diff --git a/_sources/building_the_project_with_dpcpp.rst b/_sources/building_the_project_with_dpcpp.rst index 6076117f7..efe92f285 100644 --- a/_sources/building_the_project_with_dpcpp.rst +++ b/_sources/building_the_project_with_dpcpp.rst @@ -104,6 +104,9 @@ The most important supported build options are: * - ENABLE_CURAND_BACKEND - True, False - False + * - ENABLE_CUSPARSE_BACKEND + - True, False + - False * - ENABLE_NETLIB_BACKEND - True, False - False @@ -183,8 +186,8 @@ Building for CUDA ^^^^^^^^^^^^^^^^^ The CUDA backends can be enabled with ``ENABLE_CUBLAS_BACKEND``, -``ENABLE_CUFFT_BACKEND``, ``ENABLE_CURAND_BACKEND``, and -``ENABLE_CUSOLVER_BACKEND``. +``ENABLE_CUFFT_BACKEND``, ``ENABLE_CURAND_BACKEND``, +``ENABLE_CUSOLVER_BACKEND``, and ``ENABLE_CUSPARSE_BACKEND``. No additional parameters are required for using CUDA libraries. In most cases, the CUDA libraries should be found automatically by CMake. @@ -371,6 +374,7 @@ disabled using the Ninja build system: -DENABLE_CUBLAS_BACKEND=True \ -DENABLE_CUSOLVER_BACKEND=True \ -DENABLE_CURAND_BACKEND=True \ + -DENABLE_CUSPARSE_BACKEND=True \ -DBUILD_FUNCTIONAL_TESTS=False ``$ONEMKL_DIR`` points at the oneMKL source directly. The x86 CPU (``MKLCPU``) diff --git a/_sources/domains/sparse_linear_algebra.rst b/_sources/domains/sparse_linear_algebra.rst index eab5afd56..07d90359a 100644 --- a/_sources/domains/sparse_linear_algebra.rst +++ b/_sources/domains/sparse_linear_algebra.rst @@ -20,21 +20,150 @@ Currently known limitations: - ``oneapi::mkl::sparse::set_csr_data`` and ``oneapi::mkl::sparse::set_coo_data`` functions cannot be used on a handle that has already been used for an operation or its optimize function. Doing so - will throw an ``oneapi::mkl::unimplemented`` exception. + will throw a ``oneapi::mkl::unimplemented`` exception. - Using ``spsv`` with the ``oneapi::mkl::sparse::spsv_alg::no_optimize_alg`` and a sparse matrix that does not have the - ``oneapi::mkl::sparse::matrix_property::sorted`` property will throw an + ``oneapi::mkl::sparse::matrix_property::sorted`` property will throw a ``oneapi::mkl::unimplemented`` exception. - Using ``spmm`` on Intel GPU with a sparse matrix that is ``oneapi::mkl::transpose::conjtrans`` and has the - ``oneapi::mkl::sparse::matrix_property::symmetric`` property will throw an + ``oneapi::mkl::sparse::matrix_property::symmetric`` property will throw a ``oneapi::mkl::unimplemented`` exception. - Using ``spmv`` with a sparse matrix that is ``oneapi::mkl::transpose::conjtrans`` with a ``type_view`` - ``matrix_descr::symmetric`` or ``matrix_descr::hermitian`` will throw an + ``matrix_descr::symmetric`` or ``matrix_descr::hermitian`` will throw a ``oneapi::mkl::unimplemented`` exception. - Using ``spsv`` on Intel GPU with a sparse matrix that is - ``oneapi::mkl::transpose::conjtrans`` and will throw an + ``oneapi::mkl::transpose::conjtrans`` and will throw a ``oneapi::mkl::unimplemented`` exception. - Scalar parameters ``alpha`` and ``beta`` should be host pointers to prevent synchronizations and copies to the host. + + +cuSPARSE backend +---------------- + +Currently known limitations: + +- The COO format requires the indices to be sorted by row. See the `cuSPARSE + documentation + `_. Sparse + operations using matrices with the COO format without the property + ``matrix_property::sorted_by_rows`` or ``matrix_property::sorted`` will throw + a ``oneapi::mkl::unimplemented`` exception. +- Using ``spmm`` with the algorithm ``spmm_alg::csr_alg3`` and an ``opA`` other + than ``transpose::nontrans`` or an ``opB`` ``transpose::conjtrans`` will throw + a ``oneapi::mkl::unimplemented`` exception. +- Using ``spmm`` with the algorithm ``spmm_alg::csr_alg3``, + ``opB=transpose::trans`` and real fp64 precision will throw a + ``oneapi::mkl::unimplemented`` exception. This configuration can fail as of + CUDA 12.6.2, see the related issue + `here`_. +- Using ``spmv`` with a ``type_view`` other than ``matrix_descr::general`` will + throw a ``oneapi::mkl::unimplemented`` exception. +- Using ``spsv`` with the algorithm ``spsv_alg::no_optimize_alg`` may still + perform some mandatory preprocessing. +- oneMKL Interface does not provide a way to use non-default algorithms without + calling preprocess functions such as ``cusparseSpMM_preprocess`` or + ``cusparseSpMV_preprocess``. Feel free to create an issue if this is needed. + + +Operation algorithms mapping +---------------------------- + +The following tables describe how a oneMKL SYCL Interface algorithm maps to the +backend's algorithms. Refer to the backend's documentation for a more detailed +explanation of the algorithms. + +Backends with no equivalent algorithms will fallback to the backend's default +behavior. + + +spmm +^^^^ + +.. list-table:: + :header-rows: 1 + :widths: 10 30 45 + + * - ``spmm_alg`` value + - MKLCPU/MKLGPU + - cuSPARSE + * - ``default_alg`` + - none + - ``CUSPARSE_SPMM_ALG_DEFAULT`` + * - ``no_optimize_alg`` + - none + - ``CUSPARSE_SPMM_ALG_DEFAULT`` + * - ``coo_alg1`` + - none + - ``CUSPARSE_SPMM_COO_ALG1`` + * - ``coo_alg2`` + - none + - ``CUSPARSE_SPMM_COO_ALG2`` + * - ``coo_alg3`` + - none + - ``CUSPARSE_SPMM_COO_ALG3`` + * - ``coo_alg4`` + - none + - ``CUSPARSE_SPMM_COO_ALG4`` + * - ``csr_alg1`` + - none + - ``CUSPARSE_SPMM_CSR_ALG1`` + * - ``csr_alg2`` + - none + - ``CUSPARSE_SPMM_CSR_ALG2`` + * - ``csr_alg3`` + - none + - ``CUSPARSE_SPMM_CSR_ALG3`` + + +spmv +^^^^ + +.. list-table:: + :header-rows: 1 + :widths: 10 30 45 + + * - ``spmv_alg`` value + - MKLCPU/MKLGPU + - cuSPARSE + * - ``default_alg`` + - none + - ``CUSPARSE_SPMV_ALG_DEFAULT`` + * - ``no_optimize_alg`` + - none + - ``CUSPARSE_SPMV_ALG_DEFAULT`` + * - ``coo_alg1`` + - none + - ``CUSPARSE_SPMV_COO_ALG1`` + * - ``coo_alg2`` + - none + - ``CUSPARSE_SPMV_COO_ALG2`` + * - ``csr_alg1`` + - none + - ``CUSPARSE_SPMV_CSR_ALG1`` + * - ``csr_alg2`` + - none + - ``CUSPARSE_SPMV_CSR_ALG2`` + * - ``csr_alg3`` + - none + - ``CUSPARSE_SPMV_ALG_DEFAULT`` + + +spsv +^^^^ + +.. list-table:: + :header-rows: 1 + :widths: 10 30 45 + + * - ``spsv_alg`` value + - MKLCPU/MKLGPU + - cuSPARSE + * - ``default_alg`` + - none + - ``CUSPARSE_SPSV_ALG_DEFAULT`` + * - ``no_optimize_alg`` + - none + - ``CUSPARSE_SPSV_ALG_DEFAULT`` diff --git a/building_the_project_with_dpcpp.html b/building_the_project_with_dpcpp.html index 47d0ea9d0..931da28be 100644 --- a/building_the_project_with_dpcpp.html +++ b/building_the_project_with_dpcpp.html @@ -648,47 +648,51 @@

