Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 7/13/2023
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Document Table of Contents x
Developer Reference for Intel® oneAPI Math Kernel Library - Fortran
Developer Reference for Intel® oneAPI Math Kernel Library - Fortran 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
?asum ?axpy ?copy ?copy_batch ?copy_batch_strided ?dot ?sdot ?dotc ?dotu ?nrm2 ?rot ?rotg ?rotm ?rotmg ?scal ?swap i?amax i?amin ?cabs1
BLAS Level 2 Routines x
?gbmv ?gemv ?ger ?gerc ?geru ?hbmv ?hemv ?her ?her2 ?hpmv ?hpr ?hpr2 ?sbmv ?spmv ?spr ?spr2 ?symv ?syr ?syr2 ?tbmv ?tbsv ?tpmv ?tpsv ?trmv ?trsv
BLAS Level 3 Routines x
?gemm ?hemm ?herk ?her2k ?symm ?syrk ?syr2k ?trmm ?trsm
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 ?axpyi ?doti ?dotci ?dotui ?gthr ?gthrz ?roti ?sctr
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
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 x
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
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
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 x
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_sorv_hint mkl_sparse_set_memory_hint mkl_sparse_optimize
Inspector-Executor Sparse BLAS Execution Routines x
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 mkl_sparse_?_sorv
BLAS-like Extensions x
?axpy_batch ?axpy_batch_strided ?axpby ?gem2vu ?gem2vc ?gemmt ?gemm3m ?gemm_batch ?gemm_batch_strided ?gemm3m_batch ?trsm_batch ?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 ?gemm_pack_get_size, gemm_*_pack_get_size ?gemm_pack gemm_*_pack ?gemm_compute gemm_*_compute ?gemm_free gemm_* ?gemv_batch_strided ?gemv_batch ?dgmm_batch_strided ?dgmm_batch mkl_jit_create_?gemm mkl_jit_get_?gemm_ptr mkl_jit_destroy
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
?getrf ?getrf_batch ?getrf_batch_strided mkl_?getrfnp ?getrfnp_batch_strided mkl_?getrfnpi ?getrf2 ?getri_oop_batch ?getri_oop_batch_strided ?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 x
?getrs ?getrs_batch_strided ?getrsnp_batch_strided ?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 x
?gecon ?gbcon ?gtcon ?pocon ?ppcon ?pbcon ?ptcon ?sycon ?sycon_rook ?sycon_3 ?hecon ?hecon_rook ?hecon_3 ?spcon ?hpcon ?trcon ?tpcon ?tbcon
Refining the Solution and Estimating Its Error: LAPACK Computational Routines x
?gerfs ?gerfsx ?gbrfs ?gbrfsx ?gtrfs ?porfs ?porfsx ?pprfs ?pbrfs ?ptrfs ?syrfs ?syrfsx ?herfs ?herfsx ?sprfs ?hprfs ?trrfs ?tprfs ?tbrfs
Matrix Inversion: LAPACK Computational Routines x
?getri mkl_?getrinp ?potri ?pftri ?pptri ?sytri ?sytri_rook ?hetri ?hetri_rook ?sytri2 ?hetri2 ?sytri2x ?hetri2x ?sytri_3 ?hetri_3 ?sptri ?hptri ?trtri ?tftri ?tptri
Matrix Equilibration: LAPACK Computational Routines x
?geequ ?geequb ?gbequ ?gbequb ?poequ ?poequb ?ppequ ?pbequ ?syequb ?heequb
LAPACK Linear Equation Driver Routines x
?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 ?hesv_rook ?hesvx ?hesvxx ?spsv ?spsvx ?hpsv ?hpsvx
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
?geqrf ?geqr ?geqrfp ?geqrt ?gemqrt ?geqpf ?geqp3 ?orgqr ?ormqr ?gemqr ?ungqr ?unmqr ?gelqf ?gelq ?gelqt ?gemlqt ?orglq ?ormlq ?gemlq ?unglq ?unmlq ?geqlf ?orgql ?ungql ?ormql ?unmql ?gerqf ?orgrq ?ungrq ?ormrq ?unmrq ?tzrzf ?ormrz ?unmrz ?ggqrf ?ggrqf ?tpqrt ?tpmqrt ?tplqt ?tpmlqt
Singular Value Decomposition: LAPACK Computational Routines x
?gebrd ?gbbrd ?orgbr ?ormbr ?ungbr ?unmbr ?bdsqr ?bdsdc
Symmetric Eigenvalue Problems: LAPACK Computational Routines x
