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Developer Reference for Intel® oneAPI Math Kernel Library
Getting Help and Support
What's New
Notational Conventions
Overview
Performance Enhancements
Parallelism
OpenMP* Offload
OpenMP* Offload for oneAPI Math Kernel Library
BLAS and Sparse BLAS Routines
BLAS Routines
Routine Naming Conventions
Fortran 95 Interface Conventions
Matrix Storage Schemes
BLAS Level 1 Routines and Functions
?asum
?axpy
?copy
?dot
?sdot
?dotc
?dotu
?nrm2
?rot
?rotg
?rotm
?rotmg
?scal
?swap
i?amax
i?amin
?cabs1
BLAS Level 2 Routines
?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
?gemm
?hemm
?herk
?her2k
?symm
?syrk
?syr2k
?trmm
?trsm
Sparse BLAS Level 1 Routines
Vector Arguments
Naming Conventions
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
Naming Conventions in Sparse BLAS Level 2 and Level 3
Sparse Matrix Storage Formats
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
Inspector-executor Sparse BLAS routines
Naming conventions
Sparse Matrix Storage Formats
Supported Operations
Two-stage Algorithm
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
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
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?axpy_batch
cblas_?axpy_batch_strided?axpy_batch_strided
?axpby
?gem2vu
?gem2vc
?gemmt
?gemm3m
?gemm_batch
?gemm_batch_stridedcblas_?gemm_batch_strided
?gemm3m_batch
?trsm_batch
?trsm_batch_stridedcblas_?trsm_batch_strided
mkl_?imatcopy
mkl_?omatcopy
mkl_?omatcopy2
mkl_?omatadd
?gemm_pack_get_size, gemm_*_pack_get_size
?gemm_pack
gemm_*_pack
?gemm_compute
gemm_*_compute
gemm_*
?gemv_batch_stridedcblas_?gemv_batch_strided
?gemv_batchcblas_?gemv_batch
?dgmm_batch_stridedcblas_?dgmm_batch_strided
?dgmm_batchcblas_?dgmm_batch
mkl_jit_create_?gemm
mkl_jit_get_?gemm_ptr
mkl_jit_destroy
LAPACK Routines
Routine Naming Conventions
Fortran-95 Interface Conventions
Intel® oneAPI Math Kernel Library Fortran-95 Interfaces for LAPACK Routines vs. Netlib* Implementation
Matrix Storage Schemes
Mathematical Notation
Error Analysis
Linear Equations LAPACK Routines
Computational Routines
Routines for Matrix Factorization
?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
Routines for Solving Systems of Linear Equations
?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
Routines for Estimating the Condition Number
?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
?gerfs
?gerfsx
?gbrfs
?gbrfsx
?gtrfs
?porfs
?porfsx
?pprfs
?pbrfs
?ptrfs
?syrfs
?syrfsx
?herfs
?herfsx
?sprfs
?hprfs
?trrfs
?tprfs
?tbrfs
Routines for Matrix Inversion
?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
Routines for Matrix Equilibration
?geequ
?geequb
?gbequ
?gbequb
?poequ
?poequb
?ppequ
?pbequ
?syequb
?heequb
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
?hesv_rook
?hesvx
?hesvxx
?spsv
?spsvx
?hpsv
?hpsvx
Least Squares and Eigenvalue Problems LAPACK Routines
Computational Routines
Orthogonal Factorizations
?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
?gebrd
?gbbrd
?orgbr
?ormbr
?ungbr
?unmbr
?bdsqr
?bdsdc
Symmetric Eigenvalue Problems
?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
?sygst
?hegst
?spgst
?hpgst
?sbgst
?hbgst
?pbstf
Nonsymmetric Eigenvalue Problems
?gehrd
?orghr
?ormhr
?unghr
?unmhr
?gebal
?gebak
?hseqr
?hsein
?trevc
?trevc3
?trsna
?trexc
?trsen
?trsyl
Generalized Nonsymmetric Eigenvalue Problems
?gghrd
?ggbal
?ggbak
?gghd3
?hgeqz
?tgevc
?tgexc
?tgsen
?tgsyl
?tgsna
Generalized Singular Value Decomposition
?ggsvp
?ggsvp3
?ggsvd3
?tgsja
Cosine-Sine Decomposition
?bbcsd
?orbdb/?unbdb
Driver Routines
Linear Least Squares (LLS) Problems
?gels
?gelsy
?gelss
?gelsd
?getsls
Generalized LLS Problems
?gglse
?ggglm
Symmetric Eigenproblems
?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 Eigenproblems
?gees
?geesx
?geev
?geevx
Singular Value Decomposition
?gesvd
?gesdd
?gejsv
?gesvj
?ggsvd
?gesvdx
?bdsvdx
Cosine-Sine Decomposition
?orcsd/?uncsd
?orcsd2by1/?uncsd2by1
Generalized Symmetric Definite Eigenproblems
?sygv
?hegv
?sygvd
?hegvd
?sygvx
?hegvx
?spgv
?hpgv
?spgvd
?hpgvd
