Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686
Date 12/16/2022
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Document Table of Contents
Document Table of Contents x
Developer Reference for
Developer Reference for x
Getting Help and Support What's New Notational Conventions Overview OpenMP* Offload BLAS and Sparse BLAS Routines LAPACK Routines ScaLAPACK Routines Sparse Solver Routines Extended Eigensolver Routines Vector Mathematical Functions Statistical Functions Fourier Transform Functions PBLAS Routines Partial Differential Equations Support Nonlinear Optimization Problem Solvers Support Functions BLACS Routines Data Fitting Functions Appendix A: Linear Solvers Basics Appendix B: Routine and Function Arguments Appendix C: Specific Features of Fortran 95 Interfaces for LAPACK Routines Appendix D: FFTW Interface to Intel® Math Kernel Library Appendix E: Code Examples Appendix F: oneMKL Functionality Bibliography Glossary Notices and Disclaimers
Overview x
Performance Enhancements Parallelism
OpenMP* Offload x
OpenMP* Offload for Intel® oneAPI Math Kernel Library
BLAS and Sparse BLAS Routines x
BLAS Routines Sparse BLAS Level 1 Routines Sparse BLAS Level 2 and Level 3 Routines Sparse QR Routines Inspector-executor Sparse BLAS Routines BLAS-like Extensions
BLAS Routines x
Naming Conventions for BLAS Routines Fortran 95 Interface Conventions for BLAS Routines Matrix Storage Schemes for BLAS Routines BLAS Level 1 Routines and Functions BLAS Level 2 Routines BLAS Level 3 Routines
BLAS Level 1 Routines and Functions x
<span class='option'>?asum</span> <span class='option'>?axpy</span> <span class='option'>?copy</span> ?copy_batch ?copy_batch_strided <span class='option'>?dot</span> <span class='option'>?sdot</span> <span class='option'>?dotc</span> <span class='option'>?dotu</span> <span class='option'>?nrm2</span> <span class='option'>?rot</span> <span class='option'>?rotg</span> <span class='option'>?rotm</span> <span class='option'>?rotmg</span> <span class='option'>?scal</span> <span class='option'>?swap</span> <span class='option'>i?amax</span> <span class='option'>i?amin</span> <span class='option'>?cabs1</span>
BLAS Level 2 Routines x
<span class='option'>?gbmv</span> <span class='option'>?gemv</span> <span class='option'>?ger</span> <span class='option'>?gerc</span> <span class='option'>?geru</span> <span class='option'>?hbmv</span> <span class='option'>?hemv</span> <span class='option'>?her</span> <span class='option'>?her2</span> <span class='option'>?hpmv</span> <span class='option'>?hpr</span> <span class='option'>?hpr2</span> <span class='option'>?sbmv</span> <span class='option'>?spmv</span> <span class='option'>?spr</span> <span class='option'>?spr2</span> <span class='option'>?symv</span> <span class='option'>?syr</span> <span class='option'>?syr2</span> <span class='option'>?tbmv</span> <span class='option'>?tbsv</span> <span class='option'>?tpmv</span> <span class='option'>?tpsv</span> <span class='option'>?trmv</span> <span class='option'>?trsv</span>
BLAS Level 3 Routines x
<span class='option'>?gemm</span> <span class='option'>?hemm</span> <span class='option'>?herk</span> <span class='option'>?her2k</span> <span class='option'>?symm</span> <span class='option'>?syrk</span> <span class='option'>?syr2k</span> <span class='option'>?trmm</span> <span class='option'>?trsm</span>
Sparse BLAS Level 1 Routines x
Vector Arguments Naming Conventions for Sparse BLAS Routines Routines and Data Types BLAS Level 1 Routines That Can Work With Sparse Vectors <span class='option'>?axpyi</span> <span class='option'>?doti</span> <span class='option'>?dotci</span> <span class='option'>?dotui</span> <span class='option'>?gthr</span> <span class='option'>?gthrz</span> <span class='option'>?roti</span> <span class='option'>?sctr</span>
Sparse BLAS Level 2 and Level 3 Routines x
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.
Sparse BLAS Level 2 and Level 3 Routines. x
<span class='option'>mkl_?csrgemv</span> <span class='option'>mkl_?bsrgemv</span> <span class='option'>mkl_?coogemv</span> <span class='option'>mkl_?diagemv</span> <span class='option'>mkl_?csrsymv</span> <span class='option'>mkl_?bsrsymv</span> <span class='option'>mkl_?coosymv</span> <span class='option'>mkl_?diasymv</span> <span class='option'>mkl_?csrtrsv</span> <span class='option'>mkl_?bsrtrsv</span> <span class='option'>mkl_?cootrsv</span> <span class='option'>mkl_?diatrsv</span> <span class='option'>mkl_cspblas_?csrgemv</span> <span class='option'>mkl_cspblas_?bsrgemv</span> <span class='option'>mkl_cspblas_?coogemv</span> <span class='option'>mkl_cspblas_?csrsymv</span> <span class='option'>mkl_cspblas_?bsrsymv</span> <span class='option'>mkl_cspblas_?coosymv</span> <span class='option'>mkl_cspblas_?csrtrsv</span> <span class='option'>mkl_cspblas_?bsrtrsv</span> <span class='option'>mkl_cspblas_?cootrsv</span> <span class='option'>mkl_?csrmv</span> <span class='option'>mkl_?bsrmv</span> <span class='option'>mkl_?cscmv</span> <span class='option'>mkl_?coomv</span> <span class='option'>mkl_?csrsv</span> <span class='option'>mkl_?bsrsv</span> <span class='option'>mkl_?cscsv</span> <span class='option'>mkl_?coosv</span> <span class='option'>mkl_?csrmm</span> <span class='option'>mkl_?bsrmm</span> <span class='option'>mkl_?cscmm</span> <span class='option'>mkl_?coomm</span> <span class='option'>mkl_?csrsm</span> <span class='option'>mkl_?cscsm</span> <span class='option'>mkl_?coosm</span> <span class='option'>mkl_?bsrsm</span> <span class='option'>mkl_?diamv</span> <span class='option'>mkl_?skymv</span> <span class='option'>mkl_?diasv</span> <span class='option'>mkl_?skysv</span> <span class='option'>mkl_?diamm</span> <span class='option'>mkl_?skymm</span> <span class='option'>mkl_?diasm</span> <span class='option'>mkl_?skysm</span> <span class='option'>mkl_?dnscsr</span> <span class='option'>mkl_?csrcoo</span> <span class='option'>mkl_?csrbsr</span> <span class='option'>mkl_?csrcsc</span> <span class='option'>mkl_?csrdia</span> <span class='option'>mkl_?csrsky</span> <span class='option'>mkl_?csradd</span> <span class='option'>mkl_?csrmultcsr</span> <span class='option'>mkl_?csrmultd</span>
