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Safari Chrome Edge Firefox Developer Reference for Intel® oneAPI Math Kernel Library Getting Help and Support What's New Notational Conventions Overview Performance Enhancements Parallelism C Datatypes Specific to Intel MKL OpenMP* Offload OpenMP* Offload for Intel® oneAPI Math Kernel Library BLAS and Sparse BLAS Routines BLAS Routines Naming Conventions for BLAS Routines C Interface Conventions for BLAS Routines Matrix Storage Schemes for BLAS Routines BLAS Level 1 Routines and Functions cblas_?asum cblas_?axpy cblas_?copy cblas_?copy_batch cblas_?copy_batch_strided cblas_?dot cblas_?sdot cblas_?dotc cblas_?dotu cblas_?nrm2 cblas_?rot cblas_?rotg cblas_?rotm cblas_?rotmg cblas_?scal cblas_?swap cblas_i?amax cblas_i?amin cblas_?cabs1 BLAS Level 2 Routines cblas_?gbmv cblas_?gemv cblas_?ger cblas_?gerc cblas_?geru cblas_?hbmv cblas_?hemv cblas_?her cblas_?her2 cblas_?hpmv cblas_?hpr cblas_?hpr2 cblas_?sbmv cblas_?spmv cblas_?spr cblas_?spr2 cblas_?symv cblas_?syr cblas_?syr2 cblas_?tbmv cblas_?tbsv cblas_?tpmv cblas_?tpsv cblas_?trmv cblas_?trsv BLAS Level 3 Routines cblas_?gemm cblas_?hemm cblas_?herk cblas_?her2k cblas_?symm cblas_?syrk cblas_?syr2k cblas_?trmm cblas_?trsm Sparse BLAS Level 1 Routines Vector Arguments Naming Conventions for Sparse BLAS Routines Routines and Data Types BLAS Level 1 Routines That Can Work With Sparse Vectors cblas_?axpyi cblas_?doti cblas_?dotci cblas_?dotui cblas_?gthr cblas_?gthrz cblas_?roti cblas_?sctr Sparse BLAS Level 2 and Level 3 Routines Naming Conventions in Sparse BLAS Level 2 and Level 3 Sparse Matrix Storage Formats for Sparse BLAS Routines Routines and Supported Operations Interface Consideration Sparse BLAS Level 2 and Level 3 Routines. mkl_?csrgemv mkl_?bsrgemv mkl_?coogemv mkl_?diagemv mkl_?csrsymv mkl_?bsrsymv mkl_?coosymv mkl_?diasymv mkl_?csrtrsv mkl_?bsrtrsv mkl_?cootrsv mkl_?diatrsv mkl_cspblas_?csrgemv mkl_cspblas_?bsrgemv mkl_cspblas_?coogemv mkl_cspblas_?csrsymv mkl_cspblas_?bsrsymv mkl_cspblas_?coosymv mkl_cspblas_?csrtrsv mkl_cspblas_?bsrtrsv mkl_cspblas_?cootrsv mkl_?csrmv mkl_?bsrmv mkl_?cscmv mkl_?coomv mkl_?csrsv mkl_?bsrsv mkl_?cscsv mkl_?coosv mkl_?csrmm mkl_?bsrmm mkl_?cscmm mkl_?coomm mkl_?csrsm mkl_?cscsm mkl_?coosm mkl_?bsrsm mkl_?diamv mkl_?skymv mkl_?diasv mkl_?skysv mkl_?diamm mkl_?skymm mkl_?diasm mkl_?skysm mkl_?dnscsr mkl_?csrcoo mkl_?csrbsr mkl_?csrcsc mkl_?csrdia mkl_?csrsky mkl_?csradd mkl_?csrmultcsr mkl_?csrmultd Sparse QR Routines mkl_sparse_set_qr_hint mkl_sparse_?_qr mkl_sparse_qr_reorder mkl_sparse_?_qr_factorize mkl_sparse_?_qr_solve mkl_sparse_?_qr_qmult mkl_sparse_?_qr_rsolve Compact BLAS and LAPACK Functions mkl_?gemm_compact mkl_?trsm_compact mkl_?potrf_compact mkl_?getrfnp_compact mkl_?geqrf_compact mkl_?getrinp_compact Numerical Limitations for Compact BLAS and Compact LAPACK Routines mkl_?get_size_compact mkl_get_format_compact mkl_?gepack_compact mkl_?geunpack_compact Inspector-executor Sparse BLAS Routines Naming conventions in Inspector-executor Sparse BLAS Routines Sparse Matrix Storage Formats for Inspector-executor Sparse BLAS Routines Supported Inspector-executor Sparse BLAS Operations Two-stage Algorithm in Inspector-Executor Sparse BLAS Routines Matrix Manipulation Routines mkl_sparse_?_create_csr mkl_sparse_?_create_csc mkl_sparse_?_create_coo mkl_sparse_?_create_bsr mkl_sparse_copy mkl_sparse_destroy mkl_sparse_convert_csr mkl_sparse_convert_bsr mkl_sparse_?_export_csr mkl_sparse_?_export_csc mkl_sparse_?_export_bsr mkl_sparse_?_set_value mkl_sparse_?_update_values mkl_sparse_order Inspector-executor Sparse BLAS Analysis Routines mkl_sparse_set_lu_smoother_hint mkl_sparse_set_mv_hint mkl_sparse_set_sv_hint mkl_sparse_set_mm_hint mkl_sparse_set_sm_hint mkl_sparse_set_dotmv_hint mkl_sparse_set_symgs_hint mkl_sparse_set_memory_hint mkl_sparse_optimize Inspector-Executor Sparse BLAS Execution Routines mkl_sparse_?