Math API

cunls/math contains low-level Lie-group and dense-matrix operations used by state/factor implementations.

Headers:

• cunls/math/lie_math.h

• cunls/math/dense_matrix_ops.h

Common parameter semantics

Most batched math functions in this module follow the same conventions.

Parameters

• stream - [in] CUDA stream used for asynchronous kernel/library execution.

• twist / rotation / transform / matrix - [in] Device pointer to input batched data.

• *_pitch - [in] Leading dimension (row stride) for each matrix in the batch.

• *_stride - [in] Stride between consecutive batch elements.

• size / num_matrices - [in] Number of batch elements.

• output pointer parameters (for example skew, jacobian, inverse_transform) - [out] Device pointer to destination buffer.

Returns

• All functions in this module return void.

Lie math API (lie_math.h)

SO(3) family

void ComputeSkewSO3(cudaStream_t stream, const float* twist,
                    size_t twist_stride, size_t skew_pitch,
                    size_t skew_stride, size_t size, float* skew)

void ComputeExpSO3(cudaStream_t stream, const float* twist,
                   size_t twist_stride, size_t rotation_pitch,
                   size_t rotation_stride, size_t size, float* rotation)

void ComputeLogSO3(cudaStream_t stream, const float* rotation,
                   size_t rotation_pitch, size_t rotation_stride,
                   size_t twist_stride, size_t size, float* twist)

void ComputeJacobianLeftSO3(cudaStream_t stream, const float* twist,
                            size_t twist_stride, size_t jacobian_pitch,
                            size_t jacobian_stride, size_t size,
                            float* jacobian)

void ComputeJacobianRightSO3(cudaStream_t stream, const float* twist,
                             size_t twist_stride, size_t jacobian_pitch,
                             size_t jacobian_stride, size_t size,
                             float* jacobian)

void ComputeJacobianLeftInverseSO3(cudaStream_t stream, const float* twist,
                                   size_t twist_stride,
                                   size_t jacobian_inv_pitch,
                                   size_t jacobian_inv_stride, size_t size,
                                   float* jacobian_inv)

void ComputeJacobianRightInverseSO3(cudaStream_t stream, const float* twist,
                                    size_t twist_stride,
                                    size_t jacobian_inv_pitch,
                                    size_t jacobian_inv_stride, size_t size,
                                    float* jacobian_inv)

SE(3) family

void ComputeInverseSE3(cudaStream_t stream, const float* transform,
                       size_t transform_pitch, size_t transform_stride,
                       size_t inverse_pitch, size_t inverse_stride,
                       size_t size, float* inverse_transform)

void ComputeExpSE3(cudaStream_t stream, const float* twist,
                   size_t twist_stride, size_t transform_pitch,
                   size_t transform_stride, size_t size, float* transform)

void ComputeLogSE3(cudaStream_t stream, const float* transform,
                   size_t transform_pitch, size_t transform_stride,
                   size_t twist_stride, size_t size, float* twist)

void ComputeAdjointSE3(cudaStream_t stream, const float* transform,
                       size_t transform_pitch, size_t transform_stride,
                       size_t adjoint_pitch, size_t adjoint_stride,
                       size_t size, float* adjoint)

void ComputeInverseAdjointSE3(cudaStream_t stream, const float* transform,
                              size_t transform_pitch, size_t transform_stride,
                              size_t inv_adjoint_pitch,
                              size_t inv_adjoint_stride, size_t size,
                              float* inv_adjoint)

void ComputeJacobianLeftSE3(cudaStream_t stream, const float* twist,
                            size_t twist_stride, size_t jacobian_pitch,
                            size_t jacobian_stride, size_t size,
                            float* jacobian)

void ComputeJacobianLeftInverseSE3(cudaStream_t stream, const float* twist,
                                   size_t twist_stride, size_t jacobian_pitch,
                                   size_t jacobian_stride, size_t size,
                                   float* jacobian)

void ComputeJacobianRightSE3(cudaStream_t stream, const float* twist,
                             size_t twist_stride, size_t jacobian_pitch,
                             size_t jacobian_stride, size_t size,
                             float* jacobian)

void ComputeJacobianRightInverseSE3(cudaStream_t stream, const float* twist,
                                    size_t twist_stride, size_t jacobian_pitch,
                                    size_t jacobian_stride, size_t size,
                                    float* jacobian)

General utility

void ComputeNegateMatrix(cudaStream_t stream, const float* matrix,
                         size_t rows, size_t cols, size_t pitch,
                         size_t stride, size_t size,
                         float* negated_matrix)

Additional parameter docs for ComputeNegateMatrix

• rows - [in] number of rows in each matrix.

• cols - [in] number of columns in each matrix.

Sim(3) family

void ComputeAdjointSim3(cudaStream_t stream, const float* transforms,
                        size_t transform_stride, float* adjoints,
                        size_t adjoint_stride, size_t size)

ComputeAdjointSim3 parameters

• transforms - [in] Sim(3) transforms as row-major 4x4 matrices ([[R, t], [0, 1/s]]).

• transform_stride - [in] stride between consecutive transforms (in floats).

• adjoints - [out] 7x7 adjoint matrices (row-major, flattened).

• adjoint_stride - [in] stride between consecutive adjoints (in floats).

Dense matrix API (dense_matrix_ops.h)

void ComputeSqrtMatrix(cuBLASHandle& cublas_handle, cudaStream_t stream,
                       float* spd_matrix, size_t matrix_size,
                       size_t pitch, size_t num_matrices)

ComputeSqrtMatrix parameters

• cublas_handle - [in] external cuBLAS handle wrapper.

• stream - [in] CUDA stream.

• spd_matrix - [in,out] Device pointer to SPD matrices; replaced in-place by square-root factors.

• matrix_size - [in] matrix dimension (N for N x N).

• pitch - [in] leading dimension for matrix storage.

• num_matrices - [in] batch size.

void ScatterToRightBlock(cudaStream_t stream, const float* src,
                         size_t block_dim, size_t src_stride, float* dst,
                         size_t dst_pitch, size_t dst_stride,
                         size_t num_blocks)

ScatterToRightBlock parameters

• src - [in] source dense NxN blocks (device pointer).

• block_dim - [in] block dimension N.

• src_stride - [in] stride between consecutive source blocks.

• dst - [out] destination pointer (start of right sub-block).

• dst_pitch - [in] leading dimension (row stride) of the destination.

• dst_stride - [in] stride between consecutive destination blocks.

• num_blocks - [in] number of blocks in the batch.