    // Copyright (C) 2015  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_DNN_CPU_cPP_
    #define DLIB_DNN_CPU_cPP_

    // This file contains CPU implementations of the GPU based functions in cuda_dlib.h

    #include "cpu_dlib.h"
    #include "tensor_tools.h"

    namespace dlib
    {
        namespace cpu
        {

        // -----------------------------------------------------------------------------------

            void multiply (
                bool add_to,
                tensor& dest,
                const tensor& src1,
                const tensor& src2
            )
            {
                DLIB_CASSERT(dest.k() == src1.k() && src1.k() == src2.k() &&
                    dest.nr() == src1.nr() && src1.nr() == src2.nr() &&
                    dest.nc() == src1.nc() && src1.nc() == src2.nc() );
                const long MD = std::max(std::max(dest.num_samples(),src1.num_samples()),src2.num_samples());
                DLIB_CASSERT((dest.num_samples()==1 || dest.num_samples()==MD) &&
                    (src1.num_samples()==1 || src1.num_samples()==MD) &&
                    (src2.num_samples()==1 || src2.num_samples()==MD) );

                if (dest.size() == 0)
                    return;

                const size_t max_size = std::max(std::max(dest.size(),src1.size()),src2.size());
                const auto d = dest.host();
                const auto s1 = src1.host();
                const auto s2 = src2.host();
                if (dest.size() == src1.size() && src1.size() == src2.size())
                {
                    if (add_to)
                    {
                        for (size_t i = 0; i < src1.size(); ++i)
                            d[i] += s1[i]*s2[i];
                    }
                    else
                    {
                        for (size_t i = 0; i < src1.size(); ++i)
                            d[i] = s1[i]*s2[i];
                    }
                }
                else if (dest.num_samples() == 1)
                {
                    if (!add_to)
                    {
                        for (size_t i = 0; i < dest.size(); ++i)
                            d[i] = 0;
                    }
                    for (size_t i = 0; i < max_size; ++i)
                        d[i%dest.size()] += s1[i%src1.size()]*s2[i%src2.size()];
                }
                else
                {
                    if (add_to)
                    {
                        for (size_t i = 0; i < max_size; ++i)
                            d[i] += s1[i%src1.size()]*s2[i%src2.size()];
                    }
                    else
                    {
                        for (size_t i = 0; i < max_size; ++i)
                            d[i] = s1[i%src1.size()]*s2[i%src2.size()];
                    }
                }
            }

            void multiply_conv (
                bool add_to,
                tensor& dest,
                const tensor& src1,
                const tensor& src2
            )
            {
                auto d = dest.host();
                auto s1 = src1.host();
                auto s2 = src2.host();
                if (have_same_dimensions(dest,src1))
                {
                    DLIB_CASSERT(src2.num_samples() == 1 && src2.nr() == 1 && src2.nc() == 1 && src2.k() == src1.k());

                    if (add_to)
                    {
                        for (long n = 0; n < dest.num_samples(); ++n)
                        {
                            for (long k = 0; k < dest.k(); ++k)
                            {
                                for (long r = 0; r < dest.nr(); ++r)
                                {
                                    for (long c = 0; c < dest.nc(); ++c)
                                    {
                                        *d++ += (*s1++)*s2[k];
                                    }
                                }
                            }
                        }
                    }
                    else
                    {
                        for (long n = 0; n < dest.num_samples(); ++n)
                        {
                            for (long k = 0; k < dest.k(); ++k)
                            {
                                for (long r = 0; r < dest.nr(); ++r)
                                {
                                    for (long c = 0; c < dest.nc(); ++c)
                                    {
                                        *d++ = (*s1++)*s2[k];
                                    }
                                }
                            }
                        }
                    }
                }
                else
                {
                    DLIB_CASSERT(have_same_dimensions(src1,src2));
                    DLIB_CASSERT(dest.num_samples() == 1 && dest.nr() == 1 && dest.nc() == 1 && dest.k() == src1.k());

                    if (!add_to)
                    {
                        for (long k = 0; k < src1.k(); ++k)
                            d[k] = 0;
                    }

                    for (long n = 0; n < src1.num_samples(); ++n)
                    {
                        for (long k = 0; k < src1.k(); ++k)
                        {
                            for (long r = 0; r < src1.nr(); ++r)
                            {
                                for (long c = 0; c < src1.nc(); ++c)
                                {
                                    d[k] += (*s1++)*(*s2++);
                                }
                            }
                        }
                    }
                }
            }

            void add(
                float beta,
                tensor& dest,
                float alpha,
                const tensor& src
            )
            {
                DLIB_CASSERT(
                      (have_same_dimensions(src, dest) ||
                      (src.num_samples()==1 && src.k()==dest.k() && src.nr()==1 && src.nc()==1) ||
                      (src.num_samples()==1 && src.k()==dest.k() && src.nr()==dest.nr() && src.nc()==dest.nc()) ||
                      (src.num_samples()==1 && src.k()==1 && src.nr()==dest.nr() && src.nc()==dest.nc())) &&
                      is_same_object(src,dest) == false ,
                        "\n\t dest.num_samples(): " << dest.num_samples()
                        <<"\n\t dest.k():           " << dest.k()
                        <<"\n\t dest.nr():          " << dest.nr()
                        <<"\n\t dest.nc():          " << dest.nc()
                        <<"\n\t src.num_samples():  " << src.num_samples()
                        <<"\n\t src.k():            " << src.k()
                        <<"\n\t src.nr():           " << src.nr()
                        <<"\n\t src.nc():           " << src.nc()
                        );

                if (beta == 0 && alpha == 0)
                {
                    dest = 0;
                    return;
                }

                auto d = dest.host();
                auto s = src.host();
                for (long n = 0; n < dest.num_samples(); ++n)
                {
                    const auto sn = src.num_samples()==1 ? 0:n;
                    for (long k = 0; k < dest.k(); ++k)
                    {
                        const auto sk = src.k()==1 ? 0:k;
                        for (long r = 0; r < dest.nr(); ++r)
                        {
                            const auto sr = src.nr()==1 ? 0:r;
                            for (long c = 0; c < dest.nc(); ++c)
                            {
                                const auto sc = src.nc()==1 ? 0:c;

                                const auto s_idx = ((sn*src.k() + sk)*src.nr() + sr)*src.nc() + sc;
                                *d = beta*(*d) + alpha*s[s_idx];
                                ++d;
                            }
                        }
                    }
                }
            }

        // ----------------------------------------------------------------------------------------

            void add (
                tensor& dest,
                const tensor& src1,
                const tensor& src2
            )
            {
                auto d = dest.host();
                auto s1 = src1.host();
                auto s2 = src2.host();

                // Do the simple and fast version if everything has the same dimensions
                if (have_same_dimensions(dest, src1) &&
                    have_same_dimensions(dest, src2))
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                        d[i] = s1[i] + s2[i];
                    return;
                }