?sytrd ?syrdb ?herdb ?orgtr ?ormtr ?hetrd ?ungtr ?unmtr ?orm22/?unm22 ?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 x
?sygst ?hegst ?spgst ?hpgst ?sbgst ?hbgst ?pbstf
Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines x
?gehrd ?orghr ?ormhr ?unghr ?unmhr ?gebal ?gebak ?hseqr ?hsein ?trevc ?trevc3 ?trsna ?trexc ?trsen ?trsyl
Generalized Nonsymmetric Eigenvalue Problems: LAPACK Computational Routines x
?gghrd ?ggbal ?ggbak ?gghd3 ?hgeqz ?tgevc ?tgexc ?tgsen ?tgsyl ?tgsna
Generalized Singular Value Decomposition: LAPACK Computational Routines x
?ggsvp ?ggsvp3 ?ggsvd3 ?tgsja
Cosine-Sine Decomposition: LAPACK Computational Routines x
?bbcsd ?orbdb/?unbdb
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
?gels ?gelsy ?gelss ?gelsd ?getsls
Generalized Linear Least Squares (LLS) Problems: LAPACK Driver Routines x
?gglse ?ggglm
Symmetric Eigenvalue Problems: LAPACK Driver Routines x
?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 x
?gees ?geesx ?geev ?geevx
Singular Value Decomposition: LAPACK Driver Routines x
?gesvd ?gesdd ?gejsv ?gesvj ?ggsvd ?gesvdx ?bdsvdx
Cosine-Sine Decomposition: LAPACK Driver Routines x
?orcsd/?uncsd ?orcsd2by1/?uncsd2by1
Generalized Symmetric Definite Eigenvalue Problems: LAPACK Driver Routines x
?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 x
?gges ?ggesx ?gges3 ?ggev ?ggevx ?ggev3
LAPACK Auxiliary Routines x
?lacgv ?lacrm ?lacrt ?laesy ?rot ?spmv ?spr ?syconv ?symv ?syr i?max1 ?sum1 ?gbtf2 ?gebd2 ?gehd2 ?gelq2 ?gelqt3 ?geql2 ?geqr2 ?geqr2p ?geqrt2 ?geqrt3 ?gerq2 ?gesc2 ?getc2 ?getf2 ?gtts2 ?isnan ?laisnan ?labrd ?lacn2 ?lacon ?lacpy ?ladiv ?lae2 ?laebz ?laed0 ?laed1 ?laed2 ?laed3 ?laed4 ?laed5 ?laed6 ?laed7 ?laed8 ?laed9 ?laeda ?laein ?laev2 ?laexc ?lag2 ?lags2 ?lagtf ?lagtm ?lagts ?lagv2 ?lahqr ?lahrd ?lahr2 ?laic1 ?lakf2 ?laln2 ?lals0 ?lalsa ?lalsd ?lamrg ?lamswlq ?lamtsqr ?laneg ?langb ?lange ?langt ?lanhs ?lansb ?lanhb ?lansp ?lanhp ?lanst/?lanht ?lansy ?lanhe ?lantb ?lantp ?lantr ?lanv2 ?lapll ?lapmr ?lapmt ?lapy2 ?lapy3 ?laqgb ?laqge ?laqhb ?laqp2 ?laqps ?laqr0 ?laqr1 ?laqr2 ?laqr3 ?laqr4 ?laqr5 ?laqsb ?laqsp ?laqsy ?laqtr ?laqz0 ?lar1v ?lar2v ?laran ?larf ?larfb ?larfg ?larfgp ?larft ?larfx ?larfy ?large ?largv ?larnd ?larnv ?laror ?larot ?larra ?larrb ?larrc ?larrd ?larre ?larrf ?larrj ?larrk ?larrr ?larrv ?lartg ?lartgp ?lartgs ?lartv ?laruv ?larz ?larzb ?larzt ?las2 ?lascl ?lasd0 ?lasd1 ?lasd2 ?lasd3 ?lasd4 ?lasd5 ?lasd6 ?lasd7 ?lasd8 ?lasd9 ?lasda ?lasdq ?lasdt ?laset ?lasq1 ?lasq2 ?lasq3 ?lasq4 ?lasq5 ?lasq6 ?lasr ?lasrt ?lassq ?lasv2 ?laswlq ?laswp ?lasy2 ?lasyf ?lasyf_aa ?lasyf_rook ?lahef ?lahef_aa ?lahef_rook ?latbs ?latm1 ?latm2 ?latm3 ?latm5 ?latm6 ?latme ?latmr ?latdf ?latps ?latrd ?latrs ?latrz ?latsqr ?lauu2 ?lauum ?orbdb1/?unbdb1 ?orbdb2/?unbdb2 ?orbdb3/?unbdb3 ?orbdb4/?unbdb4 Syntax Include Files Description Input Parameters Output Parameters See Also ?orbdb5/?unbdb5 ?orbdb6/?unbdb6 ?org2l/?ung2l ?org2r/?ung2r ?orgl2/?ungl2 ?orgr2/?ungr2 ?orm2l/?unm2l ?orm2r/?unm2r ?orml2/?unml2 ?ormr2/?unmr2 ?ormr3/?unmr3 ?pbtf2 ?potf2 ?ptts2 ?rscl ?syswapr ?heswapr ?syswapr1 ?sygs2/?hegs2 ?sytd2/?hetd2 ?sytf2 ?sytf2_rook ?hetf2 ?hetf2_rook ?tgex2 ?tgsy2 ?trti2 clag2z dlag2s slag2d zlag2c ?larfp ila?lc ila?lr ?gsvj0 ?gsvj1 ?sfrk ?hfrk ?tfsm ?lansf ?lanhf ?tfttp ?tfttr ?tplqt2 ?tpqrt2 ?tprfb ?tpttf ?tpttr ?trttf ?trttp ?pstf2 dlat2s zlat2c ?lacp2 ?la_gbamv ?la_gbrcond ?la_gbrcond_c ?la_gbrcond_x ?la_gbrfsx_extended ?la_gbrpvgrw ?la_geamv ?la_gercond ?la_gercond_c ?la_gercond_x ?la_gerfsx_extended ?la_heamv ?la_hercond_c ?la_hercond_x ?la_herfsx_extended ?la_herpvgrw ?la_lin_berr ?la_porcond ?la_porcond_c ?la_porcond_x ?la_porfsx_extended ?la_porpvgrw ?laqhe ?laqhp ?larcm ?la_gerpvgrw ?larscl2 ?lascl2 ?la_syamv ?la_syrcond ?la_syrcond_c ?la_syrcond_x ?la_syrfsx_extended ?la_syrpvgrw ?la_wwaddw mkl_?tppack mkl_?tpunpack Additional LAPACK Routines
