IG.Num.Matrix3d Class Reference

Matrix in a 3 dimensional space. More...

Inheritance diagram for IG.Num.Matrix3d:

Collaboration diagram for IG.Num.Matrix3d:

Public Member Functions
	Matrix3d (Matrix3d m)
	Copy constructor. Initializes components of a 3D matrix with components of another 3D matrix. More...
	Matrix3d (IMatrix m)
	Constructor. Initializes components of a 3D matrix with components of another matrix. The specified matrix should be 3*3. More...
	Matrix3d (Vector3d rowx, Vector3d rowy, Vector3d rowz)
	Initializes 3D matrix structure with the specified components. More...
	Matrix3d (mat3 m)
	Initializes components of a 3D matrix with components of the specified matrix. More...
	Matrix3d (double xx, double xy, double xz, double yx, double yy, double yz, double zx, double zy, double zz)
	Initializes 3D matrix structure with the specified components. More...
	Matrix3d (double component)
	Initializes 3D with the specified component. More...
	Matrix3d (vec3 xrow, vec3 yrow, vec3 zrow)
	Initializes 3D matrix structure with the specified components. More...
	Matrix3d (double[][] A)
	Initializes a 3D matrix with elements of a jagged array. More...
	Matrix3d (double[,] A)
	Initializes a 3D matrix with elements of a rectangular array. More...
virtual Matrix3d	GetCopyThis ()
	Returns a copy of the current 3D matrix. More...
override MatrixBase	GetCopyBase ()
	Returns a deep copy of the current 3D matrix. More...
Matrix3d	GetNewThis (int rowCount, int ColumnCount)
	Returns a copy of the current 3D matrix. More...
override MatrixBase	GetNewBase (int rowCount, int columnCount)
	Creates and returns a new 3D matrix with the specified dimensions, and of the same type as the current matrix. More...
Matrix3d	GetNewThis ()
	Creates and returns a new matrix with the same dimensions and of the same type as the current matrix. More...
override MatrixBase	GetNewBase ()
	Creates and returns a new matrix with the same dimensions and of the same type as the current matrix. More...
Vector3d	GetNewVectorThis (int length)
	Creates and returns a new 3D vector with the specified dimension (which must be null), and of the type that is consistent with the type of the current matrix. More...
override VectorBase	GetNewVectorBase (int length)
	Creates and returns a new vector with the specified dimension, and of the type that is consistent with the type of the current matrix. More...
override int	GetHashCode ()
	Returns the hashRet code (hashRet function) of the current matrix. More...
override bool	Equals (Object obj)
	Returns a value indicating whether the specified object is equal to the current matrix. More...
Matrix3d	NormalizedEuclidean ()
	Returns this matrix normalized with Euclidean norm. More...
Matrix3d	NormalizedForbenius ()
	Returns this matrix normalized with Euclidean norm. More...
Matrix3d	Normalized1 ()
	Returns this matrix normalized with 1 norm. More...
Matrix3d	NormalizedInfinity ()
	Returns this matrix normalized with infinity norm. More...
void	Read ()
	Reads 3D matrix components from a console. More...
void	Read (string name)
	Reads 3D matrix components from a console. More...
Public Member Functions inherited from IG.Num.MatrixBase
virtual IMatrix	GetCopy ()
	Creates and returns a copy of the current matrix. More...
virtual IMatrix	GetNew (int rowCount, int columnCount)
	Creates and returns a new matrix with the specified dimensions, and of the same type as the current matrix. More...
virtual IMatrix	GetNew ()
	Creates and returns a new matrix with the same dimensions and of the same type as the current matrix. More...
virtual IVector	GetNewVector (int length)
	Creates and returns a new vector with the specified dimension, and of the type that is consistent with the type of the current vector. More...
virtual double[,]	ToArray ()
	Creates and returns a rectangular 2D array that contains a component-wise copy of the matrix. More...
virtual double[][]	ToJaggedArray ()
	Creates and returns a jagged 2D array that contains a component-wise copy of the matrix. More...
virtual int	Index (int row, int column)
	Calculates and returns flat index corresponding to the specified row and column indices of the current matrix. More...
virtual void	Indices (int flatIndex, out int row, out int column)
	Returns (through output arguments) row and column indices corresponding to the specified flat index in the current matrix. More...
virtual void	SetZero ()
	Sets all components of the current matrix to 0. More...
virtual void	SetConstant (double elementValue)
	Sets all components of the current matrix to the specified value. More...
virtual void	SetIdentity ()
	Sets the current matrix to identity matrix. WARNING: Exception is thrown if a matrix is not square. For nonsquare matrices, use SetDiagonal(1.0)! More...
virtual void	SetRandom ()
	Sets the current matrix such that it contains random elements on the interval (0,1]. More...
virtual void	SetRandom (IRandomGenerator rnd)
	Sets the current matrix such that it contains random elements on the interval (0,1]. More...
virtual void	SetDiagonal (double diagonalElement)
	Sets the current matrix to the diagonal matrix with all diagonal elements equal to the specified value. Matrix does not need to be a square matrix. More...
virtual void	SetDiagonal (IVector diagonal)
	Sets the current matrix to the diagonal matrix with diagonal element specified by a vector. More...
virtual bool	IsSquare ()
	Returns true if the current matrix is a square matrix, and false if not. More...
virtual bool	IsSymmetric ()
	Returns true if the current matrix is symmetric, and false if not. If the matrix is not a square matrix then false is returned. More...
virtual bool	IsSymmetric (double relativeRMSTolerance=0.0)
	Returns true if the specified matrix is symmetric within some tolerance, and false if not. If the matrix is null then false is returned. More...
virtual void	Negate ()
	Negates the current matrix. More...
virtual void	Transpose ()
	Transposes the current matrix. WARNING: this operation can only be done on square matrices! More...
override int	GetHashCode ()
	Returns the hashRet code (hashRet function) of the current matrix. More...
override bool	Equals (Object obj)
	Returns a value indicating whether the specified object is equal to the current matrix. More...
int	GetHashFunctionInt ()
	Returns an integer valued hashRet function of the current matrix object. More...
string	GetHashFunctionString ()
	Returns a string valued hashRet function of the current matrix object. More...
override string	ToString ()
	Returns string representation of the current matrix in the standard IGLib form. Rows and elements are printed in comma separated lists in curly brackets. More...
virtual string	ToStringReadable (int accuracy=4, int padding=8)
	Returns a readable an easily string form of a matrix, accuracy and padding can be set. More...
virtual string	ToStringNewlines ()
	Returns a string representation of this matrix with newlines inserted after each row. Rows and elements are printed in comma separated lists in curly brackets. More...
virtual string	ToStringNewlines (string elementFormat)
	Returns a string representation of this matrix with newlines inserted after each row, with the specified format for elements of the matrix. Rows and elements are printed in comma separated lists in curly brackets. More...
virtual string	ToStringMath ()
	Returns string representation of the current matrix in the standard IGLib form (Mathematica-like format but with C representation of numbers). Rows and elements are printed in comma separated lists in curly brackets. More...
virtual string	ToString (string elementFormat)
	Returns a string representation of the current matrix in a standard IGLib form (Mathematica-like format but with C representation of numbers), with the specified format for elements of the matrix. More...
virtual string	ToStringMath (string elementFormat)
	Returns a string representation of the current matrix in a standard IGLib form (Mathematica-like format but with C representation of numbers), with the specified format for elements of the matrix. More...