                // Otherwise, do the more complex version with bounds checking.
                for (long n = 0; n < dest.num_samples(); ++n)
                {
                    for (long k = 0; k < dest.k(); ++k)
                    {
                        for (long r = 0; r < dest.nr(); ++r)
                        {
                            for (long c = 0; c < dest.nc(); ++c)
                            {
                                float v1 = 0;
                                float v2 = 0;

                                // if this index is inside src1
                                if (n < src1.num_samples() &&
                                    k < src1.k() &&
                                    r < src1.nr() &&
                                    c < src1.nc() )
                                {
                                    const auto s_idx = ((n*src1.k() + k)*src1.nr() + r)*src1.nc() + c;
                                    v1 = s1[s_idx];
                                }

                                // if this index is inside src2
                                if (n < src2.num_samples() &&
                                    k < src2.k() &&
                                    r < src2.nr() &&
                                    c < src2.nc() )
                                {
                                    const auto s_idx = ((n*src2.k() + k)*src2.nr() + r)*src2.nc() + c;
                                    v2 = s2[s_idx];
                                }

                                *d = v1 + v2;
                                ++d;
                            }
                        }
                    }
                }
            }

        // ----------------------------------------------------------------------------------------

            void assign_bias_gradient (
                tensor& grad,
                const tensor& gradient_input
            )
            {
                DLIB_CASSERT(
                      grad.num_samples() == 1 &&
                      gradient_input.k() == grad.k() &&
                      gradient_input.nr() == grad.nr() &&
                      gradient_input.nc() == grad.nc() &&
                      gradient_input.size() > 0);

                auto out = grad.host();
                auto in = gradient_input.host();

                for (size_t i = 0; i < grad.size(); ++i)
                    out[i] = *in++;

                for (long j = 1; j < gradient_input.num_samples(); ++j)
                {
                    for (size_t i = 0; i < grad.size(); ++i)
                        out[i] += *in++;
                }
            }

        // ------------------------------------------------------------------------------------

            void assign_conv_bias_gradient (
                tensor& grad,
                const tensor& gradient_input
            )
            {
                DLIB_CASSERT(
                      grad.num_samples() == 1 &&
                      grad.k()  >= 1 &&
                      grad.nr() == 1 &&
                      grad.nc() == 1 &&
                      gradient_input.k() == grad.k() &&
                      gradient_input.size() > 0 &&
                      is_same_object(grad,gradient_input) == false
                      );

                auto g = grad.host();
                auto gi = gradient_input.host();

                for (long k = 0; k < gradient_input.k(); ++k)
                    g[k] = 0;

                for (long n = 0; n < gradient_input.num_samples(); ++n)
                {
                    for (long k = 0; k < gradient_input.k(); ++k)
                    {
                        for (long r = 0; r < gradient_input.nr(); ++r)
                        {
                            for (long c = 0; c < gradient_input.nc(); ++c)
                            {
                                g[k] += (*gi++);
                            }
                        }
                    }
                }
            }

        // -----------------------------------------------------------------------------------

            void affine_transform(
                tensor& dest,
                const tensor& src,
                const float A,
                const float B
            )
            {
                DLIB_CASSERT(dest.size()==src.size());
                const auto d = dest.host();
                const auto s = src.host();
                for (size_t i = 0; i < src.size(); ++i)
                    d[i] = A*s[i] + B;
            }

            void affine_transform(
                tensor& dest,
                const tensor& src1,
                const tensor& src2,
                const float A,
                const float B,
                const float C
            )
            {
                DLIB_CASSERT(dest.size()==src1.size());
                DLIB_CASSERT(dest.size()==src2.size());
                const auto d = dest.host();
                const auto s1 = src1.host();
                const auto s2 = src2.host();
                for (size_t i = 0; i < src1.size(); ++i)
                    d[i] = A*s1[i] + B*s2[i] + C;
            }

            void affine_transform(
                tensor& dest,
                const tensor& src1,
                const tensor& src2,
                const tensor& src3,
                const float A,
                const float B,
                const float C,
                const float D
            )
            {
                DLIB_CASSERT(dest.size()==src1.size());
                DLIB_CASSERT(dest.size()==src2.size());
                DLIB_CASSERT(dest.size()==src3.size());
                const auto d = dest.host();
                const auto s1 = src1.host();
                const auto s2 = src2.host();
                const auto s3 = src3.host();
                for (size_t i = 0; i < src1.size(); ++i)
                    d[i] = A*s1[i] + B*s2[i] + C*s3[i] + D;
            }

            void affine_transform_range(
                size_t begin,
                size_t end,
                tensor& dest,
                const tensor& src1,
                const tensor& src2,
                const tensor& src3,
                const float A,
                const float B,
                const float C
            )
            {
                DLIB_CASSERT(dest.size()==src1.size());
                DLIB_CASSERT(dest.size()==src2.size());
                DLIB_CASSERT(dest.size()==src3.size());
                DLIB_CASSERT(begin <= end && end <= dest.size());
                const auto d = dest.host();
                const auto s1 = src1.host();
                const auto s2 = src2.host();
                const auto s3 = src3.host();
                for (size_t i = begin; i < end; ++i)
                    d[i] = A*s1[i] + B*s2[i] + C*s3[i];
            }

        // -----------------------------------------------------------------------------------

            void affine_transform(
                tensor& dest,
                const tensor& src,
                const tensor& A,
                const tensor& B
            )
            {
                DLIB_CASSERT(have_same_dimensions(dest,src));
                DLIB_CASSERT(
                      ((A.num_samples()==1 && B.num_samples()==1) ||
                      (A.num_samples()==src.num_samples() && B.num_samples()==src.num_samples())) &&
                      A.nr()==B.nr() && B.nr()==src.nr() &&
                      A.nc()==B.nc() && B.nc()==src.nc() &&
                      A.k() ==B.k()  && B.k()==src.k());

                auto d = dest.host();
                auto s = src.host();
                const auto a = A.host();
                const auto b = B.host();
                if (A.num_samples() == 1)
                {
                    const long num = src.size()/src.num_samples();
                    for (long i = 0; i < src.num_samples(); ++i)
                    {
                        for (long j = 0; j < num; ++j)
                        {
                            *d = a[j]*(*s) + b[j];
                            d++;
                            s++;
                        }
                    }
                }
                else
                {
                    for (size_t i = 0; i < src.size(); ++i)
                        d[i] = a[i]*s[i] + b[i];
                }
            }

        // -----------------------------------------------------------------------------------

            void affine_transform_conv(
                tensor& dest,
                const tensor& src,
                const tensor& A,
                const tensor& B
            )
            {
                DLIB_CASSERT(have_same_dimensions(dest,src));
                DLIB_CASSERT(have_same_dimensions(A,B));
                DLIB_CASSERT(A.num_samples() == 1 &&
                             A.nr() == 1 &&
                             A.nc() == 1 &&
                             A.k() == src.k());

                auto d = dest.host();
                auto s = src.host();
                const auto a = A.host();
                const auto b = B.host();
                for (long n = 0; n < dest.num_samples(); ++n)
                {
                    for (long k = 0; k < dest.k(); ++k)
                    {
                        for (long r = 0; r < dest.nr(); ++r)
                        {
                            for (long c = 0; c < dest.nc(); ++c)
                            {
                                *d++ = a[k]*(*s++) + b[k];
                            }
                        }
                    }
                }
            }

