/* ************************************************************************** * Copyright (C) 2021-2025 Advanced Micro Devices, Inc. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * *************************************************************************/ #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 void geblttrf_npvt_checkBadArgs(const rocblas_handle handle, const rocblas_int nb, const rocblas_int nblocks, T dA, const rocblas_int lda, const rocblas_stride stA, T dB, const rocblas_int ldb, const rocblas_stride stB, T dC, const rocblas_int ldc, const rocblas_stride stC, U dInfo, const rocblas_int bc) { // handle EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, nullptr, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc), rocblas_status_invalid_handle); // values // N/A // sizes (only check batch_count if applicable) if(STRIDED) EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, -1), rocblas_status_invalid_size); // pointers EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, (T) nullptr, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA, lda, stA, (T) nullptr, ldb, stB, dC, ldc, stC, dInfo, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, (T) nullptr, ldc, stC, dInfo, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, (U) nullptr, bc), rocblas_status_invalid_pointer); // quick return with invalid pointers EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, 0, nblocks, (T) nullptr, lda, stA, (T) nullptr, ldb, stB, (T) nullptr, ldc, stC, dInfo, bc), rocblas_status_success); EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, 0, (T) nullptr, lda, stA, (T) nullptr, ldb, stB, (T) nullptr, ldc, stC, dInfo, bc), rocblas_status_success); // quick return with zero batch_count if applicable if(STRIDED) EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, (U) nullptr, 0), rocblas_status_success); } template void testing_geblttrf_npvt_bad_arg() { // safe arguments rocblas_local_handle handle; rocblas_int nb = 1; rocblas_int nblocks = 2; rocblas_int lda = 1; rocblas_int ldb = 1; rocblas_int ldc = 1; rocblas_stride stA = 2; rocblas_stride stB = 2; rocblas_stride stC = 2; rocblas_int bc = 1; if(BATCHED) { // memory allocations device_batch_vector dA(1, 1, 1); device_batch_vector dB(1, 1, 1); device_batch_vector dC(1, 1, 1); device_strided_batch_vector dInfo(1, 1, 1, 1); CHECK_HIP_ERROR(dA.memcheck()); CHECK_HIP_ERROR(dB.memcheck()); CHECK_HIP_ERROR(dC.memcheck()); CHECK_HIP_ERROR(dInfo.memcheck()); // check bad arguments geblttrf_npvt_checkBadArgs(handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc); } else { // memory allocations device_strided_batch_vector dA(1, 1, 1, 1); device_strided_batch_vector dB(1, 1, 1, 1); device_strided_batch_vector dC(1, 1, 1, 1); device_strided_batch_vector dInfo(1, 1, 1, 1); CHECK_HIP_ERROR(dA.memcheck()); CHECK_HIP_ERROR(dB.memcheck()); CHECK_HIP_ERROR(dC.memcheck()); CHECK_HIP_ERROR(dInfo.memcheck()); // check bad arguments geblttrf_npvt_checkBadArgs(handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc); } } template void geblttrf_npvt_initData(const rocblas_handle handle, const rocblas_int nb, const rocblas_int nblocks, Td& dA, const rocblas_int lda, Td& dB, const rocblas_int ldb, Td& dC, const rocblas_int ldc, const rocblas_int bc, Th& hA, Th& hB, Th& hC, const bool singular) { if(CPU) { rocblas_init(hA, true); rocblas_init(hB, false); rocblas_init(hC, false); rocblas_int n = nb * nblocks; for(rocblas_int b = 0; b < bc; ++b) { // scale to avoid singularities // leaving matrix as diagonal dominant so that pivoting is not required for(rocblas_int i = 0; i < nb; i++) { for(rocblas_int j = 0; j < nb; j++) { for(rocblas_int k = 0; k < nblocks; k++) { if(i == j) hB[b][i + j * ldb + k * ldb * nb] += 400; else hB[b][i + j * ldb + k * ldb * nb] -= 4; } for(rocblas_int k = 0; k < nblocks - 1; k++) { hA[b][i + j * lda + k * lda * nb] -= 4; hC[b][i + j * ldc + k * ldc * nb] -= 4; } } } if(singular && (b == bc / 4 || b == bc / 2 || b == bc - 1)) { // When required, add some singularities // (always the same elements for debugging purposes) rocblas_int jj = n / 4 + b; jj -= (jj / n) * n; rocblas_int j = jj % nb; rocblas_int k = jj / nb; for(rocblas_int i = 0; i < nb; i++) { // zero the jj-th column hB[b][i + j * ldb + k * ldb * nb] = 0; if(k < nblocks - 1) hA[b][i + j * lda + k * lda * nb] = 0; if(k > 0) hC[b][i + j * ldc + (k - 1) * ldc * nb] = 0; } jj = n / 2 + b; jj -= (jj / n) * n; j = jj % nb; k = jj / nb; for(rocblas_int i = 0; i < nb; i++) { // zero the jj-th column hB[b][i + j * ldb + k * ldb * nb] = 0; if(k < nblocks - 1) hA[b][i + j * lda + k * lda * nb] = 0; if(k > 0) hC[b][i + j * ldc + (k - 1) * ldc * nb] = 0; } jj = n - 1 + b; jj -= (jj / n) * n; j = jj % nb; k = jj / nb; for(rocblas_int i = 0; i < nb; i++) { // zero the jj-th column hB[b][i + j * ldb + k * ldb * nb] = 0; if(k < nblocks - 1) hA[b][i + j * lda + k * lda * nb] = 0; if(k > 0) hC[b][i + j * ldc + (k - 1) * ldc * nb] = 0; } } } } // now copy data to the GPU if(GPU) { CHECK_HIP_ERROR(dA.transfer_from(hA)); CHECK_HIP_ERROR(dB.transfer_from(hB)); CHECK_HIP_ERROR(dC.transfer_from(hC)); } } template void geblttrf_npvt_getError(const rocblas_handle handle, const rocblas_int nb, const rocblas_int nblocks, Td& dA, const rocblas_int lda, const rocblas_stride stA, Td& dB, const rocblas_int ldb, const rocblas_stride stB, Td& dC, const rocblas_int ldc, const rocblas_stride stC, Ud& dInfo, const rocblas_int bc, Th& hA, Th& hB, Th& hBRes, Th& hC, Th& hCRes, Uh& hInfo, Uh& hInfoRes, double* max_err, const bool singular) { int n = nb * nblocks; std::vector L(n * n); std::vector U(n * n); std::vector M(n * n); std::vector MRes(n * n); // input data initialization geblttrf_npvt_initData(handle, nb, nblocks, dA, lda, dB, ldb, dC, ldc, bc, hA, hB, hC, singular); // execute computations // GPU lapack CHECK_ROCBLAS_ERROR(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc)); CHECK_HIP_ERROR(hBRes.transfer_from(dB)); CHECK_HIP_ERROR(hCRes.transfer_from(dC)); CHECK_HIP_ERROR(hInfoRes.transfer_from(dInfo)); // check info for singularities double err = 0; *max_err = 0; for(rocblas_int b = 0; b < bc; ++b) { if(singular && (b == bc / 4 || b == bc / 2 || b == bc - 1)) { EXPECT_GT(hInfoRes[b][0], 0) << "where b = " << b; if(hInfoRes[b][0] <= 0) err++; } else { EXPECT_EQ(hInfoRes[b][0], 0) << "where b = " << b; if(hInfoRes[b][0] != 0) err++; } } *max_err += err; for(rocblas_int b = 0; b < bc; ++b) { if(hInfoRes[b][0] == 0) { // compute diagonal blocks and store in full matrix L for(rocblas_int k = 0; k < nblocks; k++) { for(rocblas_int i = 0; i < nb; i++) { for(rocblas_int j = 0; j < nb; j++) { if(i <= j) L[i + j * n + k * (n + 1) * nb] = hBRes[b][i + j * ldb + k * ldb * nb]; else L[i + j * n + k * (n + 1) * nb] = 0; } } cpu_trmm(rocblas_side_left, rocblas_fill_lower, rocblas_operation_none, rocblas_diagonal_unit, nb, nb, T(1), hBRes[b] + k * ldb * nb, ldb, L.data() + k * (n + 1) * nb, n); } // move blocks A, updated C, and I into full matrices L and U for(rocblas_int k = 0; k < nblocks; k++) { for(rocblas_int i = 0; i < nb; i++) { if(k < nblocks - 1) { for(rocblas_int j = 0; j < nb; j++) { U[i + (j + nb) * n + k * (n + 1) * nb] = hCRes[b][i + j * ldc + k * ldc * nb]; L[(i + nb) + j * n + k * (n + 1) * nb] = hA[b][i + j * lda + k * lda * nb]; } } U[i + i * n + k * (n + 1) * nb] = 1; } } // reconstruct input matrix from factors and store it in MRes cpu_gemm(rocblas_operation_none, rocblas_operation_none, n, n, n, T(1), L.data(), n, U.data(), n, T(0), MRes.data(), n); // form original matrix from original blocks for(rocblas_int k = 0; k < nblocks; k++) { for(rocblas_int i = 0; i < nb; i++) { for(rocblas_int j = 0; j < nb; j++) { M[i + j * n + k * (n + 1) * nb] = hB[b][i + j * ldb + k * ldb * nb]; if(k < nblocks - 1) { M[(i + nb) + j * n + k * (n + 1) * nb] = hA[b][i + j * lda + k * lda * nb]; M[i + (j + nb) * n + k * (n + 1) * nb] = hC[b][i + j * ldc + k * ldc * nb]; } } } } // error is ||M - MRes|| / ||M|| // (THIS DOES NOT ACCOUNT FOR NUMERICAL REPRODUCIBILITY ISSUES. // IT MIGHT BE REVISITED IN THE FUTURE) // using frobenius norm err = norm_error('F', n, n, n, M.data(), MRes.data()); *max_err = err > *max_err ? err : *max_err; } } } template void geblttrf_npvt_getPerfData(const rocblas_handle handle, const rocblas_int nb, const rocblas_int nblocks, Td& dA, const rocblas_int lda, const rocblas_stride stA, Td& dB, const rocblas_int ldb, const rocblas_stride stB, Td& dC, const rocblas_int ldc, const rocblas_stride stC, Ud& dInfo, const rocblas_int bc, Th& hA, Th& hB, Th& hC, double* gpu_time_used, double* cpu_time_used, const rocblas_int hot_calls, const int profile, const bool profile_kernels, const bool perf, const bool singular) { if(!perf) { // there is no direct CPU/LAPACK equivalent for this function, therefore // we return an invalid CPU time *cpu_time_used = nan(""); } geblttrf_npvt_initData(handle, nb, nblocks, dA, lda, dB, ldb, dC, ldc, bc, hA, hB, hC, singular); // cold calls for(int iter = 0; iter < 2; iter++) { geblttrf_npvt_initData(handle, nb, nblocks, dA, lda, dB, ldb, dC, ldc, bc, hA, hB, hC, singular); CHECK_ROCBLAS_ERROR(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc)); } // 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++) { geblttrf_npvt_initData(handle, nb, nblocks, dA, lda, dB, ldb, dC, ldc, bc, hA, hB, hC, singular); timer.start(stream); rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc); timer.end(stream); } *gpu_time_used = timer.get_combined(); } template void testing_geblttrf_npvt(Arguments& argus) { // get arguments rocblas_local_handle handle; rocblas_int nb = argus.get("nb"); rocblas_int nblocks = argus.get("nblocks"); rocblas_int lda = argus.get("lda", nb); rocblas_int ldb = argus.get("ldb", nb); rocblas_int ldc = argus.get("ldc", nb); rocblas_stride stA = argus.get("strideA", lda * nb * nblocks); rocblas_stride stB = argus.get("strideB", ldb * nb * nblocks); rocblas_stride stC = argus.get("strideC", ldc * nb * nblocks); rocblas_int bc = argus.batch_count; rocblas_int hot_calls = argus.iters; rocblas_stride stBRes = (argus.unit_check || argus.norm_check) ? stB : 0; rocblas_stride stCRes = (argus.unit_check || argus.norm_check) ? stC : 0; // check non-supported values // N/A // determine sizes size_t size_A = size_t(lda) * nb * nblocks; size_t size_B = size_t(ldb) * nb * nblocks; size_t size_C = size_t(ldc) * nb * nblocks; double max_error = 0, gpu_time_used = 0, cpu_time_used = 0; size_t size_BRes = (argus.unit_check || argus.norm_check) ? size_B : 0; size_t size_CRes = (argus.unit_check || argus.norm_check) ? size_C : 0; // check invalid sizes bool invalid_size = (nb < 0 || nblocks < 0 || lda < nb || ldb < nb || ldc < nb || bc < 0); if(invalid_size) { if(BATCHED) EXPECT_ROCBLAS_STATUS( rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, (T* const*)nullptr, lda, stA, (T* const*)nullptr, ldb, stB, (T* const*)nullptr, ldc, stC, (rocblas_int*)nullptr, bc), rocblas_status_invalid_size); else EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, (T*)nullptr, lda, stA, (T*)nullptr, ldb, stB, (T*)nullptr, ldc, stC, (rocblas_int*)nullptr, bc), 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)); if(BATCHED) CHECK_ALLOC_QUERY(rocsolver_geblttrf_npvt( STRIDED, handle, nb, nblocks, (T* const*)nullptr, lda, stA, (T* const*)nullptr, ldb, stB, (T* const*)nullptr, ldc, stC, (rocblas_int*)nullptr, bc)); else CHECK_ALLOC_QUERY(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, (T*)nullptr, lda, stA, (T*)nullptr, ldb, stB, (T*)nullptr, ldc, stC, (rocblas_int*)nullptr, bc)); size_t size; CHECK_ROCBLAS_ERROR(rocblas_stop_device_memory_size_query(handle, &size)); rocsolver_bench_inform(inform_mem_query, size); return; } if(BATCHED) { // memory allocations host_batch_vector hA(size_A, 1, bc); host_batch_vector hB(size_B, 1, bc); host_batch_vector hC(size_C, 1, bc); host_batch_vector