Sparse QR Routines x
<span class='option'>mkl_sparse_set_qr_hint</span> <span class='option'>mkl_sparse_?_qr</span> <span class='option'>mkl_sparse_qr_reorder</span> <span class='option'>mkl_sparse_?_qr_factorize</span> <span class='option'>mkl_sparse_?_qr_solve</span> <span class='option'>mkl_sparse_?_qr_qmult</span> <span class='option'>mkl_sparse_?_qr_rsolve</span>
Inspector-executor Sparse BLAS Routines x
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 Inspector-Executor Sparse BLAS Analysis Routines Inspector-Executor Sparse BLAS Execution Routines
Matrix Manipulation Routines x
<span class='option'> mkl_sparse_?_create_csr</span> <span class='option'>mkl_sparse_?_create_csc</span> <span class='option'>mkl_sparse_?_create_coo</span> <span class='option'>mkl_sparse_?_create_bsr</span> <span class='option'>mkl_sparse_copy</span> <span class='option'>mkl_sparse_destroy</span> <span class='option'>mkl_sparse_convert_csr</span> <span class='option'>mkl_sparse_convert_bsr</span> <span class='option'>mkl_sparse_?_export_csr</span> <span class='option'>mkl_sparse_?_export_csc</span> <span class='option'>mkl_sparse_?_export_bsr</span> <span class='option'>mkl_sparse_?_set_value</span> <span class='option'>mkl_sparse_?_update_values</span> <span class='option'>mkl_sparse_order</span>
Inspector-Executor Sparse BLAS Analysis Routines x
<span class='option'>mkl_sparse_set_lu_smoother_hint</span> <span class='option'>mkl_sparse_set_mv_hint</span> <span class='option'>mkl_sparse_set_sv_hint</span> <span class='option'>mkl_sparse_set_mm_hint</span> <span class='option'>mkl_sparse_set_sm_hint</span> <span class='option'>mkl_sparse_set_dotmv_hint</span> <span class='option'>mkl_sparse_set_symgs_hint</span> mkl_sparse_set_sorv_hint <span class='option'>mkl_sparse_set_memory_hint</span> <span class='option'>mkl_sparse_optimize</span>
Inspector-Executor Sparse BLAS Execution Routines x
<span class='option'>mkl_sparse_?_lu_smoother</span> <span class='option'>mkl_sparse_?_mv</span> <span class='option'>mkl_sparse_?_trsv</span> <span class='option'>mkl_sparse_?_mm</span> <span class='option'>mkl_sparse_?_trsm</span> <span class='option'>mkl_sparse_?_add</span> <span class='option'>mkl_sparse_spmm</span> <span class='option'>mkl_sparse_?_spmmd</span> <span class='option'>mkl_sparse_sp2m</span> <span class='option'>mkl_sparse_?_sp2md</span> <span class='option'>mkl_sparse_sypr</span> <span class='option'>mkl_sparse_?_syprd</span> <span class='option'>mkl_sparse_?_symgs</span> <span class='option'>mkl_sparse_?_symgs_mv</span> <span class='option'>mkl_sparse_syrk</span> <span class='option'>mkl_sparse_?_syrkd</span> <span class='option'>mkl_sparse_?_dotmv</span> mkl_sparse_?_sorv
BLAS-like Extensions x
<span class='option'>?axpy_batch</span> <span class='option'>?axpy_batch_strided</span> <span class='option'>?axpby</span> <span class='option'>?gem2vu</span> <span class='option'>?gem2vc</span> <span class='option'>?gemmt</span> <span class='option'>?gemm3m</span> <span class='option'>?gemm_batch</span> <span class='option'>?gemm_batch_strided</span> <span class='option'>?gemm3m_batch</span> <span class='option'>?trsm_batch</span> <span class='option'>?trsm_batch_strided</span> <span class='option'>mkl_?imatcopy</span> <span class='option'>mkl_?imatcopy_batch</span> <span class='option'>mkl_?imatcopy_batch_strided</span> mkl_?omatadd_batch_strided <span class='option'>mkl_?omatcopy</span> <span class='option'>mkl_?omatcopy_batch</span> <span class='option'>mkl_?omatcopy_batch_strided</span> <span class='option'>mkl_?omatcopy2</span> <span class='option'>mkl_?omatadd</span> <span class='option'>?gemm_pack_get_size</span>, <span class='option'>gemm_*_pack_get_size</span> <span class='option'>?gemm_pack</span> <span class='option'>gemm_*_pack</span> <span class='option'>?gemm_compute</span> <span class='option'>gemm_*_compute</span> <span class='option'>?gemm_free</span> <span class='option'>gemm_*</span> <span class='option'>?gemv_batch_strided</span> <span class='option'>?gemv_batch</span> <span class='option'>?dgmm_batch_strided</span> <span class='option'>?dgmm_batch</span> <span class='option'>mkl_jit_create_?gemm</span> <span class='option'>mkl_jit_get_?gemm_ptr</span> <span class='option'>mkl_jit_destroy</span>
LAPACK Routines x
Naming Conventions for LAPACK Routines Fortran 95 Interface Conventions for LAPACK Routines Matrix Storage Schemes for LAPACK Routines Mathematical Notation for LAPACK Routines Error Analysis LAPACK Linear Equation Routines LAPACK Least Squares and Eigenvalue Problem Routines LAPACK Auxiliary Routines LAPACK Utility Functions and Routines LAPACK Test Functions and Routines Additional LAPACK Routines (Included for Compatibility with Netlib LAPACK)
Fortran 95 Interface Conventions for LAPACK Routines x
Intel® MKL Fortran 95 Interfaces for LAPACK Routines vs. Netlib Implementation
LAPACK Linear Equation Routines x
LAPACK Linear Equation Computational Routines LAPACK Linear Equation Driver Routines
LAPACK Linear Equation Computational Routines x
