  s  )

inline

Construct an m-by-n constant matrix.

Parameters

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

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double  A[][] )

inline

Construct a matrix from a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

System.ArgumentException

All rows must have the same length

See also

Create

References DotNetMatrix.GeneralMatrix.A, and DotNetMatrix.GeneralMatrix.m.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double  A[][], int  m, int  n  )

inline

Construct a matrix quickly without checking arguments.

Parameters

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

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.GeneralMatrix ( double[]  vals, int  m  )

inline

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.

Exceptions

System.ArgumentException

Array length must be a multiple of m.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

DotNetMatrix.GeneralMatrix.~GeneralMatrix ( )

inlineprivate

This destructor will run only if the Dispose method does not get called. It gives your base class the opportunity to finalize. Do not provide destructors in types derived from this class.

References DotNetMatrix.GeneralMatrix.Dispose().

Member Function Documentation

static GeneralMatrix DotNetMatrix.GeneralMatrix.Create ( double  A[][] )

inlinestatic

Construct a matrix from a copy of a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

System.ArgumentException

All rows must have the same length

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Copy ( )

inlinevirtual

Make a deep copy of a matrix

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.GeneralMatrix.Clone(), and DotNetMatrix.test.TestMatrix.Main().

virtual double DotNetMatrix.GeneralMatrix.GetElement ( int  i, int  j  )

inlinevirtual

Get a single element.

Parameters

i	Row index.
j	Column index.

Returns

A(i,j)

Exceptions

System.IndexOutOfRangeException

Referenced by DotNetMatrix.examples.MagicSquareExample.magic(), DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.GeneralMatrix.SetMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int  i0, int  i1, int  j0, int  j1  )

inlinevirtual

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)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.Array, and DotNetMatrix.GeneralMatrix.GeneralMatrix().

Referenced by DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.examples.MagicSquareExample.Main(), DotNetMatrix.QRDecomposition.Solve(), and DotNetMatrix.LUDecomposition.Solve().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int[]  r, int[]  c  )

inlinevirtual

Get a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.

Returns

A(r(:),c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.Array, and DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int  i0, int  i1, int[]  c  )

inlinevirtual

Get a submatrix.

Parameters

i0	Initial row index
i1	Final row index
c	Array of column indices.

Returns

A(i0:i1,c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.Array, and DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int[]  r, int  j0, int  j1  )

inlinevirtual

Get a submatrix.

Parameters

r	Array of row indices.
j0	Initial column index
j1	Final column index

Returns

A(r(:),j0:j1)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.Array, and DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual void DotNetMatrix.GeneralMatrix.SetElement ( int  i, int  j, double  s  )

inlinevirtual

Set a single element.

Parameters

i	Row index.
j	Column index.
s	A(i,j).

Exceptions

System.IndexOutOfRangeException

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int  i0, int  i1, int  j0, int  j1, GeneralMatrix  X  )

inlinevirtual

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)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GetElement().

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int[]  r, int[]  c, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.
X	A(r(:),c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GetElement().

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int[]  r, int  j0, int  j1, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

r	Array of row indices.
j0	Initial column index
j1	Final column index
X	A(r(:),j0:j1)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GetElement().

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int  i0, int  i1, int[]  c, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

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

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GetElement().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Transpose ( )

inlinevirtual

Matrix transpose.

Returns

A'

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.examples.MagicSquareExample.Main(), and DotNetMatrix.GeneralMatrix.SolveTranspose().

virtual double DotNetMatrix.GeneralMatrix.Norm1 ( )

inlinevirtual

One norm

Returns

maximum column sum.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.check(), DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

virtual double DotNetMatrix.GeneralMatrix.Norm2 ( )

inlinevirtual

Two norm

Returns

maximum singular value.

Referenced by DotNetMatrix.GeneralMatrix.Norm2().

virtual double DotNetMatrix.GeneralMatrix.NormInf ( )

inlinevirtual

Infinity norm

Returns

maximum row sum.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual double DotNetMatrix.GeneralMatrix.NormF ( )

inlinevirtual

Frobenius norm

Returns

sqrt of sum of squares of all elements.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.UnaryMinus ( )

inlinevirtual

Unary minus

Returns

-A

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Add ( GeneralMatrix  B )

inlinevirtual

C = A + B

Parameters

B	another matrix

Returns

A + B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.examples.MagicSquareExample.Main(), and DotNetMatrix.GeneralMatrix.operator+().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.AddEquals ( GeneralMatrix  B )

inlinevirtual

A = A + B

Parameters

B	another matrix

Returns

A + B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Subtract ( GeneralMatrix  B )

inlinevirtual

C = A - B

Parameters

B	another matrix

Returns

A - B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.check(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.examples.MagicSquareExample.Main(), and DotNetMatrix.GeneralMatrix.operator-().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.SubtractEquals ( GeneralMatrix  B )

inlinevirtual

A = A - B

Parameters

B	another matrix

Returns

A - B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayMultiply ( GeneralMatrix  B )

inlinevirtual

Element-by-element multiplication, C = A.*B

Parameters

B	another matrix

Returns

A.*B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element multiplication in place, A = A.*B

