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Dense Matrices

Modules

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Classes

struct  blaze::DenseMatrix< MT, SO >
 Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes. It provides an abstraction from the actual type of the dense matrix, but enables a conversion back to this type via the Matrix base class. More...
 

Functions

template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric< T1 >, bool >::Type blaze::operator== (T1 scalar, const DenseMatrix< T2, SO > &mat)
 Equality operator for the comparison of a scalar value and a dense matrix. More...
 
template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric< T1 >, bool >::Type blaze::operator!= (T1 scalar, const DenseMatrix< T2, SO > &mat)
 Inequality operator for the comparison of a scalar value and a dense matrix. More...
 
template<typename MT , bool SO>
const DMatAbsExpr< MT, SO > blaze::abs (const DenseMatrix< MT, SO > &dm)
 Returns a matrix containing the absolute values of each single element of dm. More...
 
template<typename T1 , typename T2 , bool SO>
const DMatDMatAddExpr< T1, T2, SO > blaze::operator+ (const DenseMatrix< T1, SO > &lhs, const DenseMatrix< T2, SO > &rhs)
 Addition operator for the addition of two dense matrices with identical storage order ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DMatDMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, false > &lhs, const DenseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of two row-major dense matrices ( $ A=B*C $). More...
 
template<typename T1 , typename T2 , bool SO>
const DMatDMatSubExpr< T1, T2, SO > blaze::operator- (const DenseMatrix< T1, SO > &lhs, const DenseMatrix< T2, SO > &rhs)
 Subtraction operator for the subtraction of two dense matrices with identical storage order ( $ A=B-C $). More...
 
template<typename MT , bool SO>
const DMatEvalExpr< MT, SO > blaze::eval (const DenseMatrix< MT, SO > &dm)
 Forces the evaluation of the given dense matrix expression dm. More...
 
template<typename T1 , bool SO, typename T2 >
const EnableIf< IsNumeric< T2 >, typename DivExprTrait< T1, T2 >::Type >::Type blaze::operator/ (const DenseMatrix< T1, SO > &mat, T2 scalar)
 Division operator for the division of a dense matrix by a scalar value ( $ A=B/s $). More...
 
template<typename MT , bool SO>
const DMatScalarMultExpr< MT, typename BaseElementType< MT >::Type, SO > blaze::operator- (const DenseMatrix< MT, SO > &dm)
 Unary minus operator for the negation of a dense matrix ( $ A = -B $). More...
 
template<typename T1 , bool SO, typename T2 >
const EnableIf< IsNumeric< T2 >, typename MultExprTrait< T1, T2 >::Type >::Type blaze::operator* (const DenseMatrix< T1, SO > &mat, T2 scalar)
 Multiplication operator for the multiplication of a dense matrix and a scalar value ( $ A=B*s $). More...
 
template<typename T1 , typename T2 , bool SO>
const EnableIf< IsNumeric< T1 >, typename MultExprTrait< T1, T2 >::Type >::Type blaze::operator* (T1 scalar, const DenseMatrix< T2, SO > &mat)
 Multiplication operator for the multiplication of a scalar value and a dense matrix ( $ A=s*B $). More...
 
template<typename MT , bool SO>
const DMatSerialExpr< MT, SO > blaze::serial (const DenseMatrix< MT, SO > &dm)
 Forces the serial evaluation of the given dense matrix expression dm. More...
 
template<typename T1 , typename T2 , bool SO>
const DMatSMatAddExpr< T1, T2, SO > blaze::operator+ (const DenseMatrix< T1, SO > &lhs, const SparseMatrix< T2, SO > &rhs)
 Addition operator for the addition of a dense matrix and a sparse matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 , bool SO>
const DMatSMatAddExpr< T2, T1, SO > blaze::operator+ (const SparseMatrix< T1, SO > &lhs, const DenseMatrix< T2, SO > &rhs)
 Addition operator for the addition of a sparse matrix and a dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DMatSMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, false > &lhs, const SparseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of a row-major dense matrix and a row-major sparse matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 , bool SO>
const DMatSMatSubExpr< T1, T2, SO > blaze::operator- (const DenseMatrix< T1, SO > &lhs, const SparseMatrix< T2, SO > &rhs)
 Subtraction operator for the subtraction of a dense matrix and a sparse matrix with identical storage order ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric< T1 > >, Not< IsSymmetric< T2 > > >, const DMatTDMatAddExpr< T1, T2 > >::Type blaze::operator+ (const DenseMatrix< T1, false > &lhs, const DenseMatrix< T2, true > &rhs)
 Addition operator for the addition of a row-major and a colum-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric< T1 > >, Not< IsSymmetric< T2 > > >, const DMatTDMatAddExpr< T2, T1 > >::Type blaze::operator+ (const DenseMatrix< T1, true > &lhs, const DenseMatrix< T2, false > &rhs)
 Addition operator for the addition of a column-major and a row-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DMatTDMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, false > &lhs, const DenseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of a row-major dense matrix and a column-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric< T1 > >, Not< IsSymmetric< T2 > > >, const DMatTDMatSubExpr< T1, T2 > >::Type blaze::operator- (const DenseMatrix< T1, false > &lhs, const DenseMatrix< T2, true > &rhs)
 Subtraction operator for the subtraction of a row-major and a column-major dense matrix ( $ A=B-C $). More...
 
template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric< T1 > >, Not< IsSymmetric< T2 > > >, const DMatTDMatSubExpr< T1, T2 > >::Type blaze::operator- (const DenseMatrix< T1, true > &lhs, const DenseMatrix< T2, false > &rhs)
 Subtraction operator for the subtraction of a column-major and a row-major dense matrix ( $ A=B-C $). More...
 
template<typename MT , bool SO>
const DMatTransExpr< MT,!SO > blaze::trans (const DenseMatrix< MT, SO > &dm)
 Calculation of the transpose of the given dense matrix. More...
 