_lu_smoother mkl_sparse_?_mv mkl_sparse_?_trsv mkl_sparse_?_mm mkl_sparse_?_trsm mkl_sparse_?_add mkl_sparse_spmm mkl_sparse_?_spmmd mkl_sparse_sp2m mkl_sparse_?_sp2md mkl_sparse_sypr mkl_sparse_?_syprd mkl_sparse_?_symgs mkl_sparse_?_symgs_mv mkl_sparse_syrk mkl_sparse_?_syrkd mkl_sparse_?_dotmv BLAS-like Extensions cblas_?axpy_batch cblas_?axpy_batch_strided cblas_?axpby cblas_?gemmt cblas_?gemm3m cblas_?gemm_batch cblas_?gemm_batch_strided cblas_?gemm3m_batch cblas_?trsm_batch cblas_?trsm_batch_strided mkl_?imatcopy mkl_?imatcopy_batch mkl_?imatcopy_batch_strided mkl_?omatadd_batch_strided mkl_?omatcopy mkl_?omatcopy_batch mkl_?omatcopy_batch_strided mkl_?omatcopy2 mkl_?omatadd cblas_?gemm_pack_get_size, cblas_gemm_*_pack_get_size cblas_?gemm_alloc cblas_?gemm_pack cblas_gemm_*_pack cblas_?gemm_compute cblas_gemm_*_compute cblas_gemm_bf16bf16f32_compute cblas_?gemm_free cblas_gemm_bf16bf16f32 cblas_gemm_* cblas_?gemv_batch_strided cblas_?gemv_batch cblas_?dgmm_batch_strided cblas_?dgmm_batch mkl_jit_create_?gemm mkl_jit_get_?gemm_ptr mkl_jit_destroy LAPACK Routines Choosing a LAPACK Routine C Interface Conventions for LAPACK Routines Matrix Layout for LAPACK Routines Matrix Storage Schemes for LAPACK Routines Mathematical Notation for LAPACK Routines Error Analysis LAPACK Linear Equation Routines LAPACK Linear Equation Computational Routines Matrix Factorization: LAPACK Computational Routines ?getrf mkl_?getrfnp mkl_?getrfnpi ?getrf2 ?gbtrf ?gttrf ?dttrfb ?potrf ?potrf2 ?pstrf ?pftrf ?pptrf ?pbtrf ?pttrf ?sytrf ?sytrf_aa ?sytrf_rook ?sytrf_rk ?hetrf ?hetrf_aa ?hetrf_rook ?hetrf_rk ?sptrf ?hptrf mkl_?spffrt2, mkl_?spffrtx Solving Systems of Linear Equations: LAPACK Computational Routines ?getrs ?gbtrs ?gttrs ?dttrsb ?potrs ?pftrs ?pptrs ?pbtrs ?pttrs ?sytrs ?sytrs_aa ?sytrs_rook ?hetrs ?hetrs_aa ?hetrs_rook ?sytrs2 ?hetrs2 ?sytrs_3 ?hetrs_3 ?sptrs ?hptrs ?trtrs ?tptrs ?tbtrs Estimating the Condition Number: LAPACK Computational Routines ?gecon ?gbcon ?gtcon ?pocon ?ppcon ?pbcon ?ptcon ?sycon ?sycon_3 ?hecon ?hecon_3 ?spcon ?hpcon ?trcon ?tpcon ?tbcon Refining the Solution and Estimating Its Error: LAPACK Computational Routines ?gerfs ?gerfsx ?gbrfs ?gbrfsx ?gtrfs ?porfs ?porfsx ?pprfs ?pbrfs ?ptrfs ?syrfs ?syrfsx ?herfs ?herfsx ?sprfs ?hprfs ?trrfs ?tprfs ?tbrfs Matrix Inversion: LAPACK Computational Routines ?getri mkl_?getrinp ?potri ?pftri ?pptri ?sytri ?hetri ?sytri2 ?hetri2 ?sytri2x ?hetri2x ?sytri_3 ?hetri_3 ?sptri ?hptri ?trtri ?tftri ?tptri Matrix Equilibration: LAPACK Computational Routines ?geequ ?geequb ?gbequ ?gbequb ?poequ ?poequb ?ppequ ?pbequ ?syequb ?heequb LAPACK Linear Equation Driver Routines ?gesv ?gesvx ?gesvxx ?gbsv ?gbsvx ?gbsvxx ?gtsv ?gtsvx ?dtsvb ?posv ?posvx ?posvxx ?ppsv ?ppsvx ?pbsv ?pbsvx ?ptsv ?ptsvx ?sysv ?sysv_aa ?sysv_rook ?sysv_rk ?sysvx ?sysvxx ?hesv ?hesv_aa ?hesv_rk ?hesvx ?hesvxx ?spsv ?spsvx ?hpsv ?hpsvx LAPACK Least Squares and Eigenvalue Problem Routines LAPACK Least Squares and Eigenvalue Problem Computational Routines Orthogonal Factorizations: LAPACK Computational Routines ?geqrf ?geqrfp ?geqrt ?gemqrt ?geqpf ?geqp3 ?orgqr ?ormqr ?ungqr ?unmqr ?gelqf ?orglq ?ormlq ?unglq ?unmlq ?geqlf ?orgql ?ungql ?ormql ?unmql ?gerqf ?orgrq ?ungrq ?ormrq ?unmrq ?tzrzf ?ormrz ?unmrz ?ggqrf ?ggrqf ?tpqrt ?tpmqrt Singular Value Decomposition: LAPACK Computational Routines ?gebrd ?gbbrd ?orgbr ?ormbr ?ungbr ?unmbr ?bdsqr ?bdsdc Symmetric Eigenvalue Problems: LAPACK Computational Routines ?sytrd ?orgtr ?ormtr ?hetrd ?ungtr ?unmtr ?sptrd ?opgtr ?opmtr ?hptrd ?upgtr ?upmtr ?sbtrd ?hbtrd ?sterf ?steqr ?stemr ?stedc ?stegr ?pteqr ?stebz ?stein ?disna Generalized Symmetric-Definite Eigenvalue Problems: LAPACK Computational Routines ?sygst ?hegst ?spgst ?hpgst ?sbgst ?hbgst ?pbstf Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines ?gehrd ?orghr ?ormhr ?unghr ?unmhr ?gebal ?gebak ?hseqr ?hsein ?trevc ?trevc3 ?trsna ?trexc ?trsen ?trsyl