mini_dpvo/lietorch/src/lietorch_gpu.cu

#include "lietorch_gpu.h"
#include <Eigen/Dense>

#include "common.h"
#include "dispatch.h"

#include "so3.h"
#include "rxso3.h"
#include "se3.h"
#include "sim3.h"

#define GPU_1D_KERNEL_LOOP(i, n) \
  for (size_t i = blockIdx.x * blockDim.x + threadIdx.x; i<n; i += blockDim.x * gridDim.x)

#define NUM_THREADS 256
#define NUM_BLOCKS(batch_size) ((batch_size + NUM_THREADS - 1) / NUM_THREADS)


template <typename Group, typename scalar_t>
__global__ void exp_forward_kernel(const scalar_t* a_ptr, scalar_t* X_ptr, int num_threads) {
    // exponential map forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;
    
    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Tangent a(a_ptr + i*Group::K);
        Eigen::Map<Data>(X_ptr + i*Group::N) = Group::Exp(a).data();
    }
}

template <typename Group, typename scalar_t>
__global__ void exp_backward_kernel(const scalar_t* grad, const scalar_t* a_ptr, scalar_t* da, int num_threads) {
    // exponential map backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Tangent a(a_ptr + i*Group::K);
        Grad dX(grad + i*Group::N);
        Eigen::Map<Grad>(da + i*Group::K) = dX * Group::left_jacobian(a);
    }
}

template <typename Group, typename scalar_t>
__global__ void log_forward_kernel(const scalar_t* X_ptr, scalar_t* a_ptr, int num_threads) {
    // logarithm map forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Tangent a = Group(X_ptr + i*Group::N).Log();
        Eigen::Map<Tangent>(a_ptr + i*Group::K) = a;
    }
}

template <typename Group, typename scalar_t>
__global__ void log_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, scalar_t* dX, int num_threads) {
    // logarithm map backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Tangent a = Group(X_ptr + i*Group::N).Log();
        Grad da(grad + i*Group::K);
        Eigen::Map<Grad>(dX + i*Group::N) = da * Group::left_jacobian_inverse(a);
    }
}

template <typename Group, typename scalar_t>
__global__ void inv_forward_kernel(const scalar_t* X_ptr, scalar_t* Y_ptr, int num_threads) {
    // group inverse forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Eigen::Map<Data>(Y_ptr + i*Group::N) = X.inv().data();
    }
}


template <typename Group, typename scalar_t>
__global__ void inv_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, scalar_t *dX, int num_threads) {
    // group inverse backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group Y = Group(X_ptr + i*Group::N).inv();
        Grad dY(grad + i*Group::N);
        Eigen::Map<Grad>(dX + i*Group::N) = -dY * Y.Adj();
    }
}


template <typename Group, typename scalar_t>
__global__ void mul_forward_kernel(const scalar_t* X_ptr, const scalar_t* Y_ptr, scalar_t* Z_ptr, int num_threads) {
    // group multiplication forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group Z = Group(X_ptr + i*Group::N) * Group(Y_ptr + i*Group::N);
        Eigen::Map<Data>(Z_ptr + i*Group::N) = Z.data();
    }
}

template <class Group, typename scalar_t>
__global__ void mul_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, const scalar_t* Y_ptr, scalar_t* dX, scalar_t* dY, int num_threads) {
    // group multiplication backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Grad dZ(grad + i*Group::N);
        Group X(X_ptr + i*Group::N);        
        Eigen::Map<Grad>(dX + i*Group::N) = dZ;
        Eigen::Map<Grad>(dY + i*Group::N) = dZ * X.Adj();
    }
}

template <typename Group, typename scalar_t>
__global__ void adj_forward_kernel(const scalar_t* X_ptr, const scalar_t* a_ptr, scalar_t* b_ptr, int num_threads) {
    // adjoint forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Tangent a(a_ptr + i*Group::K);
        Eigen::Map<Tangent>(b_ptr + i*Group::K) = X.Adj(a);
    }
}

template <typename Group, typename scalar_t>
__global__ void adj_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, const scalar_t* a_ptr, scalar_t* dX, scalar_t* da, int num_threads) {
    // adjoint backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Grad db(grad + i*Group::K);

        Tangent a(a_ptr + i*Group::K);
        Tangent b = X.Adj() * a;

        Eigen::Map<Grad>(da + i*Group::K) = db * X.Adj();
        Eigen::Map<Grad>(dX + i*Group::N) = -db * Group::adj(b);
    }
}


template <typename Group, typename scalar_t>
__global__ void adjT_forward_kernel(const scalar_t* X_ptr, const scalar_t* a_ptr, scalar_t* b_ptr, int num_threads) {
    // adjoint forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Tangent a(a_ptr + i*Group::K);
        Eigen::Map<Tangent>(b_ptr + i*Group::K) = X.AdjT(a);
    }
}

template <typename Group, typename scalar_t>
__global__ void adjT_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, const scalar_t* a_ptr, scalar_t* dX, scalar_t* da, int num_threads) {
    // adjoint backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);        
        Tangent db(grad + i*Group::K);
        Grad a(a_ptr + i*Group::K);