LAPACK Utility Functions and Routines x
ilaver ilaenv iparmq ieeeck ?labad ?lamch ?lamc1 ?lamc2 ?lamc3 ?lamc4 ?lamc5 chla_transtype iladiag ilaprec ilatrans ilauplo xerbla_array
LAPACK Test Functions and Routines x
?latms
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
p?getrf p?gbtrf p?dbtrf p?dttrf p?potrf p?pbtrf p?pttrf
Solving Systems of Linear Equations: ScaLAPACK Computational Routines x
p?getrs p?gbtrs p?dbtrs p?dttrs p?potrs p?pbtrs p?pttrs p?trtrs
Estimating the Condition Number: ScaLAPACK Computational Routines x
p?gecon p?pocon p?trcon
Refining the Solution and Estimating Its Error: ScaLAPACK Computational Routines x
p?gerfs p?porfs p?trrfs
Matrix Inversion: ScaLAPACK Computational Routines x
p?getri p?potri p?trtri
Matrix Equilibration: ScaLAPACK Computational Routines x
p?geequ p?poequ
Orthogonal Factorizations: ScaLAPACK Computational Routines x
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 x
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 x
p?gehrd p?ormhr p?unmhr p?lahqr p?hseqr p?trevc
Singular Value Decomposition: ScaLAPACK Driver Routines x
p?gebrd p?ormbr p?unmbr
Generalized Symmetric-Definite Eigenvalue Problems: ScaLAPACK Computational Routines x
p?sygst p?hegst
ScaLAPACK Driver Routines x
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 x
b?laapp b?laexc b?trexc 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?laqr4 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 x
p?labad p?lachkieee p?lamch p?lasnbt descinit numroc
ScaLAPACK Redistribution/Copy Routines x
p?gemr2d p?trmr2d
Sparse Solver Routines x
oneMKL PARDISO - Parallel Direct Sparse Solver Interface Parallel Direct Sparse Solver for Clusters Interface Direct Sparse Solver (DSS) Interface Routines Iterative Sparse Solvers based on Reverse Communication Interface (RCI ISS) Preconditioners based on Incomplete LU Factorization Technique Sparse Matrix Checker Routines
oneMKL PARDISO - Parallel Direct Sparse Solver Interface x
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 x
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 x
DSS Interface Description DSS Implementation Details DSS Routines
DSS Routines x
dss_create dss_define_structure dss_reorder dss_factor_real, dss_factor_complex dss_solve_real, dss_solve_complex dss_delete dss_statistics mkl_cvt_to_null_terminated_str
Iterative Sparse Solvers based on Reverse Communication Interface (RCI ISS) x
CG Interface Description FGMRES Interface Description RCI ISS Routines RCI ISS Implementation Details
RCI ISS Routines x
dcg_init dcg_check dcg dcg_get dcgmrhs_init dcgmrhs_check dcgmrhs dcgmrhs_get dfgmres_init dfgmres_check dfgmres dfgmres_get
Preconditioners based on Incomplete LU Factorization Technique x
ILU0 and ILUT Preconditioners Interface Description dcsrilu0 dcsrilut
Sparse Matrix Checker Routines x
sparse_matrix_checker sparse_matrix_checker_init
Extended Eigensolver Routines x
The FEAST Algorithm Extended Eigensolver Functionality Extended Eigensolver Interfaces for Eigenvalues within Interval Extended Eigensolver Interfaces for Extremal Eigenvalues/Singular Values
Extended Eigensolver Functionality x
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Developer Reference for Intel® oneAPI Math Kernel Library - Fortran

