Inheritance diagram for INMOST::AbstractMatrixReadOnly< Var >:

[legend]

Collaboration diagram for INMOST::AbstractMatrixReadOnly< Var >:

Public Types
typedef unsigned	enumerator

Public Member Functions
virtual enumerator	Rows () const =0
	Obtain number of rows. More...

virtual enumerator	Cols () const =0
	Obtain number of columns. More...

virtual Var	compute (enumerator i, enumerator j) const =0
	Compute element of the matrix by row and column indices without right to change the element. More...

bool	CheckNans () const
	Check all matrix entries for not a number. More...

bool	CheckInfs () const
	Check all matrix entries for infinity. More...

bool	CheckNansInfs () const
	Check all matrix entries for not a number and infinity. More...

Var	Det () const
	Matrix determinant.

bool	SVD (AbstractMatrix< Var > &U, AbstractMatrix< Var > &Sigma, AbstractMatrix< Var > &V, bool order_singular_values=true, bool nonnegative=true) const
	Singular value decomposition. More...

bool	cSVD (AbstractMatrix< Var > &U, AbstractMatrix< Var > &Sigma, AbstractMatrix< Var > &V) const
	Singular value decomposition. More...

ConstMatrixTranspose< Var >	Transpose () const
	Transpose current matrix. More...

ConstMatrixConjugateTranspose< Var >	ConjugateTranspose () const
	Transpose and conjugate current matrix. More...

ConstMatrixConjugate< Var >	Conjugate () const
	Conjugate current matrix. More...

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	CrossProduct (const AbstractMatrixReadOnly< typeB > &other) const
	Cross-product operation for a vector. More...

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	Transform (const AbstractMatrixReadOnly< typeB > &other) const
	Transformation matrix from current vector to provided vector using shortest arc rotation. More...

template<typename typeB >
MatrixDifference< Var, typeB >	operator- (const AbstractMatrixReadOnly< typeB > &other) const
	Subtract a matrix. More...

template<typename typeB >
MatrixSum< Var, typeB >	operator+ (const AbstractMatrixReadOnly< typeB > &other) const
	Add a matrix. More...

template<typename typeB >
MatrixMul< Var, typeB, typename Promote< Var, typeB >::type >	operator* (const AbstractMatrixReadOnly< typeB > &other) const
	Multiply the matrix by another matrix. More...

MatrixUnaryMinus< Var >	operator- () const
	Unary minus. Change sign of each element of the matrix.

template<typename typeB >
KroneckerProduct< Var, typeB >	Kronecker (const AbstractMatrixReadOnly< typeB > &other) const
	Kronecker product, latex symbol \otimes. More...

Matrix< Var >	Invert (int *ierr=NULL) const
	Inverts matrix using Crout-LU decomposition with full pivoting for maximum element. More...

Matrix< Var >	CholeskyInvert (int *ierr=NULL) const
	Inverts symmetric positive-definite matrix using Cholesky decomposition.

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	Solve (const AbstractMatrixReadOnly< typeB > &B, int *ierr=NULL) const
	Finds X in A*X=B, where A and B are general matrices. More...

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	CholeskySolve (const AbstractMatrixReadOnly< typeB > &B, int *ierr=NULL) const
	Finds X in A*X=B, where A is a square symmetric positive definite matrix. More...

Var	Trace () const
	Calculate sum of the diagonal elements of the matrix. More...

void	Print (INMOST_DATA_REAL_TYPE threshold=1.0e-10, std::ostream &sout=std::cout) const
	Output matrix to screen. More...

bool	isSymmetric (double eps=1.0e-7) const
	Check if the matrix is symmetric. More...

template<typename typeB >
Promote< Var, typeB >::type	DotProduct (const AbstractMatrixReadOnly< typeB > &other) const
	Computes dot product by summing up multiplication of entries with the same indices in the current and the provided matrix. More...

template<typename typeB >
Promote< Var, typeB >::type	operator^ (const AbstractMatrixReadOnly< typeB > &other) const
	Computes dot product by summing up multiplication of entries with the same indices in the current and the provided matrix. More...

SelfPromote< Var >::type	FrobeniusNorm () const
	Computes frobenius norm of the matrix. More...

Var	MaxNorm () const
	Computes maximum absolute value of the matrix. More...

Matrix< Var >	PseudoInvert (INMOST_DATA_REAL_TYPE tol=0, int *ierr=NULL) const
	Calculates Moore-Penrose pseudo-inverse of the matrix. More...

Matrix< Var >	Power (INMOST_DATA_REAL_TYPE n, int *ierr=NULL) const
	Calcuate A^n, where n is some real value. More...