        // -----------------------------------------------------------------------------------

            void compute_adam_update (
                size_t begin,
                size_t end,
                tensor& s,
                tensor& m,
                tensor& v,
                const float t,
                const float learning_rate,
                const float weight_decay,
                const float momentum1,
                const float momentum2,
                const tensor& params,
                const tensor& params_grad
            )
            {
                DLIB_CASSERT(s.size() == m.size() &&
                             s.size() == v.size() &&
                             s.size() == params.size() &&
                             s.size() == params_grad.size());
                DLIB_CASSERT(begin <= end && end <= params.size());
                const float eps = 1e-8;
                const float alpha = learning_rate*std::sqrt(1-std::pow(momentum2,t))/(1-std::pow(momentum1, t));

                // The loop is equivalent to doing this:
                //   m = momentum1*m + (1-momentum1)    *   (weight_decay*params + params_grad);
                //   v = momentum2*v + (1-momentum2)*squared(weight_decay*params + params_grad);
                //   s = -alpha*m/(sqrt(v) + eps);
                auto pm = m.host();
                auto pv = v.host();
                auto ps = s.host_write_only();
                auto pparams = params.host();
                auto ppgrad = params_grad.host();
                for (size_t i = begin; i < end; ++i)
                {
                    float g = weight_decay*pparams[i] + ppgrad[i];
                    pm[i] = momentum1*pm[i] + (1-momentum1)*g;
                    pv[i] = momentum2*pv[i] + (1-momentum2)*g*g;
                    ps[i] = -alpha*pm[i]/(std::sqrt(pv[i]) + eps);
                }
            }

        // -----------------------------------------------------------------------------------

            void batch_normalize_inference (
                const double eps,
                resizable_tensor& dest,
                const tensor& src,
                const tensor& gamma,
                const tensor& beta,
                const tensor& running_means,
                const tensor& running_variances
            )
            {
                DLIB_CASSERT(
                    gamma.num_samples() == 1 &&
                    gamma.nr() == src.nr() &&
                    gamma.nc() == src.nc() &&
                    gamma.k()  == src.k() &&
                    have_same_dimensions(gamma, beta) &&
                    have_same_dimensions(gamma, running_means) &&
                    have_same_dimensions(gamma, running_variances) &&
                    eps > 0,
                    "\ngamma.num_samples(): " << gamma.num_samples() <<
                    "\ngamma.k():  " << gamma.k() <<
                    "\ngamma.nr(): " << gamma.nr() <<
                    "\ngamma.nc(): " << gamma.nc() <<
                    "\nbeta.num_samples(): " << beta.num_samples() <<
                    "\nbeta.k():   " << beta.k() <<
                    "\nbeta.nr():  " << beta.nr() <<
                    "\nbeta.nc():  " << beta.nc() <<
                    "\nrunning_means.num_samples(): " << running_means.num_samples() <<
                    "\nrunning_means.k():   " << running_means.k() <<
                    "\nrunning_means.nr():  " << running_means.nr() <<
                    "\nrunning_means.nc():  " << running_means.nc() <<
                    "\nrunning_variances.num_samples(): " << running_variances.num_samples() <<
                    "\nrunning_variances.k():   " << running_variances.k() <<
                    "\nrunning_variances.nr():  " << running_variances.nr() <<
                    "\nrunning_variances.nc():  " << running_variances.nc() <<
                    "\nsrc.k():   " << src.k() <<
                    "\nsrc.nr():  " << src.nr() <<
                    "\nsrc.nc():  " << src.nc() <<
                    "\neps:  " << eps
                );
                dest.copy_size(src);

                auto d = dest.host();
                auto s = src.host();
                auto g = gamma.host();
                auto b = beta.host();
                auto m = running_means.host();
                auto v = running_variances.host();

                const long num = src.k()*src.nr()*src.nc();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < num; ++k)
                    {
                        *d = g[k]*(*s - m[k])/std::sqrt(v[k]+eps) + b[k];
                        ++d;
                        ++s;
                    }
                }
            }

            void batch_normalize (
                const double eps,
                resizable_tensor& dest,
                resizable_tensor& means,
                resizable_tensor& invstds,
                const double averaging_factor,
                resizable_tensor& running_means,
                resizable_tensor& running_variances,
                const tensor& src,
                const tensor& gamma,
                const tensor& beta
            )
            {
                DLIB_CASSERT(0 <= averaging_factor && averaging_factor <= 1, "averaging_factor: " << averaging_factor);
                DLIB_CASSERT(averaging_factor==1 || have_same_dimensions(running_means,means));
                DLIB_CASSERT(averaging_factor==1 || have_same_dimensions(running_variances,invstds));
                DLIB_CASSERT(
                    src.num_samples() > 1 &&
                    gamma.num_samples() == 1 &&
                    beta.num_samples() == 1 &&
                    gamma.nr() == beta.nr() && beta.nr() == src.nr() &&
                    gamma.nc() == beta.nc() && beta.nc() == src.nc() &&
                    gamma.k()  == beta.k()  && beta.k() == src.k() &&
                    eps > 0,
                    "\ngamma.num_samples(): " << gamma.num_samples() <<
                    "\ngamma.k():  " << gamma.k() <<
                    "\ngamma.nr(): " << gamma.nr() <<
                    "\ngamma.nc(): " << gamma.nc() <<
                    "\nbeta.num_samples(): " << beta.num_samples() <<
                    "\nbeta.k():   " << beta.k() <<
                    "\nbeta.nr():  " << beta.nr() <<
                    "\nbeta.nc():  " << beta.nc() <<
                    "\nsrc.k():   " << src.k() <<
                    "\nsrc.nr():  " << src.nr() <<
                    "\nsrc.nc():  " << src.nc() <<
                    "\neps:  " << eps
                );

                dest.copy_size(src);
                means.set_size(1, src.k(), src.nr(), src.nc());
                invstds.set_size(1, src.k(), src.nr(), src.nc());

                // first compute means and invstds
                means = 0;
                invstds = 0;
                const auto p_invstds = invstds.host();
                const auto p_means = means.host();
                auto p_src = src.host();
                const long num = src.k()*src.nr()*src.nc();
                // compute means, and sum of squares
                for (long i = 0; i < num; ++i)
                {
                    for (long n = 0; n < src.num_samples(); ++n)
                    {
                        float val = p_src[n*num+i];
                        p_means[i] += val;
                        p_invstds[i] += val*val;
                    }
                }
                means /= src.num_samples();
                invstds /= src.num_samples();
                // copy data back to host
                invstds.host(); means.host();