Contents

True, False

False

-

ENABLE_NETLIB_BACKEND

+

ENABLE_CUSPARSE_BACKEND

True, False

False

-

ENABLE_ROCBLAS_BACKEND

+

ENABLE_NETLIB_BACKEND

True, False

False

-

ENABLE_ROCFFT_BACKEND

+

ENABLE_ROCBLAS_BACKEND

True, False

False

-

ENABLE_ROCSOLVER_BACKEND

+

ENABLE_ROCFFT_BACKEND

True, False

False

-

ENABLE_ROCRAND_BACKEND

+

ENABLE_ROCSOLVER_BACKEND

True, False

False

-

ENABLE_MKLCPU_THREAD_TBB

+

ENABLE_ROCRAND_BACKEND

+

True, False

+

False

+ +

ENABLE_MKLCPU_THREAD_TBB

True, False

True

-

ENABLE_PORTBLAS_BACKEND

+

ENABLE_PORTBLAS_BACKEND

True, False

False

-

ENABLE_PORTFFT_BACKEND

+

ENABLE_PORTFFT_BACKEND

True, False

False

-

BUILD_FUNCTIONAL_TESTS

+

BUILD_FUNCTIONAL_TESTS

True, False

True

-

BUILD_EXAMPLES

+

BUILD_EXAMPLES

True, False

True

-

TARGET_DOMAINS (list)

+

TARGET_DOMAINS (list)

blas, lapack, rng, dft, sparse_blas

All domains

@@ -726,8 +730,8 @@

Backends

Building for CUDA#

The CUDA backends can be enabled with ENABLE_CUBLAS_BACKEND, -ENABLE_CUFFT_BACKEND, ENABLE_CURAND_BACKEND, and -ENABLE_CUSOLVER_BACKEND.

+ENABLE_CUFFT_BACKEND, ENABLE_CURAND_BACKEND, +ENABLE_CUSOLVER_BACKEND, and ENABLE_CUSPARSE_BACKEND.

No additional parameters are required for using CUDA libraries. In most cases, the CUDA libraries should be found automatically by CMake.

@@ -893,6 +897,7 @@

Backends -DENABLE_CUBLAS_BACKEND=True \ -DENABLE_CUSOLVER_BACKEND=True \ -DENABLE_CURAND_BACKEND=True \ + -DENABLE_CUSPARSE_BACKEND=True \ -DBUILD_FUNCTIONAL_TESTS=False diff --git a/domains/sparse_linear_algebra.html b/domains/sparse_linear_algebra.html index ee84b36c3..47ac635ba 100644 --- a/domains/sparse_linear_algebra.html +++ b/domains/sparse_linear_algebra.html @@ -525,6 +525,13 @@

Contents

@@ -551,26 +558,186 @@

OneMKL Intel CPU and GPU backendsoneapi::mkl::sparse::set_csr_data and oneapi::mkl::sparse::set_coo_data functions cannot be used on a handle that has already been used for an operation or its optimize function. Doing so -will throw an oneapi::mkl::unimplemented exception.

+will throw a oneapi::mkl::unimplemented exception.

  • Using spsv with the oneapi::mkl::sparse::spsv_alg::no_optimize_alg and a sparse matrix that does not have the -oneapi::mkl::sparse::matrix_property::sorted property will throw an +oneapi::mkl::sparse::matrix_property::sorted property will throw a oneapi::mkl::unimplemented exception.

  • Using spmm on Intel GPU with a sparse matrix that is oneapi::mkl::transpose::conjtrans and has the -oneapi::mkl::sparse::matrix_property::symmetric property will throw an +oneapi::mkl::sparse::matrix_property::symmetric property will throw a oneapi::mkl::unimplemented exception.

  • Using spmv with a sparse matrix that is oneapi::mkl::transpose::conjtrans with a type_view -matrix_descr::symmetric or matrix_descr::hermitian will throw an +matrix_descr::symmetric or matrix_descr::hermitian will throw a oneapi::mkl::unimplemented exception.

  • Using spsv on Intel GPU with a sparse matrix that is -oneapi::mkl::transpose::conjtrans and will throw an +oneapi::mkl::transpose::conjtrans and will throw a oneapi::mkl::unimplemented exception.

  • Scalar parameters alpha and beta should be host pointers to prevent synchronizations and copies to the host.

    • +
    +

    cuSPARSE backend#

    +

    Currently known limitations:

    +
      +

    • The COO format requires the indices to be sorted by row. See the cuSPARSE +documentation. Sparse +operations using matrices with the COO format without the property +matrix_property::sorted_by_rows or matrix_property::sorted will throw +a oneapi::mkl::unimplemented exception.

      • +

    • Using spmm with the algorithm spmm_alg::csr_alg3 and an opA other +than transpose::nontrans or an opB transpose::conjtrans will throw +a oneapi::mkl::unimplemented exception.

      • +

    • Using spmm with the algorithm spmm_alg::csr_alg3, +opB=transpose::trans and real fp64 precision will throw a +oneapi::mkl::unimplemented exception. This configuration can fail as of +CUDA 12.6.2, see the related issue +`here<https://forums.developer.nvidia.com/t/cusparse-spmm-sample-failing-with-misaligned-address/311022>`_.

      • +

    • Using spmv with a type_view other than matrix_descr::general will +throw a oneapi::mkl::unimplemented exception.

      • +

    • Using spsv with the algorithm spsv_alg::no_optimize_alg may still +perform some mandatory preprocessing.

      • +

    • oneMKL Interface does not provide a way to use non-default algorithms without +calling preprocess functions such as cusparseSpMM_preprocess or +cusparseSpMV_preprocess. Feel free to create an issue if this is needed.

      • +
    +
    +
    +

    Operation algorithms mapping#

    +

    The following tables describe how a oneMKL SYCL Interface algorithm maps to the +backend’s algorithms. Refer to the backend’s documentation for a more detailed +explanation of the algorithms.

    +

    Backends with no equivalent algorithms will fallback to the backend’s default +behavior.