hBRes(size_BRes, 1, bc); host_batch_vector hCRes(size_CRes, 1, bc); host_strided_batch_vector hInfo(1, 1, 1, bc); host_strided_batch_vector hInfoRes(1, 1, 1, bc); device_batch_vector dA(size_A, 1, bc); device_batch_vector dB(size_B, 1, bc); device_batch_vector dC(size_C, 1, bc); device_strided_batch_vector dInfo(1, 1, 1, bc); if(size_A) CHECK_HIP_ERROR(dA.memcheck()); if(size_B) CHECK_HIP_ERROR(dB.memcheck()); if(size_C) CHECK_HIP_ERROR(dC.memcheck()); CHECK_HIP_ERROR(dInfo.memcheck()); // check quick return if(nb == 0 || nblocks == 0 || bc == 0) { EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc), rocblas_status_success); if(argus.timing) rocsolver_bench_inform(inform_quick_return); return; } // check computations if(argus.unit_check || argus.norm_check) geblttrf_npvt_getError(handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc, hA, hB, hBRes, hC, hCRes, hInfo, hInfoRes, &max_error, argus.singular); // collect performance data if(argus.timing && hot_calls > 0) geblttrf_npvt_getPerfData( handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc, hA, hB, hC, &gpu_time_used, &cpu_time_used, hot_calls, argus.profile, argus.profile_kernels, argus.perf, argus.singular); } else { // memory allocations host_strided_batch_vector hA(size_A, 1, stA, bc); host_strided_batch_vector hB(size_B, 1, stB, bc); host_strided_batch_vector hC(size_C, 1, stC, bc); host_strided_batch_vector hBRes(size_BRes, 1, stBRes, bc); host_strided_batch_vector hCRes(size_CRes, 1, stCRes, bc); host_strided_batch_vector hInfo(1, 1, 1, bc); host_strided_batch_vector hInfoRes(1, 1, 1, bc); device_strided_batch_vector dA(size_A, 1, stA, bc); device_strided_batch_vector dB(size_B, 1, stB, bc); device_strided_batch_vector dC(size_C, 1, stC, bc); device_strided_batch_vector dInfo(1, 1, 1, bc); if(size_A) CHECK_HIP_ERROR(dA.memcheck()); if(size_B) CHECK_HIP_ERROR(dB.memcheck()); if(size_C) CHECK_HIP_ERROR(dC.memcheck()); CHECK_HIP_ERROR(dInfo.memcheck()); // check quick return if(nb == 0 || nblocks == 0 || bc == 0) { EXPECT_ROCBLAS_STATUS(rocsolver_geblttrf_npvt(STRIDED, handle, nb, nblocks, dA.data(), lda, stA, dB.data(), ldb, stB, dC.data(), ldc, stC, dInfo.data(), bc), rocblas_status_success); if(argus.timing) rocsolver_bench_inform(inform_quick_return); return; } // check computations if(argus.unit_check || argus.norm_check) geblttrf_npvt_getError(handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc, hA, hB, hBRes, hC, hCRes, hInfo, hInfoRes, &max_error, argus.singular); // collect performance data if(argus.timing && hot_calls > 0) geblttrf_npvt_getPerfData( handle, nb, nblocks, dA, lda, stA, dB, ldb, stB, dC, ldc, stC, dInfo, bc, hA, hB, hC, &gpu_time_used, &cpu_time_used, hot_calls, argus.profile, argus.profile_kernels, argus.perf, argus.singular); } // validate results for rocsolver-test // using nb * machine_precision as tolerance if(argus.unit_check) ROCSOLVER_TEST_CHECK(T, max_error, nb); // output results for rocsolver-bench if(argus.timing) { if(!argus.perf) { rocsolver_bench_header("Arguments:"); if(BATCHED) { rocsolver_bench_output("nb", "nblocks", "lda", "ldb", "ldc", "batch_c"); rocsolver_bench_output(nb, nblocks, lda, ldb, ldc, bc); } else if(STRIDED) { rocsolver_bench_output("nb", "nblocks", "lda", "strideA", "ldb", "strideB", "ldc", "strideC", "batch_c"); rocsolver_bench_output(nb, nblocks, lda, stA, ldb, stB, ldc, stC, bc); } else { rocsolver_bench_output("nb", "nblocks", "lda", "ldb", "ldc"); rocsolver_bench_output(nb, nblocks, lda, ldb, 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, max_error); } 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, max_error); else rocsolver_bench_output(gpu_time_used); } } // ensure all arguments were consumed argus.validate_consumed(); } #define EXTERN_TESTING_GEBLTTRF_NPVT(...) \ extern template void testing_geblttrf_npvt<__VA_ARGS__>(Arguments&); INSTANTIATE(EXTERN_TESTING_GEBLTTRF_NPVT, FOREACH_MATRIX_DATA_LAYOUT, FOREACH_SCALAR_TYPE, APPLY_STAMP)