template<typename T1 , typename T2 >
const DMatTSMatAddExpr< T1, T2 > blaze::operator+ (const DenseMatrix< T1, false > &lhs, const SparseMatrix< T2, true > &rhs)
 Addition operator for the addition of a row-major dense matrix and a column-major sparse matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DMatTSMatAddExpr< T1, T2 > blaze::operator+ (const SparseMatrix< T2, true > &lhs, const DenseMatrix< T1, false > &rhs)
 Addition operator for the addition of a column-major sparse matrix and a row-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DMatTSMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, false > &lhs, const SparseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of a row-major dense matrix and a column-major sparse matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const DMatTSMatSubExpr< T1, T2 > blaze::operator- (const DenseMatrix< T1, false > &lhs, const SparseMatrix< T2, true > &rhs)
 Subtraction operator for the subtraction of a row-major dense matrix and a column-major sparse matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const DVecTDVecMultExpr< T1, T2 > blaze::operator* (const DenseVector< T1, false > &lhs, const DenseVector< T2, true > &rhs)
 Multiplication operator for the outer product of two dense vectors ( $ A=\vec{b}*\vec{c}^T $). More...
 
template<typename T1 , typename T2 >
const SMatDMatMultExpr< T1, T2 > blaze::operator* (const SparseMatrix< T1, false > &lhs, const DenseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of a row-major sparse matrix and a row-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 , bool SO>
const SMatDMatSubExpr< T1, T2, SO > blaze::operator- (const SparseMatrix< T1, SO > &lhs, const DenseMatrix< T2, SO > &rhs)
 Subtraction operator for the subtraction of a sparse matrix and a dense matrix with identical storage order ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const SMatTDMatMultExpr< T1, T2 > blaze::operator* (const SparseMatrix< T1, false > &lhs, const DenseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of a row-major sparse matrix and a column-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const SMatTDMatSubExpr< T1, T2 > blaze::operator- (const SparseMatrix< T1, false > &lhs, const DenseMatrix< T2, true > &rhs)
 Subtraction operator for the subtraction of a row-major sparse matrix and a column-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const TDMatDMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, true > &lhs, const DenseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of a column-major dense matrix and a row-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const TDMatSMatAddExpr< T1, T2 > blaze::operator+ (const DenseMatrix< T1, true > &lhs, const SparseMatrix< T2, false > &rhs)
 Addition operator for the addition of a column-major dense matrix and a row-major sparse matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const TDMatSMatAddExpr< T1, T2 > blaze::operator+ (const SparseMatrix< T2, false > &lhs, const DenseMatrix< T1, true > &rhs)
 Addition operator for the addition of a row-major sparse matrix and a column-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const TDMatSMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, true > &lhs, const SparseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of a column-major dense matrix and a row-major sparse matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const TDMatSMatSubExpr< T1, T2 > blaze::operator- (const DenseMatrix< T1, true > &lhs, const SparseMatrix< T2, false > &rhs)
 Subtraction operator for the subtraction of a column-major dense matrix and a row-major sparse matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const TDMatTDMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, true > &lhs, const DenseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of two column-major dense matrices ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const TDMatTSMatMultExpr< T1, T2 > blaze::operator* (const DenseMatrix< T1, true > &lhs, const SparseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of a column-major dense matrix and a column-major sparse matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const DisableIf< IsMatMatMultExpr< T2 >, TDVecTDMatMultExpr< T1, T2 > >::Type blaze::operator* (const DenseVector< T1, true > &vec, const DenseMatrix< T2, true > &mat)
 Multiplication operator for the multiplication of a transpose dense vector and a column-major dense matrix ( $ \vec{y}^T=\vec{x}^T*A $). More...
 
template<typename T1 , typename T2 >
const TSMatDMatMultExpr< T1, T2 > blaze::operator* (const SparseMatrix< T1, true > &lhs, const DenseMatrix< T2, false > &rhs)
 Multiplication operator for the multiplication of a column-major sparse matrix and a row-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const TSMatDMatSubExpr< T1, T2 > blaze::operator- (const SparseMatrix< T1, true > &lhs, const DenseMatrix< T2, false > &rhs)
 Subtraction operator for the subtraction of a column-major sparse matrix and a row-major dense matrix ( $ A=B+C $). More...
 
template<typename T1 , typename T2 >
const TSMatTDMatMultExpr< T1, T2 > blaze::operator* (const SparseMatrix< T1, true > &lhs, const DenseMatrix< T2, true > &rhs)
 Multiplication operator for the multiplication of a column-major sparse matrix and a column-major dense matrix ( $ A=B*C $). More...
 
template<typename T1 , typename T2 >
const DisableIf< IsMatMatMultExpr< T2 >, TSVecDMatMultExpr< T1, T2 > >::Type blaze::operator* (const SparseVector< T1, true > &vec, const DenseMatrix< T2, false > &mat)
 Multiplication operator for the multiplication of a transpose sparse vector and a row-major dense matrix ( $ \vec{y}^T=\vec{x}^T*A $). More...
 

DenseMatrix operators

template<typename T1 , typename T2 >
bool blaze::operator== (const DenseMatrix< T1, false > &lhs, const DenseMatrix< T2, false > &rhs)
 Equality operator for the comparison of two rwo-major dense matrices. More...
 
template<typename T1 , typename T2 >
bool blaze::operator== (const DenseMatrix< T1, true > &lhs, const DenseMatrix< T2, true > &rhs)
 Equality operator for the comparison of two column-major dense matrices. More...
 
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== (const DenseMatrix< T1, SO > &lhs, const DenseMatrix< T2,!SO > &rhs)
 Equality operator for the comparison of two dense matrices with different storage order. More...
 
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== (const DenseMatrix< T1, SO > &lhs, const SparseMatrix< T2, false > &rhs)
 Equality operator for the comparison of a dense matrix and a row-major sparse matrix. More...
 