    +
    +

    spmm#

    + +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    spmm_alg value

    MKLCPU/MKLGPU

    cuSPARSE

    default_alg

    none

    CUSPARSE_SPMM_ALG_DEFAULT

    no_optimize_alg

    none

    CUSPARSE_SPMM_ALG_DEFAULT

    coo_alg1

    none

    CUSPARSE_SPMM_COO_ALG1

    coo_alg2

    none

    CUSPARSE_SPMM_COO_ALG2

    coo_alg3

    none

    CUSPARSE_SPMM_COO_ALG3

    coo_alg4

    none

    CUSPARSE_SPMM_COO_ALG4

    csr_alg1

    none

    CUSPARSE_SPMM_CSR_ALG1

    csr_alg2

    none

    CUSPARSE_SPMM_CSR_ALG2

    csr_alg3

    none

    CUSPARSE_SPMM_CSR_ALG3

    +
    +
    +

    spmv#

    + +++++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    spmv_alg value

    MKLCPU/MKLGPU

    cuSPARSE

    default_alg

    none

    CUSPARSE_SPMV_ALG_DEFAULT

    no_optimize_alg

    none

    CUSPARSE_SPMV_ALG_DEFAULT

    coo_alg1

    none

    CUSPARSE_SPMV_COO_ALG1

    coo_alg2

    none

    CUSPARSE_SPMV_COO_ALG2

    csr_alg1

    none

    CUSPARSE_SPMV_CSR_ALG1

    csr_alg2

    none

    CUSPARSE_SPMV_CSR_ALG2

    csr_alg3

    none

    CUSPARSE_SPMV_ALG_DEFAULT

    +
    +
    +

    spsv#

    + +++++ + + + + + + + + + + + + + + + + +

    spsv_alg value

    MKLCPU/MKLGPU

    cuSPARSE

    default_alg

    none

    CUSPARSE_SPSV_ALG_DEFAULT

    no_optimize_alg

    none

    CUSPARSE_SPSV_ALG_DEFAULT

    +
    +
    @@ -619,6 +786,13 @@

    OneMKL Intel CPU and GPU backends diff --git a/index.html b/index.html index 667fa7d06..c503e866c 100644 --- a/index.html +++ b/index.html @@ -599,6 +599,8 @@