Matrix Factorization: LAPACK Computational Routines Solving Systems of Linear Equations: LAPACK Computational Routines Estimating the Condition Number: LAPACK Computational Routines Refining the Solution and Estimating Its Error: LAPACK Computational Routines Matrix Inversion: LAPACK Computational Routines Matrix Equilibration: LAPACK Computational Routines
Matrix Factorization: LAPACK Computational Routines x
<span class='option'>?getrf</span> <span class='option'>?getrf_batch</span> <span class='option'>?getrf_batch_strided</span> mkl_?getrfnp <span class='option'>?getrfnp_batch_strided</span> <span class='option'>mkl_?getrfnpi</span> <span class='option'>?getrf2</span> <span class='option'>?getri_oop_batch</span> <span class='option'>?getri_oop_batch_strided</span> <span class='option'>?gbtrf</span> <span class='option'>?gttrf</span> <span class='option'>?dttrfb</span> <span class='option'>?potrf</span> <span class='option'>?potrf2</span> <span class='option'>?pstrf</span> <span class='option'>?pftrf</span> <span class='option'>?pptrf</span> <span class='option'>?pbtrf</span> <span class='option'>?pttrf</span> <span class='option'>?sytrf</span> <span class='option'>?sytrf_aa</span> <span class='option'>?sytrf_rook</span> <span class='option'>?sytrf_rk</span> <span class='option'>?hetrf</span> <span class='option'>?hetrf_aa</span> <span class='option'>?hetrf_rook</span> <span class='option'>?hetrf_rk</span> <span class='option'>?sptrf</span> <span class='option'>?hptrf</span> <span class='option'>mkl_?spffrt2</span>, <span class='option'>mkl_?spffrtx</span>
Solving Systems of Linear Equations: LAPACK Computational Routines x
<span class='option'>?getrs</span> <span class='option'>?getrs_batch_strided</span> <span class='option'>?getrsnp_batch_strided</span> <span class='option'>?gbtrs</span> <span class='option'>?gttrs</span> <span class='option'>?dttrsb</span> <span class='option'>?potrs</span> <span class='option'>?pftrs</span> <span class='option'>?pptrs</span> <span class='option'>?pbtrs</span> <span class='option'>?pttrs</span> <span class='option'>?sytrs</span> <span class='option'>?sytrs_aa</span> <span class='option'>?sytrs_rook</span> <span class='option'>?hetrs</span> <span class='option'>?hetrs_aa</span> <span class='option'>?hetrs_rook</span> <span class='option'>?sytrs2</span> <span class='option'>?hetrs2</span> <span class='option'>?sytrs_3</span> <span class='option'>?hetrs_3</span> <span class='option'>?sptrs</span> <span class='option'>?hptrs</span> <span class='option'>?trtrs</span> <span class='option'>?tptrs</span> <span class='option'>?tbtrs</span>
Estimating the Condition Number: LAPACK Computational Routines x
<span class='option'>?gecon</span> <span class='option'>?gbcon</span> <span class='option'>?gtcon</span> <span class='option'>?pocon</span> <span class='option'>?ppcon</span> <span class='option'>?pbcon</span> <span class='option'>?ptcon</span> <span class='option'>?sycon</span> <span class='option'>?sycon_rook</span> <span class='option'>?sycon_3</span> <span class='option'>?hecon</span> <span class='option'>?hecon_rook</span> <span class='option'>?hecon_3</span> <span class='option'>?spcon</span> <span class='option'>?hpcon</span> <span class='option'>?trcon</span> <span class='option'>?tpcon</span> <span class='option'>?tbcon</span>
Refining the Solution and Estimating Its Error: LAPACK Computational Routines x
<span class='option'>?gerfs</span> <span class='option'>?gerfsx</span> <span class='option'>?gbrfs</span> <span class='option'>?gbrfsx</span> <span class='option'>?gtrfs</span> <span class='option'>?porfs</span> <span class='option'>?porfsx</span> <span class='option'>?pprfs</span> <span class='option'>?pbrfs</span> <span class='option'>?ptrfs</span> <span class='option'>?syrfs</span> <span class='option'>?syrfsx</span> <span class='option'>?herfs</span> <span class='option'>?herfsx</span> <span class='option'>?sprfs</span> <span class='option'>?hprfs</span> <span class='option'>?trrfs</span> <span class='option'>?tprfs</span> <span class='option'>?tbrfs</span>
Matrix Inversion: LAPACK Computational Routines x
<span class='option'>?getri</span> mkl_?getrinp <span class='option'>?potri</span> <span class='option'>?pftri</span> <span class='option'>?pptri</span> <span class='option'>?sytri</span> <span class='option'>?sytri_rook</span> <span class='option'>?hetri</span> <span class='option'>?hetri_rook</span> <span class='option'>?sytri2</span> <span class='option'>?hetri2</span> <span class='option'>?sytri2x</span> <span class='option'>?hetri2x</span> <span class='option'>?sytri_3</span> <span class='option'>?hetri_3</span> <span class='option'>?sptri</span> <span class='option'>?hptri</span> <span class='option'>?trtri</span> <span class='option'>?tftri</span> <span class='option'>?tptri</span>
Matrix Equilibration: LAPACK Computational Routines x
<span class='option'>?geequ</span> <span class='option'>?geequb</span> <span class='option'>?gbequ</span> <span class='option'>?gbequb</span> <span class='option'>?poequ</span> <span class='option'>?poequb</span> <span class='option'>?ppequ</span> <span class='option'>?pbequ</span> <span class='option'>?syequb</span> <span class='option'>?heequb</span>
LAPACK Linear Equation Driver Routines x
