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New Major Features in Core

  • New support for bfloat16

The 16-bit Brain floating point format[1] is now available as Eigen::bfloat16. The constructor must be called explicitly, but it can otherwise be used as any other scalar type. To convert back-and-forth between uint16_t to extract the bit representation, use Eigen::numext::bit_cast.

  bfloat16 s(0.25);                                 // explicit construction
  uint16_t s_bits = numext::bit_cast<uint16_t>(s);  // bit representation
  using MatrixBf16 = Matrix<bfloat16, Dynamic, Dynamic>;
  MatrixBf16 X = s * MatrixBf16::Random(3, 3);

New backends

    • Unified with CUDA to create a generic GPU backend for NVIDIA/AMD.

Improvements/Cleanups to Core modules

  • Dense matrix decompositions and solvers
    • SVD implementations now have an info() method for checking convergence.
  MatrixXf m = MatrixXf::Random(3,2);
  JacobiSVD<MatrixXf> svd(m, ComputeThinU | ComputeThinV);
  if ( == ComputationInfo::Success) {
    // SVD computation was successful.
    VectorXf x = svd.solve(b);
    • Decompositions now fail quickly when invalid inputs are detected.
    • Fixed aliasing issues with in-place small matrix inversions.
    • Fixed several edge-cases with empty or zero inputs.
  • Sparse matrix support, decompositions and solvers
    • Enabled assignment and addition with diagonal matrices.
  SparseMatrix<float> A(10, 10);
  VectorXf x = VectorXf::Random(10);
  A = x.asDiagonal();
  A += x.asDiagonal();
    • Added new IRDS iterative linear solver.
  A.makeCompressed();   // Recommendation is to compress input before calling sparse solvers.
  IDRS<SparseMatrix<float>, DiagonalPreconditioner<float> > idrs(A);
  if ( == ComputationInfo::Success) {
    VectorXf x = idrs.solve(b);
    • Support added for SuiteSparse KLU routines.
  A.makeCompressed();   // Recommendation is to compress input before calling sparse solvers.
  KLU<SparseMatrix<T> > klu(A);
  if ( == ComputationInfo::Success) {
    VectorXf x = klu.solve(b);
    • SparseCholesky now works with row-major matrices.
    • Various bug fixes and performance improvements.
  • Improved support for half
    • Native support added for ARM __fp16, CUDA/HIP __half, Clang F16C.
    • Better vectorization support added across all backends.
  • Improved bool support
    • Partial vectorization support added for boolean operations.
    • Significantly improved performance (x25) for logical operations with Matrix or Tensor of bool.
  • Improved support for custom types
    • More custom types work out-of-the-box (see #2201[2]).
  • Improved Geometry Module
    • Transform::computeRotationScaling() and Transform::computeScalingRotation() are now more continuous across degeneracies (see !349[3]).
    • New minimal vectorization support added for Quaternion.

Backend-specific improvements

  • SSE/AVX/AVX512
    • Enabled AVX512 instructions by default if available.
    • New std::complex, half, and bfloat16 vectorization support added.
    • Better accuracy for several vectorized math functions including exp, log, pow, sqrt.
    • Many missing packet functions added.
  • GPU (CUDA and HIP)
    • Several optimized math functions added, better support for std::complex.
    • Added option to disable CUDA entirely by defining EIGEN_NO_CUDA.
    • Many more functions can now be used in device code (e.g. comparisons, matrix inversion).
  • ZVector
    • Vectorized float and std::complex<float> support added.
    • Added z14 support.
  • SYCL
    • Redesigned SYCL implementation for use with the Tensor[4] module, which can be enabled by defining EIGEN_USE_SYCL.
    • New generic memory model introduced used by TensorDeviceSycl.
    • Better integration with OpenCL devices.
    • Added many math function specializations.

Miscellaneous API Changes

  • New setOnes() method for filling a dense matrix with ones.
  • New setConstant(NoChange_t, Index, T) methods for preserving one dimension of a matrix.
MatrixXf A(10, 5);
A.setOnes();                         // 10x5  matrix of 1s
A.setConstant(NoChange_t(), 10, 1);  // 10x10 matrix of 2s.
A.setConstant(5, NoChange_t(), 2);   //  5x10 matrix of 3s.
  • Added setUnit(Index i) for vectors that sets the i th coefficient to one and all others to zero.
  • Added transpose(), adjoint(), conjugate() methods to SelfAdjointView.
  • Added shift_left<N>() and shift_right<N>() coefficient-wise array functions.
  • Enabled adding and subtracting of diagonal matrices.
  • Allow user-defined default cache sizes via defining EIGEN_DEFAULT_L1_CACHE_SIZE, ..., EIGEN_DEFAULT_L3_CACHE_SIZE.
  • Added EIGEN_ALIGNOF(X) macro for determining alignment of a provided variable.
  • Allow plugins for VectorwiseOp by defining a file EIGEN_VECTORWISEOP_PLUGIN (e.g. -DEIGEN_VECTORWISEOP_PLUGIN=my_vectorwise_op_plugins.h).
  • Allow disabling of IO operations by defining EIGEN_NO_IO.