Slicing and Indexing

This page presents the numerous possibilities offered by operator() to index sub-set of rows and columns. This API has been introduced in Eigen 3.4. It supports all the feature proposed by the block API , and much more. In particular, it supports slicing that consists in taking a set of rows, columns, or elements, uniformly spaced within a matrix or indexed from an array of indices.

Overview

All the aforementioned operations are handled through the generic DenseBase::operator()(const RowIndices&, const ColIndices&) method. Each argument can be:

• An integer indexing a single row or column, including symbolic indices.
• The symbol Eigen::placeholders::all representing the whole set of respective rows or columns in increasing order.
• An ArithmeticSequence as constructed by the Eigen::seq, Eigen::seqN, or Eigen::placeholders::lastN functions.
• Any 1D vector/array of integers including Eigen's vector/array, expressions, std::vector, std::array, as well as plain C arrays: int[N].

More generally, it can accepts any object exposing the following two member functions:

<integral type> operator[](<integral type>) const;
<integral type> size() const;

where <integral type> stands for any integer type compatible with Eigen::Index (i.e. std::ptrdiff_t).

Basic slicing

Taking a set of rows, columns, or elements, uniformly spaced within a matrix or vector is achieved through the Eigen::seq or Eigen::seqN functions where "seq" stands for arithmetic sequence. Their signatures are summarized below:

function	description	example
seq(firstIdx,lastIdx)	represents the sequence of integers ranging from firstIdx to lastIdx	seq(2,5) <=> {2,3,4,5}
seq(firstIdx,lastIdx,incr)	same but using the increment incr to advance from one index to the next	seq(2,8,2) <=> {2,4,6,8}
seqN(firstIdx,size)	represents the sequence of size integers starting from firstIdx	seqN(2,5) <=> {2,3,4,5,6}
seqN(firstIdx,size,incr)	same but using the increment incr to advance from one index to the next	seqN(2,3,3) <=> {2,5,8}

The firstIdx and lastIdx parameters can also be defined with the help of the Eigen::last symbol representing the index of the last row, column or element of the underlying matrix/vector once the arithmetic sequence is passed to it through operator(). Here are some examples for a 2D array/matrix A and a 1D array/vector v.

Intent	Code	Block-API equivalence
Bottom-left corner starting at row i with n columns	A(seq(i,last), seqN(0,n))	A.bottomLeftCorner(A.rows()-i,n)
Block starting at i,j having m rows, and n columns	A(seqN(i,m), seqN(i,n))	A.block(i,j,m,n)
Block starting at i0,j0 and ending at i1,j1	A(seq(i0,i1), seq(j0,j1)	A.block(i0,j0,i1-i0+1,j1-j0+1)
Even columns of A	A(all, seq(0,last,2))
First n odd rows A	A(seqN(1,n,2), all)
The last past one column	A(all, last-1)	A.col(A.cols()-2)
The middle row	A(last/2,all)	A.row((A.rows()-1)/2)
Last elements of v starting at i	v(seq(i,last))	v.tail(v.size()-i)
Last n elements of v	v(seq(last+1-n,last))	v.tail(n)

As seen in the last example, referencing the last n elements (or rows/columns) is a bit cumbersome to write. This becomes even more tricky and error prone with a non-default increment. Here comes Eigen::placeholders::lastN(size) , and Eigen::placeholders::lastN(size,incr) :

Intent	Code	Block-API equivalence
Last n elements of v	v(lastN(n))	v.tail(n)
Bottom-right corner of A of size m times n	A(lastN(m), lastN(n))	A.bottomRightCorner(m,n)
Bottom-right corner of A of size m times n	A(lastN(m), lastN(n))	A.bottomRightCorner(m,n)
Last n columns taking 1 column over 3	A(all, lastN(n,3))

Compile time size and increment

In terms of performance, Eigen and the compiler can take advantage of compile-time size and increment. To this end, you can enforce compile-time parameters using Eigen::fix<val>. Such compile-time value can be combined with the Eigen::last symbol:

v(seq(last-fix<7>, last-fix<2>))