    Contents
  • Sparse Linear Algebra
  • Integrating a Third-Party Library to oneAPI Math Kernel Library (oneMKL) Interfaces
      diff --git a/searchindex.js b/searchindex.js index e675ed00b..4bc6fe79b 100644 --- a/searchindex.js +++ b/searchindex.js @@ -1 +1 @@ -Search.setIndex({"alltitles": {"1. Create Header Files": [[3, "create-header-files"]], "2. Integrate Header Files": [[3, "integrate-header-files"]], "3. Create Wrappers": [[3, "create-wrappers"]], "4. Integrate Wrappers to the Build System": [[3, "integrate-wrappers-to-the-build-system"]], "5. Update the Test System": [[3, "update-the-test-system"]], "About": [[154, null]], "Additional Build Options": [[2, "additional-build-options"]], "BLAS Level 1 Routines": [[9, "blas-level-1-routines"]], "BLAS Level 2 Routines": [[10, "blas-level-2-routines"]], "BLAS Level 3 Routines": [[11, "blas-level-3-routines"]], "BLAS Routines": [[8, "blas-routines"]], "BLAS-like Extensions": [[12, "blas-like-extensions"]], "Backends": [[1, "backends"], [2, "backends"]], "Build Commands": [[1, "build-commands"], [2, "build-commands"]], "Build FAQ": [[2, "build-faq"]], "Building and Running Tests": [[0, "building-and-running-tests"]], "Building for CUDA": [[1, "building-for-cuda"], [2, "building-for-cuda"]], "Building for Intel(R) oneMKL": [[2, "building-for-intel-r-onemkl"]], "Building for ROCm": [[1, "building-for-rocm"], [2, "building-for-rocm"]], "Building for Windows": [[2, "building-for-windows"]], "Building for other SYCL devices": [[2, "building-for-other-sycl-devices"]], "Building for portBLAS": [[2, "building-for-portblas"]], "Building for portFFT": [[2, "building-for-portfft"]], "Building the Project with AdaptiveCpp": [[1, "building-the-project-with-adaptivecpp"]], "Building the Project with DPC++": [[2, "building-the-project-with-dpc"]], "CMake invocation examples": [[2, "cmake-invocation-examples"]], "Contents": [[154, "contents"]], "Dense Linear Algebra": [[69, "dense-linear-algebra"]], "Developer Reference": [[154, null]], "Environment Setup": [[1, "environment-setup"], [2, "environment-setup"]], "Get Started": [[154, null]], "Integrating a Third-Party Library to oneAPI Math Kernel Library (oneMKL) Interfaces": [[3, "integrating-a-third-party-library-to-oneapi-math-kernel-library-onemkl-interfaces"]], "Introduction": [[155, "introduction"]], "LAPACK Linear Equation Routines": [[100, "lapack-linear-equation-routines"], [102, "lapack-linear-equation-routines"]], "LAPACK Routines": [[100, "lapack-routines"]], "LAPACK Singular Value and Eigenvalue Problem Routines": [[100, "lapack-singular-value-and-eigenvalue-problem-routines"], [103, "lapack-singular-value-and-eigenvalue-problem-routines"]], "LAPACK-like Extensions Routines": [[100, "lapack-like-extensions-routines"], [101, "lapack-like-extensions-routines"]], "Matrix Storage": [[152, "matrix-storage"]], "OneMKL Intel CPU and GPU backends": [[153, "onemkl-intel-cpu-and-gpu-backends"]], "Project Cleanup": [[1, "project-cleanup"], [2, "project-cleanup"]], "Pure SYCL backends: portBLAS and portFFT": [[2, "pure-sycl-backends-portblas-and-portfft"]], "Selecting a Compiler": [[157, "selecting-a-compiler"]], "Sparse Linear Algebra": [[153, "sparse-linear-algebra"]], "TARGET_DOMAINS": [[2, "target-domains"]], "Using CMake\u2019s FetchContent": [[158, "using-cmake-s-fetchcontent"]], "Using an installed oneMKL Interfaces": [[158, "using-an-installed-onemkl-interfaces"]], "Using the oneMKL Interfaces in your project with CMake": [[158, "using-the-onemkl-interfaces-in-your-project-with-cmake"]], "asum": [[4, "asum"]], "asum (Buffer Version)": [[4, "asum-buffer-version"]], "asum (USM Version)": [[4, "asum-usm-version"]], "axpby": [[5, "axpby"]], "axpby (Buffer Version)": [[5, "axpby-buffer-version"]], "axpby (USM Version)": [[5, "axpby-usm-version"]], "axpy": [[6, "axpy"]], "axpy (Buffer Version)": [[6, "axpy-buffer-version"]], "axpy (USM Version)": [[6, "axpy-usm-version"]], "axpy_batch": [[7, "axpy-batch"]], "axpy_batch (Buffer Version)": [[7, "axpy-batch-buffer-version"]], "axpy_batch (USM Version)": [[7, "axpy-batch-usm-version"]], "copy": [[13, "copy"]], "copy (Buffer Version)": [[13, "copy-buffer-version"]], "copy (USM Version)": [[13, "copy-usm-version"]], "copy_batch": [[14, "copy-batch"]], "copy_batch (Buffer Version)": [[14, "copy-batch-buffer-version"]], "copy_batch (USM Version)": [[14, "copy-batch-usm-version"]], "dgmm_batch": [[15, "dgmm-batch"]], "dgmm_batch (Buffer Version)": [[15, "dgmm-batch-buffer-version"]], "dgmm_batch (USM Version)": [[15, "dgmm-batch-usm-version"]], "diag": [[156, "diag"]], "dot": [[16, "dot"]], "dot (Buffer Version)": [[16, "dot-buffer-version"]], "dot (USM Version)": [[16, "dot-usm-version"]], "dotc": [[17, "dotc"]], "dotc (Buffer Version)": [[17, "dotc-buffer-version"]], "dotc (USM Version)": [[17, "dotc-usm-version"]], "dotu": [[18, "dotu"]], "dotu (Buffer Version)": [[18, "dotu-buffer-version"]], "dotu (USM Version)": [[18, "dotu-usm-version"]], "gbmv": [[19, "gbmv"]], "gbmv (Buffer Version)": [[19, "gbmv-buffer-version"]], "gbmv (USM Version)": [[19, "gbmv-usm-version"]], "gebrd": [[70, "gebrd"]], "gebrd (Buffer Version)": [[70, "gebrd-buffer-version"]], "gebrd (USM Version)": [[70, "gebrd-usm-version"]], "gebrd_scratchpad_size": [[71, "gebrd-scratchpad-size"]], "gemm": [[20, "gemm"]], "gemm (Buffer Version)": [[20, "gemm-buffer-version"]], "gemm (USM Version)": [[20, "gemm-usm-version"]], "gemm_batch": [[21, "gemm-batch"]], "gemm_batch (Buffer Version)": [[21, "gemm-batch-buffer-version"]], "gemm_batch (USM Version)": [[21, "gemm-batch-usm-version"]], "gemm_bias": [[22, "gemm-bias"]], "gemm_bias (Buffer Version)": [[22, "gemm-bias-buffer-version"]], "gemm_bias (USM Version)": [[22, "gemm-bias-usm-version"]], "gemmt": [[23, "gemmt"]], "gemmt (Buffer Version)": [[23, "gemmt-buffer-version"]], "gemmt (USM Version)": [[23, "gemmt-usm-version"]], "gemv": [[24, "gemv"]], "gemv (Buffer Version)": [[24, "gemv-buffer-version"]], "gemv (USM Version)": [[24, "gemv-usm-version"]], "gemv_batch": [[25, "gemv-batch"]], "gemv_batch (Buffer Version)": [[25, "gemv-batch-buffer-version"]], "gemv_batch (USM Version)": [[25, "gemv-batch-usm-version"]], "geqrf": [[72, "geqrf"]], "geqrf (Buffer Version)": [[72, "geqrf-buffer-version"]], "geqrf (USM Version)": [[72, "geqrf-usm-version"]], "geqrf_batch": [[73, "geqrf-batch"]], "geqrf_batch (Buffer Version)": [[73, "geqrf-batch-buffer-version"]], "geqrf_batch (USM Version)": [[73, "geqrf-batch-usm-version"]], "geqrf_batch_scratchpad_size": [[74, 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103, 128, 130], "consecut": [5, 15, 25], "consequ": 2, "consist": 70, "const": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "constraint": [104, 105, 138, 139], "construct": 158, "consum": 158, "contain": [3, 7, 14, 15, 21, 25, 39, 40, 44, 45, 59, 