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== (const DenseMatrix< T1, SO > &lhs, const SparseMatrix< T2, true > &rhs)
 Equality operator for the comparison of a dense matrix and a column-major sparse matrix. More...
 
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator== (const SparseMatrix< T1, SO1 > &lhs, const DenseMatrix< T2, SO2 > &rhs)
 Equality operator for the comparison of a sparse matrix and a dense matrix. More...
 
template<typename T1 , typename T2 >
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator== (const DenseMatrix< T1, false > &mat, T2 scalar)
 Equality operator for the comparison of a row-major dense matrix and a scalar value. More...
 
template<typename T1 , typename T2 >
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator== (const DenseMatrix< T1, true > &mat, T2 scalar)
 Equality operator for the comparison of a column-major dense matrix and a scalar value. More...
 
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= (const DenseMatrix< T1, SO1 > &lhs, const DenseMatrix< T2, SO2 > &rhs)
 Inequality operator for the comparison of two dense matrices. More...
 
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= (const DenseMatrix< T1, SO1 > &lhs, const SparseMatrix< T2, SO2 > &rhs)
 Inequality operator for the comparison of a dense matrix and a sparse matrix. More...
 
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= (const SparseMatrix< T1, SO1 > &lhs, const DenseMatrix< T2, SO2 > &rhs)
 Inequality operator for the comparison of a sparse matrix and a dense matrix. More...
 
template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator!= (const DenseMatrix< T1, SO > &mat, T2 scalar)
 Inequality operator for the comparison of a dense matrix and a scalar value. More...
 

DenseMatrix functions

template<typename MT , bool SO>
bool blaze::isnan (const DenseMatrix< MT, SO > &dm)
 Checks the given dense matrix for not-a-number elements. More...
 
template<typename MT , bool SO>
bool blaze::isSymmetric (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is symmetric. More...
 
template<typename MT , bool SO>
bool blaze::isUniform (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a uniform matrix. More...
 
template<typename MT , bool SO>
bool blaze::isLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a lower triangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isUniLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a lower unitriangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isStrictlyLower (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a strictly lower triangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is an upper triangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isUniUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is an upper unitriangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isStrictlyUpper (const DenseMatrix< MT, SO > &dm)
 Checks if the given dense matrix is a strictly upper triangular matrix. More...
 
template<typename MT , bool SO>
bool blaze::isDiagonal (const DenseMatrix< MT, SO > &dm)
 Checks if the give dense matrix is diagonal. More...
 
template<typename MT , bool SO>
bool blaze::isIdentity (const DenseMatrix< MT, SO > &dm)
 Checks if the give dense matrix is an identity matrix. More...
 
template<typename MT , bool SO>
const MT::ElementType blaze::min (const DenseMatrix< MT, SO > &dm)
 Returns the smallest element of the dense matrix. More...
 
template<typename MT , bool SO>
const MT::ElementType blaze::max (const DenseMatrix< MT, SO > &dm)
 Returns the largest element of the dense matrix. More...
 

Detailed Description

Function Documentation

template<typename MT , bool SO>
const DMatAbsExpr<MT,SO> blaze::abs ( const DenseMatrix< MT, SO > &  dm)
inline

Returns a matrix containing the absolute values of each single element of dm.

Parameters
dmThe input matrix.
Returns
The absolute value of each single element of dm.

The abs function calculates the absolute value of each element of the input matrix dm. The function returns an expression representing this operation.
The following example demonstrates the use of the abs function:

// ... Resizing and initialization
B = abs( A );
template<typename MT , bool SO>
const DMatEvalExpr<MT,SO> blaze::eval ( const DenseMatrix< MT, SO > &  dm)
inline

Forces the evaluation of the given dense matrix expression dm.

Parameters
dmThe input matrix.
Returns
The evaluated dense matrix.

The eval function forces the evaluation of the given dense matrix expression dm. The function returns an expression representing the operation.
The following example demonstrates the use of the eval function

// ... Resizing and initialization
B = eval( A );
template<typename MT , bool SO>
bool blaze::isDiagonal ( const DenseMatrix< MT, SO > &  dm)

Checks if the give dense matrix is diagonal.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is diagonal, false if not.

This function tests whether the matrix is diagonal, i.e. if the non-diagonal elements are default elements. In case of integral or floating point data types, a diagonal matrix has the form

\[\left(\begin{array}{*{5}{c}} aa & 0 & 0 & \cdots & 0 \\ 0 & bb & 0 & \cdots & 0 \\ 0 & 0 & cc & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & 0 \\ 0 & 0 & 0 & 0 & xx \\ \end{array}\right)\]

$ 0 \times 0 $ or $ 1 \times 1 $ matrices are considered as trivially diagonal. The following example demonstrates the use of the function:

// ... Initialization
if( isDiagonal( A ) ) { ... }

It is also possible to check if a matrix expression results in a diagonal matrix:

if( isDiagonal( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isIdentity ( const DenseMatrix< MT, SO > &  dm)

Checks if the give dense matrix is an identity matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is an identity matrix, false if not.

This function tests whether the matrix is an identity matrix, i.e. if the diagonal elements are 1 and the non-diagonal elements are 0. In case of integral or floating point data types, an identity matrix has the form

\[\left(\begin{array}{*{5}{c}} 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & 0 \\ 0 & 0 & 0 & 0 & 1 \\ \end{array}\right)\]

The following example demonstrates the use of the function:

// ... Initialization
if( isIdentity( A ) ) { ... }

It is also possible to check if a matrix expression results in an identity matrix:

if( isIdentity( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isLower ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is a lower triangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is a lower triangular matrix, false if not.