<span class='option'>?gesv</span> <span class='option'>?gesvx</span> <span class='option'>?gesvxx</span> <span class='option'>?gbsv</span> <span class='option'>?gbsvx</span> <span class='option'>?gbsvxx</span> <span class='option'>?gtsv</span> <span class='option'>?gtsvx</span> <span class='option'>?dtsvb</span> <span class='option'>?posv</span> <span class='option'>?posvx</span> <span class='option'>?posvxx</span> <span class='option'>?ppsv</span> <span class='option'>?ppsvx</span> <span class='option'>?pbsv</span> <span class='option'>?pbsvx</span> <span class='option'>?ptsv</span> <span class='option'>?ptsvx</span> <span class='option'>?sysv</span> <span class='option'>?sysv_aa</span> <span class='option'>?sysv_rook</span> <span class='option'>?sysv_rk</span> <span class='option'>?sysvx</span> <span class='option'>?sysvxx</span> <span class='option'>?hesv</span> <span class='option'>?hesv_aa</span> <span class='option'>?hesv_rk</span> <span class='option'>?hesv_rook</span> <span class='option'>?hesvx</span> <span class='option'>?hesvxx</span> <span class='option'>?spsv</span> <span class='option'>?spsvx</span> <span class='option'>?hpsv</span> <span class='option'>?hpsvx</span>
LAPACK Least Squares and Eigenvalue Problem Routines x
LAPACK Least Squares and Eigenvalue Problem Computational Routines LAPACK Least Squares and Eigenvalue Problem Driver Routines
LAPACK Least Squares and Eigenvalue Problem Computational Routines x
Orthogonal Factorizations: LAPACK Computational Routines Singular Value Decomposition: LAPACK Computational Routines Symmetric Eigenvalue Problems: LAPACK Computational Routines Generalized Symmetric-Definite Eigenvalue Problems: LAPACK Computational Routines Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines Generalized Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines Generalized Singular Value Decomposition: LAPACK Computational Routines Cosine-Sine Decomposition: LAPACK Computational Routines
Orthogonal Factorizations: LAPACK Computational Routines x
<span class='option'>?geqrf</span> <span class='option'>?geqr</span> <span class='option'>?geqrfp</span> <span class='option'>?geqrt</span> <span class='option'>?gemqrt</span> <span class='option'>?geqpf</span> <span class='option'>?geqp3</span> <span class='option'>?orgqr</span> <span class='option'>?ormqr</span> <span class='option'>?gemqr</span> <span class='option'>?ungqr</span> <span class='option'>?unmqr</span> <span class='option'>?gelqf</span> <span class='option'>?gelq</span> <span class='option'>?gelqt</span> <span class='option'>?gemlqt</span> <span class='option'>?orglq</span> <span class='option'>?ormlq</span> <span class='option'>?gemlq</span> <span class='option'>?unglq</span> <span class='option'>?unmlq</span> <span class='option'>?geqlf</span> <span class='option'>?orgql</span> <span class='option'>?ungql</span> <span class='option'>?ormql</span> <span class='option'>?unmql</span> <span class='option'>?gerqf</span> <span class='option'>?orgrq</span> <span class='option'>?ungrq</span> <span class='option'>?ormrq</span> <span class='option'>?unmrq</span> <span class='option'>?tzrzf</span> <span class='option'>?ormrz</span> <span class='option'>?unmrz</span> <span class='option'>?ggqrf</span> <span class='option'>?ggrqf</span> <span class='option'>?tpqrt</span> <span class='option'>?tpmqrt</span> <span class='option'>?tplqt</span> <span class='option'>?tpmlqt</span>
Singular Value Decomposition: LAPACK Computational Routines x
<span class='option'>?gebrd</span> <span class='option'>?gbbrd</span> <span class='option'>?orgbr</span> <span class='option'>?ormbr</span> <span class='option'>?ungbr</span> <span class='option'>?unmbr</span> <span class='option'>?bdsqr</span> <span class='option'>?bdsdc</span>
Symmetric Eigenvalue Problems: LAPACK Computational Routines x
<span class='option'>?sytrd</span> <span class='option'>?syrdb</span> <span class='option'>?herdb</span> <span class='option'>?orgtr</span> <span class='option'>?ormtr</span> <span class='option'>?hetrd</span> <span class='option'>?ungtr</span> <span class='option'>?unmtr</span> <span class='option'>?orm22</span>/<span class='option'>?unm22</span> <span class='option'>?sptrd</span> <span class='option'>?opgtr</span> <span class='option'>?opmtr</span> <span class='option'>?hptrd</span> <span class='option'>?upgtr</span> <span class='option'>?upmtr</span> <span class='option'>?sbtrd</span> <span class='option'>?hbtrd</span> <span class='option'>?sterf</span> <span class='option'>?steqr</span> <span class='option'>?stemr</span> <span class='option'>?stedc</span> <span class='option'>?stegr</span> <span class='option'>?pteqr</span> <span class='option'>?stebz</span> <span class='option'>?stein</span> <span class='option'>?disna</span>
Generalized Symmetric-Definite Eigenvalue Problems: LAPACK Computational Routines x
<span class='option'>?sygst</span> <span class='option'>?hegst</span> <span class='option'>?spgst</span> <span class='option'>?hpgst</span> <span class='option'>?sbgst</span> <span class='option'>?hbgst</span> <span class='option'>?pbstf</span>
Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines x
<span class='option'>?gehrd</span> <span class='option'>?orghr</span> <span class='option'>?ormhr</span> <span class='option'>?unghr</span> <span class='option'>?unmhr</span> <span class='option'>?gebal</span> <span class='option'>?gebak</span> <span class='option'>?hseqr</span> <span class='option'>?hsein</span> <span class='option'>?trevc</span> <span class='option'>?trevc3</span> <span class='option'>?trsna</span> <span class='option'>?trexc</span> <span class='option'>?trsen</span> <span class='option'>?trsyl</span>
Generalized Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines x
<span class='option'>?gghrd</span> <span class='option'>?ggbal</span> <span class='option'>?ggbak</span> <span class='option'>?gghd3</span> <span class='option'>?hgeqz</span> <span class='option'>?tgevc</span> <span class='option'>?tgexc</span> <span class='option'>?tgsen</span> <span class='option'>?tgsyl</span> <span class='option'>?tgsna</span>
