Document CwiseNullaryOp

Submitted by Bruno Daniel

Assigned to Nobody

Link to original bugzilla bug (#457)
Version: 3.0

Description

I'd like to suggest a new matrix type derived from MatrixBase with roughly the

following constructor and behavior:

/**

CalcMatrix is a read-only matrix without storage recalculating the
coefficients in each coeff() call by calling the user function func lazily.
func may be a function pointer, an object with overloaded operator() or
one of C++0x's lambda functions, std::function.
coeff(i, j) is calculated as
func(rowOffset + i * rowStride, colOffset + j * colStride)
This is for matrices where the repeated recalculation of the coefficients
is less costly than creating and accessing the storage only a small but
part of the coefficients is actually accessed (which part is only known at
runtime).
The common views of CalcMatrix are easily implemented:
(Nontrivial rowStride and colStride settings are propagated to the
views. m_... is the member corresponding to the constructor parameter.)
- row(i) = CalcMatrix(1, cols(), m_func, i, 0, m_rowStride)
- col(j) = CalcMatrix(rows(), 1, m_func, 0, j, 1, m_colStride)
- diagonal() = CalcMatrix(rows(), 1, m_func, 0, 0,
```
cols() * m_colStride + m_rowStride)  
```
- block(i, j, rows, cols) = CalcMatrix(rows, cols, m_func, i, j,
```
 m_rowStride, m_colStride)  
```
Applications:
- iota(n) = CalcMatrix(n, [](Index i) { return i; })
- Permuted-rows view of another matrix A or a selection of a subset of rows
of A in any order:
permute_rows(A, perm) =
CalcMatrix(perm.size(), A.cols(),
& { return A(perm(i), j); }
- access to non-contiguous matrix layouts of external libraries.
- Kronecker delta: probably better accomplished with
VectorXd::Ones(rows).asDiagonal()

*/

template <typename Functype>

CalcMatrix(Index rows, Index cols, Functype& func,

Index rowOffset, Index colOffset, Index rowStride = 1, Index colStride = 1);

As an optimization, rowStride and colStride (and rowOffset, colOffset) could

also be offered as compile-time parameters in order to make

func(rowOffset + i * rowStride, colOffset + j * colStride)

less costly.

A similar subclass for ArrayBase would have to be added in order to be able

to call array() without significant overhead.

Depends on

Blocking