This function checks if the given dense matrix is a lower triangular matrix. The matrix is considered to be lower triangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} l_{0,0} & 0 & 0 & \cdots & 0 \\ l_{1,0} & l_{1,1} & 0 & \cdots & 0 \\ l_{2,0} & l_{2,1} & l_{2,2} & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ l_{N,0} & l_{N,1} & l_{N,2} & \cdots & l_{N,N} \\ \end{array}\right).\]

$ 0 \times 0 $ or $ 1 \times 1 $ matrices are considered as trivially lower triangular. The following code example demonstrates the use of the function:

// ... Initialization
if( isLower( A ) ) { ... }

It is also possible to check if a matrix expression results in a lower triangular matrix:

if( isLower( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isnan ( const DenseMatrix< MT, SO > &  dm)

Checks the given dense matrix for not-a-number elements.

Parameters
dmThe matrix to be checked for not-a-number elements.
Returns
true if at least one element of the matrix is not-a-number, false otherwise.

This function checks the dense matrix for not-a-number (NaN) elements. If at least one element of the matrix is not-a-number, the function returns true, otherwise it returns false.

// ... Initialization
if( isnan( A ) ) { ... }

Note that this function only works for matrices with floating point elements. The attempt to use it for a matrix with a non-floating point element type results in a compile time error.

template<typename MT , bool SO>
bool blaze::isStrictlyLower ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is a strictly lower triangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is a strictly lower triangular matrix, false if not.

This function checks if the given dense matrix is a strictly lower triangular matrix. The matrix is considered to be strictly lower triangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} 0 & 0 & 0 & \cdots & 0 \\ l_{1,0} & 0 & 0 & \cdots & 0 \\ l_{2,0} & l_{2,1} & 0 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ l_{N,0} & l_{N,1} & l_{N,2} & \cdots & 0 \\ \end{array}\right).\]

The following code example demonstrates the use of the function:

// ... Initialization
if( isStrictlyLower( A ) ) { ... }

It is also possible to check if a matrix expression results in a strictly lower triangular matrix:

if( isStrictlyLower( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isStrictlyUpper ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is a strictly upper triangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is a strictly upper triangular matrix, false if not.

This function checks if the given dense matrix is a strictly upper triangular matrix. The matrix is considered to be strictly upper triangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} 0 & u_{0,1} & u_{0,2} & \cdots & u_{0,N} \\ 0 & 0 & u_{1,2} & \cdots & u_{1,N} \\ 0 & 0 & 0 & \cdots & u_{2,N} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 0 \\ \end{array}\right).\]

The following code example demonstrates the use of the function:

// ... Initialization
if( isStrictlyUpper( A ) ) { ... }

It is also possible to check if a matrix expression results in a strictly upper triangular matrix:

if( isStrictlyUpper( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isSymmetric ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is symmetric.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is symmetric, false if not.

This function checks if the given dense matrix is symmetric. The matrix is considered to be symmetric if it is a square matrix whose transpose is equal to itself ( $ A = A^T $). The following code example demonstrates the use of the function:

// ... Initialization
if( isSymmetric( A ) ) { ... }

It is also possible to check if a matrix expression results in a symmetric matrix:

if( isSymmetric( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isUniform ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is a uniform matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is a uniform matrix, false if not.

This function checks if the given dense matrix is a uniform matrix. The matrix is considered to be uniform if all its elements are identical. The following code example demonstrates the use of the function:

// ... Initialization
if( isUniform( A ) ) { ... }

It is also possible to check if a matrix expression results in a uniform matrix:

if( isUniform( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isUniLower ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is a lower unitriangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is a lower unitriangular matrix, false if not.

This function checks if the given dense matrix is a lower unitriangular matrix. The matrix is considered to be lower unitriangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} 1 & 0 & 0 & \cdots & 0 \\ l_{1,0} & 1 & 0 & \cdots & 0 \\ l_{2,0} & l_{2,1} & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ l_{N,0} & l_{N,1} & l_{N,2} & \cdots & 1 \\ \end{array}\right).\]

The following code example demonstrates the use of the function:

// ... Initialization
if( isUniLower( A ) ) { ... }

It is also possible to check if a matrix expression results in a lower unitriangular matrix:

if( isUniLower( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isUniUpper ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is an upper unitriangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is an upper unitriangular matrix, false if not.

This function checks if the given dense matrix is an upper unitriangular matrix. The matrix is considered to be upper unitriangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} 1 & u_{0,1} & u_{0,2} & \cdots & u_{0,N} \\ 0 & 1 & u_{1,2} & \cdots & u_{1,N} \\ 0 & 0 & 1 & \cdots & u_{2,N} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \\ \end{array}\right).\]

The following code example demonstrates the use of the function:

// ... Initialization
if( isUniUpper( A ) ) { ... }

It is also possible to check if a matrix expression results in an upper unitriangular matrix:

if( isUniUpper( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
bool blaze::isUpper ( const DenseMatrix< MT, SO > &  dm)

Checks if the given dense matrix is an upper triangular matrix.

Parameters
dmThe dense matrix to be checked.
Returns
true if the matrix is an upper triangular matrix, false if not.

This function checks if the given dense matrix is an upper triangular matrix. The matrix is considered to be upper triangular if it is a square matrix of the form

\[\left(\begin{array}{*{5}{c}} u_{0,0} & u_{0,1} & u_{0,2} & \cdots & u_{0,N} \\ 0 & u_{1,1} & u_{1,2} & \cdots & u_{1,N} \\ 0 & 0 & u_{2,2} & \cdots & u_{2,N} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & u_{N,N} \\ \end{array}\right).\]

$ 0 \times 0 $ or $ 1 \times 1 $ matrices are considered as trivially upper triangular. The following code example demonstrates the use of the function:

// ... Initialization
if( isUpper( A ) ) { ... }

It is also possible to check if a matrix expression results in an upper triangular matrix:

if( isUpper( A * B ) ) { ... }

However, note that this might require the complete evaluation of the expression, including the generation of a temporary matrix.

template<typename MT , bool SO>
const MT::ElementType blaze::max ( const DenseMatrix< MT, SO > &  dm)

Returns the largest element of the dense matrix.