Matrix< Var >	Root (INMOST_DATA_ENUM_TYPE iter=25, INMOST_DATA_REAL_TYPE tol=1.0e-7, int *ierr=NULL) const
	Calculate square root of A matrix by Babylonian method. More...

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	PseudoSolve (const AbstractMatrixReadOnly< typeB > &B, INMOST_DATA_REAL_TYPE tol=0, int *ierr=NULL) const
	Solves the system of equations of the form A*X=B, with A and B matrices. More...

Matrix< Var >	ExtractSubMatrix (enumerator ibeg, enumerator iend, enumerator jbeg, enumerator jend) const
	Extract submatrix of a matrix. More...

ConstMatrixRepack< Var >	Repack (enumerator rows, enumerator cols) const
	Change representation of the matrix into matrix of another size. More...

ConstSubMatrix< Var >	operator() (enumerator first_row, enumerator last_row, enumerator first_col, enumerator last_col) const
	Extract submatrix of a matrix for in-place manipulation of elements. More...

ConstBlockOfMatrix< Var >	BlockOf (enumerator nrows, enumerator ncols, enumerator offset_row, enumerator offset_col) const
	Define matrix as a part of a matrix of larger size with in-place manipulation of elements. More...

template<typename typeB >
MatrixMulCoef< Var, typeB, typename Promote< Var, typeB >::type >	operator* (const typeB &coef) const
	Multiply the matrix by a coefficient. More...

template<class A >
MatrixMulShellCoef< Var, shell_expression< A >, typename Promote< Var, variable >::type >	operator* (shell_expression< A > const &coef) const
	Multiply the matrix by a coefficient. More...

template<typename typeB >
MatrixDivCoef< Var, typeB, typename Promote< Var, typeB >::type >	operator/ (const typeB &coef) const
	Divide the matrix by a coefficient of a different type. More...

template<class A >
MatrixDivShellCoef< Var, shell_expression< A >, typename Promote< Var, variable >::type >	operator/ (shell_expression< A > const &coef) const
	Divide the matrix by a coefficient of a different type. More...

template<typename typeB >
Matrix< typename Promote< Var, typeB >::type >	operator/ (const AbstractMatrixReadOnly< typeB > &other) const
	Performs B^{-1}*A, multiplication by inverse matrix from left. More...

ConstMatrixConcatCols< Var >	ConcatCols (const AbstractMatrixReadOnly< Var > &B) const
	Concatenate B matrix as columns of current matrix. More...

template<typename VarB >
ConstMatrixConcatCols2< Var, VarB, typename Promote< Var, VarB >::type >	ConcatCols (const AbstractMatrixReadOnly< VarB > &B) const
	Concatenate B matrix as columns of current matrix. More...

ConstMatrixConcatRows< Var >	ConcatRows (const AbstractMatrixReadOnly< Var > &B) const
	Concatenate B matrix as rows of current matrix. More...

template<typename VarB >
ConstMatrixConcatRows2< Var, VarB, typename Promote< Var, VarB >::type >	ConcatRows (const AbstractMatrixReadOnly< VarB > &B) const
	Concatenate B matrix as rows of current matrix. More...

virtual	~AbstractMatrixReadOnly ()
	Destructor.

virtual __INLINE INMOST_DATA_ENUM_TYPE	GetMatrixCount () const
	Retrieve number of indices of derivatives.

__INLINE Matrix< Promote< variable, variable >::type >	CholeskySolve (const AbstractMatrixReadOnly< variable > &B, int *ierr) const

__INLINE Matrix< Promote< INMOST_DATA_REAL_TYPE, variable >::type >	CholeskySolve (const AbstractMatrixReadOnly< variable > &B, int *ierr) const

__INLINE Matrix< Promote< variable, INMOST_DATA_REAL_TYPE >::type >	CholeskySolve (const AbstractMatrixReadOnly< INMOST_DATA_REAL_TYPE > &B, int *ierr) const

Additional Inherited Members
Static Protected Attributes inherited from INMOST::AbstractMatrixBase
static thread_private< Sparse::RowMerger >	merger

Detailed Description

template<typename Var>
class INMOST::AbstractMatrixReadOnly< Var >

Definition at line 190 of file inmost_dense.h.

Member Function Documentation

◆ BlockOf()

template<typename Var >

ConstBlockOfMatrix< Var > INMOST::AbstractMatrixReadOnly< Var >::BlockOf	(	enumerator	nrows,
		enumerator	ncols,
		enumerator	offset_row,
		enumerator	offset_col
	)		const

Define matrix as a part of a matrix of larger size with in-place manipulation of elements.

Let A = {a_ij}, i in [0,n), j in [0,m) be original matrix. Then the method returns B = {a_ij}, if i in [offset_row,offset_row+n), and j in [offset_col,offset_col+m) and B = {0} otherwise.