Generalized Singular Value Decomposition: LAPACK Computational Routines x
<span class='option'>?ggsvp</span> <span class='option'>?ggsvp3</span> <span class='option'>?ggsvd3</span> <span class='option'>?tgsja</span>
Cosine-Sine Decomposition: LAPACK Computational Routines x
<span class='option'>?bbcsd</span> <span class='option'>?orbdb/?unbdb</span>
LAPACK Least Squares and Eigenvalue Problem Driver Routines x
Linear Least Squares (LLS) Problems: LAPACK Driver Routines Generalized Linear Least Squares (LLS) Problems: LAPACK Driver Routines Symmetric Eigenvalue Problems: LAPACK Driver Routines Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines Singular Value Decomposition: LAPACK Driver Routines Cosine-Sine Decomposition: LAPACK Driver Routines Generalized Symmetric Definite Eigenvalue Problems: LAPACK Driver Routines Generalized Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines
Linear Least Squares (LLS) Problems: LAPACK Driver Routines x
<span class='option'>?gels</span> <span class='option'>?gelsy</span> <span class='option'>?gelss</span> <span class='option'>?gelsd</span> <span class='option'>?getsls</span>
Generalized Linear Least Squares (LLS) Problems: LAPACK Driver Routines x
<span class='option'>?gglse</span> <span class='option'>?ggglm</span>
Symmetric Eigenvalue Problems: LAPACK Driver Routines x
<span class='option'>?syev</span> <span class='option'>?heev</span> <span class='option'>?syevd</span> <span class='option'>?heevd</span> <span class='option'>?syevx</span> <span class='option'>?heevx</span> <span class='option'>?syevr</span> <span class='option'>?heevr</span> <span class='option'>?spev</span> <span class='option'>?hpev</span> <span class='option'>?spevd</span> <span class='option'>?hpevd</span> <span class='option'>?spevx</span> <span class='option'>?hpevx</span> <span class='option'>?sbev</span> <span class='option'>?hbev</span> <span class='option'>?sbevd</span> <span class='option'>?hbevd</span> <span class='option'>?sbevx</span> <span class='option'>?hbevx</span> <span class='option'>?stev</span> <span class='option'>?stevd</span> <span class='option'>?stevx</span> <span class='option'>?stevr</span>
Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines x
<span class='option'>?gees</span> <span class='option'>?geesx</span> <span class='option'>?geev</span> <span class='option'>?geevx</span>
Singular Value Decomposition: LAPACK Driver Routines x
<span class='option'>?gesvd</span> <span class='option'>?gesdd</span> <span class='option'>?gejsv</span> <span class='option'>?gesvj</span> <span class='option'>?ggsvd</span> <span class='option'>?gesvdx</span> <span class='option'>?bdsvdx</span>
Cosine-Sine Decomposition: LAPACK Driver Routines x
<span class='option'>?orcsd/?uncsd</span> <span class='option'>?orcsd2by1/?uncsd2by1</span>
Generalized Symmetric Definite Eigenvalue Problems: LAPACK Driver Routines x
<span class='option'>?sygv</span> <span class='option'>?hegv</span> <span class='option'>?sygvd</span> <span class='option'>?hegvd</span> <span class='option'>?sygvx</span> <span class='option'>?hegvx</span> <span class='option'>?spgv</span> <span class='option'>?hpgv</span> <span class='option'>?spgvd</span> <span class='option'>?hpgvd</span> <span class='option'>?spgvx</span> <span class='option'>?hpgvx</span> <span class='option'>?sbgv</span> <span class='option'>?hbgv</span> <span class='option'>?sbgvd</span> <span class='option'>?hbgvd</span> <span class='option'>?sbgvx</span> <span class='option'>?hbgvx</span>
Generalized Nonsymmetric Eigenvalue Problems: LAPACK Driver Routines x
<span class='option'>?gges</span> <span class='option'>?ggesx</span> <span class='option'>?gges3</span> <span class='option'>?ggev</span> <span class='option'>?ggevx</span> <span class='option'>?ggev3</span>
LAPACK Auxiliary Routines x
<span class='option'>?lacgv</span> <span class='option'>?lacrm</span> <span class='option'>?lacrt</span> <span class='option'>?laesy</span> <span class='option'>?rot</span> <span class='option'>?spmv</span> <span class='option'>?spr</span> <span class='option'>?syconv</span> <span class='option'>?symv</span> <span class='option'>?syr</span> <span class='option'>i?max1</span> <span class='option'>?sum1</span> <span class='option'>?gbtf2</span> <span class='option'>?gebd2</span> <span class='option'>?gehd2</span> <span class='option'>?gelq2</span> <span class='option'>?gelqt3</span> <span class='option'>?geql2</span> <span class='option'>?geqr2</span> <span class='option'>?geqr2p</span> <span class='option'>?geqrt2</span> <span class='option'>?geqrt3</span> <span class='option'>?gerq2</span> <span class='option'>?gesc2</span> <span class='option'>?getc2</span> <span class='option'>?getf2</span> <span class='option'>?gtts2</span> <span class='option'>?isnan</span> <span class='option'>?laisnan</span> <span class='option'>?labrd</span> <span class='option'>?lacn2</span> <span class='option'>?lacon</span> <span class='option'>?lacpy</span> <span class='option'>?ladiv</span> <span class='option'>?lae2</span> <span class='option'>?laebz</span> <span class='option'>?laed0</span> <span class='option'>?laed1</span> <span class='option'>?laed2</span> <span class='option'>?laed3</span> <span class='option'>?laed4</span> <span class='option'>?laed5</span> <span class='option'>?laed6</span> <span class='option'>?laed7</span> <span class='option'>?laed8</span> <span class='option'>?laed9</span> <span class='option'>?laeda</span> <span class='option'>?laein</span> <span class='option'>?laev2</span> <span class='option'>?laexc</span> <span class='option'>?lag2</span> <span class='option'>?lags2</span> <span class='option'>?lagtf</span> <span