Parameters
dmThe given dense matrix.
Returns
The largest dense matrix element.

This function returns the largest element of the given dense matrix. This function can only be used for element types that support the smaller-than relationship. In case the matrix currently has either 0 rows or 0 columns, the returned value is the default value (e.g. 0 in case of fundamental data types).

template<typename MT , bool SO>
const MT::ElementType blaze::min ( const DenseMatrix< MT, SO > &  dm)

Returns the smallest element of the dense matrix.

Parameters
dmThe given dense matrix.
Returns
The smallest dense matrix element.

This function returns the smallest element of the given dense matrix. This function can only be used for element types that support the smaller-than relationship. In case the matrix currently has either 0 rows or 0 columns, the returned value is the default value (e.g. 0 in case of fundamental data types).

template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= ( const DenseMatrix< T1, SO1 > &  lhs,
const DenseMatrix< T2, SO2 > &  rhs 
)
inline

Inequality operator for the comparison of two dense matrices.

Parameters
lhsThe left-hand side dense matrix for the comparison.
rhsThe right-hand side dense matrix for the comparison.
Returns
true if the two matrices are not equal, false if they are equal.
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= ( const DenseMatrix< T1, SO1 > &  lhs,
const SparseMatrix< T2, SO2 > &  rhs 
)
inline

Inequality operator for the comparison of a dense matrix and a sparse matrix.

Parameters
lhsThe left-hand side dense matrix for the comparison.
rhsThe right-hand side sparse matrix for the comparison.
Returns
true if the two matrices are not equal, false if they are equal.
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator!= ( const SparseMatrix< T1, SO1 > &  lhs,
const DenseMatrix< T2, SO2 > &  rhs 
)
inline

Inequality operator for the comparison of a sparse matrix and a dense matrix.

Parameters
lhsThe left-hand side sparse matrix for the comparison.
rhsThe right-hand side dense matrix for the comparison.
Returns
true if the two matrices are not equal, false if they are equal.
template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator!= ( const DenseMatrix< T1, SO > &  mat,
T2  scalar 
)
inline

Inequality operator for the comparison of a dense matrix and a scalar value.

Parameters
matThe left-hand side dense matrix for the comparison.
scalarThe right-hand side scalar value for the comparison.
Returns
true if at least one element of the matrix is different from the scalar, false if not.

If one value of the matrix is inequal to the scalar value, the inequality test returns true, otherwise false. Note that this function can only be used with built-in, numerical data types!

template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric<T1>, bool >::Type blaze::operator!= ( T1  scalar,
const DenseMatrix< T2, SO > &  mat 
)
inline

Inequality operator for the comparison of a scalar value and a dense matrix.

Parameters
scalarThe left-hand side scalar value for the comparison.
matThe right-hand side dense matrix for the comparison.
Returns
true if at least one element of the matrix is different from the scalar, false if not.

If one value of the matrix is inequal to the scalar value, the inequality test returns true, otherwise false. Note that this function can only be used with built-in, numerical data types!

template<typename T1 , bool SO, typename T2 >
const EnableIf< IsNumeric<T2>, typename MultExprTrait<T1,T2>::Type >::Type blaze::operator* ( const DenseMatrix< T1, SO > &  mat,
T2  scalar 
)
inline

Multiplication operator for the multiplication of a dense matrix and a scalar value ( $ A=B*s $).

Parameters
matThe left-hand side dense matrix for the multiplication.
scalarThe right-hand side scalar value for the multiplication.
Returns
The scaled result matrix.

This operator represents the multiplication between a dense matrix and a scalar value:

// ... Resizing and initialization
B = A * 1.25;

The operator returns an expression representing a dense matrix of the higher-order element type of the involved data types T1::ElementType and T2. Note that this operator only works for scalar values of built-in data type.

template<typename T1 , typename T2 , bool SO>
const EnableIf< IsNumeric<T1>, typename MultExprTrait<T1,T2>::Type >::Type blaze::operator* ( T1  scalar,
const DenseMatrix< T2, SO > &  mat 
)
inline

Multiplication operator for the multiplication of a scalar value and a dense matrix ( $ A=s*B $).

Parameters
scalarThe left-hand side scalar value for the multiplication.
matThe right-hand side dense matrix for the multiplication.
Returns
The scaled result matrix.

This operator represents the multiplication between a a scalar value and dense matrix:

// ... Resizing and initialization
B = 1.25 * A;

The operator returns an expression representing a dense matrix of the higher-order element type of the involved data types T1 and T2::ElementType. Note that this operator only works for scalar values of built-in data type.

template<typename T1 , typename T2 >
const SMatTDMatMultExpr<T1,T2> blaze::operator* ( const SparseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of a row-major sparse matrix and a column-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side sparse matrix for the multiplication.
rhsThe right-hand side dense matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a row-major sparse matrix and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatTSMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, false > &  lhs,
const SparseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of a row-major dense matrix and a column-major sparse matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side dense matrix for the multiplication.
rhsThe right-hand side sparse matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a row-major dense matrix and a column-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TSMatDMatMultExpr<T1,T2> blaze::operator* ( const SparseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of a column-major sparse matrix and a row-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side sparse matrix for the multiplication.
rhsThe right-hand side dense matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a column-major sparse matrix and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DisableIf< IsMatMatMultExpr<T2>, TSVecDMatMultExpr<T1,T2> >::Type blaze::operator* ( const SparseVector< T1, true > &  vec,
const DenseMatrix< T2, false > &  mat 
)
inline

Multiplication operator for the multiplication of a transpose sparse vector and a row-major dense matrix ( $ \vec{y}^T=\vec{x}^T*A $).

Parameters
vecThe left-hand side transpose sparse vector for the multiplication.
matThe right-hand side row-major dense matrix for the multiplication.
Returns
The resulting transpose vector.
Exceptions
std::invalid_argumentVector and matrix sizes do not match.