                // compute variances
                running_variances.copy_size(invstds);
                auto rvar = running_variances.host();
                // This scale makes the running variances unbiased.
                const double scale = (src.num_samples())/(src.num_samples()-1.0);
                for (long i = 0; i < num; ++i)
                {
                    auto actual_var = p_invstds[i] - p_means[i]*p_means[i];
                    if (averaging_factor == 1)
                        rvar[i] = scale*actual_var;
                    else
                        rvar[i] = (1-averaging_factor)*rvar[i] + scale*averaging_factor*actual_var;

                    p_invstds[i] = 1.0f/std::sqrt(actual_var + eps);
                }

                p_src = src.host();
                auto p_dest = dest.host();
                const auto p_gamma = gamma.host();
                const auto p_beta = beta.host();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long i = 0; i < num; ++i)
                    {
                        *p_dest = (*p_src - p_means[i])*p_invstds[i];
                        *p_dest = (*p_dest)*p_gamma[i] + p_beta[i];
                        ++p_src;
                        ++p_dest;
                    }
                }

                // now keep track of the running means
                running_means.copy_size(means);
                if (averaging_factor != 1)
                    running_means = (1-averaging_factor)*mat(running_means) + averaging_factor*mat(means);
                else
                    running_means = means;
            }

            void batch_normalize_gradient (
                const double eps,
                const tensor& gradient_input,
                const tensor& means,
                const tensor& invstds,
                const tensor& src,
                const tensor& gamma,
                tensor& src_grad,
                tensor& gamma_grad,
                tensor& beta_grad
            )
            {

                const long num = src.k()*src.nr()*src.nc();
                DLIB_CASSERT(src.num_samples() > 1);
                DLIB_CASSERT(num == (long)means.size());
                DLIB_CASSERT(num == (long)invstds.size());
                DLIB_CASSERT(num == (long)gamma.size());
                DLIB_CASSERT(num == (long)gamma_grad.size());
                DLIB_CASSERT(num == (long)beta_grad.size());
                DLIB_CASSERT(have_same_dimensions(gradient_input, src));
                DLIB_CASSERT(have_same_dimensions(gradient_input, src_grad));
                DLIB_CASSERT(eps > 0);

                beta_grad = 0;
                gamma_grad = 0;
                auto p_grad = gradient_input.host();
                auto p_src = src.host();
                const auto p_gamma = gamma.host();
                const auto p_gamma_grad = gamma_grad.host();
                const auto p_beta_grad = beta_grad.host();
                const auto p_invstds = invstds.host();
                const auto p_means = means.host();

                resizable_tensor dvars, dmeans;
                dvars.copy_size(invstds);
                dmeans.copy_size(means);
                dvars = 0;
                dmeans = 0;
                const auto p_dvars = dvars.host();
                const auto p_dmeans = dmeans.host();

                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long i = 0; i < num; ++i)
                    {
                        const float x_hat = (*p_src - p_means[i])*p_invstds[i];
                        p_beta_grad[i] += *p_grad;
                        p_gamma_grad[i] += (*p_grad)*x_hat;

                        const float dx = *p_grad * p_gamma[i];

                        p_dvars[i] += dx*(*p_src - p_means[i])*-0.5*std::pow(p_invstds[i], 3.0f);

                        ++p_grad;
                        ++p_src;
                    }
                }

                const float invnum = 1.0f/src.num_samples();
                p_grad = gradient_input.host();
                p_src = src.host();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long i = 0; i < num; ++i)
                    {
                        const float dx = *p_grad * p_gamma[i];

                        p_dmeans[i] += dx*-p_invstds[i] + p_dvars[i] * -2*(*p_src - p_means[i])*invnum;

                        ++p_grad;
                        ++p_src;
                    }
                }
                p_grad = gradient_input.host();
                p_src = src.host();
                auto p_src_grad = src_grad.host();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long i = 0; i < num; ++i)
                    {
                        const float dx = *p_grad * p_gamma[i];

                        *p_src_grad += dx*p_invstds[i] +
                            p_dvars[i] *2*(*p_src - p_means[i])*invnum +
                            p_dmeans[i]*invnum;

                        ++p_grad;
                        ++p_src;
                        ++p_src_grad;
                    }
                }
            }

        // ----------------------------------------------------------------------------------------

            void batch_normalize_conv_inference (
                const double eps,
                resizable_tensor& dest,
                const tensor& src,
                const tensor& gamma,
                const tensor& beta,
                const tensor& running_means,
                const tensor& running_variances
            )
            {
                DLIB_CASSERT(
                    gamma.num_samples() == 1 &&
                    gamma.nr() == 1 &&
                    gamma.nc() == 1 &&
                    gamma.k()  == src.k() &&
                    have_same_dimensions(gamma, beta) &&
                    have_same_dimensions(gamma, running_means) &&
                    have_same_dimensions(gamma, running_variances) &&
                    eps > 0,
                    "\ngamma.num_samples(): " << gamma.num_samples() <<
                    "\ngamma.k():  " << gamma.k() <<
                    "\ngamma.nr(): " << gamma.nr() <<
                    "\ngamma.nc(): " << gamma.nc() <<
                    "\nbeta.num_samples(): " << beta.num_samples() <<
                    "\nbeta.k():   " << beta.k() <<
                    "\nbeta.nr():  " << beta.nr() <<
                    "\nbeta.nc():  " << beta.nc() <<
                    "\nrunning_means.num_samples(): " << running_means.num_samples() <<
                    "\nrunning_means.k():   " << running_means.k() <<
                    "\nrunning_means.nr():  " << running_means.nr() <<
                    "\nrunning_means.nc():  " << running_means.nc() <<
                    "\nrunning_variances.num_samples(): " << running_variances.num_samples() <<
                    "\nrunning_variances.k():   " << running_variances.k() <<
                    "\nrunning_variances.nr():  " << running_variances.nr() <<
                    "\nrunning_variances.nc():  " << running_variances.nc() <<
                    "\nsrc.k():   " << src.k() <<
                    "\nsrc.nr():  " << src.nr() <<
                    "\nsrc.nc():  " << src.nc() <<
                    "\neps:  " << eps
                );
                dest.copy_size(src);

                auto d = dest.host();
                auto s = src.host();
                auto g = gamma.host();
                auto b = beta.host();
                auto m = running_means.host();
                auto v = running_variances.host();

                const long num = src.nr()*src.nc();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        const float invstd = 1.0f/std::sqrt(v[k] + eps);
                        for (long j = 0; j < num; ++j)
                        {
                            *d = g[k]*(*s - m[k])*invstd + b[k];
                            ++d;
                            ++s;
                        }
                    }
                }
            }