Parameters

B	another matrix

Returns

A.*B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayRightDivide ( GeneralMatrix  B )

inlinevirtual

Element-by-element right division, C = A./B

Parameters

B	another matrix

Returns

A./B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element right division in place, A = A./B

Parameters

B	another matrix

Returns

A./B

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayLeftDivide ( GeneralMatrix  B )

inlinevirtual

Element-by-element left division, C = A.

Parameters

B	another matrix

Returns

A.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element left division in place, A = A.

Parameters

B	another matrix

Returns

A.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Multiply ( double  s )

inlinevirtual

Multiply a matrix by a scalar, C = s*A

Parameters

s

scalar

Returns

s*A

References DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.examples.MagicSquareExample.Main(), and DotNetMatrix.GeneralMatrix.operator*().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.MultiplyEquals ( double  s )

inlinevirtual

Multiply a matrix by a scalar in place, A = s*A

Parameters

s

scalar

Returns

replace A by s*A

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Multiply ( GeneralMatrix  B )

inlinevirtual

Linear algebraic matrix multiplication, A * B

Parameters

B	another matrix

Returns

Matrix product, A * B

Exceptions

System.ArgumentException

Matrix inner dimensions must agree.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator+ ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Addition of matrices

Parameters

m1
m2

Returns

References DotNetMatrix.GeneralMatrix.Add().

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator- ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Subtraction of matrices

Parameters

m1
m2

Returns

References DotNetMatrix.GeneralMatrix.Subtract().

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator* ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Multiplication of matrices

Parameters

m1
m2

Returns

References DotNetMatrix.GeneralMatrix.Multiply().

virtual LUDecomposition DotNetMatrix.GeneralMatrix.LUD ( )

inlinevirtual

LU Decomposition

Returns

LUDecomposition

See also

LUDecomposition

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual QRDecomposition DotNetMatrix.GeneralMatrix.QRD ( )

inlinevirtual

QR Decomposition

Returns

QRDecomposition

See also

QRDecomposition

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual CholeskyDecomposition DotNetMatrix.GeneralMatrix.chol ( )

inlinevirtual

Cholesky Decomposition

Returns

CholeskyDecomposition

See also

CholeskyDecomposition

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual SingularValueDecomposition DotNetMatrix.GeneralMatrix.SVD ( )

inlinevirtual

Singular Value Decomposition

Returns

SingularValueDecomposition

See also

SingularValueDecomposition

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual EigenvalueDecomposition DotNetMatrix.GeneralMatrix.Eigen ( )

inlinevirtual

Eigenvalue Decomposition

Returns

EigenvalueDecomposition

See also

EigenvalueDecomposition

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Solve ( GeneralMatrix  B )

inlinevirtual

Solve A*X = B

Parameters

B	right hand side

Returns

solution if A is square, least squares solution otherwise

Referenced by DotNetMatrix.GeneralMatrix.Inverse(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.GeneralMatrix.Solve(), and DotNetMatrix.GeneralMatrix.SolveTranspose().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.SolveTranspose ( GeneralMatrix  B )

inlinevirtual

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.

References DotNetMatrix.GeneralMatrix.Solve(), and DotNetMatrix.GeneralMatrix.Transpose().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Inverse ( )

inlinevirtual

Matrix inverse or pseudoinverse

Returns

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

References DotNetMatrix.GeneralMatrix.Identity(), and DotNetMatrix.GeneralMatrix.Solve().

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual double DotNetMatrix.GeneralMatrix.Determinant ( )

inlinevirtual

GeneralMatrix determinant

Returns

determinant

References DotNetMatrix.LUDecomposition.Determinant().

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual int DotNetMatrix.GeneralMatrix.Rank ( )

inlinevirtual

GeneralMatrix rank

Returns

effective numerical rank, obtained from SVD.