Generalized Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines ?gghrd ?ggbal ?ggbak ?gghd3 ?hgeqz ?tgevc ?tgexc ?tgsen ?tgsyl ?tgsna Generalized Singular Value Decomposition: LAPACK Computational Routines ?ggsvp ?ggsvp3 ?ggsvd3 ?tgsja Cosine-Sine Decomposition: LAPACK Computational Routines LAPACK Least Squares and Eigenvalue Problem Driver Routines Linear Least Squares (LLS) Problems: LAPACK Driver Routines ?gels ?gelsy ?gelss ?gelsd Generalized Linear Least Squares (LLS) Problems: LAPACK Driver Routines Symmetric Eigenvalue Problems: LAPACK Driver Routines ?syev ?heev ?syevd ?heevd ?syevx ?heevx ?syevr ?heevr ?spev ?hpev ?spevd ?hpevd ?spevx ?hpevx ?sbev ?hbev ?sbevd ?hbevd ?sbevx ?hbevx ?stev ?stevd ?stevx ?stevr Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines ?gees ?geesx ?geev ?geevx Singular Value Decomposition: LAPACK Driver Routines ?gesvd ?gesdd ?gejsv ?gesvj ?ggsvd ?gesvdx ?bdsvdx Cosine-Sine Decomposition: LAPACK Driver Routines ?orcsd/?uncsd ?orcsd2by1/?uncsd2by1 Generalized Symmetric Definite Eigenvalue Problems: LAPACK Driver Routines ?sygv ?hegv ?sygvd ?hegvd ?sygvx ?hegvx ?spgv ?hpgv ?spgvd ?hpgvd ?spgvx ?hpgvx ?sbgv ?hbgv ?sbgvd ?hbgvd ?sbgvx ?hbgvx Generalized Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines ?gges ?ggesx ?gges3 ?ggev ?ggevx ?ggev3 LAPACK Auxiliary Routines ?lacgv ?lacrm ?syconv ?syr i?max1 ?sum1 ?gelq2 ?geqr2 ?geqrt2 ?geqrt3 ?getf2 ?lacn2 ?lacpy ?lakf2 ?lange ?lansy ?lanhe ?lantr LAPACKE_set_nancheck LAPACKE_get_nancheck ?lapmr ?lapmt ?lapy2 ?lapy3 ?laran ?larfb ?larfg ?larft ?larfx ?large ?larnd ?larnv ?laror ?larot ?lartgp ?lartgs ?lascl ?lasd0 ?lasd1 ?lasd2 ?lasd3 ?lasd4 ?lasd5 ?lasd6 ?lasd7 ?lasd8 ?lasd9 ?lasda ?lasdq ?lasdt ?laset ?lasrt ?laswp ?latm1 ?latm2 ?latm3 ?latm5 ?latm6 ?latme ?latmr ?lauum ?syswapr ?heswapr ?sfrk ?hfrk ?tfsm ?tfttp ?tfttr ?tpqrt2 ?tprfb ?tpttf ?tpttr ?trttf ?trttp ?lacp2 ?larcm mkl_?tppack mkl_?tpunpack LAPACK Utility Functions and Routines LAPACK Test Functions and Routines ?lagge ?laghe ?lagsy ?latms Additional LAPACK Routines (Included for Compatibility with Netlib LAPACK) ScaLAPACK Routines Overview of ScaLAPACK Routines ScaLAPACK Array Descriptors Naming Conventions for ScaLAPACK Routines ScaLAPACK Computational Routines Systems of Linear Equations: ScaLAPACK Computational Routines Matrix Factorization: ScaLAPACK Computational Routines p?getrf p?gbtrf p?dbtrf p?dttrf p?potrf p?pbtrf p?pttrf Solving Systems of Linear Equations: ScaLAPACK Computational Routines p?getrs p?gbtrs p?dbtrs p?dttrs p?potrs p?pbtrs p?pttrs p?trtrs Estimating the Condition Number: ScaLAPACK Computational Routines Refining the Solution and Estimating Its Error: ScaLAPACK Computational Routines Matrix Inversion: ScaLAPACK Computational Routines Matrix Equilibration: ScaLAPACK Computational Routines Orthogonal Factorizations: ScaLAPACK Computational Routines p?geqrf p?geqpf p?orgqr p?ungqr p?ormqr p?unmqr p?gelqf p?orglq p?unglq p?ormlq p?unmlq p?geqlf p?orgql p?ungql p?ormql p?unmql p?gerqf p?orgrq p?ungrq p?ormr3 p?unmr3 p?ormrq p?unmrq p?tzrzf p?ormrz p?unmrz p?ggqrf p?ggrqf Symmetric Eigenvalue Problems: ScaLAPACK Computational Routines p?syngst p?syntrd p?sytrd p?ormtr p?hengst p?hentrd p?hetrd p?unmtr p?stebz p?stedc p?stein Nonsymmetric Eigenvalue Problems: ScaLAPACK Computational Routines p?gehrd p?ormhr p?unmhr p?lahqr p?trevc Singular Value Decomposition: ScaLAPACK Driver Routines Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines ScaLAPACK Driver Routines p?geevx p?gesv p?gesvx p?gbsv p?dbsv p?dtsv p?posv p?posvx p?pbsv p?ptsv p?gels p?syev p?syevd p?syevr p?syevx p?heev p?heevd p?heevr p?heevx p?gesvd p?sygvx p?hegvx ScaLAPACK Auxiliary Routines p?lacgv p?max1 pilaver pmpcol pmpim2 ?combamax1 p?sum1 p?dbtrsv p?dttrsv p?gebal p?gebd2 p?gehd2 p?gelq2 p?geql2 p?geqr2 p?gerq2 p?getf2 p?labrd p?lacon p?laconsb p?lacp2 p?lacp3 p?lacpy p?laevswp p?lahrd p?laiect p?lamve p?lange p?lanhs p?lansy, p?lanhe p?lantr p?lapiv p?lapv2 