Static Public Member Functions
static Matrix3d	Create (Matrix3d mat)
	Creates and returns a 3D matrix that is a copy of another 3D matrix. More...
static Matrix3d	Create (IMatrix mat)
	Creates and returns a 3D matrix that is a copy of another (general) matrix. That matrix should be a 3*3 matrix, otherwise exception is thrown. More...
static Matrix3d	Create (double[][] A)
	Constructs a matrix from a copy of a 2-D array by deep-copy. More...
static Matrix3d	Create (double[,] A)
	Constructs a 3D matrix from a copy of a 2-D array by deep-copy. More...
static Matrix3d	CreateFromColumns (IList< IVector > columnVectors)
	Construct a complex matrix from a set of real column vectors. More...
static Matrix3d	CreateFromRows (IList< Vector > rowVectors)
	Construct a complex matrix from a set of real row vectors. More...
static Matrix3d	Identity ()
	Creates a d1*d2 identity matrix. More...
static Matrix3d	Zeros ()
	Creates a 3D matrix filled with 0. More...
static Matrix3d	Ones ()
	Creates a 3D matrix filled with 1. More...
static Matrix3d	Diagonal (IVector diagonalVector)
	Creates a new diagonal d1*d2 matrix based on the diagonal vector. More...
static Matrix3d	Random ()
	Creates and returns a 3D matrix with uniformly distributed random elements in the [0, 1) interval. More...
static Matrix3d	Random (IRandomGenerator rnd)
	Creates and returns a 3D matrix with uniformly distributed random elements in the [0, 1) interval. More...
static Matrix3d	Copy (Matrix3d m)
	Returns a copy of the specified 3D matrix. More...
static void	Negate (Matrix3d m, ref Matrix3d res)
	Negates the specified 3D matrix and stores its copy in the resulting matrix. More...
static int	EigenSystem2d (Matrix3d a, ref Matrix3d eigenvec, ref Vector3d eigenval)
	Calculates eigenvectors and eigenvalues of a 2x2 matrix a and stores eigenvectors to lines of eigenvec and eigenvalues to eigenval. eigenvec can be the same matrix as a. The number of different real eigenvalues is returned. Ref.: linalg.nb Not tested yet! More...
static Matrix3d	operator+ (Matrix3d m)
	Unary plus for 3D matrices, returns the operand. More...
static Matrix3d	operator- (Matrix3d a)
	Unary negation for 3D matrices, returns the negative operand. More...
static Matrix3d	operator+ (Matrix3d a, Matrix3d b)
	Matrix addition in 3D. More...
static Matrix3d	operator- (Matrix3d a, Matrix3d b)
	Matrix subtraction in 3D. More...
static Matrix3d	operator* (Matrix3d a, Matrix3d b)
	Matrix multiplication in 3D. More...
static Vector3d	operator* (Matrix3d a, Vector3d b)
	Matrix with vector multiplication in 3D. More...
static Matrix3d	operator* (Matrix3d a, double b)
	Product of a 3D matrix by a scalar. More...
static Matrix3d	operator* (double a, Matrix3d b)
	Product of a 3D matrix by a scalar. More...
static Matrix3d	operator/ (Matrix3d a, double b)
	Division of a 3D matrix by a scalar. More...
Static Public Member Functions inherited from IG.Num.MatrixBase
static int	Index (int dim1, int dim2, int row, int column)
	Returns flat index corresponding to the specified row and column indices of a matrix with specified dimensions. More...
static int	Index (IMatrix mat, int row, int column)
	Calculates and returns flat index corresponding to the specified row and column indices of the specified matrix. More...
static void	Indices (int dim1, int dim2, int flatIndex, out int row, out int column)
	Returns (through output arguments) row and column indices corresponding to the specified flat index in a matrix with the specified dimensions. More...
static void	Indices (IMatrix mat, int flatIndex, out int row, out int column)
	Returns (through output arguments) row and column indices corresponding to the specified flat index in the specified matrix. More...
static void	SetZero (IMatrix mat)
	Sets all components of the specified matrix to 0. More...
static void	SetConstant (IMatrix mat, double elementValue)
	Sets all components of the specified matrix to the specified value. More...
static void	SetIdentity (IMatrix mat)
	Sets the specified matrix to identity matrix. WARNING: Works only for square matrices (exception is thrown if matrix is not square). For nonsquare matrices, use SetDiagonal(1.0)! More...
static void	SetDiagonal (IMatrix mat, IVector diagonal)
	Sets the current matrix to the diagonal matrix with diagonal element specified by a vector. More...
static void	SetDiagonal (IMatrix mat, double diagonalElement)
	Sets the current matrix to the diagonal matrix with all diagonal elements equal to the specified value. Matrix does not need to be a square matrix. More...
static void	SetRandom (IMatrix mat)
	Sets the specified matrix such that it contains random elements on the interval (0,1]. More...
static void	SetRandom (IMatrix mat, IRandomGenerator rnd=null)
	Sets the current matrix such that it contains random elements on the interval (0,1]. More...
static void	SetRandomSymmetric (IMatrix mat)
	Sets the specified matrix such that it is symmetric and contains random elements on the interval (0,1]. More...
static void	SetRandomSymmetric (IMatrix mat, IRandomGenerator rnd)
	Sets the specified matrix such that it is symmetric and contains random elements on the interval (0,1]. More...
static void	SetRandomAntiSymmetric (IMatrix mat)
	Sets the specified matrix such that it is antisymmetric and contains random elements on the interval (0,1]. More...
static void	SetRandomAntiSymmetric (IMatrix mat, IRandomGenerator rnd)
	Sets the specified matrix such that it is antisymmetric and contains random elements on the interval (0,1]. More...
static void	SetRandomLowerTriangular (IMatrix mat)
	Sets the specified matrix such that it is lower triangular and contains random elements on the interval (0,1]. More...
static void	SetRandomLowerTriangular (IMatrix mat, IRandomGenerator rnd)
	Sets the specified matrix such that it is lower triangular and contains random elements on the interval (0,1]. More...
static void	SetRandomUpperTriangular (IMatrix mat)
	Sets the specified matrix such that it is upper triangular and contains random elements on the interval (0,1]. More...
static void	SetRandomUpperTriangular (IMatrix mat, IRandomGenerator rnd)
	Sets the specified matrix such that it is upper triangular and contains random elements on the interval (0,1]. More...
static void	SetRandomSymmetricPositiveDefinite (IMatrix mat)
	Sets the specified matrix such that it is positive definite and contains random elements on the interval (0,1]. More...
static void	SetRandomSymmetricPositiveDefinite (IMatrix mat, IRandomGenerator rnd)
	Sets the specified matrix such that it is positive definite and contains random elements. More...
static void	SetRandomPositiveDiagonallyDominant (IMatrix mat, IRandomGenerator rnd=null, double dominancyFactor=100.0)
	Sets the specified matrix such that it is has random elements and is diagonally dominant with positive diagonal elements, i.e. any diagonal element is greater by absolute value than sum of absolute values of nondiagonal elements in the corresponding column. More...
static void	SetRandomPositiveDiagonallyDominant (IMatrix mat, double dominancyFactor)
	Sets the specified matrix such that it is has random elements and is diagonally dominant with positive diagonal elements, i.e. any diagonal element is greater by absolute value than sum of absolute values of nondiagonal elements in the corresponding column. More...
static void	SetRandomPositiveDiagonallyDominantSymmetric (IMatrix mat, IRandomGenerator rnd=null, double dominancyFactor=100.0)
	Sets the specified matrix such that it is has random elements and is symmetric diagonally dominant with positive diagonal elements, i.e. any diagonal element is greater by absolute value than sum of absolute values of nondiagonal elements in the corresponding column. More...
static void	SetRandomPositiveDiagonallyDominantSymmetric (IMatrix mat, double dominancyFactor)
	Sets the specified matrix such that it is has random elements and is symmetric diagonally dominant with positive diagonal elements, i.e. any diagonal element is greater by absolute value than sum of absolute values of nondiagonal elements in the corresponding column. More...
static double	SetRandomInvertible (IMatrix mat, IRandomGenerator rnd=null)
	Sets the specified QUADRATIC matrix such that it is has random elements and is nonsingular. More...
static double	SetRandomPositiveDefiniteSymmetric (IMatrix mat, IRandomGenerator rnd=null)
	Sets the specified QUADRATIC matrix such that it is has random elements and is a symmetric positive definite matrix. More...
static bool	IsSquare (IMatrix mat)
	Returns true if the specified matrix is a square matrix, and false if not. If the matrix is null then false is returned. More...
static bool	IsSymmetric (IMatrix mat)
	Returns true if the specified matrix is symmetric, and false if not. If the matrix is null then false is returned. More...
static bool	IsSymmetric (IMatrix mat, double relativeRMSTolerance)
	Returns true if the specified matrix is symmetric within some tolerance, and false if not. If the matrix is null then false is returned. More...
static int	Compare (IMatrix m1, IMatrix m2)
	Compares two matrices and returns -1 if the first matrix is smaller than the second one, 0 if matrices are equal, and 1 if the first matrix is greater. Matrix that is null is considered smaller than a matrix that is not null. Two null matrices are considered equal. Matrix with smaller dimension is considered smaller than a matrix with greater dimension. Matrices with equal dimensions ar compared by elements. The first element that is different decides which matrix is considered greater. More...
static void	Resize (ref IMatrix mat, IMatrix template, int rowCount, int columnCount)
	Resizes, if necessary, the specified matrix according to the required dimensions. If the matrix is initially null then a new matrix is created. If in this case a template matrix is specified then the newly created matrix will be of the same type as that template matrix, because it is created by the GetNew() method on that matrix. If dimensions of the initial matrix do not match the required dim., then matrix is resized. If the specified matrix dimension is less or equal to 0 then matrix is resized with the same dimensions as those of the template matirx. If in this case the template matrix is null, an exception is thrown. WARNINGS: Components are NOT preserved and have in general undefined values after operation is performed. If matrix and template are both null then the type of nawly created matrix is Matrix. More...
static void	Resize (ref IMatrix mat, int rowCount, int columnCount)
	Resizes, if necessary, the specified matrix according to the required dimensions. If the matrix is initially null then a new matrix (of type Matrix) is created. If dimensions of the initial matrix do not match the required dimensions, then matrix is resized. Components are NOT preserved and have in general undefined values after operation is performed. WARNING: If the matrix is initially null then the type of the newly created matrix is Matrix. More...
static void	Resize (ref IMatrix mat, IMatrix template)
	Resizes, if necessary, the specified matrix according to the dimensions of the specified template matrix. If the matrix is initially null then a new matrix is created. In this case the newly created matrix will be of the same type as that template matrix, because it is created by the GetNew() method on that matrix. If dimensions of the initial matrix do not match the dimensions of the template matrix, then matrix is resized. If the template matrix is null, then an exception is thrown. WARNINGS: Components are NOT preserved and have in general undefined values after operation is performed. If matrix and template are null then the type of newly created matrix is Matrix. More...
static void	CopyPlain (IMatrix a, IMatrix result)
	Copies components of a matrix to another matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (IMatrix a, IMatrix result)
	Copies components of a matrix to another matrix. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (IMatrix a, ref IMatrix result)
	Copies components of a matrix to another matrix. Resulting matrix is allocated or reallocated if necessary. More...
static void	CopyPlain (MatrixBase_MathNetNumerics a, IMatrix result)
	Copies components of a matrix to another matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (MatrixBase_MathNetNumerics a, IMatrix result)
	Copies components of a matrix to another matrix. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (MatrixBase_MathNetNumerics a, ref IMatrix result)
	Copies components of a matrix to another matrix. Resulting matrix is allocated or reallocated if necessary. More...
static void	CopyPlain (IMatrix a, Matrix_MathNetNumercs result)
	Copies components of a matrix to another matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (IMatrix a, Matrix_MathNetNumercs result)
	Copies components of a matrix to another matrix. WARNING: dimensions of the copied matrix and result storage must match. More...
static void	Copy (IMatrix a, ref Matrix_MathNetNumercs result)
	Copies components of a matrix to another matrix. Resulting matrix is allocated or reallocated if necessary. More...
static void	NegatePlain (IMatrix a, IMatrix result)
	Stores a negative matrix of the operand in another matrix. Can be done in-place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the operand and result storage must match. More...
static void	Negate (IMatrix a, IMatrix result)
	Stores a negative matrix of the operand in another matrix. Can be done in-place. WARNING: dimensions of the operand and result storage must match. More...
static void	Negate (IMatrix a, ref IMatrix result)
	Stores a negative matrix of the operand in another matrix. Can be done in-place. Resulting matrix is allocated or reallocated if necessary. More...
static void	TransposePlain (IMatrix a, IMatrix result)
	Stores transpose of the operand in another matrix. Can be done in-place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the operand and result storage must match. More...
static void	Transpose (IMatrix a, IMatrix result)
	Stores transpose of the operand in another matrix. Can be done in-place. WARNING: dimensions of the operand and result storage must match. More...
static void	Transpose (IMatrix a, ref IMatrix result)
	Stores transpose of the matrix operand in another matrix. Can be done in-place. Resulting matrix is allocated or reallocated if necessary. More...
static void	SymmetrizePlain (IMatrix a, IMatrix sym, IMatrix antiSym)
	Calculates symmetric and antisymmetric part of the specified matrix (symmetric part is stored in the first result argument but is calculated last, such that it overrides antisymmetric when both arguments point to the same matrix object). More...
static void	Symmetrize (IMatrix a, IMatrix sym, IMatrix antiSym)
	Calculates symmetric and antisymmetric part of the specified matrix (symmetric part is stored in the first result argument but is calculated last, such that it overrides antisymmetric when both arguments point to the same matrix object). More...