Parameters

nrows	Number of rows in larger matrix.
ncols	Number of columns in larger matrix.
offset_row	Offset for row number.
offset_col	Offset for column number.

Returns: Submatrix of the original matrix.

Definition at line 4888 of file inmost_dense.h.

◆ CheckInfs()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::CheckInfs ( ) const

inline

Check all matrix entries for infinity.

Also checks derivatives for matrices of variables.

Definition at line 225 of file inmost_dense.h.

◆ CheckNans()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::CheckNans ( ) const

inline

Check all matrix entries for not a number.

Also checks derivatives for matrices of variables.

Definition at line 222 of file inmost_dense.h.

◆ CheckNansInfs()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::CheckNansInfs ( ) const

inline

Check all matrix entries for not a number and infinity.

Also checks derivatives for matrices of variables.

Definition at line 228 of file inmost_dense.h.

◆ CholeskySolve()

template<typename Var >

template<typename typeB >

Matrix< typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::CholeskySolve	(	const AbstractMatrixReadOnly< typeB > &	B,
		int *	ierr = `NULL`
	)		const

Finds X in A*X=B, where A is a square symmetric positive definite matrix.

Uses Cholesky decomposition algorithm.

Parameters

B	Right hand side matrix.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr equal to a positive integer that represents the row on which the failure occurred (starting from 1), in case of no failure *ierr = 0.

See also: Matrix::PseudoInvert.

Returns: Inverse matrix,

Definition at line 4120 of file inmost_dense.h.

◆ Cols()

template<typename Var >

virtual enumerator INMOST::AbstractMatrixReadOnly< Var >::Cols ( ) const

pure virtual

Obtain number of columns.

Returns: Number of columns.

Implemented in INMOST::KroneckerProduct< VarA, VarB >, INMOST::MatrixDivShellCoef< VarA, VarB, VarR >, INMOST::MatrixMulShellCoef< VarA, VarB, VarR >, INMOST::MatrixDivCoef< VarA, VarB, VarR >, INMOST::MatrixMulCoef< VarA, VarB, VarR >, INMOST::MatrixMul< variable, variable, Promote< variable, variable >::type >, INMOST::MatrixMul< variable, INMOST_DATA_REAL_TYPE, Promote< variable, INMOST_DATA_REAL_TYPE >::type >, INMOST::MatrixMul< INMOST_DATA_REAL_TYPE, variable, Promote< INMOST_DATA_REAL_TYPE, variable >::type >, INMOST::MatrixMul< VarA, VarB, VarR >, INMOST::MatrixRepack< Var >, INMOST::ConstMatrixRepack< Var >, INMOST::MatrixConcatCols< Var >, INMOST::ConstMatrixConcatCols2< VarA, VarB, VarR >, INMOST::ConstMatrixConcatCols< Var >, INMOST::MatrixConcatRows< Var >, INMOST::ConstMatrixConcatRows2< VarA, VarB, VarR >, INMOST::ConstMatrixConcatRows< Var >, INMOST::MatrixTranspose< Var >, INMOST::MatrixUnaryMinus< Var >, INMOST::ConstMatrixConjugate< Var >, INMOST::ConstMatrixConjugateTranspose< Var >, INMOST::ConstMatrixTranspose< Var >, INMOST::MatrixDifference< VarA, VarB >, INMOST::MatrixSum< VarA, VarB >, INMOST::MatrixDiag< Var >, INMOST::MatrixCol< Var >, INMOST::MatrixRow< Var >, INMOST::MatrixUnit< Var >, INMOST::ConstBlockOfMatrix< Var >, INMOST::BlockOfMatrix< Var >, INMOST::ConstSubMatrix< Var >, INMOST::SubMatrix< Var >, INMOST::Matrix< Var, storage_type >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST_DATA_REAL_TYPE >::type >, INMOST::Matrix< VarR >, INMOST::Matrix< INMOST::Promote< INMOST_DATA_REAL_TYPE, INMOST::multivar_expression >::type >, INMOST::Matrix< INMOST_DATA_REAL_TYPE >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST::multivar_expression >::type >, and INMOST::SymmetricMatrix< Var, storage_type >.

◆ compute()

template<typename Var >

virtual Var INMOST::AbstractMatrixReadOnly< Var >::compute	(	enumerator	i,
		enumerator	j
	)		const

pure virtual

Compute element of the matrix by row and column indices without right to change the element.

Parameters

i	Column index.
j	Row index.

Returns: Reference to constant element.