p?laqge p?laqr0 p?laqr1 p?laqr2 p?laqr3 p?laqr5 p?laqsy p?lared1d p?lared2d p?larf p?larfb p?larfc p?larfg p?larft p?larz p?larzb p?larzc p?larzt p?lascl p?lase2 p?laset p?lasmsub p?lasrt p?lassq p?laswp p?latra p?latrd p?latrs p?latrz p?lauu2 p?lauum p?lawil p?org2l/p?ung2l p?org2r/p?ung2r p?orgl2/p?ungl2 p?orgr2/p?ungr2 p?orm2l/p?unm2l p?orm2r/p?unm2r p?orml2/p?unml2 p?ormr2/p?unmr2 p?pbtrsv p?pttrsv p?potf2 p?rot p?rscl p?sygs2/p?hegs2 p?sytd2/p?hetd2 p?trord p?trsen p?trti2 ?lahqr2 ?lamsh ?lapst ?laqr6 ?lar1va ?laref ?larrb2 ?larrd2 ?larre2 ?larre2a ?larrf2 ?larrv2 ?lasorte ?lasrt2 ?stegr2 ?stegr2a ?stegr2b ?stein2 ?dbtf2 ?dbtrf ?dttrf ?dttrsv ?pttrsv ?steqr2 ?trmvt pilaenv pilaenvx pjlaenv Additional ScaLAPACK Routines ScaLAPACK Utility Functions and Routines p?labad p?lachkieee p?lamch p?lasnbt descinit numroc ScaLAPACK Redistribution/Copy Routines Sparse Solver Routines oneMKL PARDISO - Parallel Direct Sparse Solver Interface pardiso pardisoinit pardiso_64 mkl_pardiso_pivot pardiso_getdiag pardiso_export pardiso_handle_store pardiso_handle_restore pardiso_handle_delete pardiso_handle_store_64 pardiso_handle_restore_64 pardiso_handle_delete_64 oneMKL PARDISO Parameters in Tabular Form pardiso iparm Parameter PARDISO_DATA_TYPE Parallel Direct Sparse Solver for Clusters Interface cluster_sparse_solver cluster_sparse_solver_64 cluster_sparse_solver_get_csr_size cluster_sparse_solver_set_csr_ptrs cluster_sparse_solver_set_ptr cluster_sparse_solver_export cluster_sparse_solver iparm Parameter Direct Sparse Solver (DSS) Interface Routines DSS Interface Description DSS Implementation Details DSS Routines dss_create dss_define_structure dss_reorder dss_factor_real, dss_factor_complex dss_solve_real, dss_solve_complex dss_delete dss_statistics Iterative Sparse Solvers based on Reverse Communication Interface (RCI ISS) CG Interface Description FGMRES Interface Description RCI ISS Routines dcg_init dcg_check dcg dcg_get dcgmrhs_init dcgmrhs_check dcgmrhs dcgmrhs_get dfgmres_init dfgmres_check dfgmres dfgmres_get RCI ISS Implementation Details Preconditioners based on Incomplete LU Factorization Technique ILU0 and ILUT Preconditioners Interface Description dcsrilu0 dcsrilut Sparse Matrix Checker Routines sparse_matrix_checker sparse_matrix_checker_init Graph Routines Graph Functionality Creating/Destroying Graph Objects mkl_graph_descriptor_create mkl_graph_descriptor_destroy mkl_graph_matrix_create mkl_graph_matrix_destroy mkl_graph_vector_create mkl_graph_vector_destroy Importing/Exporting Data to or from the Graph Objects mkl_graph_matrix_set_csr mkl_graph_matrix_get_csr mkl_graph_matrix_set_csc mkl_graph_matrix_get_csc mkl_graph_vector_set_dense mkl_graph_vector_get_dense mkl_graph_vector_set_sparse mkl_graph_vector_get_sparse Graph Operations mkl_graph_mxv mkl_graph_vxm mkl_graph_mxm mkl_graph_transpose Auxiliary Routines mkl_graph_optimize_mxv mkl_graph_optimize_mxm mkl_graph_matrix_get_property mkl_graph_vector_get_property Manipulating Graph Objects mkl_graph_descriptor_set_field Graph Objects Graph API Glossary Extended Eigensolver Routines The FEAST Algorithm Extended Eigensolver Functionality Parallelism in Extended Eigensolver Routines Achieving Performance With Extended Eigensolver Routines Extended Eigensolver Interfaces for Eigenvalues within Interval Extended Eigensolver Naming Conventions feastinit Extended Eigensolver Input Parameters Extended Eigensolver Output Details Extended Eigensolver RCI Routines Extended Eigensolver RCI Interface Description ?feast_srci/?feast_hrci Extended Eigensolver Predefined Interfaces Matrix Storage ?feast_syev/?feast_heev ?feast_sygv/?feast_hegv ?feast_sbev/?feast_hbev ?feast_sbgv/?feast_hbgv ?feast_scsrev/?feast_hcsrev ?feast_scsrgv/?feast_hcsrgv Extended Eigensolver Interfaces for Extremal Eigenvalues/Singular Values Extended Eigensolver Interfaces to find largest/smallest eigenvalues mkl_sparse_?_ev mkl_sparse_?