67, 69, 70, 72, 73, 76, 78, 80, 81, 88, 89, 92, 94, 96, 98, 100, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 146, 148, 150, 152], "content": 78, "contigu": 152, "control": 2, "convent": 152, "convert": 3, "coordin": [43, 45], "copi": [9, 14, 153, 158], "correspond": [1, 3, 73, 96, 98, 107, 119, 125, 132, 134, 141, 152], "could": 2, "cpp": 3, "cpu": [0, 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112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152], "least": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89, 90, 92, 94, 96, 98, 100, 102, 104, 107, 108, 110, 112, 114, 116, 118, 119, 120, 122, 124, 125, 126, 128, 130, 132, 134, 136, 138, 141, 142, 144, 146, 148, 150, 152], "left": [15, 30, 42, 52, 53, 64, 66, 67, 78, 79, 112, 113, 114, 115, 116, 117, 146, 147, 148, 149, 150, 151, 152, 156], "left_right": [15, 30, 53, 64, 66, 67], "leftarrow": [5, 6, 13, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 62, 64, 65], "len": [15, 19, 24, 25], "length": [19, 24, 26, 27, 28, 29, 31, 32, 33, 36, 37, 38, 46, 49, 50, 51, 54, 55, 56, 60, 61, 62, 63, 65, 68], "less": [70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "level": [3, 4, 6, 8, 13, 16, 17, 18, 19, 20, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68], "level1": 8, "level2": 8, "level3": 8, "lib": [2, 3], "lib_nam": 3, "lib_obj": 3, "libnewlib": 3, "libonemkl": 3, "libonemkl_blas_mklcpu": 3, "libonemkl_blas_newlib": 3, "librari": [0, 1, 2, 12, 100, 101, 154, 155, 158], "like": [2, 5, 7, 8, 14, 15, 21, 22, 23, 25, 59, 67, 73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142, 156], "limit": [2, 153], "linear": [8, 10, 61, 63, 67, 68, 72, 75, 76, 77, 80, 83, 84, 87, 88, 89, 91, 98, 99, 101, 106, 109, 112, 113, 114, 115, 118, 121, 122, 123, 124, 125, 127, 134, 135, 136, 137, 140, 143, 146, 147, 148, 149, 154], "link": [2, 3, 158], "linux": [1, 2, 157], "list": [1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 100, 101, 102, 103, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "ll": [94, 118, 124, 127, 130], "llvm": 2, "load": 3, "loader": 3, "locat": 3, "long": 156, "longer": 156, "look": 2, "lower": [12, 23, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 80, 81, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, 150, 151, 152, 156], "lu": [80, 81, 84, 85, 88, 89, 100, 101, 102, 119, 125], "m": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 53, 54, 64, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 98, 100, 102, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 134, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152], "m1": 152, "m2": 152, "m3": 152, "m_g": [73, 74, 81, 82, 107, 108, 141, 142], "macro": 3, "magnitud": [4, 9], "mai": [1, 2, 100, 156, 158], "main": [152, 158], "main_test": 3, "major": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 34, 35, 53, 57, 58, 59, 64, 66, 67, 152], "make": [1, 2, 3], "makefil": [1, 2], "mani": [12, 100, 101], "manual": [0, 1, 2, 3, 158], "map": [3, 153], "match": 158, "math": [12, 100, 101, 141, 154], "matric": [11, 12, 15, 20, 21, 22, 23, 25, 30, 34, 53, 57, 59, 64, 66, 67, 69, 70, 73, 74, 81, 82, 85, 86, 89, 90, 94, 95, 96, 97, 98, 100, 101, 104, 107, 108, 119, 120, 125, 126, 130, 131, 132, 133, 134, 136, 138, 141, 142, 152, 156], "matrix": [4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 87, 88, 91, 92, 93, 94, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 156], "matrix_descr": 153, "matrix_properti": 153, "max": [22, 70, 72, 76, 77, 78, 80, 81, 84, 88, 92, 94, 96, 98, 110, 112, 114, 116, 117, 118, 122, 124, 128, 130, 132, 134, 136, 137, 138, 144, 146, 148, 150, 151, 152], "maxim": 39, "maximum": [9, 39], "md": 2, "mechan": 3, "memori": [5, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152], "messag": 158, "method": [3, 94, 98, 130, 134], "mi": 2, "mi200": [1, 2], "mi210": 2, "mi50": 2, "min": [70, 72, 73, 76, 78, 79, 80, 81, 104, 105, 138, 139, 152], "minim": 40, "minimum": [9, 40], "miss": 2, "mix": 16, "mkdir": [0, 1, 2], "mkl": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 156, 158], "mkl_install_prefix": 2, "mkl_link_c": 3, "mkl_root": 2, "mklcpu": [1, 2, 3], "mklgpu": [1, 2, 3], "mklroot": 2, "mn": 152, "mode": 3, "model": 3, "modifi": [3, 9, 44, 45], "more": [0, 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69], "most": [1, 2, 104, 138], "mostli": 2, "multipl": [1, 2, 3, 7, 14, 15, 21, 22, 25, 30, 34, 53, 57, 59, 64, 67, 88, 89, 100, 101, 102, 124, 125, 136, 155, 156], "multipli": [21, 66, 67, 98, 100, 102, 103, 112, 113, 114, 115, 116, 117, 134, 146, 147, 148, 149, 150, 151], "must": [1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 157], "mxn": 15, "mytarget": 158, "n": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 156], "n1": 152, "n2": 152, "n3": 152, "n_g": [73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142], "name": [1, 2, 3, 96, 156, 158], "namespac": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 156], "nan": [39, 40, 100], "ne": 78, "need": [1, 2, 3, 20, 21, 22, 23, 30, 36, 37, 38, 53, 64, 66, 67, 104, 138], "neg": 78, "never": [57, 58, 59], "new": [1, 2, 3, 156], "new_directori": 3, "newbackend": 3, "newdevic": 3, "newlib": 3, "newlib_librari": 3, "newlib_root": 3, "newlib_sasum": 3, "newlib_wrapp": 3, "newlib_wrappers_table_dyn": 3, "newlibroot": 3, "ng": 120, "ninja": [1, 2], "nn": 152, "no_optimize_alg": 153, "non": [25, 60, 61, 62, 63, 65, 68, 78], "none": 2, "nontran": [34, 35, 57, 58, 88, 89, 90, 91, 112, 113, 114, 115, 116, 117, 136, 137, 146, 147, 148, 149, 150, 151, 156], "nonunit": [136, 137, 156], "norm": [9, 41], "normal": [94, 130], "note": [2, 3, 16, 20, 21, 22, 23, 30, 39, 40, 53, 64, 66, 67, 100, 104, 138], "novec": [78, 79, 92, 93, 94, 95, 128, 129, 130, 131], "now": 3, "nrh": [88, 89, 90, 91, 124, 125, 126, 127, 136, 137], "nrhsg": 90, "nrm2": 9, "number": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151], "nvidia": [1, 2, 157], "nvptx64": 2, "obtain": [98, 134], "off": [3, 70, 96, 132], "offset": [7, 14, 15, 21, 22, 25, 59, 67, 154], "offset_typ": 22, "often": 2, "omit": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68], "omp": 1, "onc": [1, 2], "one": [1, 2, 3, 11, 13, 14, 19, 20, 21, 22, 23, 24, 25, 30, 35, 39, 40, 53, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 112, 114, 116, 146, 148, 150, 152, 156, 158], "oneapi": 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"onemkl_dft": 158, "onemkl_dft_cufft": 158, "onemkl_dir": 2, "onemkl_enable_mklcpu_backend": 3, "onemkl_enable_mklgpu_backend": 3, "onemkl_enable_newlib_backend": 3, "onemkl_interface_librari": 158, "onemkl_lapack_geqrf_batch_usm": [107, 141], "onemkl_lapack_getrf_batch_usm": 89, "onemkl_lapack_sytrd": 116, "onemkl_librari": 3, "onemkl_rng_curand": 3, "onemkl_sycl_implement": 2, "onli": [0, 1, 2, 3, 7, 12, 14, 15, 21, 23, 25, 59, 67, 73, 81, 85, 