static void	Symmetrize (IMatrix a, ref IMatrix sym, ref IMatrix antiSym)
	Stores symmetrized and antisymmetirzed matrix obtained from the specified matrix. Resulting matrix is allocated or reallocated if necessary. More...
static void	SymmetricPartPlain (IMatrix a, IMatrix result)
	Stores symmetric part of a square matrix operand in another matrix. Symmetrization is performed by averaging of non-diagonal terms and their transposed terms. Can be done in-place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the operand and result storage must match. More...
static void	SymmetricPart (IMatrix a, IMatrix result)
	Stores symmetric part of a square matrix operand in another matrix. Symmetrization is performed by averaging of non-diagonal terms and their transposed terms. Can be done in-place. WARNING: dimensions of the operand and result storage must match. More...
static void	SymmetricPart (IMatrix a, ref IMatrix result)
	Stores symmetric part of a square matrix operand in another matrix. Symmetrization is performed by averaging of non-diagonal terms and their transposed terms. Can be done in-place. Resulting matrix is allocated or reallocated if necessary. More...
static void	AntisymmetricPartPlain (IMatrix a, IMatrix result)
	Stores antisymmetric part of a square matrix operand in another matrix. Antisymmetrization is performed by subtracting non-diagonal terms and their transposed terms, division by 2 and storing result in one matrix element and its negative value in another element. Can be done in-place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of the operand and result storage must match. More...
static void	AntisymmetricPart (IMatrix a, IMatrix result)
	Stores antisymmetric part of a square matrix operand in another matrix. Antisymmetrization is performed by subtracting non-diagonal terms and their transposed terms, division by 2 and storing result in one matrix element and its negative value in another element. Can be done in-place. WARNING: dimensions of the operand and result storage must match. More...
static void	AntisymmetricPart (IMatrix a, ref IMatrix result)
	Stores antisymmetric part of a square matrix operand in another matrix. Antisymmetrization is performed by subtracting non-diagonal terms and their transposed terms, division by 2 and storing result in one matrix element and its negative value in another element. Can be done in-place. Resulting matrix is allocated or reallocated if necessary. More...
static void	AddPlain (IMatrix a, IMatrix b, IMatrix result)
	Sums two matrices and stores the result in the specified result matrix. Operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Add (IMatrix a, IMatrix b, IMatrix result)
	Sums two matrices and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Add (IMatrix a, IMatrix b, ref IMatrix result)
	Sums two matrices and stores the result in the specified result matrix. Operation can be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	SubtractPlain (IMatrix a, IMatrix b, IMatrix result)
	Subtracts two matrices and stores the result in the specified result matrix. Operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Subtract (IMatrix a, IMatrix b, IMatrix result)
	Subtracts two matrices and stores the result in the specified result matrix. Operation can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Subtract (IMatrix a, IMatrix b, ref IMatrix result)
	Subtracts two matrices and stores the result in the specified result matrix. Operation can be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	ArrayMultiplyPlain (IMatrix a, IMatrix b, IMatrix result)
	Element-by-element multiplication. This operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayMultiply (IMatrix a, IMatrix b, IMatrix result)
	Element-by-element multiplication. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayMultiply (IMatrix a, IMatrix b, ref IMatrix result)
	Element-by-element multiplication. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	ArrayDividePlain (IMatrix a, IMatrix b, IMatrix result)
	Element-by-element division. This operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayDivide (IMatrix a, IMatrix b, IMatrix result)
	Element-by-element division. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayDivide (IMatrix a, IMatrix b, ref IMatrix result)
	Element-by-element division. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	ArrayPowerPlain (IMatrix a, double power, IMatrix result)
	Element-by-element raise to power. This operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayPower (IMatrix a, double power, IMatrix result)
	Element-by-element raise to power. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayPower (IMatrix a, double power, ref IMatrix result)
	Element-by-element raise to power. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	ArrayMapPlain (IMatrix a, Converter< double, double > mapping, IMatrix result)
	Element-by-element mapping of an arbitrary function. This operation can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayMap (IMatrix a, Converter< double, double > mapping, IMatrix result)
	Element-by-element mapping of an arbitrary function. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	ArrayMap (IMatrix a, Converter< double, double > mapping, ref IMatrix result)
	Element-by-element mapping of an arbitrary function. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then teh result is re-allocated. More...
static void	MultiplyPlain (IMatrix a, IMatrix b, IMatrix result)
	R=A*B. Multiplies two matrices and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	Multiply (IMatrix a, IMatrix b, IMatrix result)
	R=A*B. Multiplies two matrices and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	Multiply (IMatrix a, IMatrix b, ref IMatrix result)
	R=A*B. Multiplies two matrices and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspMatPlain (IMatrix a, IMatrix b, IMatrix result)
	R=A^T*B Calculates product of transposed matrix and a matrix, and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMat (IMatrix a, IMatrix b, IMatrix result)
	R=A^T*B Multiplies two matrices and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMat (IMatrix a, IMatrix b, ref IMatrix result)
	R=A^T*B Multiplies two matrices and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyMatTranspPlain (IMatrix a, IMatrix b, IMatrix result)
	R=A*B^T. Multiplies a matrix by transpose of another matrix and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatTransp (IMatrix a, IMatrix b, IMatrix result)
	R=A*B^T. Multiplies a matrix by transpose of another matrix and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatTransp (IMatrix a, IMatrix b, ref IMatrix result)
	R=A*B^T. Multiplies a matrix by transpose of another matrix and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspTranspPlain (IMatrix a, IMatrix b, IMatrix result)
	R=A^T*B^T. Multiplies transposed matrix by another transposed matrix, and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspTransp (IMatrix a, IMatrix b, IMatrix result)
	R=A^T*B^T. Multiplies transposed matrix by another transposed matrix, and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspTransp (IMatrix a, IMatrix b, ref IMatrix result)
	R=A^T*B^T. Multiplies transposed matrix by another transposed matrix, and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B*C. Multiplies three matrices and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	Multiply (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B*C. Multiplies three matrices and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	Multiply (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A*B*C. Multiplies three matrices and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspMatTranspPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B*C^T. Multiplies three matrices (transposed first argument, second argument, and transposed third argument) and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of all arguments must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMatTransp (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B*C^T. Multiplies three matrices (transposed first argument, second argument, and transposed third argument) and stores the result in the specified result matrix. WARNING: dimensions of all arguments must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMatTransp (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A^T*B*C^T. Multiplies three matrices (transposed first argument, second argument, and transposed third argument) and stores the result in the specified result matrix. WARNING: dimensions of operands must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspMatMatPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B*C. Multiplies three matrices (transposed first argument, second argument, and third argument) and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of all arguments must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMatMat (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B*C. Multiplies three matrices (transposed first argument, second argument, and third argument) and stores the result in the specified result matrix. WARNING: dimensions of all arguments must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspMatMat (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A^T*B*C. Multiplies three matrices (transposed first argument, second argument, and third argument) and stores the result in the specified result matrix. WARNING: dimensions of operands must be consistent, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyMatMatTranspPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B*C^T. Multiplies three matrices (first argumet, second argumet, and transposed third argument) and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatMatTransp (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B*C^T. Multiplies three matrices (first argumet, second argumet, and transposed third argument) and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatMatTransp (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A*B*C^T. Multiplies three matrices (first argumet, second argumet, and transposed third argument) and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyMatTranspMatPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B^T*C. Multiplies three matrices (first argument, transposed second argument, and third argument) and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatTranspMat (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A*B^T*C. Multiplies three matrices (first argument, transposed second argument, and third argument) and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyMatTranspMat (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A*B^T*C. Multiplies three matrices (first argument, transposed second argument, and third argument) and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspTranspTranspPlain (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B^T*C^T. Multiplies three matrices and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspTranspTransp (IMatrix a, IMatrix b, IMatrix c, IMatrix result)
	R=A^T*B^T*C^T. Multiplies three matrices and stores the result in the specified result matrix. WARNING: dimensions of matrices must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. More...
static void	MultiplyTranspTranspTransp (IMatrix a, IMatrix b, IMatrix c, ref IMatrix result)
	R=A^T*B^T*C^T. Multiplies three matrices and stores the result in the specified result matrix. WARNING: dimensions of operands must match, otherwise an exception is thrown. WARNING: This operation can not be performed in place. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyPlain (IMatrix a, IVector b, IVector result)
	R=A*b. Multiplies a matrix with a vector and stores the result in the specified result vector. Operation can not be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Multiply (IMatrix a, IVector b, IVector result)
	R=A*b. Multiplies a matrix with a vector and stores the result in the specified result vector. Operation can not be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Multiply (IMatrix a, IVector b, ref IVector result)
	R=A*b. Multiplies matrix by scalar and stores the result in the specified result matrix. Operation can not be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyTranspVecPlain (IMatrix a, IVector b, IVector result)
	R=A^T*b. Multiplies a transposed matrix with a vector and stores the result in the specified result vector. Operation can not be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyTranspVec (IMatrix a, IVector b, IVector result)
	R=A^T*b. Multiplies a transposed matrix with a vector and stores the result in the specified result vector. Operation can not be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyTranspVec (IMatrix a, IVector b, ref IVector result)
	R=A^T*b. Multiplies transposed matrix by scalar and stores the result in the specified result matrix. Operation can not be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static double	MultiplyPlain (IVector left, IMatrix a, IVector right)
	R=a^T*M*b. Left-multiplies a matrix with a vector (transposed), right multiplies the result vith another vector, and returns the final result. Can be performed in place. This is a plain version of the method that does not perform any consistency checks. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static double	Multiply (IVector left, IMatrix a, IVector right)
	R=a^T*M*b. Left-multiplies a matrix with a vector (transposed), right multiplies the result vith another vector, and returns the final result. Can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static double	Multiply (IVector left, IMatrix a, IVector right, ref IVector result)
	R=a^T*M*b. Left-multiplies a matrix with a vector (transposed), right multiplies the result vith another vector, and returns the final result. Can be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyPlain (IMatrix a, double b, IMatrix result)
	Multiplies matrix by scalar and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. This operation can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Multiply (IMatrix a, double b, IMatrix result)
	Multiplies matrix by scalar and stores the result in the specified result matrix. This operation can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Multiply (IMatrix a, double b, ref IMatrix result)
	Multiplies matrix by scalar and stores the result in the specified result matrix. This operation can be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	DividePlain (IMatrix a, double b, IMatrix result)
	Divides matrix by scalar and stores the result in the specified result matrix. This is a plain version of the method that does not perform any consistency checks. This operation can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Divide (IMatrix a, double b, IMatrix result)
	Divides matrix by scalar and stores the result in the specified result matrix. This operation can be performed in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	Divide (IMatrix a, double b, ref IMatrix result)
	Divides matrix by scalar and stores the result in the specified result matrix. This operation can be performed in place. WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyDiagonalPlain (IVector diag, IMatrix a, IMatrix result)
	Left-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)*A This is a plain version of the method that does not perform any consistency checks. The operation can be done in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyDiagonal (IVector diag, IMatrix a, IMatrix result)
	Right-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)*A WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyDiagonal (IVector diag, IMatrix a, ref IMatrix result)
	Right-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)*A WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyInverseDiagonalPlain (IVector diag, IMatrix a, IMatrix result)
	Left-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)^-1*A This is a plain version of the method that does not perform any consistency checks. The operation can be done in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyInverseDiagonal (IVector diag, IMatrix a, IMatrix result)
	Right-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)^-1*A WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyInverseDiagonal (IVector diag, IMatrix a, ref IMatrix result)
	Right-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=diag(d)^-1*A WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyDiagonalPlain (IMatrix a, IVector diag, IMatrix result)
	Right-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d) This is a plain version of the method that does not perform any consistency checks. The operation can be done in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyDiagonal (IMatrix a, IVector diag, IMatrix result)
	Right-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d) WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyDiagonal (IMatrix a, IVector diag, ref IMatrix result)
	Right-multiplies a matrix with a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d) WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static void	MultiplyInverseDiagonalPlain (IMatrix a, IVector diag, IMatrix result)
	Right-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d)^-1 This is a plain version of the method that does not perform any consistency checks. The operation can be done in place. WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyInverseDiagonal (IMatrix a, IVector diag, IMatrix result)
	Right-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d)^-1 WARNING: dimensions of matrices must match, otherwise an exception is thrown. More...
static void	MultiplyInverseDiagonal (IMatrix a, IVector diag, ref IMatrix result)
	Right-multiplies a matrix with inverse of a diagonal matrix, and stores the result in the specified result matrix. R=A*diag(d)^-1 WARNING: dimensions of operands must match, otherwise an exception is thrown. If dimensions of the result do not match then the result is re-allocated. More...
static int	GetHashCode (IMatrix mat)
	Returns hashRet code of the specified matrix. More...
static bool	Equals (IMatrix m1, IMatrix m2)
	Returns true if the specified matrices are equal, false if not. More...
static int	GetHashFunctionInt (IMatrix mat)
	Returns an integer valued hashRet function of the specified matrix object. More...
static string	GetHashFunctionString (IMatrix mat)
	Returns a string valued hashRet function of the specified matrix object. More...
static string	ToStringReadable (IMatrix mat, int accuracy=4, int padding=8)
	Returns a readable string form of a matrix, accuracy and padding can be set. More...
static string	ToStringNewlines (IMatrix mat)
	Returns a string representation of the specified matrix with newlines inserted after each row. Rows and elements are printed in comma separated lists in curly brackets. More...
static string	ToStringNewlines (IMatrix mat, string elementFormat)
	Returns a string representation of the specified matrix with newlines inserted after each row, with the specified format for elements of the matrix. Rows and elements are printed in comma separated lists in curly brackets. More...
static string	ToString (IMatrix mat)
	Returns string representation of the current matrix in the standard IGLib form (Mathematica-like format but with C representation of numbers). Rows and elements are printed in comma separated lists in curly brackets. More...
static string	ToStringMath (IMatrix mat)
	Returns string representation of the current matrix in the standard IGLib form (Mathematica-like format but with C representation of numbers). Rows and elements are printed in comma separated lists in curly brackets. More...
static string	ToString (IMatrix mat, string elementFormat)
	Returns string representation of the current matrix in the standard IGLib form (Mathematica-like format but with C representation of numbers), with the specified format for elements of the matrix. Rows and elements are printed in comma separated lists in curly brackets. More...
static string	ToStringMath (IMatrix mat, string elementFormat)
	Returns string representation of the current matrix in the standard IGLib form (Mathematica-like format but with C representation of numbers), with the specified format for elements of the matrix. Rows and elements are printed in comma separated lists in curly brackets. More...
static void	SaveJson (IMatrix mat, string filePath)
	Saves (serializes) the specified matrix to the specified JSON file. File is owerwritten if it exists. More...
static void	SaveJson (IMatrix mat, string filePath, bool append)
	Saves (serializes) the specified matrix to the specified JSON file. More...
static void	LoadJson (string filePath, ref IMatrix matRestored)
	Restores (deserializes) a matrix object from the specified file in JSON format. More...
static MatrixBase	operator+ (MatrixBase m)
	Unary plus, returns the operand. More...
static MatrixBase	operator- (MatrixBase m)
	Unary negation, returns the negative operand. More...
static MatrixBase	operator+ (MatrixBase a, MatrixBase b)
	Matrix addition. More...
static MatrixBase	operator- (MatrixBase a, MatrixBase b)
	Matrix subtraction. More...
static MatrixBase	operator* (MatrixBase a, MatrixBase b)
	Product of two matrices. More...
static VectorBase	operator* (MatrixBase a, VectorBase b)
	Product of a matrix and a vector. More...
static MatrixBase	operator* (MatrixBase a, double b)
	Product of a matrix by a scalar. More...
static MatrixBase	operator* (double a, MatrixBase b)
	Product of a matrix by a scalar. More...
static MatrixBase	operator/ (MatrixBase a, double b)
	Matrix subtraction. More...
static double	DeterminantSlow (IMatrix A)
	Simpler but slower (compared to Determinant) implementation of determinant calculation of an arbitrary square real matrix. More...
static double	Determinant (IMatrix A, ref int[] auxPermutations, ref IMatrix auxLU)
	Calculates and returns determinant of a real-valued square matrix. More...
static void	LuDecompose (IMatrix A, out int toggle, ref int[] perm, ref IMatrix result)
	Calculates thr Doolittle LU decomposition with partial pivoting (LUP) of a square real matrix. More...
static void	LuSolve (IMatrix luMatrix, int[] perm, IVector b, ref IVector auxVec, ref IVector x)
	Solves a system of equations with the specified right-hand sides and the specified LU decomposition of the system matrix. More...
static void	LuSolve (IMatrix luMatrix, int[] perm, IMatrix B, ref IVector auxVec, ref IVector auxRight, ref IVector auxX, ref IMatrix X)
	Calculates inverse of the matrix from its specified LU decomposition. More...
static void	LuInverse (IMatrix luMatrix, int[] perm, ref IVector auxRight, ref IVector auxX, ref IMatrix res)
	Calculates inverse of the matrix from its specified LU decomposition. More...
static double	LuDeterminant (IMatrix luMatrix, int toggle)
	Calculates and returns matrix determinant form its specified LU decomposition. More...
static void	LuExtractLower (IMatrix matLu, ref IMatrix result)
	Extracts the lower part of the Doolittle specified LU decomposition (1s on diagonal, 0s in above diagonal) and stores it in the specified result matrix. More...
static IMatrix	LuExtractUpper (IMatrix matLu, ref IMatrix result)
	Extracts the upper part of the specified Doolittle LU decomposition 0s below diagonal) and stores it in the specified result matrix. More...
static void	PermutationArrayToMatrix (int[] perm, ref IMatrix res)
	Calculates and stores permutation matrix that correspond to the specified permutation array. More...
static void	Permute (IMatrix A, int[] permutations, ref IMatrix result)
	Permutes rows of the specified aquare matrix according to the specified permutations array. More...
static void	UnPermute (IMatrix Apermuted, int[] permutations, ref int[] auxArray, ref IMatrix result)
	Unpermutes the product of the specified DooLittle LU decomposition according to permutations array. More...
static bool	TestLuDecomposition (int dim, int numRepetitions=1, double tol=1e-6, int outputLevel=0, IRandomGenerator randomGenerator=null, IMatrix A=null, IVector b=null)
	Performs a test of calculatons performed via LU decomposition of a matrix. Calculation times and error extents are measured and reported (if specified). More...
static void	TestLuDecompositionDemo ()
	Demonstration of usae of LU decomposition. More...
static bool	LdltDecompose (IMatrix A, ref IMatrix result, double tol=1e-12)
	Calculates LDLT decomposition of a real symmetric square matrix. More...
static void	LdltSolve (IMatrix decomposed, IVector b, ref IVector x)
	Solves a system of eauations with the specified LDLT decomposition of a real symmetric square matrix. More...
static void	LdltSolve (IMatrix ldltMatrix, IMatrix B, ref IVector auxX, ref IMatrix X)
	Calculates inverse of the matrix from its specified LDLT-decomposed matrix. More...
static void	LdltInverse (IMatrix ldltMatrix, ref IVector auxX, ref IMatrix res)
	Calculates inverse of the matrix from its specified LDLT decomposition. More...
static double	LdltDeterminant (IMatrix ldltMatrix)
	Calculates and returns determinant of a square symmetric matrix form its specified LDLT decomposition. More...
static void	LdltExtractLower (IMatrix matLdlt, ref IMatrix result)
	Extracts the lower part of the specified LDLT decomposition (1s on diagonal, 0s above diagonal) and stores it in the specified result matrix. More...
static IMatrix	LdltExtractUpper (IMatrix matLdlt, ref IMatrix result)
	Extracts the upper part of the specified LDLT decomposition (1s on diagonal, 0s in below diagonal) and stores it in the specified result matrix. More...
static IMatrix	LdltExtractDiagonal (IMatrix matLdlt, ref IMatrix result)
	Extracts the diagonal part of the specified LDLT decomposition and stores it in the specified result matrix. More...
static bool	TestLdltDecomposition (int dim, int numRepetitions=1, double tol=1e-6, int outputLevel=0, IRandomGenerator randomGenerator=null, IMatrix A=null, IVector b=null)
	Performs a test of calculatons performed via LDLT decomposition of a matrix. Calculation times and error extents are measured and reported (if specified). More...
static bool	CholeskyDecompose (IMatrix A, ref IMatrix result, double tol=1e-12)
	Calculates Cholesky decomposition of a real symmetric square matrix. More...
static void	CholeskySolve (IMatrix decomposed, IVector b, ref IVector x)
	Solves a system of eauations with the specified Cholesky decomposition of a real symmetric square matrix. More...
static void	CholeskySolve (IMatrix CholeskyMatrix, IMatrix B, ref IVector auxX, ref IMatrix X)
	Calculates inverse of the matrix from its specified Cholesky-decomposed matrix. More...
static void	CholeskyInverse (IMatrix CholeskyMatrix, ref IVector auxX, ref IMatrix res)
	Calculates inverse of the matrix from its specified Cholesky decomposition. More...
static double	CholeskyDeterminant (IMatrix CholeskyMatrix)
	Calculates and returns determinant of a square symmetric matrix form its specified Cholesky decomposition. More...
static void	CholeskyExtractLower (IMatrix matCholesky, ref IMatrix result)
	Extracts the lower part of the specified Cholesky decomposition (0s above diagonal) and stores it in the specified result matrix. More...
static IMatrix	CholeskyExtractUpper (IMatrix matCholesky, ref IMatrix result)
	Extracts the upper part of the specified Cholesky decomposition (0s in below diagonal) and stores it in the specified result matrix. More...
static bool	TestCholeskyDecomposition (int dim, int numRepetitions=1, double tol=1e-6, int outputLevel=0, IRandomGenerator randomGenerator=null, IMatrix A=null, IVector b=null)
	Performs test of calculatons performed via Cholesky decomposition of a matrix. Calculation times and error extents are measured and reported (if specified so). More...
static void	TestCholeskyDecompositionDemo ()
	Demonstration of usae of Cholesky decomposition. More...
static bool	QrDecomposeGrammSchmidt (IMatrix A, ref IMatrix resQ, ref IMatrix resR, double tol=1e-12)
	Calculates QR decomposition of a real invertible matrix by using Gramm-Schmidt orthogonalization. More...
static bool	QrDecompose (IMatrix A, ref IMatrix resQ, ref IMatrix resR, double tol=1e-12)
	Calculates QR decomposition of a real invertible matrix. More...
static void	QrSolve (IMatrix factorQ, IMatrix factorR, IVector b, ref IVector x)
	Solves a system of eauations with the specified QR decomposition of a real symmetric square matrix. More...
static void	QrSolve (IMatrix factorQ, IMatrix factorR, IMatrix B, ref IVector auxB, ref IVector auxX, ref IMatrix X)
	Calculates inverse of the matrix from its specified LDLT-decomposed matrix. More...
static void	QrInverse (IMatrix factorQ, IMatrix factorR, ref IVector auxB, ref IVector auxX, ref IMatrix res)
	Calculates inverse of the matrix from its specified LDLT decomposition. More...
static bool	TestMatrixProducts (bool printReports)
	Tests various matrix and vector products with fixed tolerance of 1.0E-6. More...
static bool	TestMatrixProducts (double tolerance)
	Tests various matrix and vector products, without printing reports. More...
static bool	TestMatrixProducts ()
	Tests various matrix and vector products with fixed tolerance of 1.0E-6 and without printing reports. More...
static bool	TestMatrixProducts (double tolerance, bool printReports)
	Tests various matrix and vector products. More...
static void	TestStaticMethodCommon ()
	A test method, just prints some output. More...
static void	TestStaticMethodSpecific ()
	A test method, just prints some output. More...
static bool	TestIndices (int dim1=3, int dim2=4, IMatrix providedMatrix=null)
	Performs test of converson between double indexing and flat indexing of matric elements,. Returns true if successful, false othwrwise. More...