_gv Extended Eigensolver Interfaces to find largest/smallest singular values mkl_sparse_ee_init Extended Eigensolver Input Parameters for Extremal Eigenvalue Problem Vector Mathematical Functions VM Data Types, Accuracy Modes, and Performance Tips VM Naming Conventions VM Function Interfaces VM Mathematical Function Interfaces VM Pack Function Interfaces VM Unpack Function Interfaces VM Service Function Interfaces VM Input Parameters VM Output Parameters Vector Indexing Methods VM Error Diagnostics VM Mathematical Functions Special Value Notations Arithmetic Functions v?Add v?Sub v?Sqr v?Mul v?MulByConj v?Conj v?Abs v?Arg v?LinearFrac v?Fmod v?Remainder Power and Root Functions v?Inv v?Div v?Sqrt v?InvSqrt v?Cbrt v?InvCbrt v?Pow2o3 v?Pow3o2 v?Pow v?Powx v?Powr v?Hypot Exponential and Logarithmic Functions v?Exp v?Exp2 v?Exp10 v?Expm1 v?Ln v?Log2 v?Log10 v?Log1p v?Logb Trigonometric Functions v?Cos v?Sin v?SinCos v?CIS v?Tan v?Acos v?Asin v?Atan v?Atan2 v?Cospi v?Sinpi v?Tanpi v?Acospi v?Asinpi v?Atanpi v?Atan2pi v?Cosd v?Sind v?Tand Hyperbolic Functions v?Cosh v?Sinh v?Tanh v?Acosh v?Asinh v?Atanh Special Functions v?Erf v?Erfc v?CdfNorm v?ErfInv v?ErfcInv v?CdfNormInv v?LGamma v?TGamma v?ExpInt1 Rounding Functions v?Floor v?Ceil v?Trunc v?Round v?NearbyInt v?Rint v?Modf v?Frac VM Pack/Unpack Functions VM Service Functions vmlSetMode vmlGetMode MKLFreeTls vmlSetErrStatus vmlGetErrStatus vmlClearErrStatus vmlSetErrorCallBack vmlGetErrorCallBack vmlClearErrorCallBack Miscellaneous VM Functions v?CopySign v?NextAfter v?Fdim v?Fmax v?Fmin v?MaxMag v?MinMag Statistical Functions Random Number Generators Random Number Generators Conventions Random Number Generators Mathematical Notation Random Number Generators Naming Conventions Basic Generators BRNG Parameter Definition Random Streams BRNG Data Types Error Reporting VS RNG Usage Model Intel® oneMKL RNG Usage Model Service Routines vslNewStream vslNewStreamEx vsliNewAbstractStream vsldNewAbstractStream vslsNewAbstractStream vslDeleteStream vslCopyStream vslCopyStreamState vslSaveStreamF vslLoadStreamF vslSaveStreamM vslLoadStreamM vslGetStreamSize vslLeapfrogStream vslSkipAheadStream vslSkipAheadStreamEx vslGetStreamStateBrng vslGetNumRegBrngs Distribution Generators Continuous Distributions vRngUniform Continuous Distribution Generators vRngGaussian vRngGaussianMV vRngExponential vRngLaplace vRngWeibull vRngCauchy vRngRayleigh vRngLognormal vRngGumbel vRngGamma vRngBeta vRngChiSquare Discrete Distributions vRngUniform Discrete Distribution Generators vRngUniformBits vRngUniformBits32 vRngUniformBits64 vRngBernoulli vRngGeometric vRngBinomial vRngHypergeometric vRngPoisson vRngPoissonV vRngNegBinomial vRngMultinomial Advanced Service Routines Advanced Service Routine Data Types vslRegisterBrng vslGetBrngProperties Formats for User-Designed Generators Convolution and Correlation Convolution and Correlation Naming Conventions Convolution and Correlation Data Types Convolution and Correlation Parameters Convolution and Correlation Task Status and Error Reporting Convolution and Correlation Task Constructors vslConvNewTask/vslCorrNewTask vslConvNewTask1D/vslCorrNewTask1D vslConvNewTaskX/vslCorrNewTaskX vslConvNewTaskX1D/vslCorrNewTaskX1D Convolution and Correlation Task Editors vslConvSetMode/vslCorrSetMode vslConvSetInternalPrecision/vslCorrSetInternalPrecision vslConvSetStart/vslCorrSetStart vslConvSetDecimation/vslCorrSetDecimation Task Execution Routines vslConvExec/vslCorrExec vslConvExec1D/vslCorrExec1D vslConvExecX/vslCorrExecX vslConvExecX1D/vslCorrExecX1D Convolution and Correlation Task Destructors vslConvDeleteTask/vslCorrDeleteTask Convolution and Correlation Task Copiers vslConvCopyTask/vslCorrCopyTask Convolution and Correlation Usage Examples Convolution and Correlation Mathematical Notation and Definitions Convolution and Correlation Data Allocation Summary Statistics Summary Statistics Naming Conventions Summary Statistics Data Types