References DotNetMatrix.SingularValueDecomposition.Rank().

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

virtual double DotNetMatrix.GeneralMatrix.Condition ( )

inlinevirtual

Matrix condition (2 norm)

Returns

ratio of largest to smallest singular value.

References DotNetMatrix.SingularValueDecomposition.Condition().

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

virtual double DotNetMatrix.GeneralMatrix.Trace ( )

inlinevirtual

Matrix trace.

Returns

sum of the diagonal elements.

Referenced by DotNetMatrix.test.TestMatrix.Main(), and DotNetMatrix.examples.MagicSquareExample.Main().

static GeneralMatrix DotNetMatrix.GeneralMatrix.Random ( int  m, int  n  )

inlinestatic

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.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.test.TestMatrix.Main().

static GeneralMatrix DotNetMatrix.GeneralMatrix.Identity ( int  m, int  n  )

inlinestatic

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.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.Array, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.GeneralMatrix.Inverse(), and DotNetMatrix.test.TestMatrix.Main().

void DotNetMatrix.GeneralMatrix.CheckMatrixDimensions ( GeneralMatrix  B )

inlineprivate

Check if size(A) == size(B) *

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.AddEquals(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals(), DotNetMatrix.GeneralMatrix.Subtract(), and DotNetMatrix.GeneralMatrix.SubtractEquals().

void DotNetMatrix.GeneralMatrix.Dispose ( )

inline

Do not make this method virtual. A derived class should not be able to override this method.

Referenced by DotNetMatrix.GeneralMatrix.~GeneralMatrix().

void DotNetMatrix.GeneralMatrix.Dispose ( bool  disposing )

inlineprivate

Dispose(bool disposing) executes in two distinct scenarios. If disposing equals true, the method has been called directly or indirectly by a user's code. Managed and unmanaged resources can be disposed. If disposing equals false, the method has been called by the runtime from inside the finalizer and you should not reference other objects. Only unmanaged resources can be disposed.

Parameters

disposing

System.Object DotNetMatrix.GeneralMatrix.Clone ( )

inline

Clone the GeneralMatrix object.

References DotNetMatrix.GeneralMatrix.Copy().

void ISerializable. DotNetMatrix.GeneralMatrix.GetObjectData ( SerializationInfo  info, StreamingContext  context  )

inlineprivate

A method called when serializing this class

Parameters

info
context

static GeneralMatrix DotNetMatrix.GeneralMatrix.Create ( double  A[][] )

inlinestatic

Construct a matrix from a copy of a 2-D array.

Parameters

A	Two-dimensional array of doubles.

Exceptions

System.ArgumentException

All rows must have the same length

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Copy ( )

inlinevirtual

Make a deep copy of a matrix

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual double DotNetMatrix.GeneralMatrix.GetElement ( int  i, int  j  )

inlinevirtual

Get a single element.

Parameters

i	Row index.
j	Column index.

Returns

A(i,j)

Exceptions

System.IndexOutOfRangeException

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int  i0, int  i1, int  j0, int  j1  )

inlinevirtual

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)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int[]  r, int[]  c  )

inlinevirtual

Get a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.

Returns

A(r(:),c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int  i0, int  i1, int[]  c  )

inlinevirtual

Get a submatrix.

Parameters

i0	Initial row index
i1	Final row index
c	Array of column indices.

Returns

A(i0:i1,c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.GetMatrix ( int[]  r, int  j0, int  j1  )

inlinevirtual

Get a submatrix.

Parameters

r	Array of row indices.
j0	Initial column index
j1	Final column index

Returns

A(r(:),j0:j1)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

References DotNetMatrix.GeneralMatrix.GeneralMatrix().

virtual void DotNetMatrix.GeneralMatrix.SetElement ( int  i, int  j, double  s  )

inlinevirtual

Set a single element.

Parameters

i	Row index.
j	Column index.
s	A(i,j).

Exceptions

System.IndexOutOfRangeException

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int  i0, int  i1, int  j0, int  j1, GeneralMatrix  X  )

inlinevirtual

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)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int[]  r, int[]  c, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

r	Array of row indices.
c	Array of column indices.
X	A(r(:),c(:))

Exceptions

System.IndexOutOfRangeException

Submatrix indices

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int[]  r, int  j0, int  j1, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

r	Array of row indices.
j0	Initial column index
j1	Final column index
X	A(r(:),j0:j1)

Exceptions

System.IndexOutOfRangeException

Submatrix indices

virtual void DotNetMatrix.GeneralMatrix.SetMatrix ( int  i0, int  i1, int[]  c, GeneralMatrix  X  )

inlinevirtual

Set a submatrix.

Parameters

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

Exceptions

System.IndexOutOfRangeException

Submatrix indices

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Transpose ( )

inlinevirtual

Matrix transpose.

Returns

A'

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual double DotNetMatrix.GeneralMatrix.Norm1 ( )

inlinevirtual

One norm

Returns

maximum column sum.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual double DotNetMatrix.GeneralMatrix.Norm2 ( )

inlinevirtual

Two norm

Returns

maximum singular value.

References DotNetMatrix.GeneralMatrix.Norm2().

virtual double DotNetMatrix.GeneralMatrix.NormInf ( )

inlinevirtual

Infinity norm

Returns

maximum row sum.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual double DotNetMatrix.GeneralMatrix.NormF ( )

inlinevirtual

Frobenius norm

Returns

sqrt of sum of squares of all elements.

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.UnaryMinus ( )

inlinevirtual

Unary minus

Returns

-A

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Add ( GeneralMatrix  B )

inlinevirtual

C = A + B

Parameters

B	another matrix

Returns

A + B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.AddEquals ( GeneralMatrix  B )

inlinevirtual

A = A + B

Parameters

B	another matrix

Returns

A + B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Subtract ( GeneralMatrix  B )

inlinevirtual

C = A - B

Parameters

B	another matrix

Returns

A - B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.SubtractEquals ( GeneralMatrix  B )

inlinevirtual

A = A - B

Parameters

B	another matrix

Returns

A - B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayMultiply ( GeneralMatrix  B )

inlinevirtual

Element-by-element multiplication, C = A.*B

Parameters

B	another matrix

Returns

A.*B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element multiplication in place, A = A.*B

Parameters

B	another matrix

Returns

A.*B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayRightDivide ( GeneralMatrix  B )

inlinevirtual

Element-by-element right division, C = A./B

Parameters

B	another matrix

Returns

A./B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element right division in place, A = A./B

Parameters

B	another matrix

Returns

A./B

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayLeftDivide ( GeneralMatrix  B )

inlinevirtual

Element-by-element left division, C = A.

Parameters

B	another matrix

Returns

A.

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals ( GeneralMatrix  B )

inlinevirtual

Element-by-element left division in place, A = A.

Parameters

B	another matrix

Returns

A.

References DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Multiply ( double  s )

inlinevirtual

Multiply a matrix by a scalar, C = s*A

Parameters

s

scalar

Returns

s*A

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.MultiplyEquals ( double  s )

inlinevirtual

Multiply a matrix by a scalar in place, A = s*A

Parameters

s

scalar

Returns

replace A by s*A

References DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Multiply ( GeneralMatrix  B )

inlinevirtual

Linear algebraic matrix multiplication, A * B

Parameters

B	another matrix

Returns

Matrix product, A * B

Exceptions

System.ArgumentException

Matrix inner dimensions must agree.

References DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator+ ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Addition of matrices

Parameters

m1
m2

Returns

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator- ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Subtraction of matrices

Parameters

m1
m2

Returns

static GeneralMatrix DotNetMatrix.GeneralMatrix.operator* ( GeneralMatrix  m1, GeneralMatrix  m2  )

inlinestatic

Multiplication of matrices

Parameters

m1
m2

Returns

virtual LUDecomposition DotNetMatrix.GeneralMatrix.LUD ( )

inlinevirtual

LU Decomposition

Returns

LUDecomposition

See also

LUDecomposition

virtual QRDecomposition DotNetMatrix.GeneralMatrix.QRD ( )

inlinevirtual

QR Decomposition

Returns

QRDecomposition

See also

QRDecomposition

virtual CholeskyDecomposition DotNetMatrix.GeneralMatrix.chol ( )

inlinevirtual

Cholesky Decomposition

Returns

CholeskyDecomposition

See also

CholeskyDecomposition

virtual SingularValueDecomposition DotNetMatrix.GeneralMatrix.SVD ( )

inlinevirtual

Singular Value Decomposition

Returns

SingularValueDecomposition

See also

SingularValueDecomposition

virtual EigenvalueDecomposition DotNetMatrix.GeneralMatrix.Eigen ( )

inlinevirtual

Eigenvalue Decomposition

Returns

EigenvalueDecomposition

See also

EigenvalueDecomposition

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Solve ( GeneralMatrix  B )

inlinevirtual

Solve A*X = B

Parameters

B	right hand side

Returns

solution if A is square, least squares solution otherwise

References DotNetMatrix.GeneralMatrix.Solve().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.SolveTranspose ( GeneralMatrix  B )

inlinevirtual

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.

References DotNetMatrix.GeneralMatrix.Solve(), and DotNetMatrix.GeneralMatrix.Transpose().

virtual GeneralMatrix DotNetMatrix.GeneralMatrix.Inverse ( )

inlinevirtual

Matrix inverse or pseudoinverse

Returns

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

References DotNetMatrix.GeneralMatrix.Identity(), and DotNetMatrix.GeneralMatrix.Solve().

virtual double DotNetMatrix.GeneralMatrix.Determinant ( )

inlinevirtual

GeneralMatrix determinant

Returns

determinant

References DotNetMatrix.LUDecomposition.Determinant().

virtual int DotNetMatrix.GeneralMatrix.Rank ( )

inlinevirtual

GeneralMatrix rank

Returns

effective numerical rank, obtained from SVD.

References DotNetMatrix.SingularValueDecomposition.Rank().

virtual double DotNetMatrix.GeneralMatrix.Condition ( )

inlinevirtual

Matrix condition (2 norm)

Returns

ratio of largest to smallest singular value.

References DotNetMatrix.SingularValueDecomposition.Condition().

virtual double DotNetMatrix.GeneralMatrix.Trace ( )

inlinevirtual

Matrix trace.

Returns

sum of the diagonal elements.

static GeneralMatrix DotNetMatrix.GeneralMatrix.Random ( int  m, int  n  )

inlinestatic

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.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

static GeneralMatrix DotNetMatrix.GeneralMatrix.Identity ( int  m, int  n  )

inlinestatic

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.

References DotNetMatrix.GeneralMatrix.A, DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.m, and DotNetMatrix.GeneralMatrix.n.

void DotNetMatrix.GeneralMatrix.CheckMatrixDimensions ( GeneralMatrix  B )

inlineprivate

Check if size(A) == size(B) *

void DotNetMatrix.GeneralMatrix.Dispose ( )

inline

Do not make this method virtual. A derived class should not be able to override this method.

void DotNetMatrix.GeneralMatrix.Dispose ( bool  disposing )

inlineprivate

Dispose(bool disposing) executes in two distinct scenarios. If disposing equals true, the method has been called directly or indirectly by a user's code. Managed and unmanaged resources can be disposed. If disposing equals false, the method has been called by the runtime from inside the finalizer and you should not reference other objects. Only unmanaged resources can be disposed.

Parameters

disposing

System.Object DotNetMatrix.GeneralMatrix.Clone ( )

inline

Clone the GeneralMatrix object.

References DotNetMatrix.GeneralMatrix.Copy().

void ISerializable. DotNetMatrix.GeneralMatrix.GetObjectData ( SerializationInfo  info, StreamingContext  context  )

inlineprivate

A method called when serializing this class

Parameters

info
context

Member Data Documentation

double [][] DotNetMatrix.GeneralMatrix.A

private

Array for internal storage of elements. internal array storage.

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.AddEquals(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.Identity(), DotNetMatrix.GeneralMatrix.Multiply(), DotNetMatrix.GeneralMatrix.Random(), DotNetMatrix.GeneralMatrix.Subtract(), and DotNetMatrix.GeneralMatrix.SubtractEquals().

int DotNetMatrix.GeneralMatrix.m

private

Row and column dimensions. row dimension. column dimension.

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.AddEquals(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals(), DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.Copy(), DotNetMatrix.GeneralMatrix.Create(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.Identity(), DotNetMatrix.GeneralMatrix.Multiply(), DotNetMatrix.GeneralMatrix.MultiplyEquals(), DotNetMatrix.GeneralMatrix.Norm1(), DotNetMatrix.GeneralMatrix.NormF(), DotNetMatrix.GeneralMatrix.NormInf(), DotNetMatrix.GeneralMatrix.Random(), DotNetMatrix.GeneralMatrix.Subtract(), DotNetMatrix.GeneralMatrix.SubtractEquals(), DotNetMatrix.GeneralMatrix.Transpose(), and DotNetMatrix.GeneralMatrix.UnaryMinus().

int DotNetMatrix.GeneralMatrix.n

private

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.AddEquals(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayLeftDivideEquals(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayMultiplyEquals(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.GeneralMatrix.ArrayRightDivideEquals(), DotNetMatrix.GeneralMatrix.CheckMatrixDimensions(), DotNetMatrix.GeneralMatrix.Copy(), DotNetMatrix.GeneralMatrix.Create(), DotNetMatrix.GeneralMatrix.GeneralMatrix(), DotNetMatrix.GeneralMatrix.Identity(), DotNetMatrix.GeneralMatrix.Multiply(), DotNetMatrix.GeneralMatrix.MultiplyEquals(), DotNetMatrix.GeneralMatrix.Norm1(), DotNetMatrix.GeneralMatrix.NormF(), DotNetMatrix.GeneralMatrix.NormInf(), DotNetMatrix.GeneralMatrix.Random(), DotNetMatrix.GeneralMatrix.Subtract(), DotNetMatrix.GeneralMatrix.SubtractEquals(), DotNetMatrix.GeneralMatrix.Transpose(), and DotNetMatrix.GeneralMatrix.UnaryMinus().

Property Documentation

virtual double [][] DotNetMatrix.GeneralMatrix.Array

get

Access the internal two-dimensional array.

Returns

Pointer to the two-dimensional array of matrix elements.

Referenced by DotNetMatrix.GeneralMatrix.Add(), DotNetMatrix.GeneralMatrix.ArrayLeftDivide(), DotNetMatrix.GeneralMatrix.ArrayMultiply(), DotNetMatrix.GeneralMatrix.ArrayRightDivide(), DotNetMatrix.CholeskyDecomposition.CholeskyDecomposition(), DotNetMatrix.GeneralMatrix.Copy(), DotNetMatrix.GeneralMatrix.Create(), DotNetMatrix.EigenvalueDecomposition.EigenvalueDecomposition(), DotNetMatrix.GeneralMatrix.GetMatrix(), DotNetMatrix.GeneralMatrix.Identity(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.GeneralMatrix.Multiply(), DotNetMatrix.GeneralMatrix.Random(), DotNetMatrix.LUDecomposition.Solve(), DotNetMatrix.GeneralMatrix.Subtract(), DotNetMatrix.GeneralMatrix.Transpose(), and DotNetMatrix.GeneralMatrix.UnaryMinus().

virtual double [][] DotNetMatrix.GeneralMatrix.ArrayCopy

get

Copy the internal two-dimensional array.

Returns

Two-dimensional array copy of matrix elements.

Referenced by DotNetMatrix.LUDecomposition.LUDecomposition(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.QRDecomposition.QRDecomposition(), DotNetMatrix.SingularValueDecomposition.SingularValueDecomposition(), DotNetMatrix.CholeskyDecomposition.Solve(), and DotNetMatrix.QRDecomposition.Solve().

virtual double [] DotNetMatrix.GeneralMatrix.ColumnPackedCopy

get

Make a one-dimensional column packed copy of the internal array.

Returns

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

Referenced by DotNetMatrix.test.TestMatrix.Main().

virtual double [] DotNetMatrix.GeneralMatrix.RowPackedCopy

get

Make a one-dimensional row packed copy of the internal array.

Returns

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

Referenced by DotNetMatrix.test.TestMatrix.Main().

int DotNetMatrix.GeneralMatrix.RowDimension

get

Get row dimension.

Returns

m, the number of rows.

Referenced by DotNetMatrix.CholeskyDecomposition.CholeskyDecomposition(), DotNetMatrix.LUDecomposition.LUDecomposition(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.QRDecomposition.QRDecomposition(), DotNetMatrix.SingularValueDecomposition.SingularValueDecomposition(), DotNetMatrix.CholeskyDecomposition.Solve(), DotNetMatrix.QRDecomposition.Solve(), and DotNetMatrix.LUDecomposition.Solve().

int DotNetMatrix.GeneralMatrix.ColumnDimension

get

Get column dimension.

Returns

n, the number of columns.

Referenced by DotNetMatrix.CholeskyDecomposition.CholeskyDecomposition(), DotNetMatrix.EigenvalueDecomposition.EigenvalueDecomposition(), DotNetMatrix.LUDecomposition.LUDecomposition(), DotNetMatrix.test.TestMatrix.Main(), DotNetMatrix.QRDecomposition.QRDecomposition(), DotNetMatrix.SingularValueDecomposition.SingularValueDecomposition(), DotNetMatrix.CholeskyDecomposition.Solve(), DotNetMatrix.QRDecomposition.Solve(), and DotNetMatrix.LUDecomposition.Solve().

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The documentation for this class was generated from the following file:

• igtest/numerics/DotMatrix/Backup/GeneralMatrix.cs