class='option'>?lagtm</span> <span class='option'>?lagts</span> <span class='option'>?lagv2</span> <span class='option'>?lahqr</span> <span class='option'>?lahrd</span> <span class='option'>?lahr2</span> <span class='option'>?laic1</span> <span class='option'>?lakf2</span> <span class='option'>?laln2</span> <span class='option'>?lals0</span> <span class='option'>?lalsa</span> <span class='option'>?lalsd</span> <span class='option'>?lamrg</span> <span class='option'>?lamswlq</span> <span class='option'>?lamtsqr</span> <span class='option'>?laneg</span> <span class='option'>?langb</span> <span class='option'>?lange</span> <span class='option'>?langt</span> <span class='option'>?lanhs</span> <span class='option'>?lansb</span> <span class='option'>?lanhb</span> <span class='option'>?lansp</span> <span class='option'>?lanhp</span> <span class='option'>?lanst/?lanht</span> <span class='option'>?lansy</span> <span class='option'>?lanhe</span> <span class='option'>?lantb</span> <span class='option'>?lantp</span> <span class='option'>?lantr</span> <span class='option'>?lanv2</span> <span class='option'>?lapll</span> <span class='option'>?lapmr</span> <span class='option'>?lapmt</span> <span class='option'>?lapy2</span> <span class='option'>?lapy3</span> <span class='option'>?laqgb</span> <span class='option'>?laqge</span> <span class='option'>?laqhb</span> <span class='option'>?laqp2</span> <span class='option'>?laqps</span> <span class='option'>?laqr0</span> <span class='option'>?laqr1</span> <span class='option'>?laqr2</span> <span class='option'>?laqr3</span> <span class='option'>?laqr4</span> <span class='option'>?laqr5</span> <span class='option'>?laqsb</span> <span class='option'>?laqsp</span> <span class='option'>?laqsy</span> <span class='option'>?laqtr</span> ?laqz0 <span class='option'>?lar1v</span> <span class='option'>?lar2v</span> <span class='option'>?laran</span> <span class='option'>?larf</span> <span class='option'>?larfb</span> <span class='option'>?larfg</span> <span class='option'>?larfgp</span> <span class='option'>?larft</span> <span class='option'>?larfx</span> <span class='option'>?larfy</span> <span class='option'>?large</span> <span class='option'>?largv</span> <span class='option'>?larnd</span> <span class='option'>?larnv</span> <span class='option'>?laror</span> <span class='option'>?larot</span> <span class='option'>?larra</span> <span class='option'>?larrb</span> <span class='option'>?larrc</span> <span class='option'>?larrd</span> <span class='option'>?larre</span> <span class='option'>?larrf</span> <span class='option'>?larrj</span> <span class='option'>?larrk</span> <span class='option'>?larrr</span> <span class='option'>?larrv</span> <span class='option'>?lartg</span> <span class='option'>?lartgp</span> <span class='option'>?lartgs</span> <span class='option'>?lartv</span> <span class='option'>?laruv</span> <span class='option'>?larz</span> <span class='option'>?larzb</span> <span class='option'>?larzt</span> <span class='option'>?las2</span> <span class='option'>?lascl</span> <span class='option'>?lasd0</span> <span class='option'>?lasd1</span> <span class='option'>?lasd2</span> <span class='option'>?lasd3</span> <span class='option'>?lasd4</span> <span class='option'>?lasd5</span> <span class='option'>?lasd6</span> <span class='option'>?lasd7</span> <span class='option'>?lasd8</span> <span class='option'>?lasd9</span> <span class='option'>?lasda</span> <span class='option'>?lasdq</span> <span class='option'>?lasdt</span> <span class='option'>?laset</span> <span class='option'>?lasq1</span> <span class='option'>?lasq2</span> <span class='option'>?lasq3</span> <span class='option'>?lasq4</span> <span class='option'>?lasq5</span> <span class='option'>?lasq6</span> <span class='option'>?lasr</span> <span class='option'>?lasrt</span> <span class='option'>?lassq</span> <span class='option'>?lasv2</span> <span class='option'>?laswlq</span> <span class='option'>?laswp</span> <span class='option'>?lasy2</span> <span class='option'>?lasyf</span> <span class='option'>?lasyf_aa</span> <span class='option'>?lasyf_rook</span> <span class='option'>?lahef</span> <span class='option'>?lahef_aa</span> <span class='option'>?lahef_rook</span> <span class='option'>?latbs</span> <span class='option'>?latm1</span> <span class='option'>?latm2</span> <span class='option'>?latm3</span> <span class='option'>?latm5</span> <span class='option'>?latm6</span> <span class='option'>?latme</span> <span class='option'>?latmr</span> <span class='option'>?latdf</span> <span class='option'>?latps</span> <span class='option'>?latrd</span> <span class='option'>?latrs</span> <span class='option'>?latrz</span> <span class='option'>?latsqr</span> <span class='option'>?lauu2</span> <span class='option'>?lauum</span> <span class='option'>?orbdb1/?unbdb1</span> <span class='option'>?orbdb2/?unbdb2</span> <span class='option'>?orbdb3/?unbdb3</span> <span class='option'>?orbdb4/?unbdb4</span> <span class='option'>?orbdb5/?unbdb5</span> <span class='option'>?orbdb6/?unbdb6</span> <span class='option'>?org2l/?ung2l</span> <span class='option'>?org2r/?ung2r</span> <span class='option'>?orgl2/?ungl2</span> <span class='option'>?orgr2/?ungr2</span> <span class='option'>?orm2l/?unm2l</span> <span class='option'>?orm2r/?unm2r</span> <span class='option'>?orml2/?unml2</span> <span class='option'>?ormr2/?unmr2</span> <span class='option'>?ormr3/?unmr3</span> <span class='option'>?pbtf2</span> <span class='option'>?potf2</span> <span class='option'>?ptts2</span> <span class='option'>?rscl</span> <span class='option'>?syswapr</span> <span class='option'>?heswapr</span> <span