        Eigen::Map<Tangent>(da + i*Group::K) = X.Adj(db);
        Eigen::Map<Grad>(dX + i*Group::N) = -a * Group::adj(X.Adj(db));
    }
}

template <typename Group, typename scalar_t>
__global__ void act_forward_kernel(const scalar_t* X_ptr, const scalar_t* p_ptr, scalar_t* q_ptr, int num_threads) {
    // action on point forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;
    using Point = Eigen::Matrix<scalar_t,3,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Point p(p_ptr + i*3);
        Eigen::Map<Point>(q_ptr + i*3) = X * p;
    }
}

template <typename Group, typename scalar_t>
__global__ void act_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, const scalar_t* p_ptr, scalar_t* dX, scalar_t* dp, int num_threads) {
    // adjoint backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Point = Eigen::Matrix<scalar_t,3,1>;
    using PointGrad = Eigen::Matrix<scalar_t,1,3>;
    using Transformation = Eigen::Matrix<scalar_t,4,4>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Point p(p_ptr + i*3);
        PointGrad dq(grad + i*3);

        Eigen::Map<PointGrad>(dp + i*3) = dq * X.Matrix4x4().block<3,3>(0,0);
        Eigen::Map<Grad>(dX + i*Group::N) = dq * Group::act_jacobian(X*p);
    }
}


template <typename Group, typename scalar_t>
__global__ void act4_forward_kernel(const scalar_t* X_ptr, const scalar_t* p_ptr, scalar_t* q_ptr, int num_threads) {
    // action on point forward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;
    using Point = Eigen::Matrix<scalar_t,4,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Point p(p_ptr + i*4);
        Eigen::Map<Point>(q_ptr + i*4) = X.act4(p);
    }
}

template <typename Group, typename scalar_t>
__global__ void act4_backward_kernel(const scalar_t* grad, const scalar_t* X_ptr, const scalar_t* p_ptr, scalar_t* dX, scalar_t* dp, int num_threads) {
    // adjoint backward kernel
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Grad = Eigen::Matrix<scalar_t,1,Group::K>;
    using Point = Eigen::Matrix<scalar_t,4,1>;
    using PointGrad = Eigen::Matrix<scalar_t,1,4>;
    using Transformation = Eigen::Matrix<scalar_t,4,4>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Point p(p_ptr + i*4);
        PointGrad dq(grad + i*4);

        Eigen::Map<PointGrad>(dp + i*4) = dq * X.Matrix4x4();
        const Point q = X.act4(p);
        Eigen::Map<Grad>(dX + i*Group::N) = dq * Group::act4_jacobian(q);
    }
}

template <typename Group, typename scalar_t>
__global__ void as_matrix_forward_kernel(const scalar_t* X_ptr, scalar_t* T_ptr, int num_threads) {
    // convert to 4x4 matrix representation
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;
    using Matrix4 = Eigen::Matrix<scalar_t,4,4,Eigen::RowMajor>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Eigen::Map<Matrix4>(T_ptr + i*16) = X.Matrix4x4();
    }
}

template <typename Group, typename scalar_t>
__global__ void orthogonal_projector_kernel(const scalar_t* X_ptr, scalar_t* P_ptr, int num_threads) {
    // orthogonal projection matrix
    using Proj = Eigen::Matrix<scalar_t,Group::N,Group::N,Eigen::RowMajor>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Eigen::Map<Proj>(P_ptr + i*Group::N*Group::N) = X.orthogonal_projector();
    }
}

template <typename Group, typename scalar_t>
__global__ void jleft_forward_kernel(const scalar_t* X_ptr, const scalar_t* a_ptr, scalar_t* b_ptr, int num_threads) {
    // left jacobian inverse action
    using Tangent = Eigen::Matrix<scalar_t,Group::K,1>;
    using Data = Eigen::Matrix<scalar_t,Group::N,1>;

    GPU_1D_KERNEL_LOOP(i, num_threads) {
        Group X(X_ptr + i*Group::N);
        Tangent a(a_ptr + i*Group::K);
        Tangent b = Group::left_jacobian_inverse(X.Log()) * a;
        Eigen::Map<Tangent>(b_ptr + i*Group::K) = b;
    }
}

// unary operations

torch::Tensor exp_forward_gpu(int group_id, torch::Tensor a) {
    int batch_size = a.size(0);
    torch::Tensor X;

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, a.type(), "exp_forward_kernel", ([&] {
        X = torch::zeros({batch_size, group_t::N}, a.options());
        exp_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            a.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return X;
}

std::vector<torch::Tensor> exp_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor a) {
    int batch_size = a.size(0);
    torch::Tensor da = torch::zeros(a.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, a.type(), "exp_backward_kernel", ([&] {
        exp_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            da.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {da};
}

torch::Tensor log_forward_gpu(int group_id, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor a;