            void batch_normalize_conv (
                const double eps,
                resizable_tensor& dest,
                resizable_tensor& means,
                resizable_tensor& invstds,
                const double averaging_factor,
                resizable_tensor& running_means,
                resizable_tensor& running_variances,
                const tensor& src,
                const tensor& gamma,
                const tensor& beta
            )
            {
                DLIB_CASSERT(0 <= averaging_factor && averaging_factor <= 1, "averaging_factor: " << averaging_factor);
                DLIB_CASSERT(averaging_factor==1 || have_same_dimensions(running_means,means));
                DLIB_CASSERT(averaging_factor==1 || have_same_dimensions(running_variances,invstds));
                DLIB_CASSERT(
                    src.num_samples() > 1 &&
                    gamma.num_samples() == 1 &&
                    beta.num_samples() == 1 &&
                    gamma.nr() == 1 &&
                    beta.nr() == 1 &&
                    gamma.nc() == 1 &&
                    beta.nc() == 1 &&
                    gamma.k()  == beta.k()  && beta.k() == src.k() &&
                    eps > 0,
                    "\ngamma.num_samples(): " << gamma.num_samples() <<
                    "\ngamma.k():  " << gamma.k() <<
                    "\ngamma.nr(): " << gamma.nr() <<
                    "\ngamma.nc(): " << gamma.nc() <<
                    "\nbeta.num_samples(): " << beta.num_samples() <<
                    "\nbeta.k():   " << beta.k() <<
                    "\nbeta.nr():  " << beta.nr() <<
                    "\nbeta.nc():  " << beta.nc() <<
                    "\nsrc.k():   " << src.k() <<
                    "\nsrc.nr():  " << src.nr() <<
                    "\nsrc.nc():  " << src.nc()  <<
                    "\neps:  " << eps
                );

                dest.copy_size(src);
                means.set_size(1, src.k());
                invstds.set_size(1, src.k());

                // first compute means and invstds
                means = 0;
                invstds = 0;
                const auto p_invstds = invstds.host();
                const auto p_means = means.host();
                const auto p_gamma = gamma.host();
                const auto p_beta = beta.host();
                auto p_src = src.host();
                const long num = src.nr()*src.nc();
                // compute means, and sum of squares
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        for (long i = 0; i < num; ++i)
                        {
                            p_means[k] += *p_src;
                            p_invstds[k] += (*p_src)*(*p_src);
                            ++p_src;
                        }
                    }
                }
                means /= src.num_samples()*num;
                invstds /= src.num_samples()*num;
                // copy data back to host
                invstds.host(); means.host();

                p_src = src.host();
                // compute variances
                running_variances.copy_size(invstds);
                auto rvar = running_variances.host();
                // This scale makes the running variances unbiased.
                const double scale = (src.num_samples()*num)/(src.num_samples()*num-1.0);
                for (long k = 0; k < src.k(); ++k)
                {
                    float actual_var = p_invstds[k] - p_means[k]*p_means[k];
                    if (averaging_factor == 1)
                        rvar[k] = scale*actual_var;
                    else
                        rvar[k] = (1-averaging_factor)*rvar[k] + scale*averaging_factor*actual_var;

                    p_invstds[k] = 1.0f/std::sqrt(actual_var + eps);
                }

                p_src = src.host();
                auto p_dest = dest.host();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        for (long i = 0; i < num; ++i)
                        {
                            *p_dest = (*p_src - p_means[k])*p_invstds[k];
                            *p_dest = (*p_dest)*p_gamma[k] + p_beta[k];
                            ++p_src;
                            ++p_dest;
                        }
                    }
                }

                // now keep track of the running means
                running_means.copy_size(means);
                if (averaging_factor != 1)
                    running_means = (1-averaging_factor)*mat(running_means) + averaging_factor*mat(means);
                else
                    running_means = means;
            }

            void batch_normalize_conv_gradient(
                const double eps,
                const tensor& gradient_input,
                const tensor& means,
                const tensor& invstds,
                const tensor& src,
                const tensor& gamma,
                tensor& src_grad,
                tensor& gamma_grad,
                tensor& beta_grad
            )
            {

                const long num = src.nr()*src.nc();
                DLIB_CASSERT(src.num_samples() > 1);
                DLIB_CASSERT(src.k() == (long)means.size());
                DLIB_CASSERT(src.k() == (long)invstds.size());
                DLIB_CASSERT(src.k() == (long)gamma.size());
                DLIB_CASSERT(src.k() == (long)gamma_grad.size());
                DLIB_CASSERT(src.k() == (long)beta_grad.size());
                DLIB_CASSERT(have_same_dimensions(gradient_input, src));
                DLIB_CASSERT(have_same_dimensions(gradient_input, src_grad));
                DLIB_CASSERT(eps > 0);

                beta_grad = 0;
                gamma_grad = 0;

                auto p_grad = gradient_input.host();
                auto p_src = src.host();
                const auto p_gamma = gamma.host();
                const auto p_gamma_grad = gamma_grad.host();
                const auto p_beta_grad = beta_grad.host();
                const auto p_invstds = invstds.host();
                const auto p_means = means.host();

                resizable_tensor dvars, dmeans;
                dvars.copy_size(invstds);
                dmeans.copy_size(means);
                dvars = 0;
                dmeans = 0;
                const auto p_dvars = dvars.host();
                const auto p_dmeans = dmeans.host();

                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        const float invstd_pow = -0.5*std::pow(p_invstds[k], 3.0f);
                        for (long i = 0; i < num; ++i)
                        {
                            const float x_hat = (*p_src - p_means[k])*p_invstds[k];
                            p_beta_grad[k] += *p_grad;
                            p_gamma_grad[k] += (*p_grad)*x_hat;

                            const float dx = *p_grad * p_gamma[k];

                            p_dvars[k] += dx*(*p_src - p_means[k])*invstd_pow;

                            ++p_grad;
                            ++p_src;
                        }
                    }
                }

                p_grad = gradient_input.host();
                p_src = src.host();
                const float invnum = 1.0f/(src.num_samples()*num);
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        for (long i = 0; i < num; ++i)
                        {
                            const float dx = *p_grad * p_gamma[k];

                            p_dmeans[k] += -dx*p_invstds[k] + p_dvars[k] * -2*(*p_src - p_means[k])*invnum;

                            ++p_grad;
                            ++p_src;
                        }
                    }
                }
                p_grad = gradient_input.host();
                p_src = src.host();
                auto p_src_grad = src_grad.host();
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    for (long k = 0; k < src.k(); ++k)
                    {
                        for (long i = 0; i < num; ++i)
                        {
                            const float dx = *p_grad * p_gamma[k];

                            *p_src_grad += dx*p_invstds[k] +
                                p_dvars[k]*2*(*p_src - p_means[k])*invnum +
                                p_dmeans[k]*invnum;

                            ++p_grad;
                            ++p_src;
                            ++p_src_grad;
                        }
                    }
                }
            }

        // -----------------------------------------------------------------------------------

            void threshold (
                tensor& data,
                float thresh
            )
            {
                const auto d = data.host();
                for (size_t i = 0; i < data.size(); ++i)
                    d[i] = d[i]>thresh ? 1:0;
            }

            void dot (
                const tensor& a,
                const tensor& b,
                tensor& result,
                size_t idx
            )
            {
                DLIB_CASSERT(a.size() == b.size());
                DLIB_CASSERT(idx < result.size());

                const auto aa = a.host();
                const auto bb = b.host();
                auto r = result.host();
                for (size_t i = 0; i < a.size(); ++i)
                    r[idx] += aa[i]*bb[i];
            }

