This page explains how to work with "raw" C/C++ arrays. This can be useful in a variety of contexts, particularly when "importing" vectors and matrices from other libraries into Eigen.

Introduction

Occasionally you may have a pre-defined array of numbers that you want to use within Eigen as a vector or matrix. While one option is to make a copy of the data, most commonly you probably want to re-use this memory as an Eigen type. Fortunately, this is very easy with the Map class.

Map types and declaring Map variables

A Map object has a type defined by its Eigen equivalent:

Map<Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime> >

Note that, in this default case, a Map requires just a single template parameter.

To construct a Map variable, you need two other pieces of information: a pointer to the region of memory defining the array of coefficients, and the desired shape of the matrix or vector. For example, to define a matrix of float with sizes determined at compile time, you might do the following:

Map<MatrixXf> mf(pf,rows,columns);

where pf is a float * pointing to the array of memory. A fixed-size read-only vector of integers might be declared as

Map<const Vector4i> mi(pi);

where pi is an int *. In this case the size does not have to be passed to the constructor, because it is already specified by the Matrix/Array type.

Note that Map does not have a default constructor; you must pass a pointer to initialize the object. However, you can work around this requirement (see Changing the mapped array).

Map is flexible enough to accommodate a variety of different data representations. There are two other (optional) template parameters:

Map<typename MatrixType,
    int MapOptions,
    typename StrideType>

• MapOptions specifies whether the pointer is Aligned, or Unaligned. The default is Unaligned.
• StrideType allows you to specify a custom layout for the memory array, using the Stride class. One example would be to specify that the data array is organized in row-major format:

  Example:	Output:
  int array[8]; for(int i = 0; i < 8; ++i) array[i] = i; cout << "Column-major:\n" << Map<Matrix<int,2,4> >(array) << endl; cout << "Row-major:\n" << Map<Matrix<int,2,4,RowMajor> >(array) << endl; cout << "Row-major using stride:\n" << Map<Matrix<int,2,4>, Unaligned, Stride<1,4> >(array) << endl;	Column-major: 0 2 4 6 1 3 5 7 Row-major: 0 1 2 3 4 5 6 7 Row-major using stride: 0 1 2 3 4 5 6 7

  However, Stride is even more flexible than this; for details, see the documentation for the Map and Stride classes.

Using Map variables

You can use a Map object just like any other Eigen type:

typedef Matrix<float,1,Dynamic> MatrixType;
typedef Map<MatrixType> MapType;
typedef Map<const MatrixType> MapTypeConst;   // a read-only map
const int n_dims = 5;
  
MatrixType m1(n_dims), m2(n_dims);
m1.setRandom();
m2.setRandom();
float *p = &m2(0);  // get the address storing the data for m2
MapType m2map(p,m2.size());   // m2map shares data with m2
MapTypeConst m2mapconst(p,m2.size());  // a read-only accessor for m2
 
cout << "m1: " << m1 << endl;
cout << "m2: " << m2 << endl;
cout << "Squared euclidean distance: " << (m1-m2).squaredNorm() << endl;
cout << "Squared euclidean distance, using map: " <<
  (m1-m2map).squaredNorm() << endl;
m2map(3) = 7;   // this will change m2, since they share the same array
cout << "Updated m2: " << m2 << endl;
cout << "m2 coefficient 2, constant accessor: " << m2mapconst(2) << endl;
/* m2mapconst(2) = 5; */   // this yields a compile-time error

m1:   0.68 -0.211  0.566  0.597  0.823
m2: -0.605  -0.33  0.536 -0.444  0.108
Squared euclidean distance: 3.26
Squared euclidean distance, using map: 3.26
Updated m2: -0.605  -0.33  0.536      7  0.108
m2 coefficient 2, constant accessor: 0.536

All Eigen functions are written to accept Map objects just like other Eigen types. However, when writing your own functions taking Eigen types, this does not happen automatically: a Map type is not identical to its Dense equivalent. See Writing Functions Taking Eigen Types as Parameters for details.

Changing the mapped array

It is possible to change the array of a Map object after declaration, using the C++ "placement new" syntax:

int data[] = {1,2,3,4,5,6,7,8,9};
Map<RowVectorXi> v(data,4);
cout << "The mapped vector v is: " << v << "\n";
new (&v) Map<RowVectorXi>(data+4,5);
cout << "Now v is: " << v << "\n";

The mapped vector v is: 1 2 3 4
Now v is: 5 6 7 8 9

Despite appearances, this does not invoke the memory allocator, because the syntax specifies the location for storing the result.

This syntax makes it possible to declare a Map object without first knowing the mapped array's location in memory:

Map<Matrix3f> A(NULL);  // don't try to use this matrix yet!
VectorXf b(n_matrices);
for (int i = 0; i < n_matrices; i++)
{
  new (&A) Map<Matrix3f>(get_matrix_pointer(i));
  b(i) = A.trace();
}