class='option'>?syswapr1</span> <span class='option'>?sygs2/?hegs2</span> <span class='option'>?sytd2/?hetd2</span> <span class='option'>?sytf2</span> <span class='option'>?sytf2_rook</span> <span class='option'>?hetf2</span> <span class='option'>?hetf2_rook</span> <span class='option'>?tgex2</span> <span class='option'>?tgsy2</span> <span class='option'>?trti2</span> <span class='option'>clag2z</span> <span class='option'>dlag2s</span> <span class='option'>slag2d</span> <span class='option'>zlag2c</span> <span class='option'>?larfp</span> <span class='option'>ila?lc</span> <span class='option'>ila?lr</span> <span class='option'>?gsvj0</span> <span class='option'>?gsvj1</span> <span class='option'>?sfrk</span> <span class='option'>?hfrk</span> <span class='option'>?tfsm</span> <span class='option'>?lansf</span> <span class='option'>?lanhf</span> <span class='option'>?tfttp</span> <span class='option'>?tfttr</span> <span class='option'>?tplqt2</span> <span class='option'>?tpqrt2</span> <span class='option'>?tprfb</span> <span class='option'>?tpttf</span> <span class='option'>?tpttr</span> <span class='option'>?trttf</span> <span class='option'>?trttp</span> <span class='option'>?pstf2</span> <span class='option'>dlat2s </span> <span class='option'>zlat2c </span> <span class='option'>?lacp2</span> <span class='option'>?la_gbamv</span> <span class='option'>?la_gbrcond</span> <span class='option'>?la_gbrcond_c</span> <span class='option'>?la_gbrcond_x</span> <span class='option'>?la_gbrfsx_extended</span> <span class='option'>?la_gbrpvgrw</span> <span class='option'>?la_geamv</span> <span class='option'>?la_gercond</span> <span class='option'>?la_gercond_c</span> <span class='option'>?la_gercond_x</span> <span class='option'>?la_gerfsx_extended</span> <span class='option'>?la_heamv</span> <span class='option'>?la_hercond_c</span> <span class='option'>?la_hercond_x</span> <span class='option'>?la_herfsx_extended</span> <span class='option'>?la_herpvgrw</span> <span class='option'>?la_lin_berr</span> <span class='option'>?la_porcond</span> <span class='option'>?la_porcond_c</span> <span class='option'>?la_porcond_x</span> <span class='option'>?la_porfsx_extended</span> <span class='option'>?la_porpvgrw</span> <span class='option'>?laqhe</span> <span class='option'>?laqhp</span> ?larcm <span class='option'>?la_gerpvgrw</span> <span class='option'>?larscl2</span> <span class='option'>?lascl2</span> <span class='option'>?la_syamv</span> <span class='option'>?la_syrcond</span> <span class='option'>?la_syrcond_c</span> <span class='option'>?la_syrcond_x</span> <span class='option'>?la_syrfsx_extended</span> <span class='option'>?la_syrpvgrw</span> <span class='option'>?la_wwaddw</span> <span class='option'>mkl_?tppack</span> <span class='option'>mkl_?tpunpack</span> Additional LAPACK Routines
LAPACK Utility Functions and Routines x
<span class='option'>ilaver</span> <span class='option'>ilaenv</span> <span class='option'>iparmq</span> <span class='option'>ieeeck</span> <span class='option'>?labad</span> <span class='option'>?lamch</span> <span class='option'>?lamc1</span> <span class='option'>?lamc2</span> <span class='option'>?lamc3</span> <span class='option'>?lamc4</span> <span class='option'>?lamc5</span> <span class='option'>chla_transtype</span> <span class='option'>iladiag</span> <span class='option'>ilaprec</span> <span class='option'>ilatrans</span> <span class='option'>ilauplo</span> <span class='option'>xerbla_array</span>
LAPACK Test Functions and Routines x
<span class='option'>?latms</span>
ScaLAPACK Routines x
Overview of ScaLAPACK Routines ScaLAPACK Array Descriptors Naming Conventions for ScaLAPACK Routines ScaLAPACK Computational Routines ScaLAPACK Driver Routines ScaLAPACK Auxiliary Routines ScaLAPACK Utility Functions and Routines ScaLAPACK Redistribution/Copy Routines
ScaLAPACK Computational Routines x
Systems of Linear Equations: ScaLAPACK Computational Routines Matrix Factorization: ScaLAPACK Computational Routines Solving Systems of Linear Equations: ScaLAPACK Computational Routines 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 Symmetric Eigenvalue Problems: ScaLAPACK Computational Routines Nonsymmetric Eigenvalue Problems: ScaLAPACK Computational Routines Singular Value Decomposition: ScaLAPACK Driver Routines Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines
Matrix Factorization: ScaLAPACK Computational Routines x
<span class='option'>p?getrf</span> <span class='option'>p?gbtrf</span> <span class='option'>p?dbtrf</span> <span class='option'>p?dttrf</span> <span class='option'>p?potrf</span> <span class='option'>p?pbtrf</span> <span class='option'>p?pttrf</span>
Solving Systems of Linear Equations: ScaLAPACK Computational Routines x
<span class='option'>p?getrs</span> <span class='option'>p?gbtrs</span> <span class='option'>p?dbtrs</span> <span class='option'>p?dttrs</span> <span class='option'>p?potrs</span> <span class='option'>p?pbtrs</span> <span class='option'>p?pttrs</span> <span class='option'>p?trtrs</span>
Estimating the Condition Number: ScaLAPACK Computational Routines x
<span class='option'>p?gecon</span> <span class='option'>p?pocon</span> <span class='option'>p?trcon</span>
Refining the Solution and Estimating Its Error: ScaLAPACK Computational Routines x
<span class='option'>p?gerfs</span> <span class='option'>p?porfs</span> <span class='option'>p?trrfs</span>
Matrix Inversion: ScaLAPACK Computational Routines x
<span class='option'>p?getri</span> <span class='option'>p?potri</span> <span class='option'>p?trtri</span>
Matrix Equilibration: ScaLAPACK Computational Routines x