Summary Statistics Parameters Summary Statistics Task Status and Error Reporting Summary Statistics Task Constructors Summary Statistics Task Editors vslSSEditTask vslSSEditMoments vslSSEditSums vslSSEditCovCor vslSSEditCP vslSSEditPartialCovCor vslSSEditQuantiles vslSSEditStreamQuantiles vslSSEditPooledCovariance vslSSEditRobustCovariance vslSSEditOutliersDetection vslSSEditMissingValues vslSSEditCorParameterization Summary Statistics Task Computation Routines Summary Statistics Task Destructor Summary Statistics Usage Examples Summary Statistics Mathematical Notation and Definitions Fourier Transform Functions FFT Functions FFT Interface Computing an FFT Configuration Settings DFTI_PRECISION DFTI_FORWARD_DOMAIN DFTI_DIMENSION, DFTI_LENGTHS DFTI_PLACEMENT DFTI_FORWARD_SCALE, DFTI_BACKWARD_SCALE DFTI_NUMBER_OF_USER_THREADS DFTI_THREAD_LIMIT DFTI_INPUT_STRIDES, DFTI_OUTPUT_STRIDES DFTI_NUMBER_OF_TRANSFORMS DFTI_INPUT_DISTANCE, DFTI_OUTPUT_DISTANCE DFTI_COMPLEX_STORAGE, DFTI_REAL_STORAGE, DFTI_CONJUGATE_EVEN_STORAGE DFTI_PACKED_FORMAT DFTI_WORKSPACE DFTI_COMMIT_STATUS DFTI_ORDERING DFTI_DESTROY_INPUT FFT Descriptor Manipulation Functions DftiCreateDescriptor DftiCommitDescriptor DftiFreeDescriptor DftiCopyDescriptor FFT Descriptor Configuration Functions DftiSetValue DftiGetValue FFT Computation Functions DftiComputeForward DftiComputeBackward Configuring and Computing an FFT in C/C++ Status Checking Functions DftiErrorClass DftiErrorMessage Cluster FFT Functions Computing Cluster FFT Distributing Data Among Processes Cluster FFT Interface Cluster FFT Descriptor Manipulation Functions DftiCreateDescriptorDM DftiCommitDescriptorDM DftiFreeDescriptorDM Cluster FFT Computation Functions DftiComputeForwardDM DftiComputeBackwardDM Cluster FFT Descriptor Configuration Functions DftiSetValueDM DftiGetValueDM Error Codes PBLAS Routines PBLAS Routines Overview PBLAS Routine Naming Conventions PBLAS Level 1 Routines p?amax p?asum p?axpy p?copy p?dot p?dotc p?dotu p?nrm2 p?scal p?swap PBLAS Level 2 Routines p?gemv p?agemv p?ger p?gerc p?geru p?hemv p?ahemv p?her p?her2 p?symv p?asymv p?syr p?syr2 p?trmv p?atrmv p?trsv PBLAS Level 3 Routines p?geadd p?tradd p?gemm p?hemm p?herk p?her2k p?symm p?syrk p?syr2k p?tran p?tranu p?tranc p?trmm p?trsm Partial Differential Equations Support Trigonometric Transform Routines Trigonometric Transforms Implemented Sequence of Invoking TT Routines Trigonometric Transform Interface Description TT Routines ?_init_trig_transform ?_commit_trig_transform ?_forward_trig_transform ?_backward_trig_transform free_trig_transform Common Parameters of the Trigonometric Transforms Trigonometric Transform Implementation Details Fast Poisson Solver Routines Poisson Solver Implementation Sequence of Invoking Poisson Solver Routines Fast Poisson Solver Interface Description Routines for the Cartesian Solver ?_init_Helmholtz_2D/?_init_Helmholtz_3D _commit_Helmholtz_2D/?_commit_Helmholtz_3D ?_Helmholtz_2D/?_Helmholtz_3D free_Helmholtz_2D/free_Helmholtz_3D Routines for the Spherical Solver ?_init_sph_p/?_init_sph_np ?_commit_sph_p/?_commit_sph_np ?_sph_p/?_sph_np free_sph_p/free_sph_np Common Parameters for the Poisson Solver ipar dpar and spar Caveat on Parameter Modifications Parameters That Define Boundary Conditions Poisson Solver Implementation Details Nonlinear Optimization Problem Solvers Nonlinear Solver Organization and Implementation Nonlinear Solver Routine Naming Conventions Nonlinear Least Squares Problem without Constraints ?trnlsp_init ?trnlsp_check ?trnlsp_solve ?trnlsp_get ?trnlsp_delete Nonlinear Least Squares Problem with Linear (Bound) Constraints ?trnlspbc_init ?trnlspbc_check ?trnlspbc_solve ?trnlspbc_get ?trnlspbc_delete Jacobian Matrix Calculation Routines ?jacobi_init ?jacobi_solve ?jacobi_delete ?jacobi ?jacobix Support Functions Version Information mkl_get_version mkl_get_version_string Threading Control mkl_set_num_threads mkl_domain_set_num_threads