This operator represents the multiplication between a transpose sparse vector and a row-major dense matrix:

// ... Resizing and initialization
y = x * A;

The operator returns an expression representing a transpose sparse vector of the higher-order element type of the two involved element types T1::ElementType and T2::ElementType. Both the dense matrix type T1 and the dense vector type T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current size of the vector vec doesn't match the current number of rows of the matrix mat, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DVecTDVecMultExpr<T1,T2> blaze::operator* ( const DenseVector< T1, false > &  lhs,
const DenseVector< T2, true > &  rhs 
)
inline

Multiplication operator for the outer product of two dense vectors ( $ A=\vec{b}*\vec{c}^T $).

Parameters
lhsThe left-hand side dense vector for the outer product.
rhsThe right-hand side transpose dense vector for the outer product.
Returns
The resulting dense matrix.

This operator represents the outer product between a dense vector and a transpose dense vector:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved element types T1::ElementType and T2::ElementType. Both dense vector types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.

template<typename T1 , typename T2 >
const TSMatTDMatMultExpr<T1,T2> blaze::operator* ( const SparseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of a column-major sparse matrix and a column-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side sparse matrix for the multiplication.
rhsThe right-hand side dense matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a column-major sparse matrix and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatSMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, false > &  lhs,
const SparseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of a row-major dense matrix and a row-major sparse matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side dense matrix for the multiplication.
rhsThe right-hand side sparse matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a row-major dense matrix and a row-major sparse matrix:

// ... Resizing and initialization
C = A * B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const SMatDMatMultExpr<T1,T2> blaze::operator* ( const SparseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of a row-major sparse matrix and a row-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side sparse matrix for the multiplication.
rhsThe right-hand side dense matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a row-major sparse matrix and a row-major dense matrix:

// ... Resizing and initialization
C = A * B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatTSMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, true > &  lhs,
const SparseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of a column-major dense matrix and a column-major sparse matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side dense matrix for the multiplication.
rhsThe right-hand side sparse matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a column-major dense matrix and a column-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatSMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, true > &  lhs,
const SparseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of a column-major dense matrix and a row-major sparse matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side dense matrix for the multiplication.
rhsThe right-hand side sparse matrix for the multiplication.
Returns
The resulting matrix.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the multiplication of a column-major dense matrix and a row-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DisableIf< IsMatMatMultExpr<T2>, TDVecTDMatMultExpr<T1,T2> >::Type blaze::operator* ( const DenseVector< T1, true > &  vec,
const DenseMatrix< T2, true > &  mat 
)
inline

Multiplication operator for the multiplication of a transpose dense vector and a column-major dense matrix ( $ \vec{y}^T=\vec{x}^T*A $).

Parameters
vecThe left-hand side transpose dense vector for the multiplication.
matThe right-hand side column-major dense matrix for the multiplication.
Returns
The resulting transpose vector.
Exceptions
std::invalid_argumentVector and matrix sizes do not match.

This operator represents the multiplication between a transpose dense vector and a column-major dense matrix:

The operator returns an expression representing a transpose dense vector of the higher-order element type of the two involved element types T1::ElementType and T2::ElementType. Both the dense matrix type T1 and the dense vector type T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current size of the vector vec doesn't match the current number of rows of the matrix mat, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatTDMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of a row-major dense matrix and a column-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side matrix for the multiplication.
rhsThe right-hand side matrix for the multiplication.
Returns
The resulting matrix.

This operator represents the multiplication of a row-major dense matrix and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current number of columns of lhs and the current number of rows of rhs don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatDMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of two row-major dense matrices ( $ A=B*C $).

Parameters
lhsThe left-hand side matrix for the multiplication.
rhsThe right-hand side matrix for the multiplication.
Returns
The resulting matrix.

This operator represents the multiplication of two row-major dense matrices:

// ... Resizing and initialization
C = A * B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current number of columns of lhs and the current number of rows of rhs don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatTDMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Multiplication operator for the multiplication of two column-major dense matrices ( $ A=B*C $).

Parameters
lhsThe left-hand side matrix for the multiplication.
rhsThe right-hand side matrix for the multiplication.
Returns
The resulting matrix.

This operator represents the multiplication of two column-major dense matrices:

// ... Resizing and initialization
C = A * B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current number of columns of lhs and the current number of rows of rhs don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatDMatMultExpr<T1,T2> blaze::operator* ( const DenseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Multiplication operator for the multiplication of a column-major dense matrix and a row-major dense matrix ( $ A=B*C $).

Parameters
lhsThe left-hand side matrix for the multiplication.
rhsThe right-hand side matrix for the multiplication.
Returns
The resulting matrix.

This operator represents the multiplication of a column-major dense matrix and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the MultTrait class template.
In case the current number of columns of lhs and the current number of rows of rhs don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 , bool SO>
const DMatSMatAddExpr<T1,T2,SO> blaze::operator+ ( const DenseMatrix< T1, SO > &  lhs,
const SparseMatrix< T2, SO > &  rhs 
)
inline

Addition operator for the addition of a dense matrix and a sparse matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side sparse matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a dense matrix and a sparse matrix:

// ... Resizing and initialization
C = A + B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatSMatAddExpr<T1,T2> blaze::operator+ ( const DenseMatrix< T1, true > &  lhs,
const SparseMatrix< T2, false > &  rhs 
)

Addition operator for the addition of a column-major dense matrix and a row-major sparse matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side sparse matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a column-major dense matrix and a row-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatTSMatAddExpr<T1,T2> blaze::operator+ ( const DenseMatrix< T1, false > &  lhs,
const SparseMatrix< T2, true > &  rhs 
)