<span class='option'>p?geequ</span> <span class='option'>p?poequ</span>
Orthogonal Factorizations: ScaLAPACK Computational Routines x
<span class='option'>p?geqrf</span> <span class='option'>p?geqpf</span> <span class='option'>p?orgqr</span> <span class='option'>p?ungqr</span> <span class='option'>p?ormqr</span> <span class='option'>p?unmqr</span> <span class='option'>p?gelqf</span> <span class='option'>p?orglq</span> <span class='option'>p?unglq</span> <span class='option'>p?ormlq</span> <span class='option'>p?unmlq</span> <span class='option'>p?geqlf</span> <span class='option'>p?orgql</span> <span class='option'>p?ungql</span> <span class='option'>p?ormql</span> <span class='option'>p?unmql</span> <span class='option'>p?gerqf</span> <span class='option'>p?orgrq</span> <span class='option'>p?ungrq</span> <span class='option'>p?ormr3</span> <span class='option'>p?unmr3</span> <span class='option'>p?ormrq</span> <span class='option'>p?unmrq</span> <span class='option'>p?tzrzf</span> <span class='option'>p?ormrz</span> <span class='option'>p?unmrz</span> <span class='option'>p?ggqrf</span> <span class='option'>p?ggrqf</span>
Symmetric Eigenvalue Problems: ScaLAPACK Computational Routines x
<span class='option'>p?syngst</span> <span class='option'>p?syntrd</span> <span class='option'>p?sytrd</span> <span class='option'>p?ormtr</span> <span class='option'>p?hengst</span> <span class='option'>p?hentrd</span> <span class='option'>p?hetrd</span> <span class='option'>p?unmtr</span> <span class='option'>p?stebz</span> <span class='option'>p?stedc</span> <span class='option'>p?stein</span>
Nonsymmetric Eigenvalue Problems: ScaLAPACK Computational Routines x
<span class='option'>p?gehrd</span> <span class='option'>p?ormhr</span> <span class='option'>p?unmhr</span> <span class='option'>p?lahqr</span> <span class='option'>p?hseqr</span> <span class='option'>p?trevc</span>
Singular Value Decomposition: ScaLAPACK Driver Routines x
<span class='option'>p?gebrd</span> <span class='option'>p?ormbr</span> <span class='option'>p?unmbr</span>
Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines x
<span class='option'>p?sygst</span> <span class='option'>p?hegst</span>
ScaLAPACK Driver Routines x
<span class='option'>p?geevx</span> <span class='option'>p?gesv</span> <span class='option'>p?gesvx</span> <span class='option'>p?gbsv</span> <span class='option'>p?dbsv</span> <span class='option'>p?dtsv</span> <span class='option'>p?posv</span> <span class='option'>p?posvx</span> <span class='option'>p?pbsv</span> <span class='option'>p?ptsv</span> <span class='option'>p?gels</span> <span class='option'>p?syev</span> <span class='option'>p?syevd</span> <span class='option'>p?syevr</span> <span class='option'>p?syevx</span> <span class='option'>p?heev</span> <span class='option'>p?heevd</span> <span class='option'>p?heevr</span> <span class='option'>p?heevx</span> <span class='option'>p?gesvd</span> <span class='option'>p?sygvx</span> <span class='option'>p?hegvx</span>
ScaLAPACK Auxiliary Routines x
<span class='option'>b?laapp</span> <span class='option'>b?laexc</span> <span class='option'>b?trexc</span> <span class='option'>p?lacgv</span> <span class='option'>p?max1</span> <span class='option'>pilaver</span> <span class='option'>pmpcol</span> <span class='option'>pmpim2</span> <span class='option'>?combamax1</span> <span class='option'>p?sum1</span> <span class='option'>p?dbtrsv</span> <span class='option'>p?dttrsv</span> <span class='option'>p?gebal</span> <span class='option'>p?gebd2</span> <span class='option'>p?gehd2</span> <span class='option'>p?gelq2</span> <span class='option'>p?geql2</span> <span class='option'>p?geqr2</span> <span class='option'>p?gerq2</span> <span class='option'>p?getf2</span> <span class='option'>p?labrd</span> <span class='option'>p?lacon</span> <span class='option'>p?laconsb</span> <span class='option'>p?lacp2</span> <span class='option'>p?lacp3</span> <span class='option'>p?lacpy</span> <span class='option'>p?laevswp</span> <span class='option'>p?lahrd</span> <span class='option'>p?laiect</span> <span class='option'>p?lamve</span> <span class='option'>p?lange</span> <span class='option'>p?lanhs</span> <span class='option'>p?lansy</span>, <span class='option'>p?lanhe</span> <span class='option'>p?lantr</span> <span class='option'>p?lapiv</span> <span class='option'>p?lapv2</span> <span class='option'>p?laqge</span> <span class='option'>p?laqr0</span> <span class='option'>p?laqr1</span> <span class='option'>p?laqr2</span> <span class='option'>p?laqr3</span> <span class='option'>p?laqr4</span> <span class='option'>p?laqr5</span> <span class='option'>p?laqsy</span> <span class='option'>p?lared1d</span> <span class='option'>p?lared2d</span> <span class='option'>p?larf</span> <span class='option'>p?larfb</span> <span class='option'>p?larfc</span> <span class='option'>p?larfg</span> <span class='option'>p?larft</span> <span class='option'>p?larz</span> <span class='option'>p?larzb</span> <span class='option'>p?larzc</span> <span class='option'>p?larzt</span> <span class='option'>p?lascl</span> <span class='option'>p?lase2</span> <span class='option'>p?laset</span> <span class='option'>p?lasmsub</span> <span class='option'>p?lasrt</span> <span class='option'>p?lassq</span> <span class='option'>p?laswp</span> <span class='option'>p?latra</span> <span class='option'>p?latrd</span> <span class='option'>p?latrs</span> <span class='option'>p?latrz</span> <span class='option'>p?lauu2</span> <span class='option'>p?lauum</span> <span class='option'>p?lawil</span> <span class='option'>p?org2l/p?ung2l</span> <span class='option'>p?org2r/p?ung2r</span> <span class='option'>p?orgl2/p?ungl2</span>