* \brief Generic expression of a matrix where all coefficients are defined by a functor
*
* \param NullaryOp template functor implementing the operator
* \param PlainObjectType the underlying plain matrix/array type
* \tparam NullaryOp template functor implementing the operator
* \tparam PlainObjectType the underlying plain matrix/array type
*
* This class represents an expression of a generic nullary operator.
* It is the return type of the Ones(), Zero(), Constant(), Identity() and Random() methods,
...
...
@@ -27,33 +38,33 @@ namespace Eigen {
* However, if you want to write a function returning such an expression, you
* will need to use this class.
*
* \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr()
* The functor NullaryOp must expose one of the following method:
<table class="manual">
<tr ><td>\c operator()() </td><td>if the procedural generation does not depend on the coefficient entries (e.g., random numbers)</td></tr>
<tr class="alt"><td>\c operator()(Index i)</td><td>if the procedural generation makes sense for vectors only and that it depends on the coefficient index \c i (e.g., linspace) </td></tr>
<tr ><td>\c operator()(Index i,Index j)</td><td>if the procedural generation depends on the matrix coordinates \c i, \c j (e.g., to generate a checkerboard with 0 and 1)</td></tr>
</table>
* It is also possible to expose the last two operators if the generation makes sense for matrices but can be optimized for vectors.
*
* See DenseBase::NullaryExpr(Index,const CustomNullaryOp&) for an example binding
* C++11 random number generators.
*
* A nullary expression can also be used to implement custom sophisticated matrix manipulations
* that cannot be covered by the existing set of natively supported matrix manipulations.
* See this \ref TopicCustomizing_NullaryExpr "page" for some examples and additional explanations
* on the behavior of CwiseNullaryOp.
*
* \sa class CwiseUnaryOp, class CwiseBinaryOp, DenseBase::NullaryExpr
/** \internal \returns the index of the first element of the array that is well aligned for vectorization.
/** \internal \returns the index of the first element of the array stored by \a m that is properly aligned with respect to \a Alignment for vectorization.
*
* \tparam Alignment requested alignment in Bytes.
*
* There is also the variant first_aligned(const Scalar*, Integer) defined in Memory.h. See it for more
Flags=(unsignedint)_MatrixTypeNested::Flags&(RowMajorBit|MaskLvalueBit|DirectAccessBit)&~RowMajorBit,// FIXME DirectAccessBit should not be handled by expressions
/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
* of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
* norm, that is the maximum of the absolute values of the coefficients of *this.
/** \returns the \b coefficient-wise \f$ \ell^p \f$ norm of \c *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
* of the coefficients of \c *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
* norm, that is the maximum of the absolute values of the coefficients of \c *this.
*
* In all cases, if \c *this is empty, then the value 0 is returned.
*
* \note For matrices, this function does not compute the <a href="https://en.wikipedia.org/wiki/Operator_norm">operator-norm</a>. That is, if \c *this is a matrix, then its coefficients are interpreted as a 1D vector. Nonetheless, you can easily compute the 1-norm and \f$\infty\f$-norm matrix operator norms using \link TutorialReductionsVisitorsBroadcastingReductionsNorm partial reductions \endlink.