?spgvx
?hpgvx
?sbgv
?hbgv
?sbgvd
?hbgvd
?sbgvx
?hbgvx
Generalized Nonsymmetric Eigenproblems
?gges
?ggesx
?gges3
?ggev
?ggevx
?ggev3
Auxiliary Routines
?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
?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
?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_rpvgrw
?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
Utility Functions and Routines
ilaver
ilaenv
iparmq
ieeeck
?labad
?lamch
?lamc1
?lamc2
?lamc3
?lamc4
?lamc5
chla_transtype
iladiag
ilaprec
ilatrans
ilauplo
xerbla_array
Test Routines
latms
Additional LAPACK Routines (added for NETLIB compatibility)
ScaLAPACK Routines
Overview
ScaLAPACK Array Descriptors
Routine Naming Conventions
Computational Routines
Linear Equations
Routines for Matrix Factorization
p?getrf
p?gbtrf
p?dbtrf
p?dttrf
p?potrf
p?pbtrf
p?pttrf
Routines for Solving Systems of Linear Equations
p?getrs
p?gbtrs
p?dbtrs
p?dttrs
p?potrs
p?pbtrs
p?pttrs
p?trtrs
Routines for Estimating the Condition Number
p?gecon
p?pocon
p?trcon
Refining the Solution and Estimating Its Error
p?gerfs
p?porfs
p?trrfs
Routines for Matrix Inversion
p?getri
p?potri
p?trtri
Routines for Matrix Equilibration
p?geequ
p?poequ
Orthogonal Factorizations
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 Eigenproblems
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
p?gehrd
p?ormhr
p?unmhr
p?lahqr
p?hseqr
p?trevc
Singular Value Decomposition
p?gebrd
p?ormbr
p?unmbr
Generalized Symmetric-Definite Eigen Problems
p?sygst
p?hegst
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
Auxiliary Routines
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
Utility Functions and Routines
p?labad
p?lachkieee
p?lamch
p?lasnbt
descint
descint
Matrix Redistribution/Copy Routines
p?gemr2d
p?trmr2d
Sparse Solver Routines
PARDISO* - Parallel Direct Sparse Solver Interface
pardiso
pardisoinit
pardiso_64
mkl_pardiso_pivot
pardiso_getdiag
pardiso_export
pardiso_handle_dump
pardiso_handle_load
pardiso_handle_wipe
pardiso_handle_dump_64
pardiso_handle_load_64
pardiso_handle_wipe_64
PARDISO Parameters in Tabular Form
pardiso iparm Parameter
PARDISO_DATA_TYPE
Intel® oneAPI Math Kernel Library Parallel Direct Sparse Solver for Clusters
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
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
mkl_cvt_to_null_terminated_str
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
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_init
Extended Eigensolver Routines
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_?_svd
mkl_sparse_ee_init
Extended Eigensolver Input Parameters for Extremal Eigenvalue Problem
Vector Mathematical Functions
Data Types and Accuracy Modes
Function Naming Conventions
Function Interfaces
VML Mathematical Functions
Pack Functions
Unpack Functions
Service Functions
Input Parameters
Output Parameters
Vector Indexing Methods
Error Diagnostics
VML 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
VML Pack/Unpack Functions
v?pack
v?unpack
VML Service Functions
vmlsetmode
vmlgetmode
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
Conventions
Mathematical Notation
Naming Conventions
Basic Generators
BRNG Parameter Definition
Random Streams
Data Types
Error Reporting
VSL 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
VRngGaussian
VRngGaussianMV
VRngExponential
VRngLaplace
VRngWeibull
VRngCauchy
VRngRayleigh
VRngLognormal
VRngGumbel
VRngGamma
VRngBeta
VRngChiSquare
Discrete Distributions
vRngUniform
vRngUniformBits
vRngUniformBits32
vRngUniformBits64
vRngBernoulli
vRngGeometric
vRngBinomial
vRngHypergeometric
vRngPoisson
vRngPoissonV
vRngNegBinomial
vRngMultinomial
Advanced Service Routines
Data types
vslGetBrngProperties
Convolution and Correlation
Naming Conventions
Data Types
Parameters
Task Status
Task Constructors
vslConvNewTask/vslCorrNewTask
vslConvNewTask1D/vslCorrNewTask1D
vslConvNewTaskX/vslCorrNewTaskX
vslConvNewTaskX1D/vslCorrNewTaskX1D
Task Editors
vslConvSetMode/vslCorrSetMode
vslConvSetInternalPrecision/vslCorrSetInternalPrecision
vslConvSetStart/vslCorrSetStart