mkl_set_num_threads_local mkl_set_dynamic mkl_get_max_threads mkl_domain_get_max_threads mkl_get_dynamic mkl_set_num_stripes mkl_get_num_stripes Error Handling Error Handling for Linear Algebra Routines xerbla pxerbla LAPACKE_xerbla Handling Fatal Errors Character Equality Testing Timing second/dsecnd mkl_get_cpu_clocks mkl_get_cpu_frequency mkl_get_max_cpu_frequency mkl_get_clocks_frequency Memory Management mkl_free_buffers mkl_thread_free_buffers mkl_disable_fast_mm mkl_mem_stat mkl_peak_mem_usage mkl_malloc mkl_calloc mkl_realloc mkl_free mkl_set_memory_limit Usage Examples for the Memory Functions Single Dynamic Library Control mkl_set_interface_layer mkl_set_threading_layer mkl_set_xerbla mkl_set_progress mkl_set_pardiso_pivot Conditional Numerical Reproducibility Control mkl_cbwr_set mkl_cbwr_get mkl_cbwr_get_auto_branch Named Constants for CNR Control Reproducibility Conditions Usage Examples for CNR Support Functions Miscellaneous mkl_progress mkl_enable_instructions mkl_set_env_mode mkl_verbose mkl_verbose_output_file mkl_set_mpi mkl_finalize BLACS Routines Matrix Shapes Repeatability and Coherence BLACS Combine Operations BLACS Point To Point Communication ?gesd2d ?trsd2d ?gerv2d ?trrv2d BLACS Broadcast Routines ?gebs2d ?trbs2d ?gebr2d ?trbr2d BLACS Support Routines Initialization Routines blacs_pinfo blacs_setup blacs_get blacs_set blacs_gridinit blacs_gridmap Destruction Routines blacs_freebuff blacs_gridexit blacs_abort blacs_exit Informational Routines blacs_gridinfo blacs_pnum blacs_pcoord Miscellaneous Routines BLACS Routines Usage Examples Data Fitting Functions Data Fitting Function Naming Conventions Data Fitting Function Data Types Mathematical Conventions for Data Fitting Functions Data Fitting Usage Model Data Fitting Usage Examples Data Fitting Function Task Status and Error Reporting Data Fitting Task Creation and Initialization Routines Task Configuration Routines df?EditPPSpline1D df?EditPtr dfiEditVal df?EditIdxPtr df?QueryPtr dfiQueryVal df?QueryIdxPtr Data Fitting Computational Routines df?Construct1D df?Interpolate1D/df?InterpolateEx1D df?Integrate1D/df?IntegrateEx1D df?SearchCells1D/df?SearchCellsEx1D df?InterpCallBack df?IntegrCallBack df?SearchCellsCallBack Data Fitting Task Destructors Appendix A: Linear Solvers Basics Sparse Linear Systems Matrix Fundamentals Direct Method Sparse Matrix Storage Formats DSS Symmetric Matrix Storage DSS Nonsymmetric Matrix Storage DSS Structurally Symmetric Matrix Storage DSS Distributed Symmetric Matrix Storage Sparse BLAS CSR Matrix Storage Format Sparse BLAS CSC Matrix Storage Format Sparse BLAS Coordinate Matrix Storage Format Sparse BLAS Diagonal Matrix Storage Format Sparse BLAS Skyline Matrix Storage Format Sparse BLAS BSR Matrix Storage Format Appendix B: Routine and Function Arguments Vector Arguments in BLAS Vector Arguments in Vector Math Matrix Arguments Appendix C: FFTW Interface to Intel® oneAPI Math Kernel Library Notational Conventions FFTW2 Interface to Intel® oneAPI Math Kernel Library Wrappers Reference One-dimensional Complex-to-complex FFTs Multi-dimensional Complex-to-complex FFTs One-dimensional Real-to-half-complex/Half-complex-to-real FFTs Multi-dimensional Real-to-complex/Complex-to-real FFTs Multi-threaded FFTW FFTW Support Functions Limitations of the FFTW2 Interface to Intel® oneAPI Math Kernel Library Installing FFTW2 Interface Wrappers Creating the Wrapper Library Application Assembling Running FFTW2 Interface Wrapper Examples MPI FFTW2 Wrappers MPI FFTW Wrappers Reference Complex MPI FFTW Real MPI FFTW Creating MPI FFTW2 Wrapper Library Application Assembling with MPI FFTW Wrapper Library Running MPI FFTW2 Wrapper Examples FFTW3 Interface to Intel® oneAPI Math Kernel Library Using FFTW3 Wrappers Building Your Own Wrapper Library Building an Application With FFTW3 Interface Wrappers Running FFTW3 Interface Wrapper Examples MPI FFTW3 Wrappers Building Your Own Wrapper