        // -----------------------------------------------------------------------------------
        // -----------------------------------------------------------------------------------
        // -----------------------------------------------------------------------------------

            void softmax (
                tensor& dest,
                const tensor& src
            )
            {
                DLIB_CASSERT(have_same_dimensions(dest,src));
                const auto d = dest.host();
                const auto s = src.host();

                const long num = src.nr()*src.nc();
                // Note that we subtract out the max values in each channel before applying
                // exp() to avoid numeric overflow in the subsequent computations.  Doing this
                // doesn't change the resulting output, it just makes it more numerically
                // stable.
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    auto ss = s + num*src.k()*n;
                    auto dd = d + num*src.k()*n;
                    for (long i = 0; i < num; ++i)
                    {
                        float max_val = -std::numeric_limits<float>::infinity();
                        for (long k = 0; k < src.k(); ++k)
                            max_val = std::max(max_val, ss[k*num]);

                        for (long k = 0; k < src.k(); ++k)
                            dd[k*num] = std::exp(ss[k*num]-max_val);

                        ++ss;
                        ++dd;
                    }
                }

                // Now normalize each channel so they sum to 1.
                for (long n = 0; n < src.num_samples(); ++n)
                {
                    const auto dd = d + num*src.k()*n;
                    for (long r = 0; r < src.nr(); ++r)
                    {
                        for (long c = 0; c < src.nc(); ++c)
                        {
                            const auto ddd = dd+r*src.nc()+c;

                            float temp = 0;
                            for (long k = 0; k < src.k(); ++k)
                                temp += ddd[k*num];
                            for (long k = 0; k < src.k(); ++k)
                                ddd[k*num] /= temp;
                        }
                    }
                }
            }

            void softmax_gradient (
                tensor& grad,
                const tensor& dest,
                const tensor& gradient_input
            )
            {
                DLIB_CASSERT(have_same_dimensions(grad,dest));
                DLIB_CASSERT(have_same_dimensions(grad,gradient_input));
                const auto d = dest.host();
                const auto g = grad.host();
                const auto in = gradient_input.host();

                const long num = grad.nr()*grad.nc();

                for (long n = 0; n < grad.num_samples(); ++n)
                {
                    const auto d2 = d + num*grad.k()*n;
                    const auto g2 = g + num*grad.k()*n;
                    const auto in2 = in + num*grad.k()*n;
                    for (long r = 0; r < grad.nr(); ++r)
                    {
                        for (long c = 0; c < grad.nc(); ++c)
                        {
                            const auto d3 = d2+r*grad.nc()+c;
                            const auto g3 = g2+r*grad.nc()+c;
                            const auto in3 = in2+r*grad.nc()+c;

                            float temp = 0;
                            for (long k = 0; k < grad.k(); ++k)
                                temp += -d3[k*num]*in3[k*num];
                            if (is_same_object(gradient_input, grad))
                            {
                                for (long k = 0; k < grad.k(); ++k)
                                    g3[k*num] = d3[k*num]*(temp+in3[k*num]);
                            }
                            else
                            {
                                for (long k = 0; k < grad.k(); ++k)
                                    g3[k*num] += d3[k*num]*(temp+in3[k*num]);
                            }
                        }
                    }
                }
            }

        // ------------------------------------------------------------------------------------

            void sigmoid (
                tensor& dest,
                const tensor& src
            )
            {
                const auto d = dest.host();
                const auto s = src.host();
                for (size_t i = 0; i < src.size(); ++i)
                    d[i] = 1/(1+std::exp(-s[i]));
            }

            void sigmoid_gradient (
                tensor& grad,
                const tensor& dest,
                const tensor& gradient_input
            )
            {
                const auto g = grad.host();
                const auto d = dest.host();
                const auto in = gradient_input.host();
                if (is_same_object(gradient_input, grad))
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                        g[i] = in[i]*d[i]*(1-d[i]);
                }
                else
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                        g[i] += in[i]*d[i]*(1-d[i]);
                }
            }

        // ------------------------------------------------------------------------------------

            void relu (
                tensor& dest,
                const tensor& src
            )
            {
                dest = lowerbound(mat(src), 0);
            }

            void relu_gradient (
                tensor& grad,
                const tensor& dest,
                const tensor& gradient_input
            )
            {
                const float* gi = gradient_input.host();
                const float* in = dest.host();
                float* out = grad.host();
                if (is_same_object(grad, gradient_input))
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                    {
                        if (in[i] > 0)
                            out[i] = gi[i];
                        else
                            out[i] = 0;
                    }
                }
                else
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                    {
                        if (in[i] > 0)
                            out[i] += gi[i];
                    }
                }
            }

        // ----------------------------------------------------------------------------------------

            void prelu (
                tensor& dest,
                const tensor& src,
                const tensor& param
            )
            {
                const float p = param.host()[0];
                const float* s = src.host();
                float* d = dest.host();
                for (size_t i = 0; i < dest.size(); ++i)
                {
                    if (s[i] > 0)
                        d[i] = s[i];
                    else
                        d[i] = p*s[i];
                }
            }

            void prelu_gradient (
                tensor& grad,
                const tensor& src,
                const tensor& gradient_input,
                const tensor& param,
                tensor& params_grad
            )
            {
                DLIB_CASSERT(is_same_object(grad, gradient_input) == false);
                const float p = param.host()[0];
                const float* gi = gradient_input.host();
                const float* s = src.host();
                float* out = grad.host();
                float pgrad = 0;
                for (size_t i = 0; i < src.size(); ++i)
                {
                    if (s[i] > 0)
                    {
                        out[i] += gi[i];
                    }
                    else
                    {
                        out[i] += p*gi[i];
                        pgrad += gi[i]*s[i];
                    }
                }
                params_grad.host()[0] = pgrad;
            }

        // ------------------------------------------------------------------------------------

            void tanh (
                tensor& dest,
                const tensor& src
            )
            {
                const auto d = dest.host();
                const auto s = src.host();
                for (size_t i = 0; i < src.size(); ++i)
                    d[i] = std::tanh(s[i]);
            }

            void tanh_gradient (
                tensor& grad,
                const tensor& dest,
                const tensor& gradient_input
            )
            {
                const auto g = grad.host();
                const auto d = dest.host();
                const auto in = gradient_input.host();
                if (is_same_object(grad, gradient_input))
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                        g[i] = in[i]*(1-d[i]*d[i]);
                }
                else
                {
                    for (size_t i = 0; i < dest.size(); ++i)
                        g[i] += in[i]*(1-d[i]*d[i]);
                }
            }

        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------

            pooling::pooling (
            ) : window_height(0),window_width(0),stride_y(0),stride_x(0),padding_y(0),padding_x(0),do_max_pooling(true)
            {
            }

            void pooling::
            clear(
            )
            {
                window_height = 0;
                window_width = 0;
                stride_y = 0;
                stride_x = 0;
                padding_y = 0;
                padding_x = 0;
            }

            void pooling::
            setup_max_pooling(
                int window_height_,
                int window_width_,
                int stride_y_,
                int stride_x_,
                int padding_y_,
                int padding_x_
            )
            {
                DLIB_CASSERT(window_width_ > 0);
                DLIB_CASSERT(window_height_ > 0);
                DLIB_CASSERT(stride_y_ > 0);
                DLIB_CASSERT(stride_x_ > 0);
                DLIB_CASSERT(0 <= padding_y_ && padding_y_ < window_height_);
                DLIB_CASSERT(0 <= padding_x_ && padding_x_ < window_width_);

                window_height = window_height_;
                window_width = window_width_;
                stride_y = stride_y_;
                stride_x = stride_x_;
                padding_y = padding_y_;
                padding_x = padding_x_;
                do_max_pooling = true;
            }

            void pooling::
            setup_avg_pooling(
                int window_height_,
                int window_width_,
                int stride_y_,
                int stride_x_,
                int padding_y_,
                int padding_x_
            )
            {
                DLIB_CASSERT(window_width_ > 0);
                DLIB_CASSERT(window_height_ > 0);
                DLIB_CASSERT(stride_y_ > 0);
                DLIB_CASSERT(stride_x_ > 0);
                DLIB_CASSERT(0 <= padding_y_ && padding_y_ < window_height_);
                DLIB_CASSERT(0 <= padding_x_ && padding_x_ < window_width_);

                window_height = window_height_;
                window_width = window_width_;
                stride_y = stride_y_;
                stride_x = stride_x_;
                padding_y = padding_y_;
                padding_x = padding_x_;
                do_max_pooling = false;
            }

            void pooling::
            operator() (
                resizable_tensor& dest,
                const tensor& src
            )
            {
                DLIB_CASSERT(window_width > 0);
                DLIB_CASSERT(window_height > 0);
                DLIB_CASSERT(stride_y > 0);
                DLIB_CASSERT(stride_x > 0);
                DLIB_CASSERT(0 <= padding_y && padding_y < window_height);
                DLIB_CASSERT(0 <= padding_x && padding_x < window_width);
                DLIB_CASSERT(window_width  <= src.nc() + 2*padding_x,
                    "Pooling windows must be small enough to fit into the padded image.");
                DLIB_CASSERT(window_height <= src.nr() + 2*padding_y,
                    "Pooling windows must be small enough to fit into the padded image.");

                dest.set_size(
                     src.num_samples(),
                     src.k(),
                     1+(src.nr()+2*padding_y-window_height)/stride_y,
                     1+(src.nc()+2*padding_x-window_width)/stride_x
                    );

                if (src.size() == 0)
                {
                    dest = 0;
                    return;
                }

                auto d = dest.host();
                const long x_offset = window_width/2 - padding_x;
                const long y_offset = window_height/2 - padding_y;
                if (does_max_pooling())
                {
                    for (long n = 0; n < dest.num_samples(); ++n)
                    {
                        for (long k = 0; k < dest.k(); ++k)
                        {
                            auto simg = image_plane(src,n,k);
                            auto dimg = d + (n*dest.k() + k)*dest.nr()*dest.nc();

                            for (long r = 0; r < dest.nr(); ++r)
                            {
                                for (long c = 0; c < dest.nc(); ++c)
                                {
                                    auto win = centered_rect(c*stride_x+x_offset,
                                        r*stride_y+y_offset,
                                        window_width,
                                        window_height);
                                    dimg[r*dest.nc() + c] = max(subm_clipped(simg,win));
                                }
                            }
                        }
                    }
                }
                else
                {
                    for (long n = 0; n < dest.num_samples(); ++n)
                    {
                        for (long k = 0; k < dest.k(); ++k)
                        {
                            auto simg = image_plane(src,n,k);
                            auto dimg = d + (n*dest.k() + k)*dest.nr()*dest.nc();

                            for (long r = 0; r < dest.nr(); ++r)
                            {
                                for (long c = 0; c < dest.nc(); ++c)
                                {
                                    auto win = centered_rect(c*stride_x+x_offset,
                                        r*stride_y+y_offset,
                                        window_width,
                                        window_height);
                                    dimg[r*dest.nc() + c] = mean(subm_clipped(simg,win));
                                }
                            }
                        }
                    }
                }

            }

            void pooling::get_gradient(
                const tensor& gradient_input,
                const tensor& dest,
                const tensor& src,
                tensor& grad
            )
            {
                DLIB_CASSERT(have_same_dimensions(gradient_input,dest));
                DLIB_CASSERT(have_same_dimensions(src,grad));

                if (src.size() == 0)
                {
                    return;
                }

                auto gi = gradient_input.host();
                auto g = grad.host();
                const long x_offset = window_width/2 - padding_x;
                const long y_offset = window_height/2 - padding_y;
                if (does_max_pooling())
                {
                    for (long n = 0; n < dest.num_samples(); ++n)
                    {
                        for (long k = 0; k < dest.k(); ++k)
                        {
                            auto simg = image_plane(src,n,k);
                            auto gimg = g + (n*grad.k() + k)*grad.nr()*grad.nc();
                            auto giimg = gi + (n*dest.k() + k)*dest.nr()*dest.nc();
                            auto imgbox = get_rect(simg);

                            for (long r = 0; r < dest.nr(); ++r)
                            {
                                for (long c = 0; c < dest.nc(); ++c)
                                {
                                    auto win = centered_rect(c*stride_x+x_offset,
                                        r*stride_y+y_offset,
                                        window_width,
                                        window_height).intersect(imgbox);
                                    auto p = max_point(subm(simg,win))+win.tl_corner();
                                    gimg[p.y()*grad.nc()+p.x()] += giimg[r*dest.nc()+c];
                                }
                            }
                        }
                    }
                }
                else
                {
                    for (long n = 0; n < dest.num_samples(); ++n)
                    {
                        for (long k = 0; k < dest.k(); ++k)
                        {
                            auto simg = image_plane(src,n,k);
                            auto gimg = g + (n*grad.k() + k)*grad.nr()*grad.nc();
                            auto giimg = gi + (n*dest.k() + k)*dest.nr()*dest.nc();
                            auto imgbox = get_rect(simg);

                            for (long r = 0; r < dest.nr(); ++r)
                            {
                                for (long c = 0; c < dest.nc(); ++c)
                                {
                                    auto win = centered_rect(c*stride_x+x_offset,
                                        r*stride_y+y_offset,
                                        window_width,
                                        window_height).intersect(imgbox);
                                    const float delta = giimg[r*dest.nc()+c]/win.area();
                                    for (long y = win.top(); y <= win.bottom(); ++y)
                                    {
                                        for (long x = win.left(); x <= win.right(); ++x)
                                        {
                                            gimg[y*grad.nc()+x] += delta;
                                        }
                                    }
                                }
                            }
                        }
                    }
                }

            }

        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------

            void img2col(
                matrix<float>& output,
                const tensor& data,
                long n,
                long filter_nr,
                long filter_nc,
                long stride_y,
                long stride_x,
                long padding_y,
                long padding_x
            )
            {
                const auto d = data.host() + data.k()*data.nr()*data.nc()*n;
                const rectangle boundary = get_rect(data);

                const long out_nr = 1+(data.nr()+2*padding_y-filter_nr)/stride_y;
                const long out_nc = 1+(data.nc()+2*padding_x-filter_nc)/stride_x;

                output.set_size(out_nr*out_nc,
                                data.k()*filter_nr*filter_nc);
                DLIB_CASSERT(output.size() != 0);
                float* t = &output(0,0);

                // now fill in the Toeplitz output matrix for the n-th sample in data.
                size_t cnt = 0;
                const long max_r = data.nr() + padding_y-(filter_nr-1);
                const long max_c = data.nc() + padding_x-(filter_nc-1);
                for (long r = -padding_y; r < max_r; r+=stride_y)
                {
                    for (long c = -padding_x; c < max_c; c+=stride_x)
                    {
                        for (long k = 0; k < data.k(); ++k)
                        {
                            for (long y = 0; y < filter_nr; ++y)
                            {
                                for (long x = 0; x < filter_nc; ++x)
                                {
                                    DLIB_ASSERT(cnt < output.size());
                                    long xx = c+x;
                                    long yy = r+y;
                                    if (boundary.contains(xx,yy))
                                        *t = d[(k*data.nr() + yy)*data.nc() + xx];
                                    else
                                        *t = 0;
                                    ++t;
                                    ++cnt;
                                }
                            }
                        }
                    }
                }
            }

            void col2img(
                const matrix<float>& output,
                tensor& data,
                long n,
                long filter_nr,
                long filter_nc,
                long stride_y,
                long stride_x,
                long padding_y,
                long padding_x
            )
            {
                const auto d = data.host() + data.k()*data.nr()*data.nc()*n;
                const rectangle boundary = get_rect(data);

                DLIB_CASSERT(output.size() != 0);
                const float* t = &output(0,0);

                // now fill in the Toeplitz output matrix for the n-th sample in data.
                const long max_r = data.nr() + padding_y-(filter_nr-1);
                const long max_c = data.nc() + padding_x-(filter_nc-1);
                for (long r = -padding_y; r < max_r; r+=stride_y)
                {
                    for (long c = -padding_x; c < max_c; c+=stride_x)
                    {
                        for (long k = 0; k < data.k(); ++k)
                        {
                            for (long y = 0; y < filter_nr; ++y)
                            {
                                for (long x = 0; x < filter_nc; ++x)
                                {
                                    long xx = c+x;
                                    long yy = r+y;
                                    if (boundary.contains(xx,yy))
                                        d[(k*data.nr() + yy)*data.nc() + xx] += *t;
                                    ++t;
                                }
                            }
                        }
                    }
                }
            }

            void tensor_conv::operator() (
                resizable_tensor& output,
                const tensor& data,
                const tensor& filters,
                int stride_y,
                int stride_x,
                int padding_y,
                int padding_x
            )
            {
                DLIB_CASSERT(is_same_object(output,data) == false);
                DLIB_CASSERT(is_same_object(output,filters) == false);
                DLIB_CASSERT(filters.k() == data.k());
                DLIB_CASSERT(stride_y > 0 && stride_x > 0);
                DLIB_CASSERT(0 <= padding_y && padding_y < filters.nr());
                DLIB_CASSERT(0 <= padding_x && padding_x < filters.nc());
                DLIB_CASSERT(filters.nr() <= data.nr() + 2*padding_y,
                    "Filter windows must be small enough to fit into the padded image.");
                DLIB_CASSERT(filters.nc() <= data.nc() + 2*padding_x,
                    "Filter windows must be small enough to fit into the padded image.");

                output.set_size(data.num_samples(),
                                filters.num_samples(),
                                1+(data.nr()+2*padding_y-filters.nr())/stride_y,
                                1+(data.nc()+2*padding_x-filters.nc())/stride_x);

                matrix<float> temp;
                for (long n = 0; n < data.num_samples(); ++n)
                {
                    img2col(temp, data, n, filters.nr(), filters.nc(), stride_y, stride_x, padding_y, padding_x);
                    output.set_sample(n, mat(filters)*trans(temp));
                }

                last_stride_y = stride_y;
                last_stride_x = stride_x;
                last_padding_y = padding_y;
                last_padding_x = padding_x;
            }

        // ------------------------------------------------------------------------------------

            void tensor_conv::
            get_gradient_for_data (
                const tensor& gradient_input,
                const tensor& filters,
                tensor& data_gradient
            )
            {
                matrix<float> temp;
                for (long n = 0; n < gradient_input.num_samples(); ++n)
                {
                    auto gi = mat(gradient_input.host()+gradient_input.k()*gradient_input.nr()*gradient_input.nc()*n,
                                  gradient_input.k(),
                                  gradient_input.nr()*gradient_input.nc());

                    temp = trans(gi)*mat(filters);
                    col2img(temp, data_gradient, n, filters.nr(), filters.nc(), last_stride_y, last_stride_x, last_padding_y, last_padding_x);
                }
            }

        // ------------------------------------------------------------------------------------

            void tensor_conv::
            get_gradient_for_filters (
                const tensor& gradient_input,
                const tensor& data,
                tensor& filters_gradient
            )
            {
                matrix<float> temp;
                for (long n = 0; n < gradient_input.num_samples(); ++n)
                {
                    auto gi = mat(gradient_input.host()+gradient_input.k()*gradient_input.nr()*gradient_input.nc()*n,
                                  gradient_input.k(),
                                  gradient_input.nr()*gradient_input.nc());

                    img2col(temp, data, n, filters_gradient.nr(), filters_gradient.nc(), last_stride_y, last_stride_x, last_padding_y, last_padding_x);
                    if (n == 0)
                        filters_gradient = gi*temp;
                    else
                        filters_gradient += gi*temp;
                }
            }
        // ------------------------------------------------------------------------------------
        void copy_tensor(
                tensor& dest,
                size_t dest_k_offset,
                const tensor& src,
                size_t src_k_offset,
                size_t count_k
        )
        {
            const size_t dest_sample_size = static_cast<size_t>(dest.nc() * dest.nr() * dest.k());
            const size_t src_sample_size = static_cast<size_t>(src.nc() * src.nr() * src.k());

            const size_t block_size = count_k * dest.nc() * dest.nr();

            DLIB_CASSERT(dest.num_samples() == src.num_samples() &&
                         dest.nc() == src.nc() && dest.nr() == src.nr(), "All sources should fit into dest tensor size");
            DLIB_CASSERT(dest.k() - dest_k_offset >= count_k, "Not enough space in dest tensor");
            DLIB_CASSERT(src.k() - src_k_offset >= count_k, "Not enough space in src tensor");

            float* dest_p = dest.host() + dest_k_offset * dest.nc() * dest.nr();
            const float* src_p = src.host() + src_k_offset * src.nc() * src.nr();

            for (long i = 0; i < src.num_samples(); ++i)
            {
                ::memcpy(dest_p, src_p, block_size * sizeof(float));

                dest_p += dest_sample_size;
                src_p  += src_sample_size;
            }
        }

        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------
        // ------------------------------------------------------------------------------------

        }
    }

    #endif // DLIB_DNN_CPU_cPP_