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首页MKL 2018开发者指南:Fortran中的高性能数学库函数详解
MKL 2018开发者指南:Fortran中的高性能数学库函数详解
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更新于2024-07-17
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Intel Math Kernel Library (MKL) 2018 Developer Reference是一份详细的文档,专注于介绍FORTRAN编程语言中Intel提供的高性能数学函数库。MKL是Intel针对科学计算、工程和数据分析等领域开发的一套数学运算加速工具,它集合了BLAS (Basic Linear Algebra Subprograms)、稀疏BLAS以及更高级别的矩阵操作。
在FORTRAN中,MKL包含了广泛的功能,如基本线性代数运算,如矩阵加法(gemm)、矩阵乘法(gemv)、向量内积(dot)和范数计算(nrm2),这些都是BLAS Level 1至Level 3的基础操作。例如,gemv支持向量与矩阵的乘法,gemm则处理两个矩阵的乘法,这些操作对于解决线性方程组、特征值问题等数学问题至关重要。
除了标准的BLAS,MKL还提供了对稀疏矩阵的支持,如hbmv(对稀疏矩阵-向量乘法)和spr/spr2(对稀疏矩阵-稀疏向量乘法),这对于处理大规模的数据集时性能优化非常关键。同时,MKL还提供了用于复数运算的特定函数,如dotc(复数向量内积)和herk/her2k(复数矩阵的Hermitian和非Hermitian卷积运算)。
值得注意的是,MKL文档强调了性能增强和并行计算能力,这意味着开发者可以利用多核处理器的优势,通过MKL的并行接口实现高效的并行化算法。此外,文档中还提供了详细的命名约定和函数接口规范,以帮助用户正确理解和使用这些库函数。
新版本的MKL2018可能引入了新的功能、改进的算法或优化的性能特性,开发者应查阅"What's New"章节获取具体更新内容。同时,文档中包含的帮助和支持部分为遇到问题的用户提供了指导途径,无论是寻求解答还是技术文档,都是开发过程中不可或缺的资源。
Intel MKL 2018 Developer Reference是FORTRAN开发者进行高性能数学计算和并行处理的强大工具,其丰富的功能和详细的文档支持使得它成为科学研究和工程应用中的首选库。要深入掌握和利用MKL,理解其内部运作机制、函数特性和使用方法至关重要。
p?larzt........................................................................................2333
p?lascl ........................................................................................2336
p?lase2.......................................................................................2337
p?laset .......................................................................................2339
p?lasmsub...................................................................................2340
p?lasrt........................................................................................2342
p?lassq .......................................................................................2344
p?laswp ......................................................................................2345
p?latra........................................................................................2347
p?latrd........................................................................................2348
p?latrs........................................................................................2352
p?latrz........................................................................................2354
p?lauu2 ......................................................................................2356
p?lauum .....................................................................................2357
p?lawil........................................................................................2359
p?org2l/p?ung2l...........................................................................2360
p?org2r/p?ung2r ..........................................................................2362
p?orgl2/p?ungl2...........................................................................2364
p?orgr2/p?ungr2 ..........................................................................2367
p?orm2l/p?unm2l.........................................................................2369
p?orm2r/p?unm2r ........................................................................2372
p?orml2/p?unml2.........................................................................2376
p?ormr2/p?unmr2 ........................................................................2379
p?pbtrsv .....................................................................................2383
p?pttrsv......................................................................................2387
p?potf2.......................................................................................2390
p?rot ..........................................................................................2392
p?rscl .........................................................................................2394
p?sygs2/p?hegs2 .........................................................................2395
p?sytd2/p?hetd2 ..........................................................................2397
p?trord .......................................................................................2400
p?trsen .......................................................................................2404
p?trti2 ........................................................................................2409
?lahqr2 .......................................................................................2410
?lamsh .......................................................................................2412
?lapst .........................................................................................2414
?laqr6.........................................................................................2414
?lar1va .......................................................................................2417
?laref .........................................................................................2420
?larrb2 .......................................................................................2423
?larrd2 .......................................................................................2425
?larre2........................................................................................2429
?larre2a ......................................................................................2433
?larrf2 ........................................................................................2438
?larrv2........................................................................................2440
?lasorte ......................................................................................2445
?lasrt2........................................................................................2446
?stegr2 .......................................................................................2448
?stegr2a .....................................................................................2451
?stegr2b .....................................................................................2455
?stein2 .......................................................................................2459
?dbtf2 ........................................................................................2461
?dbtrf .........................................................................................2462
?dttrf..........................................................................................2464
?dttrsv........................................................................................2465
Intel
®
Math Kernel Library Developer Reference
16
?pttrsv........................................................................................2466
?steqr2 .......................................................................................2468
?trmvt ........................................................................................2469
pilaenv .......................................................................................2472
pilaenvx......................................................................................2473
pjlaenv .......................................................................................2475
Additional ScaLAPACK Routines ......................................................2476
ScaLAPACK Utility Functions and Routines................................................2477
p?labad ......................................................................................2477
p?lachkieee .................................................................................2478
p?lamch......................................................................................2479
p?lasnbt......................................................................................2480
descinit.......................................................................................2481
numroc.......................................................................................2482
ScaLAPACK Redistribution/Copy Routines.................................................2483
p?gemr2d ...................................................................................2483
p?trmr2d ....................................................................................2485
Chapter 5: Sparse Solver Routines
Intel MKL PARDISO - Parallel Direct Sparse Solver Interface.......................2488
pardiso .......................................................................................2494
pardisoinit...................................................................................2501
pardiso_64..................................................................................2503