Addition operator for the addition of a row-major dense matrix and a column-major sparse matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side sparse matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a row-major dense matrix and a column-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 , bool SO>
const DMatSMatAddExpr<T2,T1,SO> blaze::operator+ ( const SparseMatrix< T1, SO > &  lhs,
const DenseMatrix< T2, SO > &  rhs 
)
inline

Addition operator for the addition of a sparse matrix and a dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a sparse matrix and a dense matrix:

// ... Resizing and initialization
C = A + B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatSMatAddExpr<T1,T2> blaze::operator+ ( const SparseMatrix< T2, false > &  lhs,
const DenseMatrix< T1, true > &  rhs 
)

Addition operator for the addition of a row-major sparse matrix and a column-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a row-major sparse matrix and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatTSMatAddExpr<T1,T2> blaze::operator+ ( const SparseMatrix< T2, true > &  lhs,
const DenseMatrix< T1, false > &  rhs 
)

Addition operator for the addition of a column-major sparse matrix and a row-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the addition of a column-major sparse matrix and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric<T1> >, Not< IsSymmetric<T2> > > , const DMatTDMatAddExpr<T1,T2> >::Type blaze::operator+ ( const DenseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Addition operator for the addition of a row-major and a colum-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the addition of a row-major and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric<T1> >, Not< IsSymmetric<T2> > > , const DMatTDMatAddExpr<T2,T1> >::Type blaze::operator+ ( const DenseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Addition operator for the addition of a column-major and a row-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the addition of a column-major and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 , bool SO>
const DMatDMatAddExpr<T1,T2,SO> blaze::operator+ ( const DenseMatrix< T1, SO > &  lhs,
const DenseMatrix< T2, SO > &  rhs 
)
inline

Addition operator for the addition of two dense matrices with identical storage order ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix addition.
rhsThe right-hand side dense matrix to be added to the left-hand side matrix.
Returns
The sum of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the addition of two dense matrices with identical storage order:

// ... Resizing and initialization
C = A + B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the AddTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 , bool SO>
const SMatDMatSubExpr<T1,T2,SO> blaze::operator- ( const SparseMatrix< T1, SO > &  lhs,
const DenseMatrix< T2, SO > &  rhs 
)
inline

Subtraction operator for the subtraction of a sparse matrix and a dense matrix with identical storage order ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the sparse matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a sparse matrix and a dense matrix with identical storage order:

// ... Resizing and initialization
C = A - B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TSMatDMatSubExpr<T1,T2> blaze::operator- ( const SparseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Subtraction operator for the subtraction of a column-major sparse matrix and a row-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the sparse matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a column-major sparse matrix and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const SMatTDMatSubExpr<T1,T2> blaze::operator- ( const SparseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Subtraction operator for the subtraction of a row-major sparse matrix and a column-major dense matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side sparse matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the sparse matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a row-major sparse matrix and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 , bool SO>
const DMatSMatSubExpr<T1,T2,SO> blaze::operator- ( const DenseMatrix< T1, SO > &  lhs,
const SparseMatrix< T2, SO > &  rhs 
)
inline

Subtraction operator for the subtraction of a dense matrix and a sparse matrix with identical storage order ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side sparse matrix to be subtracted from the dense matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a dense matrix and a sparse matrix with identical storage order:

// ... Resizing and initialization
C = A - B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const TDMatSMatSubExpr<T1,T2> blaze::operator- ( const DenseMatrix< T1, true > &  lhs,
const SparseMatrix< T2, false > &  rhs 
)
inline

Subtraction operator for the subtraction of a column-major dense matrix and a row-major sparse matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side sparse matrix to be subtracted from the dense matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a column-major dense matrix and a row-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
const DMatTSMatSubExpr<T1,T2> blaze::operator- ( const DenseMatrix< T1, false > &  lhs,
const SparseMatrix< T2, true > &  rhs 
)
inline

Subtraction operator for the subtraction of a row-major dense matrix and a column-major sparse matrix ( $ A=B+C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side sparse matrix to be subtracted from the dense matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match.

This operator represents the subtraction of a row-major dense matrix and a column-major sparse matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current sizes of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric<T1> >, Not< IsSymmetric<T2> > > , const DMatTDMatSubExpr<T1,T2> >::Type blaze::operator- ( const DenseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Subtraction operator for the subtraction of a row-major and a column-major dense matrix ( $ A=B-C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the left-hand side matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the subtraction of a row-major and a column-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , typename T2 >
EnableIf< And< Not< IsSymmetric<T1> >, Not< IsSymmetric<T2> > > , const DMatTDMatSubExpr<T1,T2> >::Type blaze::operator- ( const DenseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Subtraction operator for the subtraction of a column-major and a row-major dense matrix ( $ A=B-C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the left-hand side matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the subtraction of a column-major and a row-major dense matrix:

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename MT , bool SO>
const DMatScalarMultExpr<MT,typename BaseElementType<MT>::Type,SO> blaze::operator- ( const DenseMatrix< MT, SO > &  dm)
inline

Unary minus operator for the negation of a dense matrix ( $ A = -B $).

Parameters
dmThe dense matrix to be negated.
Returns
The negation of the matrix.

This operator represents the negation of a dense matrix:

// ... Resizing and initialization
B = -A;

The operator returns an expression representing the negation of the given dense matrix.

template<typename T1 , typename T2 , bool SO>
const DMatDMatSubExpr<T1,T2,SO> blaze::operator- ( const DenseMatrix< T1, SO > &  lhs,
const DenseMatrix< T2, SO > &  rhs 
)
inline

Subtraction operator for the subtraction of two dense matrices with identical storage order ( $ A=B-C $).