Implemented in INMOST::KroneckerProduct< VarA, VarB >, INMOST::MatrixMul< variable, variable, Promote< variable, variable >::type >, INMOST::MatrixMul< variable, INMOST_DATA_REAL_TYPE, Promote< variable, INMOST_DATA_REAL_TYPE >::type >, INMOST::MatrixMul< INMOST_DATA_REAL_TYPE, variable, Promote< INMOST_DATA_REAL_TYPE, variable >::type >, INMOST::MatrixRepack< Var >, INMOST::ConstMatrixRepack< Var >, INMOST::MatrixConcatCols< Var >, INMOST::ConstMatrixConcatCols< Var >, INMOST::MatrixConcatRows< Var >, INMOST::ConstMatrixConcatRows< Var >, INMOST::MatrixTranspose< Var >, INMOST::MatrixUnaryMinus< Var >, INMOST::ConstMatrixConjugate< Var >, INMOST::ConstMatrixConjugateTranspose< Var >, INMOST::ConstMatrixTranspose< Var >, INMOST::MatrixDifference< VarA, VarB >, INMOST::MatrixSum< VarA, VarB >, INMOST::MatrixDiag< Var >, INMOST::MatrixCol< Var >, INMOST::MatrixRow< Var >, INMOST::MatrixUnit< Var >, INMOST::ConstBlockOfMatrix< Var >, INMOST::BlockOfMatrix< Var >, INMOST::ConstSubMatrix< Var >, INMOST::SubMatrix< Var >, INMOST::Matrix< Var, storage_type >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST_DATA_REAL_TYPE >::type >, INMOST::Matrix< VarR >, INMOST::Matrix< INMOST::Promote< INMOST_DATA_REAL_TYPE, INMOST::multivar_expression >::type >, INMOST::Matrix< INMOST_DATA_REAL_TYPE >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST::multivar_expression >::type >, and INMOST::SymmetricMatrix< Var, storage_type >.

◆ ConcatCols() [1/2]

template<typename Var >

ConstMatrixConcatCols<Var> INMOST::AbstractMatrixReadOnly< Var >::ConcatCols ( const AbstractMatrixReadOnly< Var > & B ) const

inline

Concatenate B matrix as columns of current matrix.

Assumes that number of rows of current matrix is equal to number of rows of B matrix.

Parameters

B	Matrix to be concatenated to current matrix.

Returns: Result of concatenation of current matrix and parameter.

See also: Matrix::ConcatRows

Definition at line 592 of file inmost_dense.h.

◆ ConcatCols() [2/2]

template<typename Var >

template<typename VarB >

ConstMatrixConcatCols2<Var, VarB, typename Promote<Var, VarB>::type> INMOST::AbstractMatrixReadOnly< Var >::ConcatCols ( const AbstractMatrixReadOnly< VarB > & B ) const

inline

Concatenate B matrix as columns of current matrix.

Assumes that number of rows of current matrix is equal to number of rows of B matrix.

Parameters

B	Matrix to be concatenated to current matrix.

Returns: Result of concatenation of current matrix and parameter.

See also: Matrix::ConcatRows

Definition at line 604 of file inmost_dense.h.

◆ ConcatRows() [1/2]

template<typename Var >

ConstMatrixConcatRows<Var> INMOST::AbstractMatrixReadOnly< Var >::ConcatRows ( const AbstractMatrixReadOnly< Var > & B ) const

inline

Concatenate B matrix as rows of current matrix.

Assumes that number of colums of current matrix is equal to number of columns of B matrix.

Parameters

B	Matrix to be concatenated to current matrix.

Returns: Result of concatenation of current matrix and parameter.

See also: Matrix::ConcatCols

Definition at line 614 of file inmost_dense.h.

◆ ConcatRows() [2/2]

template<typename Var >

template<typename VarB >

ConstMatrixConcatRows2<Var,VarB,typename Promote<Var,VarB>::type> INMOST::AbstractMatrixReadOnly< Var >::ConcatRows ( const AbstractMatrixReadOnly< VarB > & B ) const

inline

Concatenate B matrix as rows of current matrix.

Assumes that number of colums of current matrix is equal to number of columns of B matrix.

Parameters

B	Matrix to be concatenated to current matrix.

Returns: Result of concatenation of current matrix and parameter.

See also: Matrix::ConcatCols

Definition at line 626 of file inmost_dense.h.

◆ Conjugate()

template<typename Var >

ConstMatrixConjugate<Var> INMOST::AbstractMatrixReadOnly< Var >::Conjugate ( ) const

inline

Conjugate current matrix.

Returns: Conjugated matrix.

Definition at line 286 of file inmost_dense.h.

◆ ConjugateTranspose()

template<typename Var >

ConstMatrixConjugateTranspose<Var> INMOST::AbstractMatrixReadOnly< Var >::ConjugateTranspose ( ) const

inline

Transpose and conjugate current matrix.

Returns: Transposed and conjugated matrix.

Definition at line 283 of file inmost_dense.h.

◆ CrossProduct()

template<typename Var >

template<typename typeB >

Matrix< typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::CrossProduct ( const AbstractMatrixReadOnly< typeB > & other ) const

Cross-product operation for a vector.

Both right hand side and left hand side should be a vector

Parameters

other The right hand side of cross product.

Returns: The cross product of current and right hand side vector.

Warning: Works for 3x1 vector and 3xm m-vectors as right hand side.

Definition at line 3676 of file inmost_dense.h.

◆ cSVD()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::cSVD	(	AbstractMatrix< Var > &	U,
		AbstractMatrix< Var > &	Sigma,
		AbstractMatrix< Var > &	V
	)		const

Singular value decomposition.

Specific for complex matrices.

Definition at line 5209 of file inmost_dense.h.

◆ DotProduct()

template<typename Var >

template<typename typeB >

Promote<Var, typeB>::type INMOST::AbstractMatrixReadOnly< Var >::DotProduct ( const AbstractMatrixReadOnly< typeB > & other ) const

inline

Computes dot product by summing up multiplication of entries with the same indices in the current and the provided matrix.

Parameters

other Provided matrix.

Returns: Dot product of two matrices.

Definition at line 428 of file inmost_dense.h.

◆ ExtractSubMatrix()

template<typename Var >

Matrix< Var > INMOST::AbstractMatrixReadOnly< Var >::ExtractSubMatrix	(	enumerator	ibeg,
		enumerator	iend,
		enumerator	jbeg,
		enumerator	jend
	)		const

Extract submatrix of a matrix.

Let A = {a_ij}, i in [0,n), j in [0,m) be original matrix. Then the method returns B = {a_ij}, i in [ibeg,iend), and j in [jbeg,jend).

Parameters

ibeg	Starting row in the original matrix.
iend	Last row (excluded) in the original matrix.
jbeg	Starting column in the original matrix.
jend	Last column (excluded) in the original matrix.

Returns: Submatrix of the original matrix.

Definition at line 4745 of file inmost_dense.h.

◆ FrobeniusNorm()

template<typename Var >

SelfPromote<Var>::type INMOST::AbstractMatrixReadOnly< Var >::FrobeniusNorm ( ) const

inline

Computes frobenius norm of the matrix.

Returns: Frobenius norm of the matrix.

Definition at line 449 of file inmost_dense.h.

◆ Invert()

template<typename Var >

Matrix< Var > INMOST::AbstractMatrixReadOnly< Var >::Invert ( int * ierr = NULL ) const

Inverts matrix using Crout-LU decomposition with full pivoting for maximum element.

Works well for non-singular matrices, for singular matrices look see Matrix::PseudoInvert.

Parameters

ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr equal to a positive integer that represents the row on which the failure occurred (starting from 1), in case of no failure *ierr = 0.

Returns: Inverse matrix.

See also: Matrix::PseudoInvert.

Todo:: (test) Activate and test implementation with Solve.

Definition at line 4100 of file inmost_dense.h.

◆ isSymmetric()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::isSymmetric ( double eps = 1.0e-7 ) const

inline

Check if the matrix is symmetric.

Returns: Returns true if the matrix is symmetric, otherwise false.

Definition at line 411 of file inmost_dense.h.

◆ Kronecker()

template<typename Var >

template<typename typeB >

KroneckerProduct< Var, typeB > INMOST::AbstractMatrixReadOnly< Var >::Kronecker ( const AbstractMatrixReadOnly< typeB > & other ) const

Kronecker product, latex symbol \otimes.

Parameters

other Matrix on the right of the Kronecker product.

Returns: Result of the Kronecker product of current and another matrix.

Definition at line 4093 of file inmost_dense.h.

◆ MaxNorm()

template<typename Var >

Var INMOST::AbstractMatrixReadOnly< Var >::MaxNorm ( ) const

inline

Computes maximum absolute value of the matrix.

Returns: Maximum norm of the matrix.

Definition at line 459 of file inmost_dense.h.

◆ operator()()

template<typename Var >

ConstSubMatrix< Var > INMOST::AbstractMatrixReadOnly< Var >::operator()	(	enumerator	first_row,
		enumerator	last_row,
		enumerator	first_col,
		enumerator	last_col
	)		const

Extract submatrix of a matrix for in-place manipulation of elements.

Let A = {a_ij}, i in [0,n), j in [0,m) be original matrix. Then the method returns B = {a_ij}, i in [ibeg,iend), and j in [jbeg,jend).

Parameters

first_row	Starting row in the original matrix.
last_row	Last row (excluded) in the original matrix.
first_col	Starting column in the original matrix.
last_col	Last column (excluded) in the original matrix.

Returns: Submatrix of the original matrix.

Definition at line 4877 of file inmost_dense.h.