pardiso_getenv_f, pardiso_setenv_f, pardiso_getenv, pardiso_setenv ..2504
mkl_pardiso_pivot........................................................................2506
pardiso_getdiag ...........................................................................2506
pardiso_handle_store ...................................................................2508
pardiso_handle_restore.................................................................2509
pardiso_handle_delete ..................................................................2510
pardiso_handle_store_64 ..............................................................2510
pardiso_handle_restore_64 ...........................................................2511
pardiso_handle_delete_64.............................................................2512
Intel MKL PARDISO Parameters in Tabular Form ...............................2513
pardiso iparm Parameter ...............................................................2518
PARDISO_DATA_TYPE ...................................................................2530
Parallel Direct Sparse Solver for Clusters Interface....................................2530
cluster_sparse_solver ...................................................................2532
cluster_sparse_solver_64..............................................................2537
cluster_sparse_solver iparm Parameter ...........................................2538
Direct Sparse Solver (DSS) Interface Routines .........................................2547
DSS Interface Description .............................................................2548
DSS Implementation Details ..........................................................2549
DSS Routines ..............................................................................2550
dss_create ..........................................................................2550
dss_define_structure ............................................................2551
dss_reorder ........................................................................2553
dss_factor_real, dss_factor_complex ......................................2554
dss_solve_real, dss_solve_complex........................................2556
dss_delete ..........................................................................2559
dss_statistics ......................................................................2559
mkl_cvt_to_null_terminated_str ............................................2562
Iterative Sparse Solvers based on Reverse Communication Interface (RCI
ISS) ...............................................................................................2563
CG Interface Description ...............................................................2564
FGMRES Interface Description........................................................2569
Contents
17
RCI ISS Routines .........................................................................2577
dcg_init ..............................................................................2577
dcg_check ..........................................................................2578
dcg ....................................................................................2579
dcg_get ..............................................................................2580
dcgmrhs_init .......................................................................2581
dcgmrhs_check ...................................................................2582
dcgmrhs .............................................................................2583
dcgmrhs_get.......................................................................2585
dfgmres_init........................................................................2586
dfgmres_check ....................................................................2586
dfgmres..............................................................................2587
dfgmres_get .......................................................................2589
RCI ISS Implementation Details .....................................................2590
Preconditioners based on Incomplete LU Factorization Technique ................2591
ILU0 and ILUT Preconditioners Interface Description .........................2593
dcsrilu0 ......................................................................................2593
dcsrilut .......................................................................................2596
Sparse Matrix Checker Routines .............................................................2600
sparse_matrix_checker .................................................................2600
sparse_matrix_checker_init ...........................................................2601
Chapter 6: Extended Eigensolver Routines
The FEAST Algorithm ............................................................................2604
Extended Eigensolver Functionality .........................................................2605
Parallelism in Extended Eigensolver Routines ...................................2606
Achieving Performance With Extended Eigensolver Routines...............2606
Extended Eigensolver Interfaces.............................................................2607
Extended Eigensolver Naming Conventions ......................................2607
feastinit ......................................................................................2608
Extended Eigensolver Input Parameters ..........................................2609
Extended Eigensolver Output Details...............................................2610
Extended Eigensolver RCI Routines.................................................2611
Extended Eigensolver RCI Interface Description .......................2611
?feast_srci/?feast_hrci..........................................................2613
Extended Eigensolver Predefined Interfaces .....................................2617
Matrix Storage.....................................................................2617
?feast_syev/?feast_heev.......................................................2617
?feast_sygv/?feast_hegv.......................................................2619
?feast_sbev/?feast_hbev.......................................................2622
?feast_sbgv/?feast_hbgv ......................................................2624
?feast_scsrev/?feast_hcsrev..................................................2627
?feast_scsrgv/?feast_hcsrgv..................................................2629
Chapter 7: Vector Mathematical Functions
VM Data Types, Accuracy Modes, and Performance Tips .............................2633
VM Naming Conventions........................................................................2634
VM Function Interfaces .................................................................2635
VM Mathematical Function Interfaces......................................2635
VM Pack Function Interfaces..................................................2635
VM Unpack Function Interfaces ..............................................2635
VM Service Function Interfaces ..............................................2635
VM Input Function Interfaces.................................................2635
VM Output Function Interfaces...............................................2636
Vector Indexing Methods .......................................................................2636
Intel
®
Math Kernel Library Developer Reference
18
VM Error Diagnostics.............................................................................2637
VM Mathematical Functions....................................................................2637
Special Value Notations.................................................................2640
Arithmetic Functions.....................................................................2640
v?Add ................................................................................2640
v?Sub ................................................................................2642
v?Sqr .................................................................................2644
v?Mul .................................................................................2645
v?MulByConj .......................................................................2647
v?Conj................................................................................2648
v?Abs.................................................................................2649
v?Arg .................................................................................2651
v?LinearFrac........................................................................2652
v?Fmod .............................................................................2654
