Vectors, matrices, linear Algebra


Dynamic and fixed-size vectors and matrices, basic linear Algebra

Design rationale

Unlike in older MRPT 1.x versions, matrices and vectors since MRPT v2.0.0 do no longer inherit from Eigen classes. Instead, they are now thin wrappers around static/dynamic memory containers, which can be casted to Eigen-compatible classes, but which allow most common operations to be done without Eigen.

The reason for this scheme is two-fold:

  • Including Eigen in all headers significantly slows down build times.

  • Backwards-compatible MRPT code required using Eigen’s plugin mechanism to inject code inside Eigen::DenseBase. This was a source of problems when using MRPT in an application that uses Eigen on its own, since an error would be raised in MRPT math headers were not always included first.

Important facts

  • Fixed-size containers should be preferred where possible, since they allow more compile-time optimizations and avoid dynamic memory (de)allocations.

  • Most common uses of vectors and matrices require #include -ing just the corresponding MRPT headers.

  • If some particular feature is not exposed in the MRPT API, then you can map the MRPT container into an Eigen Map and use the regular Eigen API.

  • For fixed-sized matrices and vectors, only a subset of all infinite possible sizes are explicitly instantiated in the mrpt-math library. This means that if you use a non-supported size, you will not have any build error but your program will fail to link. The alternative then is to either use .asEigen() or casting to a dynamic-sized container.

  • Exact list of explicitly-instantiated vectors:

    • mrpt::math::CVectorDynamic<T>: For T = float and T = double. Any dynamic size.

    • mrpt::math::CVectorFixed<T,N> : For T = float and T = double, and N =2,3,4,5,6,7,12.

  • Exact list of explicitly-instantiated matrices:

    • mrpt::math::CMatrixDynamic<T>: For T = float and T = double. Any dynamic size.

    • mrpt::math::CMatrixFixed<T,N,N>: For T = float and T = double, and N =2,3,4,6,7.

  • All matrices and vectors support build-time generation of constexpr strings describing their types, via: [mrpt-typemeta]

  • For binary serialization of dynamic-sized matrices, the following classes are provided which implements the CSerializable interface (see: [mrpt-serialization]):

Example: matrix sum (MRPT methods, no explicit call to Eigen)

#include <mrpt/math/CMatrixDynamic.h>
#include <iostream>
// ...
mrpt::math::CMatrixDouble M1;

auto M2 = mrpt::math::CMatrixDouble::Identity(4);

// Sum:
mrpt::math::CMatrixDouble R = M1 + M2;
std::cout << "R:\n" << R << "\n";

Example: QR-based linear system solving (With explicit call to Eigen)

#include <mrpt/math/CMatrixDynamic.h>
#include <Eigen/Dense>  // Must add this one to use .asEigen()
#include <iostream>
// ...
mrpt::math::CMatrixDouble33 A;

mrpt::math::CVectorDouble<3> b;

mrpt::math::CVectorDouble<3> x;

// Solve Ax=b
x.asEigen() = A.asEigen().fullPivHouseholderQr().solve(x);

std::cout << "x:\n" << x.asString() << "\n";

See list of classes below.