In this example Eigen knowns at compile-time that the returned expression has 6 elements. It is equivalent to:

v(seqN(last-7, fix<6>))

We can revisit the even columns of A example as follows:

A(all, seq(0,last,fix<2>))

Reverse order

Row/column indices can also be enumerated in decreasing order using a negative increment. For instance, one over two columns of A from the column 20 to 10:

A(all, seq(20, 10, fix<-2>))

The last n rows starting from the last one:

A(seqN(last, n, fix<-1>), all)

You can also use the ArithmeticSequence::reverse() method to reverse its order. The previous example can thus also be written as:

A(lastN(n).reverse(), all)

Array of indices

The generic operator() can also takes as input an arbitrary list of row or column indices stored as either an ArrayXi, a std::vector<int>, std::array<int,N>, etc.

Example:	Output:
std::vector<int> ind{4,2,5,5,3}; MatrixXi A = MatrixXi::Random(4,6); cout << "Initial matrix A:\n" << A << "\n\n"; cout << "A(all,ind):\n" << A(Eigen::placeholders::all,ind) << "\n\n";	Initial matrix A: 7 9 -5 -3 3 -10 -2 -6 1 0 5 -5 6 -3 0 9 -8 -8 6 6 3 9 2 6 A(all,ind): 3 -5 -10 -10 -3 5 1 -5 -5 0 -8 0 -8 -8 9 2 3 6 6 9

You can also directly pass a static array:

Example:	Output:
MatrixXi A = MatrixXi::Random(4,6); cout << "Initial matrix A:\n" << A << "\n\n"; cout << "A(all,{4,2,5,5,3}):\n" << A(Eigen::placeholders::all,{4,2,5,5,3}) << "\n\n";	Initial matrix A: 7 9 -5 -3 3 -10 -2 -6 1 0 5 -5 6 -3 0 9 -8 -8 6 6 3 9 2 6 A(all,{4,2,5,5,3}): 3 -5 -10 -10 -3 5 1 -5 -5 0 -8 0 -8 -8 9 2 3 6 6 9

or expressions:

Example:	Output:
ArrayXi ind(5); ind<<4,2,5,5,3; MatrixXi A = MatrixXi::Random(4,6); cout << "Initial matrix A:\n" << A << "\n\n"; cout << "A(all,ind-1):\n" << A(Eigen::placeholders::all,ind-1) << "\n\n";	Initial matrix A: 7 9 -5 -3 3 -10 -2 -6 1 0 5 -5 6 -3 0 9 -8 -8 6 6 3 9 2 6 A(all,ind-1): -3 9 3 3 -5 0 -6 5 5 1 9 -3 -8 -8 0 9 6 2 2 3

When passing an object with a compile-time size such as Array4i, std::array<int,N>, or a static array, then the returned expression also exhibit compile-time dimensions.

Custom index list

More generally, operator() can accept as inputs any object ind of type T compatible with:

Index s = ind.size(); or Index s = size(ind);
Index i;
i = ind[i];

This means you can easily build your own fancy sequence generator and pass it to operator(). Here is an example enlarging a given matrix while padding the additional first rows and columns through repetition:

Example:	Output:
struct pad { Index size() const { return out_size; } Index operator[] (Index i) const { return std::max<Index>(0,i-(out_size-in_size)); } Index in_size, out_size; }; Matrix3i A; A.reshaped() = VectorXi::LinSpaced(9,1,9); cout << "Initial matrix A:\n" << A << "\n\n"; MatrixXi B(5,5); B = A(pad{3,5}, pad{3,5}); cout << "A(pad{3,N}, pad{3,N}):\n" << B << "\n\n";	Initial matrix A: 1 4 7 2 5 8 3 6 9 A(pad{3,N}, pad{3,N}): 1 1 1 4 7 1 1 1 4 7 1 1 1 4 7 2 2 2 5 8 3 3 3 6 9