v?Remainder .......................................................................2655
Power and Root Functions .............................................................2657
v?Inv .................................................................................2657
v?Div .................................................................................2658
v?Sqrt ................................................................................2660
v?InvSqrt ...........................................................................2662
v?Cbrt ................................................................................2663
v?InvCbrt ...........................................................................2664
v?Pow2o3 ...........................................................................2665
v?Pow3o2 ...........................................................................2666
v?Pow ................................................................................2667
v?Powx...............................................................................2671
v?Powr ...............................................................................2673
v?Hypot..............................................................................2674
Exponential and Logarithmic Functions............................................2676
v?Exp.................................................................................2676
v?Exp2 ...............................................................................2678
v?Exp10 .............................................................................2679
v?Expm1 ............................................................................2680
v?Ln...................................................................................2682
v?Log2 ...............................................................................2684
v?Log10 .............................................................................2685
v?Log1p .............................................................................2687
v?Logb ...............................................................................2688
Trigonometric Functions ................................................................2689
v?Cos.................................................................................2689
v?Sin .................................................................................2691
v?SinCos ............................................................................2693
v?CIS.................................................................................2695
v?Tan .................................................................................2696
v?Acos ...............................................................................2698
v?Asin ................................................................................2700
v?Atan ...............................................................................2702
v?Atan2..............................................................................2704
v?Cospi ..............................................................................2705
v?Sinpi ...............................................................................2707
v?Tanpi...............................................................................2708
v?Acospi .............................................................................2709
v?Asinpi..............................................................................2711
v?Atanpi .............................................................................2712
v?Atan2pi ...........................................................................2713
Contents
19
v?Cosd ...............................................................................2715
v?Sind................................................................................2716
v?Tand ...............................................................................2718
Hyperbolic Functions ....................................................................2719
v?Cosh ...............................................................................2719
v?Sinh................................................................................2721
v?Tanh ...............................................................................2724
v?Acosh..............................................................................2726
v?Asinh ..............................................................................2728
v?Atanh..............................................................................2730
Special Functions .........................................................................2732
v?Erf ..................................................................................2732
v?Erfc ................................................................................2734
v?CdfNorm..........................................................................2736
v?ErfInv .............................................................................2738
v?ErfcInv ............................................................................2741
v?CdfNormInv .....................................................................2742
v?LGamma..........................................................................2744
v?TGamma .........................................................................2745
v?ExpInt1 ...........................................................................2746
Rounding Functions ......................................................................2747
v?Floor ...............................................................................2747
v?Ceil.................................................................................2748
v?Trunc ..............................................................................2750
v?Round .............................................................................2751
v?NearbyInt ........................................................................2752
v?Rint ................................................................................2753
v?Modf ...............................................................................2755
v?Frac ................................................................................2756
VM Pack/Unpack Functions ....................................................................2757
v?Pack........................................................................................2757
v?Unpack....................................................................................2759
VM Service Functions ............................................................................2761
vmlSetMode ................................................................................2761
vmlgetmode ................................................................................2763
vmlSetErrStatus...........................................................................2764
vmlgeterrstatus ...........................................................................2765
vmlclearerrstatus .........................................................................2765
vmlSetErrorCallBack .....................................................................2766
vmlGetErrorCallBack.....................................................................2768
vmlClearErrorCallBack ..................................................................2768
Miscellaneous VM Functions ...................................................................2768
v?CopySign .................................................................................2768
v?NextAfter .................................................................................2769
v?Fdim .......................................................................................2770
v?Fmax.......................................................................................2771
v?Fmin .......................................................................................2773
v?MaxMag...................................................................................2774
v?MinMag....................................................................................2775
Chapter 8: Statistical Functions
Random Number Generators ..................................................................2777
Random Number Generators Conventions........................................2778
Random Number Generators Mathematical Notation .................2779
Random Number Generators Naming Conventions ....................2780
Intel
®
Math Kernel Library Developer Reference
20
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