89, 92, 93, 94, 95, 107, 119, 125, 128, 129, 130, 131, 136, 141, 156], "op": [19, 20, 21, 22, 23, 24, 25, 35, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68], "open": [2, 155], "oper": [2, 7, 9, 10, 11, 12, 14, 15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 153, 157], "opt": 2, "optim": 153, "option": [0, 1, 3, 78, 79, 92, 94, 100, 103, 128, 130, 154], "order": [78, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, 146, 148, 150, 156], "orgbr": [70, 100, 103, 105], "orgbr_scratchpad_s": [100, 103, 104], "orgqr": [100, 102, 109], "orgqr_batch": [100, 101, 108], "orgqr_batch_scratchpad_s": [100, 101, 107], "orgqr_scratchpad_s": [100, 102, 106], "orgtr": [100, 103, 111], "orgtr_scratchpad_s": [100, 103, 110], "origin": [104, 105, 138, 139], "ormqr": [100, 102, 113], "ormqr_scratchpad_s": [100, 102, 112], "ormrq": [100, 102, 115], "ormrq_scratchpad_s": [100, 102, 114], "ormtr": [100, 103, 117], "ormtr_scratchpad_s": [100, 103, 116], "orthogon": [70, 72, 73, 76, 78, 96, 100, 101, 102, 103, 104, 106, 107, 110, 112, 114, 116, 128, 132, 140, 141], "orthonorm": [106, 107, 140, 141], "os": 1, "other": [1, 3, 44, 45, 52, 92, 128, 152], "otherwis": [15, 25, 43], "out": 2, "output": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150, 156], "over": [112, 114, 146, 148], "overlap": 100, "overlin": 17, "overwrit": [112, 114, 116, 146, 148, 150], "overwritevec": [78, 79], "overwritten": [7, 14, 15, 20, 21, 22, 23, 25, 30, 34, 35, 53, 57, 58, 59, 64, 66, 67, 70, 72, 76, 78, 79, 80, 84, 88, 92, 94, 96, 98, 104, 106, 110, 112, 114, 116, 118, 122, 124, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "own": 158, "p": [0, 70, 80, 100, 103, 104, 105, 106, 107, 138, 139, 140, 141], "p_": 70, "p_i": 81, "p_il_iu_i": 81, "pack": [10, 36, 37, 38, 49, 50, 51, 62, 63, 152], "packag": [1, 2, 100], "page": [0, 2, 153], "pal": [92, 128], "parallel": [3, 155, 156], "param": [44, 45], "paramet": 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23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 39, 40, 46, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 94, 100, 101, 102, 118, 119, 122, 124, 125, 130, 152], "possibl": 2, "post": 3, "potr": [100, 102, 127], "potrf": [100, 102, 121, 122, 124], "potrf_batch": [100, 101, 120, 125], "potrf_batch_scratchpad_s": [100, 101, 119], "potrf_scratchpad_s": [100, 102, 118], "potri": [100, 102, 123], "potri_scratchpad_s": [100, 102, 122], "potrs_batch": [100, 101, 126], "potrs_batch_scratchpad_s": [100, 101, 125], "potrs_scratchpad_s": [100, 102, 124], "pre": 3, "precis": [4, 5, 6, 7, 9, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 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69, 70, 72, 73, 76, 81, 85, 89, 96, 100, 101, 119, 120, 125, 126, 132], "public": 3, "push_back": 3, "py": 3, "python": 3, "q": [3, 70, 72, 76, 96, 100, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 132, 138, 139, 140, 143, 144, 145, 146, 147, 148, 149, 150, 151], "q_": 70, "q_1b_1p_1": 70, "q_1b_1p_h": 70, "q_i": [73, 100, 101, 107, 108, 141, 142], "q_ir_i": 73, "qbp": 70, "qc": [112, 114, 116, 146, 148, 150], "ql": [92, 128], "qr": [72, 73, 92, 100, 101, 102, 106, 107, 112, 128, 140, 141, 146], "qtq": [96, 110, 116, 132, 144, 150], "quad": 152, "queri": 3, "queue": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 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141, 142, 143, 146, 147, 148, 149, 150, 151], "relat": [69, 100, 103], "relev": [0, 1, 2], "reli": 2, "remain": 76, "replac": [44, 52], "repositori": [1, 2, 157], "repres": [70, 72, 73, 74, 76, 96, 132, 152], "represent": [70, 72, 73, 76, 96, 132], "request": [92, 128], "requir": [0, 1, 2, 3, 44, 45, 71, 74, 75, 77, 79, 82, 83, 86, 87, 90, 91, 92, 93, 95, 97, 99, 105, 108, 109, 111, 113, 115, 117, 120, 121, 123, 126, 127, 128, 129, 131, 133, 135, 137, 139, 142, 143, 145, 147, 149, 151, 153, 157, 158], "required_var": 3, "respect": [2, 44, 45, 152], "result": [3, 4, 6, 12, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 39, 40, 41, 45, 46, 48, 49, 50, 53, 54, 55, 56, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 100, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "retain": [1, 2], "retriev": 2, "return": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151], "rhs_g": 126, "riangular": 156, "right": [15, 30, 42, 52, 53, 63, 64, 66, 67, 68, 78, 88, 89, 90, 91, 100, 101, 102, 112, 113, 114, 115, 116, 117, 124, 125, 126, 127, 136, 137, 146, 147, 148, 149, 150, 151, 152, 156], "rng": [1, 2], "rocbla": 2, "rocminfo": 2, "rocrand": 2, "rocsolv": 2, "root": [1, 2], "rot": 9, "rotat": [9, 42, 43, 44, 45], "rotg": 9, "rotm": 9, "rotmg": 9, "routin": [4, 5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 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26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68], "rowwis": 78, "rq": [76, 100, 102, 112, 114, 146, 148], "rt": 2, "run": [1, 2, 3, 154, 158], "runtime_error": 3, "rx": 2, "safe": 156, "sai": 156, "same": [2, 3, 39, 40, 110, 111, 116, 117, 144, 145, 150, 151, 152, 156], "sb": 48, "sbmv": 10, "scal": 9, "scalar": [4, 5, 6, 7, 9, 12, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 64, 66, 67, 70, 72, 73, 76, 96, 104, 132, 153], "scale": [5, 7, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 45, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 64, 66, 67], "scratchpad": [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151], "scratchpad_s": [70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 105, 106, 107, 110, 112, 113, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 139, 140, 141, 144, 146, 147, 148, 150], "script": [2, 3], "scriptscriptstyl": 152, "scriptstyl": [22, 152], "sdsdot": 9, "second": [45, 70, 76, 78, 80, 88, 92, 94, 96, 98, 110, 112, 114, 116, 118, 122, 124, 128, 130, 132, 134, 136, 144, 146, 148, 150], "section": [1, 2, 69, 158], "see": [1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 98, 104, 105, 118, 119, 134, 138, 139, 153, 158], "segment": 152, "select": [1, 2, 100, 154, 156], "semicolon": 1, "separ": [1, 3], "sequenti": 152, "seri": [1, 2], "set": [0, 1, 2, 3, 32, 33, 35, 36, 37, 38, 44, 45, 64, 66, 67, 158], "set_coo_data": 153, "set_csr_data": 153, "set_target_properti": 3, "setup": 154, "sever": [2, 8, 100, 152, 156], "share": 0, "short": [3, 156], "should": [1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 156, 158], "side": [15, 30, 53, 63, 64, 66, 67, 68, 88, 89, 90, 91, 100, 101, 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85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142], "bax": [94, 95, 130, 131], "becom": 100, "been": [2, 122, 123, 124, 125, 126, 127, 153, 158], "befor": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150, 152, 158], "begin": [42, 43, 44, 45, 52, 70, 73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142, 152], "behavior": 