◆ operator*() [1/3]

template<typename Var >

template<typename typeB >

MatrixMul< Var, typeB, typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::operator* ( const AbstractMatrixReadOnly< typeB > & other ) const

Multiply the matrix by another matrix.

Parameters

other Matrix to be multiplied from right.

Returns: Matrix multipled by another matrix.

Definition at line 3917 of file inmost_dense.h.

◆ operator*() [2/3]

template<typename Var >

template<typename typeB >

MatrixMulCoef< Var, typeB, typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::operator* ( const typeB & coef ) const

Multiply the matrix by a coefficient.

Parameters

coef	Coefficient.

Returns: Matrix multiplied by the coefficient.

Definition at line 4036 of file inmost_dense.h.

◆ operator*() [3/3]

template<typename Var >

template<typename A >

MatrixMulShellCoef< Var, shell_expression< A >, typename Promote< Var, variable >::type > INMOST::AbstractMatrixReadOnly< Var >::operator* ( shell_expression< A > const & coef ) const

Multiply the matrix by a coefficient.

Parameters

coef	Coefficient.

Returns: Matrix multiplied by the coefficient.

Definition at line 4045 of file inmost_dense.h.

◆ operator+()

template<typename Var >

template<typename typeB >

MatrixSum< Var, typeB > INMOST::AbstractMatrixReadOnly< Var >::operator+ ( const AbstractMatrixReadOnly< typeB > & other ) const

Add a matrix.

Parameters

other The matrix to be added.

Returns: Sum of current matrix with another matrix.

Definition at line 3883 of file inmost_dense.h.

◆ operator-()

template<typename Var >

template<typename typeB >

MatrixDifference< Var, typeB > INMOST::AbstractMatrixReadOnly< Var >::operator- ( const AbstractMatrixReadOnly< typeB > & other ) const

Subtract a matrix.

Parameters

other The matrix to be subtracted.

Returns: Difference of current matrix with another matrix.

Definition at line 3849 of file inmost_dense.h.

◆ operator/() [1/3]

template<typename Var >

template<typename typeB >

Matrix<typename Promote<Var, typeB>::type> INMOST::AbstractMatrixReadOnly< Var >::operator/ ( const AbstractMatrixReadOnly< typeB > & other ) const

inline

Performs B^{-1}*A, multiplication by inverse matrix from left.

Throws exception if matrix is not invertible. See Mesh::PseudoSolve for singular matrices.

Parameters

other Matrix to be inverted and multiplied from left.

Returns: Multiplication of current matrix by inverse of another

See also: Matrix::PseudoInvert.

Definition at line 580 of file inmost_dense.h.

◆ operator/() [2/3]

template<typename Var >

template<typename typeB >

MatrixDivCoef< Var, typeB, typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::operator/ ( const typeB & coef ) const

Divide the matrix by a coefficient of a different type.

Parameters

coef	Coefficient.

Returns: Matrix divided by the coefficient.

Definition at line 4074 of file inmost_dense.h.

◆ operator/() [3/3]

template<typename Var >

template<typename A >

MatrixDivShellCoef< Var, shell_expression< A >, typename Promote< Var, variable >::type > INMOST::AbstractMatrixReadOnly< Var >::operator/ ( shell_expression< A > const & coef ) const

Divide the matrix by a coefficient of a different type.

Parameters

coef	Coefficient.

Returns: Matrix divided by the coefficient.

Definition at line 4065 of file inmost_dense.h.

◆ operator^()

template<typename Var >

template<typename typeB >

Promote<Var, typeB>::type INMOST::AbstractMatrixReadOnly< Var >::operator^ ( const AbstractMatrixReadOnly< typeB > & other ) const

inline

Computes dot product by summing up multiplication of entries with the same indices in the current and the provided matrix.

Parameters

other Provided matrix.

Returns: Dot product of two matrices.

Definition at line 443 of file inmost_dense.h.

◆ Power()

template<typename Var >

Matrix< Var > INMOST::AbstractMatrixReadOnly< Var >::Power	(	INMOST_DATA_REAL_TYPE	n,
		int *	ierr = `NULL`
	)		const

Calcuate A^n, where n is some real value.

Warning: Currently works for symmetric matrices only!

Parameters

n	Real value.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr = 1, in case of no failure *ierr = 0. The error may be caused by error in SVD algorithm.

Returns: Matrix in power of n.

Definition at line 4817 of file inmost_dense.h.

◆ Print()

template<typename Var >

void INMOST::AbstractMatrixReadOnly< Var >::Print	(	INMOST_DATA_REAL_TYPE	threshold = `1.0e-10`,
		std::ostream &	sout = `std::cout`
	)		const

inline

Output matrix to screen.

Does not output derivatices.