Properties
override int	RowCount [get]
	Gets the first dimension (number of rows) of the 3D matrix, i.e. 3. More...
override int	ColumnCount [get]
	Gets the second dimension (number of columns) of the 3D matrix, i.e. 3. More...
mat3	Mat [get, set]
	Gets the struct representation of this 3D matrix. More...
double	XX [get, set]
	XX component. More...
double	XY [get, set]
	XY component. More...
double	XZ [get, set]
	XZ component. More...
double	YX [get, set]
	YX component. More...
double	YY [get, set]
	YY component. More...
double	YZ [get, set]
	YZ component. More...
double	ZX [get, set]
	ZX component. More...
double	ZY [get, set]
	ZY component. More...
double	ZZ [get, set]
	ZZ component. More...
override double	this[int i, int j] [get, set]
	Index operator. More...
Vector3d	RowX [get, set]
	Gets or sets the x-row of the 3D matrix. More...
Vector3d	RowY [get, set]
	Gets or sets the y-row of the 3D matrix. More...
Vector3d	RowZ [get, set]
	Gets or sets the z-row of the 3D matrix. More...
Vector3d	ColumnX [get, set]
	Gets or sets the x-column of the 3D matrix. More...
Vector3d	ColumnY [get, set]
	Gets or sets the y-column of the 3D matrix. More...
Vector3d	ColumnZ [get, set]
	Gets or sets the z-column of the 3D matrix. More...
override double	NormForbenius [get]
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...
override double	NormEuclidean [get]
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...
override double	Norm [get]
	Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components. More...
double	Norm1 [get]
	Get the 1 norm of the matrix - maximum over columns of sum of absolute values of components. More...
double	NormInfinity [get]
	Get the infinity norm of the matrix - maximum over rows of sum of absolute values of components. More...
double	Determinant [get]
	Gets matrix determinant. More...
double	Det [get]
	Gets matrix determinant. More...
override double	Trace [get]
	Gets matrix trace (sum of diagonal elements). More...
new Matrix3d	T [get]
	Gets transpose of the current matrix. More...
Matrix3d	Inverse [get]
	Gets inverse of the current matrix. More...
Matrix3d	Inv [get]
	Gets inverse of the current matrix. More...
Properties inherited from IG.Num.MatrixBase
abstract int	RowCount [get]
	Gets the number of rows of the current matrix. More...
abstract int	ColumnCount [get]
	Gets the number of columns of the current matrix. More...
virtual int	Count [get]
	Gets total number of elements. More...
virtual IMatrix	T [get]
	Returns a new matrix that is transpose of the current matrix. More...
virtual double	this[int flatIndex] [get, set]
	Gets or set the element indexed by a flat index in the Matrix. More...
virtual double	this[int row, int column] [get, set]
	Gets or set the element indexed by (i, j) in the Matrix. More...
virtual double	Trace [get]
	Gets matrix trace (sum of diagonal terms). More...
virtual double	NormForbenius [get]
	Gets Forbenious (or Euclidean) norm of the matrix - square root of sum of squares of elements. More...
virtual double	NormEuclidean [get]
	Gets Forbenious (or Euclidean) norm of the matrix - square root of sum of squares of elements. More...
virtual double	Norm [get]
	Gets Forbenious (or Euclidean) norm of the matrix - square root of sum of squares of elements. More...
static MatrixStore	MatrixStore [get]
	Gets the matrix store for recycling auxiliary matrices. More...