?orbdb4/?unbdb4

Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns.

Syntax

call sorbdb4( m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, phantom, work, lwork, info )

call dorbdb4( m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, phantom, work, lwork, info )

call cunbdb4( m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, phantom, work, lwork, info )

call zunbdb4( m, p, q, x11, ldx11, x21, ldx21, theta, phi, taup1, taup2, tauq1, phantom, work, lwork, info )

Include Files

  • mkl.fi, lapack.f90

Description

The routines ?orbdb4/?unbdb4 simultaneously bidiagonalize the blocks of a tall and skinny matrix X with orthonormal columns:

The size of x11 is p by q, and x12 is (m - p) by q. m-q must not be larger than q, p, or m-p.

Tall and Skinny Matrix Routines

q≤ min(p, m - p, m - q)

?orbdb1/?unbdb1

p≤ min(q, m - p, m - q)

?orbdb2/?unbdb2

m - p≤ min(p, q, m - q)

?orbdb3/?unbdb3

m - q≤ min(p, q, m - p)

?orbdb4/?unbdb4

The orthogonal/unitary matrices p1, p2, and q1 are p-by-p, (m-p)-by-(m-p), (m-q)-by-(m-q), respectively.

p1, p2, and q1 are represented as products of elementary reflectors. See the description of ?orcsd2by1/?uncsd2by1 for details on generating p1, p2, and q1 using ?orgqr and ?orglq.

The upper-bidiagonal matrices b11 and b12 of size (m-q) by (m-q) are represented implicitly by angles theta(1), ..., theta(q) and phi(1), ..., phi(q-1). Every entry in each bidiagonal band is a product of a sine or cosine of theta with a sine or cosine of phi. See [Sutton09] or the description of ?orcsd/?uncsd for details.

Input Parameters

m

INTEGER. The number of rows in x11 plus the number of rows in x21.

p

INTEGER. The number of rows in x11. 0 ≤p≤m.

q

INTEGER. The number of columns in x11 and x21. 0 ≤q≤m and 0 ≤m-q≤ min(p,m-p,q).

x11

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (ldx11,q).

On entry, the top block of the orthogonal/unitary matrix to be reduced.

ldx11

INTEGER. The leading dimension of the array X11. ldx11≥p.

x21

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (ldx21,q).

On entry, the bottom block of the orthogonal/unitary matrix to be reduced.

ldx21

INTEGER. The leading dimension of the array X21. ldx21≥m-p.

work

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Workspace array, DIMENSION (lwork).

lwork

INTEGER. The size of the work array. lwork≥m-q

If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

Output Parameters

x11

On exit: the columns of tril(x11) specify reflectors for p1 and the rows of triu(x11,1) specify reflectors for q1.

x21

On exit, the columns of tril(x21) specify the reflectors for p2

theta

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (q). The entries of bidiagonal blocks b11 and b21 can be computed from the angles theta and phi. See the Description section for details.

phi

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (q-1). The entries of bidiagonal blocks b11 and b21 can be computed from the angles theta and phi. See the Description section for details.

taup1

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (p).

Scalar factors of the elementary reflectors that define p1.
taup2

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (m-p).

Scalar factors of the elementary reflectors that define p2.
tauq1

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (q).

Scalar factors of the elementary reflectors that define q1.
phantom

REAL for sorbdb4

DOUBLE PRECISION for dorbdb4

COMPLEX for cunbdb4

DOUBLE COMPLEX for zunbdb4

Array, DIMENSION (m).

The routine computes an m-by-1 column vector y that is orthogonal to the columns of [ x11; x21 ]. phantom(1:p) and phantom(p+1:m) contain Householder vectors for y(1:p) and y(p+1:m), respectively.

info

INTEGER.

= 0: successful exit

< 0: if info = -i, the i-th argument has an illegal value.

Parent topic: LAPACK Auxiliary Routines

See Also

?orcsd2by1/?uncsd2by1 Computes the CS decomposition of a block-partitioned orthogonal/unitary matrix.
?orbdb1/?unbdb1 Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns.
?orbdb2/?unbdb2 Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns.
?orbdb3/?unbdb3 Simultaneously bidiagonalizes the blocks of a tall and skinny matrix with orthonormal columns.
?orbdb5/?unbdb5 Orthogonalizes a column vector with respect to the orthonormal basis matrix.
?orbdb6/?unbdb6 Orthogonalizes a column vector with respect to the orthonormal basis matrix.
Level Two Title