153, "being": [1, 119], "belong": [73, 74, 81, 82, 85, 86, 89, 90, 119, 120, 125, 126, 156], "below": [1, 2, 3, 22, 70, 72, 73, 96, 116, 117, 132, 150], "best": 2, "beta": [5, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 34, 35, 36, 46, 49, 53, 54, 57, 58, 59, 153], "between": [1, 5, 7, 14, 15, 16, 17, 18, 21, 25, 48, 59, 67, 73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142], "bfloat16": 20, "bia": [12, 22], "bias": 22, "bidiagon": [70, 100, 103], "bin": 2, "binari": [0, 158], "bit": 0, "bla": [0, 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 152, 154, 156], "blas_ct": 3, "blas_ct_templ": 3, "blas_load": 3, "blas_mklcpu": 3, "blas_newlib": 3, "block": [98, 134], "bmatrix": [43, 44, 45, 152], "bo": 22, "both": [0, 2, 3, 34, 57, 76, 78, 156], "bottom": 152, "buffer": [3, 77, 79, 99, 135], "build": [154, 157, 158], "build_doc": 2, "build_exampl": [1, 2, 158], "build_functional_test": [1, 2, 158], "build_shared_lib": [2, 3], "built": [0, 2, 3, 158], "builtin": 2, "bunch": [98, 100, 102, 134], "butter": 92, "bx": [94, 95, 130, 131], "bya": 116, "byte": 153, "bz": [94, 130], "c": [3, 15, 20, 21, 22, 23, 30, 34, 35, 42, 43, 52, 53, 57, 58, 59, 112, 113, 114, 115, 116, 117, 146, 147, 148, 149, 150, 151, 155, 156], "c_arrai": 15, "c_compil": 2, "c_offset": [22, 156], "calcul": [21, 25, 59, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 95, 97, 99, 105, 107, 108, 109, 111, 113, 115, 117, 119, 120, 121, 123, 125, 126, 127, 129, 131, 133, 135, 137, 139, 141, 142, 143, 145, 147, 149, 151], "call": [3, 7, 14, 15, 20, 21, 22, 23, 25, 30, 53, 59, 67, 70, 71, 75, 77, 79, 83, 84, 85, 87, 88, 89, 91, 93, 95, 97, 99, 105, 107, 109, 110, 111, 113, 115, 116, 117, 121, 122, 123, 124, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 144, 145, 147, 149, 150, 151, 153, 158], "can": [0, 1, 2, 3, 92, 112, 114, 116, 128, 146, 148, 150, 153, 155, 156, 157, 158], "cannot": [2, 78, 153], "capabl": 1, "card": 2, "cartesian": [43, 45], "case": [1, 2, 3, 34, 44, 45, 57, 76, 104, 138, 156], "caus": [2, 100], "cbla": 2, "cd": [0, 1, 2, 3], "cdot": [72, 73, 84, 98, 119, 125, 134], "cgh": 3, "chang": [2, 3], "char": 3, "charact": 156, "check": [3, 158], "chetrd": 96, "choleski": [94, 100, 101, 102, 118, 119, 122, 124, 125, 130], "choos": 157, "chosen": 3, "cl": [3, 157], "clang": [2, 157], "clangrt": 2, "class": 3, "clean": [1, 2], "cleanup": 154, "clone": [0, 1, 2], "cmake": [0, 1, 3, 154], "cmake_cxx_flag": 2, "cmake_library_output_directori": 3, "cmakedefin": 3, "cmakelist": 3, "co": [22, 156], "code": 3, "codeplai": 2, "coeffici": [61, 63, 68, 88, 89, 100, 101, 102, 124, 136], "col": 22, "colon": 2, "column": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 88, 89, 92, 98, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 124, 125, 128, 134, 136, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152, 156], "column_major": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68], "columnwis": 78, "com": [0, 153, 158], "combin": [104, 138], "come": 156, "comma": 1, "command": [3, 154, 158], "common": [1, 2], "compat": 2, "compil": [1, 2, 3, 154, 158], "complet": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "complex": [4, 5, 6, 7, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 47, 52, 53, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 112, 114, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 156], "compon": [44, 45], "comput": [1, 2, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151], "condit": 3, "config": 3, "configur": [1, 2, 153], "conjg": [33, 34, 38], "conjtran": [34, 35, 57, 58, 59, 88, 89, 90, 91, 136, 137, 146, 147, 148, 149, 150, 151, 153, 156], "conjug": [9, 10, 17, 27, 57, 58, 59, 156], "conquer": [92, 94, 100, 103, 128, 130], "consecut": [5, 15, 25], "consequ": 2, "consist": 70, "const": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "constraint": [104, 105, 138, 139], "construct": 158, "consum": 158, "contain": [3, 7, 14, 15, 21, 25, 39, 40, 44, 45, 59, 67, 69, 70, 72, 73, 76, 78, 80, 81, 88, 89, 92, 94, 96, 98, 100, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 146, 148, 150, 152], "content": 78, "contigu": 152, "control": 2, "convent": 152, "convert": 3, "coo": 153, "coo_alg1": 153, "coo_alg2": 153, "coo_alg3": 153, "coo_alg4": 153, "coordin": [43, 45], "copi": [9, 14, 153, 158], "correspond": [1, 3, 73, 96, 98, 107, 119, 125, 132, 134, 141, 152], "could": 2, "cpp": 3, "cpu": [0, 2, 3, 154], "cq": [112, 114, 116, 146, 148, 150], "creat": [1, 2, 153, 154], "csr_alg1": 153, "csr_alg2": 153, "csr_alg3": 153, "ctest": [0, 2, 3], "cubla": 3, "cuda": [153, 157], "cufft": 158, "current": [2, 95, 97, 129, 153], "cuspars": 154, "cusparse_spmm_alg_default": 153, "cusparse_spmm_coo_alg1": 153, "cusparse_spmm_coo_alg2": 153, "cusparse_spmm_coo_alg3": 153, "cusparse_spmm_coo_alg4": 153, "cusparse_spmm_csr_alg1": 153, "cusparse_spmm_csr_alg2": 153, "cusparse_spmm_csr_alg3": 153, "cusparse_spmv_alg_default": 153, "cusparse_spmv_coo_alg1": 153, "cusparse_spmv_coo_alg2": 153, "cusparse_spmv_csr_alg1": 153, "cusparse_spmv_csr_alg2": 153, "cusparse_spsv_alg_default": 153, 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142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 156], "desir": [1, 2], "destroi": [78, 94, 130], "detail": [1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 98, 134, 153], "detect": [2, 3], "determin": [30, 53, 64, 84, 85, 100, 103, 104, 106, 107, 110, 116, 138, 140, 141, 144, 150], "develop": [153, 158], "devic": [1, 3, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 95, 97, 99, 105, 107, 108, 109, 111, 113, 115, 117, 119, 120, 121, 123, 125, 126, 127, 129, 131, 133, 135, 137, 139, 141, 142, 143, 145, 147, 149, 151, 155], "device_id": 3, "dft": 2, "dgmm": 15, "dhip_cxx_compil": 2, "dhip_target": 2, "dhipsycl_target": 1, "diag": [15, 60, 61, 62, 63, 64, 65, 66, 67, 68, 136, 137, 154], "diagon": [15, 19, 29, 32, 33, 35, 36, 37, 38, 45, 46, 60, 61, 64, 66, 67, 70, 72, 73, 78, 80, 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85, 100, 101, 102, 122], "invert": [100, 102], "invoc": 154, "involv": [1, 2], "ipiv": [80, 81, 82, 84, 85, 86, 88, 89, 90, 98, 134], "ipiv_i": [81, 86], "ipivi": 90, "is_host": 3, "issu": [2, 153], "its": [3, 23, 30, 34, 35, 53, 57, 58, 59, 72, 73, 76, 153], "ityp": [94, 95, 130, 131], "j": [0, 7, 14, 15, 21, 25, 59, 67, 152], "j4": 3, "jit": 2, "job": [78, 79, 92, 93, 94, 95, 128, 129, 130, 131], "jobu": [78, 79], "jobvt": [78, 79], "jobz": [92, 93, 94, 95, 128, 129, 130, 131], "k": [11, 15, 20, 21, 22, 23, 29, 34, 35, 46, 57, 58, 59, 60, 61, 63, 68, 81, 98, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 134, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152], "k_g": [107, 108, 141, 142], "kahan": [92, 128], "kaufman": [98, 100, 102, 134], "kernel": [12, 100, 101, 154], "kg": 