Private Member Functions
Vector3d	Solve (Vector3d b)
	Returns solution of system of equations with the current system matrix and the specified right-hand sides. More...
Matrix3d	Add (Matrix3d a)
	Returns sum of the current matrix and the specified matrix. More...
Matrix3d	Subtract (Matrix3d a)
	Returns difference between the current matrix and the specified matrix. More...
Matrix3d	MultiplyRight (Matrix3d b)
	Right-multiplies the current 3D matrix with the specified matrix and returns the product. More...
Matrix3d	MultiplyLeft (Matrix3d b)
	Left-multiplies the current 3D matrix with the specified matrix and returns the product. More...
Vector3d	Multiply (Vector3d b)
	Right-multiplies the current 3D matrix with the specified 3D vector and returns the product. More...
Matrix3d	Multiply (double b)
	Multiplies the current 3D matrix with the specified scalar and returns the product. More...

Private Attributes
mat3	_m

Additional Inherited Members
Static Protected Member Functions inherited from IG.Num.MatrixBase
static void	LuSolveNoPermutationsPlain (IMatrix luMatrix, IVector b, IVector x)
	Solves a system of equations with the specified LU decomposition with already permuted b. More...
static bool	CheckTestResult (IMatrix result, IMatrix referenceResult, double tolerance, bool printReports)
	Checks whether the difference between matrix result of the tested operation and some reference result is within the specified tolerance. More...
static bool	CheckTestResult (IVector result, IVector referenceResult, double tolerance, bool printReports)
	Checks whether the difference between matrix result of the tested operation and some reference result is within the specified tolerance. More...

Detailed Description

Matrix in a 3 dimensional space.

$A Igor Jul08; Oct10;

Constructor & Destructor Documentation

IG.Num.Matrix3d.Matrix3d ( Matrix3d  m )

inline

Copy constructor. Initializes components of a 3D matrix with components of another 3D matrix.

Parameters

m	Matrix whose components are copied to the initialized matrix.

References IG.Num.Matrix3d.XX, IG.Num.Matrix3d.XY, IG.Num.Matrix3d.XZ, IG.Num.Matrix3d.YX, IG.Num.Matrix3d.YY, IG.Num.Matrix3d.YZ, IG.Num.Matrix3d.ZX, IG.Num.Matrix3d.ZY, and IG.Num.Matrix3d.ZZ.

IG.Num.Matrix3d.Matrix3d ( IMatrix  m )

inline

Constructor. Initializes components of a 3D matrix with components of another matrix. The specified matrix should be 3*3.