Parameters
lhsThe left-hand side dense matrix for the matrix subtraction.
rhsThe right-hand side dense matrix to be subtracted from the left-hand side matrix.
Returns
The difference of the two matrices.
Exceptions
std::invalid_argumentMatrix sizes do not match

This operator represents the subtraction of two dense matrices with identical storage order:

// ... Resizing and initialization
C = A - B;

The operator returns an expression representing a dense matrix of the higher-order element type of the two involved matrix element types T1::ElementType and T2::ElementType. Both matrix types T1 and T2 as well as the two element types T1::ElementType and T2::ElementType have to be supported by the SubTrait class template.
In case the current number of rows and columns of the two given matrices don't match, a std::invalid_argument is thrown.

template<typename T1 , bool SO, typename T2 >
const EnableIf< IsNumeric<T2>, typename DivExprTrait<T1,T2>::Type >::Type blaze::operator/ ( const DenseMatrix< T1, SO > &  mat,
T2  scalar 
)
inline

Division operator for the division of a dense matrix by a scalar value ( $ A=B/s $).

Parameters
matThe left-hand side dense matrix for the division.
scalarThe right-hand side scalar value for the division.
Returns
The scaled result matrix.

This operator represents the division of a dense matrix by a scalar value:

// ... Resizing and initialization
B = A / 0.24;

The operator returns an expression representing a dense matrix of the higher-order element type of the involved data types T1::ElementType and T2. Note that this operator only works for scalar values of built-in data type.

Note: A division by zero is only checked by an user assert.

template<typename T1 , typename T2 >
bool blaze::operator== ( const DenseMatrix< T1, false > &  lhs,
const DenseMatrix< T2, false > &  rhs 
)
inline

Equality operator for the comparison of two rwo-major dense matrices.

Parameters
lhsThe left-hand side matrix for the comparison.
rhsThe right-hand side matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , typename T2 >
bool blaze::operator== ( const DenseMatrix< T1, true > &  lhs,
const DenseMatrix< T2, true > &  rhs 
)
inline

Equality operator for the comparison of two column-major dense matrices.

Parameters
lhsThe left-hand side matrix for the comparison.
rhsThe right-hand side matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== ( const DenseMatrix< T1, SO > &  lhs,
const DenseMatrix< T2,!SO > &  rhs 
)
inline

Equality operator for the comparison of two dense matrices with different storage order.

Parameters
lhsThe left-hand side matrix for the comparison.
rhsThe right-hand side matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== ( const DenseMatrix< T1, SO > &  lhs,
const SparseMatrix< T2, false > &  rhs 
)
inline

Equality operator for the comparison of a dense matrix and a row-major sparse matrix.

Parameters
lhsThe left-hand side dense matrix for the comparison.
rhsThe right-hand side row-major sparse matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , typename T2 , bool SO>
bool blaze::operator== ( const DenseMatrix< T1, SO > &  lhs,
const SparseMatrix< T2, true > &  rhs 
)
inline

Equality operator for the comparison of a dense matrix and a column-major sparse matrix.

Parameters
lhsThe left-hand side dense matrix for the comparison.
rhsThe right-hand side column-major sparse matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , bool SO1, typename T2 , bool SO2>
bool blaze::operator== ( const SparseMatrix< T1, SO1 > &  lhs,
const DenseMatrix< T2, SO2 > &  rhs 
)
inline

Equality operator for the comparison of a sparse matrix and a dense matrix.

Parameters
lhsThe left-hand side sparse matrix for the comparison.
rhsThe right-hand side dense matrix for the comparison.
Returns
true if the two matrices are equal, false if not.
template<typename T1 , typename T2 >
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator== ( const DenseMatrix< T1, false > &  mat,
T2  scalar 
)
inline

Equality operator for the comparison of a row-major dense matrix and a scalar value.

Parameters
matThe left-hand side row-major dense matrix for the comparison.
scalarThe right-hand side scalar value for the comparison.
Returns
true if all elements of the matrix are equal to the scalar, false if not.

If all values of the matrix are equal to the scalar value, the equality test returns true, otherwise false. Note that this function can only be used with built-in, numerical data types!

template<typename T1 , typename T2 >
EnableIf< IsNumeric< T2 >, bool >::Type blaze::operator== ( const DenseMatrix< T1, true > &  mat,
T2  scalar 
)
inline

Equality operator for the comparison of a column-major dense matrix and a scalar value.

Parameters
matThe left-hand side column-major dense matrix for the comparison.
scalarThe right-hand side scalar value for the comparison.
Returns
true if all elements of the matrix are equal to the scalar, false if not.

If all values of the matrix are equal to the scalar value, the equality test returns true, otherwise false. Note that this function can only be used with built-in, numerical data types!

template<typename T1 , typename T2 , bool SO>
EnableIf< IsNumeric<T1>, bool >::Type blaze::operator== ( T1  scalar,
const DenseMatrix< T2, SO > &  mat 
)
inline

Equality operator for the comparison of a scalar value and a dense matrix.

Parameters
scalarThe left-hand side scalar value for the comparison.
matThe right-hand side dense matrix for the comparison.
Returns
true if all elements of the matrix are equal to the scalar, false if not.

If all values of the matrix are equal to the scalar value, the equality test returns true, otherwise false. Note that this function can only be used with built-in, numerical data types!

template<typename MT , bool SO>
const DMatSerialExpr< MT, SO > blaze::serial ( const DenseMatrix< MT, SO > &  dm)
inline

Forces the serial evaluation of the given dense matrix expression dm.

Parameters
dmThe input matrix.
Returns
The evaluated dense matrix.

The serial function forces the serial evaluation of the given dense matrix expression dm. The function returns an expression representing the operation.
The following example demonstrates the use of the serial function

// ... Resizing and initialization
B = serial( A );
template<typename MT , bool SO>
const DMatTransExpr< MT,!SO > blaze::trans ( const DenseMatrix< MT, SO > &  dm)
inline

Calculation of the transpose of the given dense matrix.

Parameters
dmThe dense matrix to be transposed.
Returns
The transpose of the matrix.

This function returns an expression representing the transpose of the given dense matrix: