TheRock/rocm-libraries/projects/rocsolver/clients/common/auxiliary/testing_stedcj.hpp

/* **************************************************************************
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#pragma once

#include "common/misc/client_util.hpp"
#include "common/misc/clientcommon.hpp"
#include "common/misc/lapack_host_reference.hpp"
#include "common/misc/norm.hpp"
#include "common/misc/rocsolver.hpp"
#include "common/misc/rocsolver_arguments.hpp"
#include "common/misc/rocsolver_test.hpp"
#include "common/misc/rocsolver_timer.hpp"

template <typename T, typename S, typename U>
void stedcj_checkBadArgs(const rocblas_handle handle,
                         const rocblas_evect evect,
                         const rocblas_int n,
                         S dD,
                         S dE,
                         T dC,
                         const rocblas_int ldc,
                         U dInfo)
{
    // handle
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(nullptr, evect, n, dD, dE, dC, ldc, dInfo),
                          rocblas_status_invalid_handle);

    // values
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, rocblas_evect(0), n, dD, dE, dC, ldc, dInfo),
                          rocblas_status_invalid_value);

    // pointers
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, evect, n, (S) nullptr, dE, dC, ldc, dInfo),
                          rocblas_status_invalid_pointer);
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, evect, n, dD, (S) nullptr, dC, ldc, dInfo),
                          rocblas_status_invalid_pointer);
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, evect, n, dD, dE, (T) nullptr, ldc, dInfo),
                          rocblas_status_invalid_pointer);
    EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, evect, n, dD, dE, dC, ldc, (U) nullptr),
                          rocblas_status_invalid_pointer);

    // quick return with invalid pointers
    EXPECT_ROCBLAS_STATUS(
        rocsolver_stedcj(handle, evect, 0, (S) nullptr, (S) nullptr, (T) nullptr, ldc, dInfo),
        rocblas_status_success);
}

template <typename T>
void testing_stedcj_bad_arg()
{
    using S = decltype(std::real(T{}));

    // safe arguments
    rocblas_local_handle handle;
    rocblas_evect evect = rocblas_evect_original;
    rocblas_int n = 2;
    rocblas_int ldc = 2;

    // memory allocations
    device_strided_batch_vector<S> dD(1, 1, 1, 1);
    device_strided_batch_vector<S> dE(1, 1, 1, 1);
    device_strided_batch_vector<T> dC(1, 1, 1, 1);
    device_strided_batch_vector<rocblas_int> dInfo(1, 1, 1, 1);
    CHECK_HIP_ERROR(dD.memcheck());
    CHECK_HIP_ERROR(dE.memcheck());
    CHECK_HIP_ERROR(dC.memcheck());
    CHECK_HIP_ERROR(dInfo.memcheck());

    // check bad arguments
    stedcj_checkBadArgs(handle, evect, n, dD.data(), dE.data(), dC.data(), ldc, dInfo.data());
}

template <bool CPU, bool GPU, typename T, typename Sd, typename Td, typename Ud, typename Sh, typename Th, typename Uh>
void stedcj_initData(const rocblas_handle handle,
                     const rocblas_evect evect,
                     const rocblas_int n,
                     Sd& dD,
                     Sd& dE,
                     Td& dC,
                     const rocblas_int ldc,
                     Ud& dInfo,
                     Sh& hD,
                     Sh& hE,
                     Th& hC,
                     Uh& hInfo)
{
    if(CPU)
    {
        using S = decltype(std::real(T{}));

        // if the matrix is too small (n < 4), simply initialize D and E
        if(n < 4)
        {
            rocblas_init<S>(hD, true);
            rocblas_init<S>(hE, true);
        }

        // otherwise, the marix will be divided in exactly 2 independent blocks, if the size is even,
        // or 3 if the size is odd. The 2 main independent blocks will have the same eigenvalues.
        // The last block, when the size is odd, will have eigenvalue equal 1.
        else
        {
            rocblas_int N1 = n / 2;
            rocblas_int E = n - 2 * N1;

            // a. initialize the eigenvalues for the uppermost sub-blocks of the main independent blocks.
            // The second sub-block will have some repeated eigenvalues in order to test the deflation process
            S d;
            rocblas_int NN1 = N1 / 2;
            rocblas_int NN2 = N1 - NN1;
            rocblas_int s1 = NN1 * NN1;
            rocblas_int s2 = NN2 * NN2;
            rocblas_int sw = NN2 * 32;
            std::vector<S> A1(s1);
            std::vector<S> A2(s2);
            for(rocblas_int i = 0; i < NN1; ++i)
            {
                for(rocblas_int j = 0; j < NN1; ++j)
                {
                    if(i == j)
                    {
                        d = (i + 1) / S(NN1);
                        A1[i + i * NN1] = d;
                        A2[i + i * NN2] = (i % 2 == 0) ? d : -d;
                    }
                    else
                    {
                        A1[i + j * NN1] = 0;
                        A2[i + j * NN2] = 0;
                    }
                }
            }
            if(NN2 > NN1)
            {
                for(rocblas_int i = 0; i < NN1; ++i)
                {
                    A2[NN1 + i * NN2] = 0;
                    A2[i + NN1 * NN2] = 0;
                }
                A2[NN1 + NN1 * NN2] = 0;
            }

            // b. find the corresponding tridiagonal matrices containing the setup eigenvalues of each sub-block
            // first find random orthogonal matrices Q1 and Q2
            Sh Q1(s1, 1, s1, 1);
            Sh Q2(s2, 1, s2, 1);
            rocblas_init<S>(Q1, true);
            rocblas_init<S>(Q2, true);
            std::vector<S> hW(sw);
            std::vector<S> ipiv1(NN1);
            std::vector<S> ipiv2(NN2);
            cpu_geqrf<S>(NN1, NN1, Q1.data(), NN1, ipiv1.data(), hW.data(), sw);
            cpu_geqrf<S>(NN2, NN2, Q2.data(), NN2, ipiv2.data(), hW.data(), sw);
            // now multiply the orthogonal matrices by the diagonals A1 and A2 to hide the eigenvalues
            cpu_ormqr_unmqr<S>(rocblas_side_left, rocblas_operation_transpose, NN1, NN1, NN1,
                               Q1.data(), NN1, ipiv1.data(), A1.data(), NN1, hW.data(), sw);
            cpu_ormqr_unmqr<S>(rocblas_side_right, rocblas_operation_none, NN1, NN1, NN1, Q1.data(),
                               NN1, ipiv1.data(), A1.data(), NN1, hW.data(), sw);
            cpu_ormqr_unmqr<S>(rocblas_side_left, rocblas_operation_transpose, NN2, NN2, NN2,
                               Q2.data(), NN2, ipiv2.data(), A2.data(), NN2, hW.data(), sw);
            cpu_ormqr_unmqr<S>(rocblas_side_right, rocblas_operation_none, NN2, NN2, NN2, Q2.data(),
                               NN2, ipiv2.data(), A2.data(), NN2, hW.data(), sw);
            // finally, perform tridiagonalization
            cpu_sytrd_hetrd<S>(rocblas_fill_upper, NN1, A1.data(), NN1, hD[0], hE[0], ipiv1.data(),
                               hW.data(), sw);
            cpu_sytrd_hetrd<S>(rocblas_fill_upper, NN2, A2.data(), NN2, hD[0] + NN1, hE[0] + NN1,
                               ipiv2.data(), hW.data(), sw);

            // c. integrate blocks into final matrix
            // integrate the 2 sub-blocks into the first independent block
            hE[0][NN1 - 1] = 1;
            hD[0][NN1 - 1] += 1;
            hD[0][NN1] += 1;
            // copy the independent block over
            for(rocblas_int i = 0; i < N1; ++i)
            {
                hD[0][N1 + i] = hD[0][i];
                hE[0][N1 + i] = hE[0][i];
            }
            hE[0][N1 - 1] = 0;
            hE[0][2 * N1 - 1] = 0;
            // integrate the 2 sub-blocks into the second independent block
            // (using negative p to test secular eqn algorithm)
            hE[0][N1 + NN1 - 1] = -1;
            hD[0][N1 + NN1 - 1] -= 2;
            hD[0][N1 + NN1] -= 2;
            // if there is a third independent block, initialize it with 1
            if(E == 1)
                hD[0][n - 1] = 1;
        }

        // initialize C to the identity matrix
        if(evect == rocblas_evect_original)
        {
            for(rocblas_int j = 0; j < n; j++)
            {
                for(rocblas_int i = 0; i < n; i++)
                {
                    if(i == j)
                        hC[0][i + j * ldc] = 1;
                    else
                        hC[0][i + j * ldc] = 0;
                }
            }
        }
    }

    if(GPU)
    {
        // now copy to the GPU
        CHECK_HIP_ERROR(dD.transfer_from(hD));
        CHECK_HIP_ERROR(dE.transfer_from(hE));

        if(evect == rocblas_evect_original)
            CHECK_HIP_ERROR(dC.transfer_from(hC));
    }
}

template <typename T, typename Sd, typename Td, typename Ud, typename Sh, typename Th, typename Uh>
void stedcj_getError(const rocblas_handle handle,
                     const rocblas_evect evect,
                     const rocblas_int n,
                     Sd& dD,
                     Sd& dE,
                     Td& dC,
                     const rocblas_int ldc,
                     Ud& dInfo,
                     Sh& hD,
                     Sh& hDRes,
                     Sh& hE,
                     Sh& hERes,
                     Th& hC,
                     Th& hCRes,
                     Uh& hInfo,
                     Uh& hInfoRes,
                     double* max_err,
                     double* max_errv)
{
    constexpr bool COMPLEX = rocblas_is_complex<T>;
    using S = decltype(std::real(T{}));

    int lgn = floor(log(n - 1) / log(2)) + 1;
    size_t lwork = (COMPLEX) ? n * n : 0;
    size_t lrwork = (evect == rocblas_evect_none || n <= 1) ? 1 : 1 + 3 * n + 4 * n * n + 2 * n * lgn;
    size_t liwork = (evect == rocblas_evect_none || n <= 1) ? 1 : 6 + 6 * n + 5 * n * lgn;
    std::vector<T> work(lwork);
    std::vector<S> rwork(lrwork);
    std::vector<rocblas_int> iwork(liwork);

    // input data initialization
    stedcj_initData<true, true, T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hE, hC, hInfo);

    // execute computations
    // GPU lapack
    CHECK_ROCBLAS_ERROR(
        rocsolver_stedcj(handle, evect, n, dD.data(), dE.data(), dC.data(), ldc, dInfo.data()));
    CHECK_HIP_ERROR(hDRes.transfer_from(dD));
    CHECK_HIP_ERROR(hERes.transfer_from(dE));
    CHECK_HIP_ERROR(hInfoRes.transfer_from(dInfo));
    if(evect != rocblas_evect_none)
        CHECK_HIP_ERROR(hCRes.transfer_from(dC));

    // if eigenvectors were required, prepare matrix A (upper triangular) for implicit tests
    rocblas_int lda = n;
    size_t size_A = lda * n;
    host_strided_batch_vector<T> hA(size_A, 1, size_A, 1);
    if(evect != rocblas_evect_none)
    {
        for(rocblas_int i = 0; i < n; i++)
        {
            for(rocblas_int j = i; j < n; j++)
            {
                if(i == j)
                    hA[0][i + j * lda] = hD[0][i];
                else if(i + 1 == j)
                    hA[0][i + j * lda] = hE[0][i];
                else
                    hA[0][i + j * lda] = 0;
            }
        }
    }

    // CPU lapack
    cpu_stedc(evect, n, hD[0], hE[0], hC[0], ldc, work.data(), lwork, rwork.data(), lrwork,
              iwork.data(), liwork, hInfo[0]);

    // check info
    EXPECT_EQ(hInfo[0][0], hInfoRes[0][0]);
    if(hInfo[0][0] != hInfoRes[0][0])
        *max_err = 1;
    else
        *max_err = 0;

    double err;

    if(hInfo[0][0] == 0)
    {
        // check that eigenvalues are correct and in order
        // error is ||hD - hDRes|| / ||hD||
        // using frobenius norm
        err = norm_error('F', 1, n, 1, hD[0], hDRes[0]);
        *max_err = err > *max_err ? err : *max_err;

        // check eigenvectors if required
        if(evect != rocblas_evect_none)
        {
            // both eigenvalues and eigenvectors needed; need to implicitly test
            // eigenvectors due to non-uniqueness of eigenvectors under scaling

            // multiply A with each of the n eigenvectors and divide by corresponding
            // eigenvalues
            T alpha;
            T beta = 0;
            for(int j = 0; j < n; j++)
            {
                alpha = T(1) / hDRes[0][j];
                cpu_symv_hemv(rocblas_fill_upper, n, alpha, hA[0], lda, hCRes[0] + j * ldc, 1, beta,
                              hC[0] + j * ldc, 1);
            }

            // error is ||hC - hCRes|| / ||hC||
            // using frobenius norm
            *max_errv = norm_error('F', n, n, ldc, hCRes[0], hC[0]);
        }
    }
}

template <typename T, typename Sd, typename Td, typename Ud, typename Sh, typename Th, typename Uh>
void stedcj_getPerfData(const rocblas_handle handle,
                        const rocblas_evect evect,
                        const rocblas_int n,
                        Sd& dD,
                        Sd& dE,
                        Td& dC,
                        const rocblas_int ldc,
                        Ud& dInfo,
                        Sh& hD,
                        Sh& hE,
                        Th& hC,
                        Uh& hInfo,
                        double* gpu_time_used,
                        double* cpu_time_used,
                        const rocblas_int hot_calls,
                        const int profile,
                        const bool profile_kernels,
                        const bool perf)
{
    constexpr bool COMPLEX = rocblas_is_complex<T>;
    using S = decltype(std::real(T{}));

    int lgn = floor(log(n - 1) / log(2)) + 1;
    size_t lwork = (COMPLEX ? n * n : 0);
    size_t lrwork = (evect == rocblas_evect_none ? 1 : 1 + 3 * n + 4 * n * n + 2 * n * lgn);
    size_t liwork = (evect == rocblas_evect_none ? 1 : 6 + 6 * n + 5 * n * lgn);
    std::vector<T> work(lwork);
    std::vector<S> rwork(lrwork);
    std::vector<rocblas_int> iwork(liwork);

    if(!perf)
    {
        // cpu-lapack performance (only if not in perf mode)
        *cpu_time_used = nan("");
    }

    stedcj_initData<true, false, T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hE, hC, hInfo);

    // cold calls
    for(int iter = 0; iter < 2; iter++)
    {
        stedcj_initData<false, true, T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hE, hC, hInfo);

        CHECK_ROCBLAS_ERROR(
            rocsolver_stedcj(handle, evect, n, dD.data(), dE.data(), dC.data(), ldc, dInfo.data()));
    }

    // gpu-lapack performance
    hipStream_t stream;
    CHECK_ROCBLAS_ERROR(rocblas_get_stream(handle, &stream));
    rocsolver_timer timer;

    if(profile > 0)
    {
        if(profile_kernels)
            rocsolver_log_set_layer_mode(rocblas_layer_mode_log_profile
                                         | rocblas_layer_mode_ex_log_kernel);
        else
            rocsolver_log_set_layer_mode(rocblas_layer_mode_log_profile);
        rocsolver_log_set_max_levels(profile);
    }

    for(rocblas_int iter = 0; iter < hot_calls; iter++)
    {
        stedcj_initData<false, true, T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hE, hC, hInfo);

        timer.start(stream);
        rocsolver_stedcj(handle, evect, n, dD.data(), dE.data(), dC.data(), ldc, dInfo.data());
        timer.end(stream);
    }
    *gpu_time_used = timer.get_combined();
}

template <typename T>
void testing_stedcj(Arguments& argus)
{
    using S = decltype(std::real(T{}));

    // get arguments
    rocblas_local_handle handle;
    char evectC = argus.get<char>("evect");
    rocblas_int n = argus.get<rocblas_int>("n");
    rocblas_int ldc = argus.get<rocblas_int>("ldc", n);

    rocblas_evect evect = char2rocblas_evect(evectC);
    rocblas_int hot_calls = argus.iters;

    // check non-supported values
    // N/A

    // determine sizes
    size_t size_D = n;
    size_t size_E = n;
    size_t size_C = ldc * n;
    double max_err = 0, max_errv = 0, gpu_time_used = 0, cpu_time_used = 0;

    size_t size_DRes = (argus.unit_check || argus.norm_check) ? size_D : 0;
    size_t size_ERes = (argus.unit_check || argus.norm_check) ? size_E : 0;
    size_t size_CRes = (argus.unit_check || argus.norm_check) ? size_C : 0;

    // check invalid sizes
    bool invalid_size = (n < 0 || (evect != rocblas_evect_none && ldc < n));
    if(invalid_size)
    {
        EXPECT_ROCBLAS_STATUS(rocsolver_stedcj(handle, evect, n, (S*)nullptr, (S*)nullptr,
                                               (T*)nullptr, ldc, (rocblas_int*)nullptr),
                              rocblas_status_invalid_size);

        if(argus.timing)
            rocsolver_bench_inform(inform_invalid_size);

        return;
    }

    // memory size query is necessary
    if(argus.mem_query)
    {
        CHECK_ROCBLAS_ERROR(rocblas_start_device_memory_size_query(handle));
        CHECK_ALLOC_QUERY(rocsolver_stedcj(handle, evect, n, (S*)nullptr, (S*)nullptr, (T*)nullptr,
                                           ldc, (rocblas_int*)nullptr));

        size_t size;
        CHECK_ROCBLAS_ERROR(rocblas_stop_device_memory_size_query(handle, &size));

        rocsolver_bench_inform(inform_mem_query, size);
        return;
    }

    // memory allocations
    host_strided_batch_vector<S> hD(size_D, 1, size_D, 1);
    host_strided_batch_vector<S> hDRes(size_DRes, 1, size_DRes, 1);
    host_strided_batch_vector<S> hE(size_E, 1, size_E, 1);
    host_strided_batch_vector<S> hERes(size_ERes, 1, size_ERes, 1);
    host_strided_batch_vector<T> hC(size_C, 1, size_C, 1);
    host_strided_batch_vector<T> hCRes(size_CRes, 1, size_CRes, 1);
    host_strided_batch_vector<rocblas_int> hInfo(1, 1, 1, 1);
    host_strided_batch_vector<rocblas_int> hInfoRes(1, 1, 1, 1);
    device_strided_batch_vector<S> dD(size_D, 1, size_D, 1);
    device_strided_batch_vector<S> dE(size_E, 1, size_E, 1);
    device_strided_batch_vector<T> dC(size_C, 1, size_C, 1);
    device_strided_batch_vector<rocblas_int> dInfo(1, 1, 1, 1);
    if(size_D)
        CHECK_HIP_ERROR(dD.memcheck());
    if(size_E)
        CHECK_HIP_ERROR(dE.memcheck());
    if(size_C)
        CHECK_HIP_ERROR(dC.memcheck());
    CHECK_HIP_ERROR(dInfo.memcheck());

    // check quick return
    if(n == 0)
    {
        EXPECT_ROCBLAS_STATUS(
            rocsolver_stedcj(handle, evect, n, dD.data(), dE.data(), dC.data(), ldc, dInfo.data()),
            rocblas_status_success);
        if(argus.timing)
            rocsolver_bench_inform(inform_quick_return);

        return;
    }

    // check computations
    if(argus.unit_check || argus.norm_check)
        stedcj_getError<T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hDRes, hE, hERes, hC,
                           hCRes, hInfo, hInfoRes, &max_err, &max_errv);

    // collect performance data
    if(argus.timing && hot_calls > 0)
        stedcj_getPerfData<T>(handle, evect, n, dD, dE, dC, ldc, dInfo, hD, hE, hC, hInfo,
                              &gpu_time_used, &cpu_time_used, hot_calls, argus.profile,
                              argus.profile_kernels, argus.perf);

    // validate results for rocsolver-test
    // using n * machine_precision as tolerance
    if(argus.unit_check)
    {
        ROCSOLVER_TEST_CHECK(T, max_err, n);
        if(evect != rocblas_evect_none)
            ROCSOLVER_TEST_CHECK(T, max_errv, n * n);
    }

    // output results for rocsolver-bench
    if(argus.timing)
    {
        if(!argus.perf)
        {
            rocsolver_bench_header("Arguments:");
            rocsolver_bench_output("evect", "n", "ldc");
            rocsolver_bench_output(evectC, n, ldc);

            rocsolver_bench_header("Results:");
            if(argus.norm_check)
            {
                rocsolver_bench_output("cpu_time_us", "gpu_time_us", "error");
                rocsolver_bench_output(cpu_time_used, gpu_time_used, std::max(max_err, max_errv));
            }
            else
            {
                rocsolver_bench_output("cpu_time_us", "gpu_time_us");
                rocsolver_bench_output(cpu_time_used, gpu_time_used);
            }
            rocsolver_bench_endl();
        }
        else
        {
            if(argus.norm_check)
                rocsolver_bench_output(gpu_time_used, std::max(max_err, max_errv));
            else
                rocsolver_bench_output(gpu_time_used);
        }
    }

    // ensure all arguments were consumed
    argus.validate_consumed();
}

#define EXTERN_TESTING_STEDCJ(...) extern template void testing_stedcj<__VA_ARGS__>(Arguments&);

INSTANTIATE(EXTERN_TESTING_STEDCJ, FOREACH_SCALAR_TYPE, APPLY_STAMP)