Parameters

m	Matrix whose components are copied to the initialized matrix (should be 3*3).

IG.Num.Matrix3d.Matrix3d ( Vector3d  rowx, Vector3d  rowy, Vector3d  rowz  )

inline

Initializes 3D matrix structure with the specified components.

References IG.Num.Vector3d.X, IG.Num.Vector3d.Y, and IG.Num.Vector3d.Z.

IG.Num.Matrix3d.Matrix3d ( mat3  m )

inline

Initializes components of a 3D matrix with components of the specified matrix.

Parameters

m	Matrix whose components are copied to the initialized matrix.

IG.Num.Matrix3d.Matrix3d ( double  xx, double  xy, double  xz, double  yx, double  yy, double  yz, double  zx, double  zy, double  zz  )

inline

Initializes 3D matrix structure with the specified components.

IG.Num.Matrix3d.Matrix3d ( double  component )

inline

Initializes 3D with the specified component.

Parameters

component

Value that is assigned to all matrix components.

IG.Num.Matrix3d.Matrix3d ( vec3  xrow, vec3  yrow, vec3  zrow  )

inline

Initializes 3D matrix structure with the specified components.

IG.Num.Matrix3d.Matrix3d ( double  A[][] )

inline

Initializes a 3D matrix with elements of a jagged array.

Parameters

A	Array from which a 3D matrix is constructed.

IG.Num.Matrix3d.Matrix3d ( double  A[,] )

inline

Initializes a 3D matrix with elements of a rectangular array.

Parameters

A	Array from which a 3D matrix is constructed.

References IG.Num.A.

Member Function Documentation

static Matrix3d IG.Num.Matrix3d.Create ( Matrix3d  mat )

inlinestatic

Creates and returns a 3D matrix that is a copy of another 3D matrix.

Parameters

mat

Returns

static Matrix3d IG.Num.Matrix3d.Create ( IMatrix  mat )

inlinestatic

Creates and returns a 3D matrix that is a copy of another (general) matrix. That matrix should be a 3*3 matrix, otherwise exception is thrown.

Parameters

mat	Matrix whose components are copied to the created matrix. Should be a 3*3 matrix, otherwisee exception is thrown.

Returns

static Matrix3d IG.Num.Matrix3d.Create ( double  A[][] )

inlinestatic

Constructs a matrix from a copy of a 2-D array by deep-copy.

Parameters

A	Two-dimensional array of doubles.

static Matrix3d IG.Num.Matrix3d.Create ( double  A[,] )

inlinestatic

Constructs a 3D matrix from a copy of a 2-D array by deep-copy.

Parameters

A	Two-dimensional array of doubles.

References IG.Num.A.

static Matrix3d IG.Num.Matrix3d.CreateFromColumns ( IList< IVector >  columnVectors )

inlinestatic

Construct a complex matrix from a set of real column vectors.

static Matrix3d IG.Num.Matrix3d.CreateFromRows ( IList< Vector >  rowVectors )

inlinestatic

Construct a complex matrix from a set of real row vectors.

static Matrix3d IG.Num.Matrix3d.Identity ( )

inlinestatic

Creates a d1*d2 identity matrix.

Returns

An d1*d2 matrix with ones on the diagonal and zeros elsewhere.

static Matrix3d IG.Num.Matrix3d.Zeros ( )

inlinestatic

Creates a 3D matrix filled with 0.

static Matrix3d IG.Num.Matrix3d.Ones ( )

inlinestatic

Creates a 3D matrix filled with 1.

static Matrix3d IG.Num.Matrix3d.Diagonal ( IVector  diagonalVector )

inlinestatic

Creates a new diagonal d1*d2 matrix based on the diagonal vector.

Parameters

diagonalVector

The values of the matrix diagonal.

Returns

A d1*d2 matrix with the values from the diagonal vector on the diagonal and zeros elsewhere.

static Matrix3d IG.Num.Matrix3d.Random ( )

inlinestatic

Creates and returns a 3D matrix with uniformly distributed random elements in the [0, 1) interval.

Returns

A 3D matrix with uniformly distributed random elements in [0, 1) interval.

References IG.Num.MatrixBase.SetRandom().

static Matrix3d IG.Num.Matrix3d.Random ( IRandomGenerator  rnd )

inlinestatic

Creates and returns a 3D matrix with uniformly distributed random elements in the [0, 1) interval.

Parameters

rnd	Random generator that is used for generation of elements.

Returns

A 3D matrix with uniformly distributed random elements in [0, 1) interval.

References IG.Num.MatrixBase.SetRandom().

virtual Matrix3d IG.Num.Matrix3d.GetCopyThis ( )

inlinevirtual

Returns a copy of the current 3D matrix.

Returns

override MatrixBase IG.Num.Matrix3d.GetCopyBase ( )

inlinevirtual

Returns a deep copy of the current 3D matrix.

Implements IG.Num.MatrixBase.

Matrix3d IG.Num.Matrix3d.GetNewThis ( int  rowCount, int  ColumnCount  )

inline

Returns a copy of the current 3D matrix.

override MatrixBase IG.Num.Matrix3d.GetNewBase ( int  rowCount, int  columnCount  )

inlinevirtual

Creates and returns a new 3D matrix with the specified dimensions, and of the same type as the current matrix.

Parameters

rowCount	Number fo rows of the newly created matrix. Must be 3.
columnCount	Number of columns of the newly created matrix. Must be 3.

Returns

A newly created matrix of the specified dimensions and of the same type as the current matrix.

Implements IG.Num.MatrixBase.

Matrix3d IG.Num.Matrix3d.GetNewThis ( )

inline

Creates and returns a new matrix with the same dimensions and of the same type as the current matrix.

override MatrixBase IG.Num.Matrix3d.GetNewBase ( )

inlinevirtual

Creates and returns a new matrix with the same dimensions and of the same type as the current matrix.

Implements IG.Num.MatrixBase.

Vector3d IG.Num.Matrix3d.GetNewVectorThis ( int  length )

inline

Creates and returns a new 3D vector with the specified dimension (which must be null), and of the type that is consistent with the type of the current matrix.

Parameters

length

Dimension of the newly created vector.

Returns

A newly created vector of the specified dimension and of the same type as the current vector.

override VectorBase IG.Num.Matrix3d.GetNewVectorBase ( int  length )

inlinevirtual

Creates and returns a new vector with the specified dimension, and of the type that is consistent with the type of the current matrix.

Parameters

length

Dimension of the newly created vector.

Returns

A newly created vector of the specified dimension and of the same type as the current vector.

Implements IG.Num.MatrixBase.

override int IG.Num.Matrix3d.GetHashCode ( )

inline

Returns the hashRet code (hashRet function) of the current matrix.

This method calls the MatrixBase.GetHashCode() to calculate the hashRet code, which is standard for all implementations of the IMatrix interface.

Two matrices that have the same dimensions and equal elements will produce the same hashRet codes.

Probability that two different matrices will produce the same hashRet code is small but it exists.

Overrides the object.GetHashCode method.

References IG.Num.MatrixBase.GetHashCode().

override bool IG.Num.Matrix3d.Equals ( Object  obj )

inline

Returns a value indicating whether the specified object is equal to the current matrix.

True is returned if the object is a non-null matrix (i.e. it implements the IMatrix interface), and has the same dimension and equal elements as the current matrix.

This method calls the MatrixBase.Equals(object) to obtain the returned value, which is standard for all implementations of the IMatrix interface.

Overrides the object.Equals(object) method.

References IG.Num.MatrixBase.Equals().

Matrix3d IG.Num.Matrix3d.NormalizedEuclidean ( )

inline

Returns this matrix normalized with Euclidean norm.

Matrix3d IG.Num.Matrix3d.NormalizedForbenius ( )

inline

Returns this matrix normalized with Euclidean norm.

Matrix3d IG.Num.Matrix3d.Normalized1 ( )

inline

Returns this matrix normalized with 1 norm.

Matrix3d IG.Num.Matrix3d.NormalizedInfinity ( )

inline

Returns this matrix normalized with infinity norm.

Vector3d IG.Num.Matrix3d.Solve ( Vector3d  b )

inlineprivate

Returns solution of system of equations with the current system matrix and the specified right-hand sides.

Parameters

b	Vector of right-hand sides of equations.

Returns

References IG.Num.Vector3d.Vec.

Matrix3d IG.Num.Matrix3d.Add ( Matrix3d  a )

inlineprivate

Returns sum of the current matrix and the specified matrix.

References IG.Num.Matrix3d.Mat.

Referenced by IG.Num.Matrix3d.operator+().