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "log_forward_kernel", ([&] {
        a = torch::zeros({batch_size, group_t::K}, X.options());
        log_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return a;
}

std::vector<torch::Tensor> log_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "log_backward_kernel", ([&] {
        log_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX};
}

torch::Tensor inv_forward_gpu(int group_id, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor Y = torch::zeros_like(X);

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "inv_forward_kernel", ([&] {
        inv_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            Y.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return Y;
}

std::vector<torch::Tensor> inv_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "inv_backward_kernel", ([&] {
        inv_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX};
}

// binary operations
torch::Tensor mul_forward_gpu(int group_id, torch::Tensor X, torch::Tensor Y) {
    int batch_size = X.size(0);
    torch::Tensor Z = torch::zeros_like(X);

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "mul_forward_kernel", ([&] {
        mul_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            Y.data_ptr<scalar_t>(), 
            Z.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return Z;
}

std::vector<torch::Tensor> mul_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X, torch::Tensor Y) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());
    torch::Tensor dY = torch::zeros(Y.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "mul_backward_kernel", ([&] {
        mul_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            Y.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            dY.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX, dY};
}

torch::Tensor adj_forward_gpu(int group_id, torch::Tensor X, torch::Tensor a) {
    int batch_size = X.size(0);
    torch::Tensor b = torch::zeros(a.sizes(), a.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "adj_forward_kernel", ([&] {
        adj_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            b.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return b;
}

std::vector<torch::Tensor> adj_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X, torch::Tensor a) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());
    torch::Tensor da = torch::zeros(a.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "adj_backward_kernel", ([&] {
        adj_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            da.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX, da};
}


torch::Tensor adjT_forward_gpu(int group_id, torch::Tensor X, torch::Tensor a) {
    int batch_size = X.size(0);
    torch::Tensor b = torch::zeros(a.sizes(), a.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "adjT_forward_kernel", ([&] {
        adjT_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            b.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return b;
}

std::vector<torch::Tensor> adjT_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X, torch::Tensor a) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());
    torch::Tensor da = torch::zeros(a.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "adjT_backward_kernel", ([&] {
        adjT_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            da.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX, da};
}



torch::Tensor act_forward_gpu(int group_id, torch::Tensor X, torch::Tensor p) {
    int batch_size = X.size(0);
    torch::Tensor q = torch::zeros(p.sizes(), p.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "act_forward_kernel", ([&] {
        act_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            p.data_ptr<scalar_t>(), 
            q.data_ptr<scalar_t>(),
            batch_size);
    }));

    return q;
}

std::vector<torch::Tensor> act_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X, torch::Tensor p) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());
    torch::Tensor dp = torch::zeros(p.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "act_backward_kernel", ([&] {
        act_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            p.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            dp.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX, dp};
}

torch::Tensor act4_forward_gpu(int group_id, torch::Tensor X, torch::Tensor p) {
    int batch_size = X.size(0);
    torch::Tensor q = torch::zeros(p.sizes(), p.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "act4_forward_kernel", ([&] {
        act4_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            p.data_ptr<scalar_t>(), 
            q.data_ptr<scalar_t>(),
            batch_size);
    }));

    return q;
}

std::vector<torch::Tensor> act4_backward_gpu(int group_id, torch::Tensor grad, torch::Tensor X, torch::Tensor p) {
    int batch_size = X.size(0);
    torch::Tensor dX = torch::zeros(X.sizes(), grad.options());
    torch::Tensor dp = torch::zeros(p.sizes(), grad.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "act4_backward_kernel", ([&] {
        act4_backward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            grad.data_ptr<scalar_t>(), 
            X.data_ptr<scalar_t>(), 
            p.data_ptr<scalar_t>(), 
            dX.data_ptr<scalar_t>(), 
            dp.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return {dX, dp};
}


torch::Tensor as_matrix_forward_gpu(int group_id, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor T4x4 = torch::zeros({X.size(0), 4, 4}, X.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "as_matrix_forward_kernel", ([&] {
        as_matrix_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            T4x4.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return T4x4;
}


torch::Tensor orthogonal_projector_gpu(int group_id, torch::Tensor X) {
    int batch_size = X.size(0);
    torch::Tensor P;

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "orthogonal_projector_kernel", ([&] {
        P = torch::zeros({X.size(0), group_t::N, group_t::N}, X.options());
        orthogonal_projector_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            P.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return P;
}


torch::Tensor jleft_forward_gpu(int group_id, torch::Tensor X, torch::Tensor a) {
    int batch_size = X.size(0);
    torch::Tensor b = torch::zeros(a.sizes(), a.options());

    DISPATCH_GROUP_AND_FLOATING_TYPES(group_id, X.type(), "jleft_forward_kernel", ([&] {
        jleft_forward_kernel<group_t, scalar_t><<<NUM_BLOCKS(batch_size), NUM_THREADS>>>(
            X.data_ptr<scalar_t>(), 
            a.data_ptr<scalar_t>(), 
            b.data_ptr<scalar_t>(), 
            batch_size);
    }));

    return b;
}