vslConvSetDecimation/vslCorrSetDecimation
Task Execution Routines
vslConvExec/vslCorrExec
vslConvExec1D/vslCorrExec1D
vslConvExecX/vslCorrExecX
vslConvExecX1D/vslCorrExecX1D
Task Destructors
vslConvDeleteTask/vslCorrDeleteTask
Task Copy
vslConvCopyTask/vslCorrCopyTask
Usage Examples
Mathematical Notation and Definitions
Data Allocation
Summary Statistics
Naming Conventions
Data Types
Parameters
Task Status and Error Reporting
Task Constructors
vslSSNewTask
Task Editors
vslSSEditTask
vslSSEditMoments
vslSSEditSums
vslSSEditCovCor
vslSSEditCP
vslSSEditPartialCovCor
vslSSEditQuantiles
vslSSEditStreamQuantiles
vslSSEditPooledCovariance
vslSSEditRobustCovariance
vslSSEditOutliersDetection
vslSSEditMissingValues
vslSSEditCorParameterization
Task Computation Routine
vslSSCompute
Task Destructors
vslSSDeleteTask
Usage Examples
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
Descriptor Manipulation Functions
DftiCreateDescriptor
DftiCommitDescriptor
DftiFreeDescriptor
DftiCopyDescriptor
Descriptor Configuration Functions
DftiSetValue
DftiGetValue
FFT Computation Functions
DftiComputeForward
DftiComputeBackward
Configuring and Computing an FFT in Fortran
Status Checking Functions
DftiErrorClass
DftiErrorMessage
Cluster FFT Functions
Computing Cluster FFT
Distributing Data among Processes
Cluster FFT Interface
Descriptor Manipulation Functions
DftiCreateDescriptorDM
DftiCommitDescriptorDM
DftiFreeDescriptorDM
FFT Computation Functions
DftiComputeForwardDM
DftiComputeBackwardDM
Descriptor Configuration Functions
DftiSetValueDM
DftiGetValueDM
Error Codes
PBLAS Routines
Overview
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
Transforms Implemented
Sequence of Invoking TT Routines
Interface Description
TT Routines
?_init_trig_transform
?_commit_trig_transform
?_forward_trig_transform
?_backward_trig_transform
free_trig_transform
Common Parameters
Implementation Details
Fast Poisson Solver Routines
Poisson Solver Implementation
Sequence of Invoking Poisson Solver Routines
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
ipar
dpar and spar
Caveat on Parameter Modifications
Parameters That Define Boundary Conditions
Implementation Details
Calling PDE Support Routines from Fortran
Nonlinear Optimization Problem Solvers
Organization and Implementation
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
Using a Fortran Interface Module for Support Functions
Version Information
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
Handling Fatal Errors
mkl_set_exit_handler
Character Equality Testing
lsame
lsamen
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
?gamx2d
?gamn2d
?gsum2d
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_barrier
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
df?newtask1d
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
dfdeletetask
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 Format
Sparse BLAS CSC Format
Sparse BLAS Coordinate Format
Sparse BLAS Diagonal Format
Sparse BLAS Skyline Format
Sparse BLAS BSR Format
Appendix B: Routine and Function Arguments
Vector Arguments in BLAS
Vector Arguments in VML
Matrix Arguments
Appendix C: Specific Features of Fortran 95 Interfaces for LAPACK Routines
Appendix D: 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
Calling Wrappers from Fortran
Limitations of the FFTW2 Interface to Intel® oneAPI Math Kernel Library
Installation
Creating the Wrapper Library
Application Assembling
Running Examples
FFTW3 Interface to Intel® oneAPI Math Kernel Library
Using FFTW3 Wrappers
Calling Wrappers from Fortran
Building Your Own Wrapper Library
Building an Application
Running Examples
MPI FFTW Wrappers
Building Your Own Wrapper Library
Building an Application
Running Examples
Appendix E: Code Examples
BLAS Code Examples
Fourier Transform Functions Code Examples
FFT Code Examples
Examples of Using Multi-Threading for FFT Computation
Examples for Cluster FFT Functions
Auxiliary Data Transformations
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
Legal InformationNotices and Disclaimers