Matrix3d IG.Num.Matrix3d.Subtract ( Matrix3d  a )

inlineprivate

Returns difference between the current matrix and the specified matrix.

References IG.Num.Matrix3d.Mat.

Referenced by IG.Num.Matrix3d.operator-().

Matrix3d IG.Num.Matrix3d.MultiplyRight ( Matrix3d  b )

inlineprivate

Right-multiplies the current 3D matrix with the specified matrix and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns

this*b

References IG.Num.Matrix3d.Mat.

Referenced by IG.Num.Matrix3d.operator*().

Matrix3d IG.Num.Matrix3d.MultiplyLeft ( Matrix3d  b )

inlineprivate

Left-multiplies the current 3D matrix with the specified matrix and returns the product.

Parameters

b	Left-hand side factor of multiplication.

Returns

b*this

References IG.Num.Matrix3d.Mat.

Vector3d IG.Num.Matrix3d.Multiply ( Vector3d  b )

inlineprivate

Right-multiplies the current 3D matrix with the specified 3D vector and returns the product.

Parameters

b	Right-hand side factor of multiplication.

Returns

this*b

References IG.Num.Vector3d.Vec.

Referenced by IG.Num.Matrix3d.operator*(), and IG.Num.Matrix3d.operator/().

Matrix3d IG.Num.Matrix3d.Multiply ( double  b )

inlineprivate

Multiplies the current 3D matrix with the specified scalar and returns the product.

Parameters

b	Factor of multiplication.

Returns

this*b

static Matrix3d IG.Num.Matrix3d.Copy ( Matrix3d  m )

inlinestatic

Returns a copy of the specified 3D matrix.

Parameters

m	Matrix whose copy is returned.

static void IG.Num.Matrix3d.Negate ( Matrix3d  m, ref Matrix3d  res  )

inlinestatic

Negates the specified 3D matrix and stores its copy in the resulting matrix.

Parameters

m	Matrix to be negated.
res	Matrix where the result is stored.

References IG.Num.Matrix3d.Mat, and IG.Num.mat3.Negate().

static int IG.Num.Matrix3d.EigenSystem2d ( Matrix3d  a, ref Matrix3d  eigenvec, ref Vector3d  eigenval  )

inlinestatic

Calculates eigenvectors and eigenvalues of a 2x2 matrix a and stores eigenvectors to lines of eigenvec and eigenvalues to eigenval. eigenvec can be the same matrix as a. The number of different real eigenvalues is returned. Ref.: linalg.nb Not tested yet!

Parameters

a	2D Matrix whose eigenvalues and eigenvectors are calculated.
eigenvec	Matrix where eigenvectors are stored as rows.
eigenval	Vector where eigenvalues are stored.

Returns

The number of different real eigenvalues.

$A Igor Aug08, Oct10;

References IG.Num.mat3.EigenSystem2d(), and IG.Num.Matrix3d.Mat.

static Matrix3d IG.Num.Matrix3d.operator+ ( Matrix3d  m )

inlinestatic

Unary plus for 3D matrices, returns the operand.

static Matrix3d IG.Num.Matrix3d.operator- ( Matrix3d  a )

inlinestatic

Unary negation for 3D matrices, returns the negative operand.

References IG.Num.Matrix3d.XX, IG.Num.Matrix3d.XY, IG.Num.Matrix3d.XZ, IG.Num.Matrix3d.YX, IG.Num.Matrix3d.YY, IG.Num.Matrix3d.YZ, IG.Num.Matrix3d.ZX, IG.Num.Matrix3d.ZY, and IG.Num.Matrix3d.ZZ.

static Matrix3d IG.Num.Matrix3d.operator+ ( Matrix3d  a, Matrix3d  b  )

inlinestatic

Matrix addition in 3D.

References IG.Num.Matrix3d.Add().

static Matrix3d IG.Num.Matrix3d.operator- ( Matrix3d  a, Matrix3d  b  )

inlinestatic

Matrix subtraction in 3D.

References IG.Num.Matrix3d.Subtract().

static Matrix3d IG.Num.Matrix3d.operator* ( Matrix3d  a, Matrix3d  b  )

inlinestatic

Matrix multiplication in 3D.

References IG.Num.Matrix3d.MultiplyRight().

static Vector3d IG.Num.Matrix3d.operator* ( Matrix3d  a, Vector3d  b  )

inlinestatic

Matrix with vector multiplication in 3D.

References IG.Num.Matrix3d.Multiply().

static Matrix3d IG.Num.Matrix3d.operator* ( Matrix3d  a, double  b  )

inlinestatic

Product of a 3D matrix by a scalar.

References IG.Num.Matrix3d.Multiply().

static Matrix3d IG.Num.Matrix3d.operator* ( double  a, Matrix3d  b  )

inlinestatic

Product of a 3D matrix by a scalar.

References IG.Num.Matrix3d.Multiply().

static Matrix3d IG.Num.Matrix3d.operator/ ( Matrix3d  a, double  b  )

inlinestatic

Division of a 3D matrix by a scalar.

References IG.Num.Matrix3d.Multiply().

void IG.Num.Matrix3d.Read ( )

inline

Reads 3D matrix components from a console.

void IG.Num.Matrix3d.Read ( string  name )

inline

Reads 3D matrix components from a console.

Parameters

name	Name of the matrix to be read; it is written as orientation to the user and can be null.

References IG.Num.mat3.Read().

Member Data Documentation

mat3 IG.Num.Matrix3d._m

private

Property Documentation

override int IG.Num.Matrix3d.RowCount

get

Gets the first dimension (number of rows) of the 3D matrix, i.e. 3.

override int IG.Num.Matrix3d.ColumnCount

get

Gets the second dimension (number of columns) of the 3D matrix, i.e. 3.

mat3 IG.Num.Matrix3d.Mat

getsetprotected

Gets the struct representation of this 3D matrix.

Referenced by IG.Num.Matrix3d.Add(), IG.Num.Matrix3d.EigenSystem2d(), IG.Num.Matrix3d.MultiplyLeft(), IG.Num.Matrix3d.MultiplyRight(), IG.Num.Matrix3d.Negate(), and IG.Num.Matrix3d.Subtract().

double IG.Num.Matrix3d.XX

getset

XX component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.XY

getset

XY component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.XZ

getset

XZ component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.YX

getset

YX component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.YY

getset

YY component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.YZ

getset

YZ component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.ZX

getset

ZX component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.ZY

getset

ZY component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

double IG.Num.Matrix3d.ZZ

getset

ZZ component.

Referenced by IG.Num.Matrix3d.Matrix3d(), and IG.Num.Matrix3d.operator-().

override double IG.Num.Matrix3d.this[int i, int j]

getset

Index operator.

Parameters

i	Component index.
j	Component index.

Returns

The specified component of a 3D vector.

Vector3d IG.Num.Matrix3d.RowX

getset

Gets or sets the x-row of the 3D matrix.

Vector3d IG.Num.Matrix3d.RowY

getset

Gets or sets the y-row of the 3D matrix.

Vector3d IG.Num.Matrix3d.RowZ

getset

Gets or sets the z-row of the 3D matrix.

Vector3d IG.Num.Matrix3d.ColumnX

getset

Gets or sets the x-column of the 3D matrix.

Vector3d IG.Num.Matrix3d.ColumnY

getset

Gets or sets the y-column of the 3D matrix.

Vector3d IG.Num.Matrix3d.ColumnZ

getset

Gets or sets the z-column of the 3D matrix.

override double IG.Num.Matrix3d.NormForbenius

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

override double IG.Num.Matrix3d.NormEuclidean

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

override double IG.Num.Matrix3d.Norm

get

Get Forbenius (or euclidean) norm of the matrix - square root of sum of squares of components.

double IG.Num.Matrix3d.Norm1

get

Get the 1 norm of the matrix - maximum over columns of sum of absolute values of components.

double IG.Num.Matrix3d.NormInfinity

get

Get the infinity norm of the matrix - maximum over rows of sum of absolute values of components.

double IG.Num.Matrix3d.Determinant

getprivate

Gets matrix determinant.

double IG.Num.Matrix3d.Det

getprivate

Gets matrix determinant.

override double IG.Num.Matrix3d.Trace

get

Gets matrix trace (sum of diagonal elements).

new Matrix3d IG.Num.Matrix3d.T

get

Gets transpose of the current matrix.

Matrix3d IG.Num.Matrix3d.Inverse

getprivate

Gets inverse of the current matrix.

Matrix3d IG.Num.Matrix3d.Inv

getprivate

Gets inverse of the current matrix.

---

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

• igbase/numeric/geometry/Matrix3DClass.cs