Parameters

threshold Elements smaller then the number are considered to be zero.

Definition at line 389 of file inmost_dense.h.

◆ PseudoInvert()

template<typename Var >

Matrix< Var > INMOST::AbstractMatrixReadOnly< Var >::PseudoInvert	(	INMOST_DATA_REAL_TYPE	tol = `0`,
		int *	ierr = `NULL`
	)		const

Calculates Moore-Penrose pseudo-inverse of the matrix.

Parameters

tol	Thershold for singular values. Singular values smaller then threshold are considered to be zero.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr = 1, in case of no failure *ierr = 0.

Returns: A pseudo-inverse of the matrix.

Definition at line 4762 of file inmost_dense.h.

◆ PseudoSolve()

template<typename Var >

template<typename typeB >

Matrix< typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::PseudoSolve	(	const AbstractMatrixReadOnly< typeB > &	B,
		INMOST_DATA_REAL_TYPE	tol = `0`,
		int *	ierr = `NULL`
	)		const

Solves the system of equations of the form A*X=B, with A and B matrices.

Uses Moore-Penrose pseudo-inverse of the matrix A and calculates X = A^+*B.

Parameters

B	Matrix at the right hand side.
tol	Thershold for singular values. Singular values smaller then threshold are considered to be zero.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr = 1, in case of no failure *ierr = 0.

Returns: A pair of the solution matrix X and boolean. If boolean is true, then the matrix was inverted successfully.

Definition at line 4845 of file inmost_dense.h.

◆ Repack()

template<typename Var >

ConstMatrixRepack<Var> INMOST::AbstractMatrixReadOnly< Var >::Repack	(	enumerator	rows,
		enumerator	cols
	)		const

inline

Change representation of the matrix into matrix of another size.

Useful to change representation from matrix into vector and back. Replaces original number of columns and rows with a new one.

Returns: Matrix with same entries and provided number of rows and columns.

Definition at line 519 of file inmost_dense.h.

◆ Root()

template<typename Var >

Matrix< Var > INMOST::AbstractMatrixReadOnly< Var >::Root	(	INMOST_DATA_ENUM_TYPE	iter = `25`,
		INMOST_DATA_REAL_TYPE	tol = `1.0e-7`,
		int *	ierr = `NULL`
	)		const

Calculate square root of A matrix by Babylonian method.

Parameters

iter	Number of iterations.
tol	Convergence tolerance.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr = 1, in case of no failure *ierr = 0.

Returns: Square root of a matrix.

Definition at line 4792 of file inmost_dense.h.

◆ Rows()

template<typename Var >

virtual enumerator INMOST::AbstractMatrixReadOnly< Var >::Rows ( ) const

pure virtual

Obtain number of rows.

Returns: Number of rows.

Implemented in INMOST::KroneckerProduct< VarA, VarB >, INMOST::MatrixDivShellCoef< VarA, VarB, VarR >, INMOST::MatrixMulShellCoef< VarA, VarB, VarR >, INMOST::MatrixDivCoef< VarA, VarB, VarR >, INMOST::MatrixMulCoef< VarA, VarB, VarR >, INMOST::MatrixMul< variable, variable, Promote< variable, variable >::type >, INMOST::MatrixMul< variable, INMOST_DATA_REAL_TYPE, Promote< variable, INMOST_DATA_REAL_TYPE >::type >, INMOST::MatrixMul< INMOST_DATA_REAL_TYPE, variable, Promote< INMOST_DATA_REAL_TYPE, variable >::type >, INMOST::MatrixMul< VarA, VarB, VarR >, INMOST::MatrixRepack< Var >, INMOST::ConstMatrixRepack< Var >, INMOST::MatrixConcatCols< Var >, INMOST::ConstMatrixConcatCols2< VarA, VarB, VarR >, INMOST::ConstMatrixConcatCols< Var >, INMOST::MatrixConcatRows< Var >, INMOST::ConstMatrixConcatRows2< VarA, VarB, VarR >, INMOST::ConstMatrixConcatRows< Var >, INMOST::MatrixTranspose< Var >, INMOST::MatrixUnaryMinus< Var >, INMOST::ConstMatrixConjugate< Var >, INMOST::ConstMatrixConjugateTranspose< Var >, INMOST::ConstMatrixTranspose< Var >, INMOST::MatrixDifference< VarA, VarB >, INMOST::MatrixSum< VarA, VarB >, INMOST::MatrixDiag< Var >, INMOST::MatrixCol< Var >, INMOST::MatrixRow< Var >, INMOST::MatrixUnit< Var >, INMOST::ConstBlockOfMatrix< Var >, INMOST::BlockOfMatrix< Var >, INMOST::ConstSubMatrix< Var >, INMOST::SubMatrix< Var >, INMOST::Matrix< Var, storage_type >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST_DATA_REAL_TYPE >::type >, INMOST::Matrix< VarR >, INMOST::Matrix< INMOST::Promote< INMOST_DATA_REAL_TYPE, INMOST::multivar_expression >::type >, INMOST::Matrix< INMOST_DATA_REAL_TYPE >, INMOST::Matrix< INMOST::Promote< INMOST::multivar_expression, INMOST::multivar_expression >::type >, and INMOST::SymmetricMatrix< Var, storage_type >.