Library Building an Application Running Examples Appendix D: Code Examples BLAS Code Examples Fourier Transform Functions Code Examples FFT Code Examples Examples of Using OpenMP* Threading for FFT Computation Examples for Cluster FFT Functions Auxiliary Data Transformations Appendix E: Graph Basics Graphs in Linear Algebra Graph Fundamentals Appendix F: oneMKL Functionality BLAS Functionality Transposition Functionality LAPACK Functionality DFT Functionality Sparse BLAS Functionality Sparse Solvers Functionality Graphs Functionality Random Number Generators Functionality Vector Math Functionality Data Fitting Functionality Summary Statistics Functionality Bibliography Glossary Notices and Disclaimers Computes a matrix-matrix product with general matrices.
The
routines compute a scalar-matrix-matrix product and add the result to a scalar-matrix product, with general matrices. The operation is defined as
C := alpha*op(A)*op(B) + beta*C
for the Fortran language interface to this routine
, BLAS-like extension routines, that use matrix multiplication for similar matrix-matrix operations
Specifies whether two-dimensional array storage is row-major ( ) or column-major ( ).
Specifies the form of
used in the matrix multiplication:
Specifies the form of
used in the matrix multiplication:
Specifies the number of rows of the matrix and of the matrix . The value of must be at least zero.
Specifies the number of columns of the matrix and the number of columns of the matrix . The value of must be at least zero.
Specifies the number of columns of the matrix and the number of rows of the matrix . The value of must be at least zero.
transa
=
CblasTrans
or
transa
=
CblasConjTrans
Before entry, the leading
m
-by-
k
part of the array
a
must contain the matrix
A
.
Before entry, the leading
k
-by-
m
part of the array
a
must contain the matrix
A
.
Before entry, the leading
k
-by-
m
part of the array
a
must contain the matrix
A
.
Before entry, the leading
m
-by-
k
part of the array
a
must contain the matrix
A
.
Specifies the leading dimension of as declared in the calling (sub)program.
transa
=
CblasTrans
or
transa
=
CblasConjTrans
transb
=
CblasTrans
or
transb
=
CblasConjTrans
Array, size
ldb
by
n
. Before entry, the leading
k
-by-
n
part of the array
b
must contain the matrix
B
.
Array, size
ldb
by
k
. Before entry the leading
n
-by-
k
part of the array
b
must contain the matrix
B
.
Array, size
ldb
by
k
. Before entry the leading
n
-by-
k
part of the array
b
must contain the matrix
B
.
Array, size
ldb
by
n
. Before entry, the leading
k
-by-
n
part of the array
b
must contain the matrix
B
.
Specifies the leading dimension of as declared in the calling (sub)program.
When = , then must be at least , otherwise must be at least .
transb
=
CblasTrans
or
transb
=
CblasConjTrans
Specifies the scalar . When is equal to zero, then need not be set on input.
Array, size
ldc
by
n
. Before entry, the leading
m
-by-
n
part of the array
c
must contain the matrix
C
, except when
beta
is equal to zero, in which case
c
need not be set on entry.
Array, size
ldc
by
m
. Before entry, the leading
n
-by-
m
part of the array
c
must contain the matrix
C
, except when
beta
is equal to zero, in which case
c
need not be set on entry.
Specifies the leading dimension of as declared in the calling (sub)program.
Overwritten by the -by- matrix .
For examples of
usage, see these code examples in the
Intel® oneAPI Math Kernel Library
installation directory:
:
examples\cblas\source\cblas_hgemmx.c
:
examples\cblas\source\cblas_sgemmx.c
:
examples\cblas\source\cblas_dgemmx.c
:
examples\cblas\source\cblas_cgemmx.c
:
examples\cblas\source\cblas_zgemmx.c
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Source: https://www.intel.com/content/www/us/en/develop/documentation/onemkl-developer-reference-c/top/blas-and-sparse-blas-routines/blas-routines/blas-level-3-routines/cblas-gemm.html
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