108, "kl": [19, 152], "know": 158, "known": 153, "ku": [19, 152], "l": [80, 94, 98, 118, 124, 127, 130, 134, 156], "l_i": [81, 119, 125, 126], "l_il_i": [119, 125, 126], "lambda": [92, 94, 95, 128, 130, 131], "lambda_i": [92, 128], "lapack": [0, 2, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 156, 157], "largest": 39, "last": [44, 45], "latest": [153, 157], "layer": 3, "layout": [15, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 53, 64, 66, 67, 152], "lda": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152], "lda_g": [74, 81], "ldag": 120, "ldb": [20, 21, 22, 23, 30, 34, 53, 57, 64, 66, 67, 88, 89, 90, 91, 94, 95, 124, 125, 126, 127, 130, 131, 136, 137], "ldc": [15, 20, 21, 22, 23, 30, 34, 35, 53, 57, 58, 59, 112, 113, 114, 115, 116, 117, 146, 147, 148, 149, 150, 151], "ldl": [98, 99, 134, 135], "ldm": 152, "ldot": 152, "ldu": [78, 79], "ldvt": [78, 79], "le": [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151], "lead": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152], "least": [4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 89, 90, 92, 94, 96, 98, 100, 102, 104, 107, 108, 110, 112, 114, 116, 118, 119, 120, 122, 124, 125, 126, 128, 130, 132, 134, 136, 138, 141, 142, 144, 146, 148, 150, 152], "left": [15, 30, 42, 52, 53, 64, 66, 67, 78, 79, 112, 113, 114, 115, 116, 117, 146, 147, 148, 149, 150, 151, 152, 156], "left_right": [15, 30, 53, 64, 66, 67], "leftarrow": [5, 6, 13, 19, 20, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 42, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 62, 64, 65], "len": [15, 19, 24, 25], "length": [19, 24, 26, 27, 28, 29, 31, 32, 33, 36, 37, 38, 46, 49, 50, 51, 54, 55, 56, 60, 61, 62, 63, 65, 68], "less": [70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "level": [3, 4, 6, 8, 13, 16, 17, 18, 19, 20, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68], "level1": 8, "level2": 8, "level3": 8, "lib": [2, 3], "lib_nam": 3, "lib_obj": 3, "libnewlib": 3, "libonemkl": 3, "libonemkl_blas_mklcpu": 3, "libonemkl_blas_newlib": 3, "librari": [0, 1, 2, 12, 100, 101, 154, 155, 158], "like": [2, 5, 7, 8, 14, 15, 21, 22, 23, 25, 59, 67, 73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142, 156], "limit": [2, 153], "linear": [8, 10, 61, 63, 67, 68, 72, 75, 76, 77, 80, 83, 84, 87, 88, 89, 91, 98, 99, 101, 106, 109, 112, 113, 114, 115, 118, 121, 122, 123, 124, 125, 127, 134, 135, 136, 137, 140, 143, 146, 147, 148, 149, 154], "link": [2, 3, 158], "linux": [1, 2, 157], "list": [1, 2, 3, 4, 5, 6, 7, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 78, 80, 81, 84, 85, 88, 89, 92, 94, 96, 98, 100, 101, 102, 103, 104, 106, 107, 110, 112, 114, 116, 118, 119, 122, 124, 125, 128, 130, 132, 134, 136, 138, 140, 141, 144, 146, 148, 150], "ll": [94, 118, 124, 127, 130], "llvm": 2, "load": 3, "loader": 3, "locat": 3, "long": 156, "longer": 156, "look": 2, "lower": [12, 23, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 80, 81, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, 150, 151, 152, 156], "lu": [80, 81, 84, 85, 88, 89, 100, 101, 102, 119, 125], "m": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 53, 54, 64, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 98, 100, 102, 104, 105, 106, 107, 108, 109, 112, 113, 114, 115, 116, 117, 134, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 151, 152], "m1": 152, "m2": 152, "m3": 152, "m_g": [73, 74, 81, 82, 107, 108, 141, 142], "macro": 3, "magnitud": [4, 9], "mai": [1, 2, 100, 153, 156, 158], "main": [152, 158], "main_test": 3, "major": [15, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 34, 35, 53, 57, 58, 59, 64, 66, 67, 152], "make": [1, 2, 3], "makefil": [1, 2], "mandatori": 153, "mani": [12, 100, 101], "manual": [0, 1, 2, 3, 158], "map": [3, 154], "match": 158, "math": [12, 100, 101, 141, 154], "matric": [11, 12, 15, 20, 21, 22, 23, 25, 30, 34, 53, 57, 59, 64, 66, 67, 69, 70, 73, 74, 81, 82, 85, 86, 89, 90, 94, 95, 96, 97, 98, 100, 101, 104, 107, 108, 119, 120, 125, 126, 130, 131, 132, 133, 134, 136, 138, 141, 142, 152, 153, 156], "matrix": [4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 87, 88, 91, 92, 93, 94, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 125, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 154, 156], "matrix_descr": 153, "matrix_properti": 153, "max": [22, 70, 72, 76, 77, 78, 80, 81, 84, 88, 92, 94, 96, 98, 110, 112, 114, 116, 117, 118, 122, 124, 128, 130, 132, 134, 136, 137, 138, 144, 146, 148, 150, 151, 152], "maxim": 39, "maximum": [9, 39], "md": 2, "mechan": 3, "memori": [5, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152], "messag": 158, "method": [3, 94, 98, 130, 134], "mi": 2, "mi200": [1, 2], "mi210": 2, "mi50": 2, "min": [70, 72, 73, 76, 78, 79, 80, 81, 104, 105, 138, 139, 152], "minim": 40, "minimum": [9, 40], "misalign": 153, "miss": 2, "mix": 16, "mkdir": [0, 1, 2], "mkl": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 153, 156, 158], "mkl_install_prefix": 2, "mkl_link_c": 3, "mkl_root": 2, "mklcpu": [1, 2, 3, 153], "mklgpu": [1, 2, 3, 153], "mklroot": 2, "mn": 152, "mode": 3, "model": 3, "modifi": [3, 9, 44, 45], "more": [0, 1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 153], "most": [1, 2, 104, 138], "mostli": 2, "multipl": [1, 2, 3, 7, 14, 15, 21, 22, 25, 30, 34, 53, 57, 59, 64, 67, 88, 89, 100, 101, 102, 124, 125, 136, 155, 156], "multipli": [21, 66, 67, 98, 100, 102, 103, 112, 113, 114, 115, 116, 117, 134, 146, 147, 148, 149, 150, 151], "must": [1, 2, 3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 157], "mxn": 15, "mytarget": 158, "n": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 156], "n1": 152, "n2": 152, "n3": 152, "n_g": [73, 74, 81, 82, 85, 86, 89, 90, 107, 108, 119, 120, 125, 126, 141, 142], "name": [1, 2, 3, 96, 156, 158], "namespac": [3, 4, 5, 6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 156], "nan": [39, 40, 100], "ne": 78, "need": [1, 2, 3, 20, 21, 22, 23, 30, 36, 37, 38, 53, 64, 66, 67, 104, 138, 153], "neg": 78, "never": [57, 58, 59], "new": [1, 2, 3, 156], "new_directori": 3, "newbackend": 3, "newdevic": 3, "newlib": 3, "newlib_librari": 3, "newlib_root": 3, "newlib_sasum": 3, "newlib_wrapp": 3, "newlib_wrappers_table_dyn": 3, "newlibroot": 3, "ng": 120, "ninja": [1, 2], "nn": 152, "no_optimize_alg": 153, "non": [25, 60, 61, 62, 63, 65, 68, 78, 153], "none": [2, 153], "nontran": [34, 35, 57, 58, 88, 89, 90, 91, 112, 113, 114, 115, 116, 117, 136, 137, 146, 147, 148, 149, 150, 151, 153, 156], "nonunit": [136, 137, 156], "norm": [9, 41], "normal": [94, 130], "note": [2, 3, 16, 20, 21, 22, 23, 30, 39, 40, 53, 64, 66, 67, 100, 104, 138], "novec": [78, 79, 92, 93, 94, 95, 128, 129, 130, 131], "now": 3, "nrh": [88, 89, 90, 91, 124, 125, 126, 127, 136, 137], "nrhsg": 90, "nrm2": 9, "number": [4, 5, 6, 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