◆ Solve()

template<typename Var >

template<typename typeB >

Matrix< typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::Solve	(	const AbstractMatrixReadOnly< typeB > &	B,
		int *	ierr = `NULL`
	)		const

Finds X in A*X=B, where A and B are general matrices.

Converts system into A^T*A*X=A^T*B. Inverts matrix A^T*A using Crout-LU decomposition with full pivoting for maximum element. Works well for non-singular matrices, for singular matrices see Matrix::PseudoInvert.

Parameters

B	Right hand side matrix.
ierr	Returns error on fail. If ierr is NULL, then throws an exception. If ierr == -1 on input, then prints out information in case of failure. In case of failure ierr equal to a positive integer that represents the row on which the failure occurred (starting from 1), in case of no failure *ierr = 0.

Returns: Inverse matrix,

See also: Matrix::PseudoInvert.

Warning: Number of rows in matrices A and B should match.

Todo:

Test implementation.
Maximum product transversal + block pivoting instead of pivoting by maximum element.

Definition at line 4588 of file inmost_dense.h.

◆ SVD()

template<typename Var >

bool INMOST::AbstractMatrixReadOnly< Var >::SVD	(	AbstractMatrix< Var > &	U,
		AbstractMatrix< Var > &	Sigma,
		AbstractMatrix< Var > &	V,
		bool	order_singular_values = `true`,
		bool	nonnegative = `true`
	)		const

Singular value decomposition.

Reconstruct matrix: A = U*Sigma*V.Transpose(). Source http://www.public.iastate.edu/~dicook/JSS/paper/code/svd.c With few corrections for robustness.

Parameters

U	Left unitary matrix, U^T U = I.
Sigma	Diagonal matrix with singular values.
V	Right unitary matrix, not transposed.
order_singular_values	Return singular values in descending order.
nonnegative	Change sign of singular values.

Warning: Somehow result differ in auto-differential mode.

Todo:: Test implementation for auto-differentiation.

Definition at line 5514 of file inmost_dense.h.

◆ Trace()

template<typename Var >

Var INMOST::AbstractMatrixReadOnly< Var >::Trace ( ) const

inline

Calculate sum of the diagonal elements of the matrix.

Returns: Trace of the matrix.

Definition at line 379 of file inmost_dense.h.

◆ Transform()

template<typename Var >

template<typename typeB >

Matrix< typename Promote< Var, typeB >::type > INMOST::AbstractMatrixReadOnly< Var >::Transform ( const AbstractMatrixReadOnly< typeB > & other ) const

Transformation matrix from current vector to provided vector using shortest arc rotation.

Parameters

other Vector to transform to.

Returns: A sqaure (rotation) matrix that transforms current vector into right hand side vector.

Warning: Works only for 3x1 vectors.

Definition at line 3735 of file inmost_dense.h.

◆ Transpose()

template<typename Var >

ConstMatrixTranspose<Var> INMOST::AbstractMatrixReadOnly< Var >::Transpose ( ) const

inline

Transpose current matrix.

Returns: Transposed matrix.

Definition at line 280 of file inmost_dense.h.

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

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename Var> class INMOST::AbstractMatrixReadOnly< Var >

Member Function Documentation

◆ BlockOf()

◆ CheckInfs()

◆ CheckNans()

◆ CheckNansInfs()

◆ CholeskySolve()

◆ Cols()

◆ compute()

◆ ConcatCols() [1/2]

◆ ConcatCols() [2/2]

◆ ConcatRows() [1/2]

◆ ConcatRows() [2/2]

◆ Conjugate()

◆ ConjugateTranspose()

◆ CrossProduct()

◆ cSVD()

◆ DotProduct()

◆ ExtractSubMatrix()

◆ FrobeniusNorm()

◆ Invert()

◆ isSymmetric()

◆ Kronecker()

◆ MaxNorm()

◆ operator()()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator^()

◆ Power()

◆ Print()

◆ PseudoInvert()

◆ PseudoSolve()

◆ Repack()

◆ Root()

◆ Rows()

◆ Solve()

◆ SVD()

◆ Trace()

◆ Transform()

◆ Transpose()

template<typename Var>
class INMOST::AbstractMatrixReadOnly< Var >