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首页Intel MKL开发手册:BLAS与稀疏BLAS函数详解
Intel MKL开发手册:BLAS与稀疏BLAS函数详解
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更新于2023-03-16
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Intel Math Kernel Library (MKL) 是一款由英特尔公司开发的高度优化的数学库,主要用于加速高性能科学计算、工程分析和其他数值密集型应用中的基本线性代数运算。该开发手册提供了对MKL的重要功能和接口的详细介绍,特别是针对BLAS (Basic Linear Algebra Subprograms) 和 Sparse BLAS (Basic Linear Algebra Subprograms for Sparse Matrices) 的支持。
手册的核心内容包括性能增强和并行处理的概述,以及针对不同级别的BLAS操作的详细指导。MKL的CBLAS (Compaq Portable Basic Linear Algebra Subprograms) 接口是其标准接口之一,用户可以通过这些函数来利用MKL的优化算法和硬件加速。
在CBLAS Level 1操作部分,手册介绍了诸如`cblas_?asum`(计算数组元素绝对值之和)、`cblas_?axpy`(向量加法)等基础函数,这些都是矩阵乘法和向量操作的基础。`cblas_?copy`用于矩阵元素复制,`cblas_?dot`和相关变体如`cblas_?dotc`和`cblas_?dotu`负责计算内积,而`cblas_?nrm2`则计算向量的欧几里得范数。旋转函数如`cblas_?rot`、`cblas_?rotg`等用于处理向量和矩阵的旋转变换。
在更高级别的BLAS Level 2中,有如`cblas_?gemv`(通用矩阵-向量乘法)、`cblas_?ger`(矩阵-向量外积)等,它们在解决大规模线性方程组和矩阵乘法时非常关键。对于稀疏矩阵的支持,MKL也提供了一些特定的函数,如`cblas_?sbmv`和`cblas_?spmv`,这些函数针对稀疏矩阵的操作进行了优化。
此外,手册还强调了如何利用MKL的并行特性,这对于现代多核处理器环境下的高性能计算至关重要。开发者可以借助MKL提供的并行化策略,充分利用硬件资源,提升程序的性能。
总体来说,Intel MKL参考手册是开发人员在设计高性能计算应用程序时不可或缺的参考资料,无论是对于理解BLAS操作原理,还是掌握如何通过MKL实现高效计算,都有着重要的指导作用。通过学习和熟悉这个手册,开发者能够更好地利用MKL进行科学计算任务,提高代码的执行效率。
v?Cos.................................................................................1900
v?Sin .................................................................................1902
v?SinCos ............................................................................1903
v?CIS.................................................................................1905
v?Tan .................................................................................1906
v?Acos ...............................................................................1908
v?Asin ................................................................................1909
v?Atan ...............................................................................1911
v?Atan2..............................................................................1912
v?Cospi ..............................................................................1914
v?Sinpi ...............................................................................1915
v?Tanpi...............................................................................1916
v?Acospi .............................................................................1918
v?Asinpi..............................................................................1919
v?Atanpi .............................................................................1920
v?Atan2pi ...........................................................................1921
v?Cosd ...............................................................................1923
v?Sind................................................................................1924
v?Tand ...............................................................................1926
Hyperbolic Functions ....................................................................1927
v?Cosh ...............................................................................1927
v?Sinh................................................................................1929
v?Tanh ...............................................................................1931
v?Acosh..............................................................................1933
v?Asinh ..............................................................................1934
v?Atanh..............................................................................1936
Special Functions .........................................................................1938
v?Erf ..................................................................................1938
v?Erfc ................................................................................1940
v?CdfNorm..........................................................................1942
v?ErfInv .............................................................................1943
v?ErfcInv ............................................................................1946
v?CdfNormInv .....................................................................1947
v?LGamma..........................................................................1949
v?TGamma .........................................................................1950
v?ExpInt1 ...........................................................................1951
Rounding Functions ......................................................................1952
v?Floor ...............................................................................1952
v?Ceil.................................................................................1953
v?Trunc ..............................................................................1954
v?Round .............................................................................1955
v?NearbyInt ........................................................................1956
v?Rint ................................................................................1957
v?Modf ...............................................................................1958
v?Frac ................................................................................1959
VM Pack/Unpack Functions ....................................................................1960
v?Pack........................................................................................1961
v?Unpack....................................................................................1962
VM Service Functions ............................................................................1963
vmlSetMode ................................................................................1964
vmlGetMode ................................................................................1966
MKLFreeTls..................................................................................1966
vmlSetErrStatus...........................................................................1967
vmlGetErrStatus ..........................................................................1968
vmlClearErrStatus ........................................................................1968
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Math Kernel Library Developer Reference
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vmlSetErrorCallBack .....................................................................1969
vmlGetErrorCallBack.....................................................................1971
vmlClearErrorCallBack ..................................................................1971
Miscellaneous VM Functions ...................................................................1971
v?CopySign .................................................................................1971
v?NextAfter .................................................................................1972
v?Fdim .......................................................................................1973
v?Fmax.......................................................................................1974
v?Fmin .......................................................................................1975
v?MaxMag...................................................................................1977
v?MinMag....................................................................................1978
Chapter 8: Statistical Functions
Random Number Generators ..................................................................1980
Random Number Generators Conventions........................................1981
Random Number Generators Mathematical Notation .................1981
Random Number Generators Naming Conventions ....................1982
Basic Generators..........................................................................1986
BRNG Parameter Definition....................................................1987
Random Streams .................................................................1988
BRNG Data Types.................................................................1989
Error Reporting ............................................................................1989
VS RNG Usage Model ....................................................................1991
Service Routines ..........................................................................1992
vslNewStream .....................................................................1993
vslNewStreamEx..................................................................1994
vsliNewAbstractStream.........................................................1995
vsldNewAbstractStream ........................................................1997
vslsNewAbstractStream ........................................................1998
vslDeleteStream ..................................................................1999
vslCopyStream ....................................................................2000
vslCopyStreamState.............................................................2001
vslSaveStreamF...................................................................2001
vslLoadStreamF...................................................................2002
vslSaveStreamM ..................................................................2004
vslLoadStreamM ..................................................................2004
vslGetStreamSize ................................................................2006
vslLeapfrogStream ...............................................................2006
vslSkipAheadStream ............................................................2008
vslGetStreamStateBrng ........................................................2010
vslGetNumRegBrngs.............................................................2010
Distribution Generators.................................................................2011
Continuous Distributions .......................................................2014
Discrete Distributions ...........................................................2038
Advanced Service Routines ............................................................2056
Advanced Service Routine Data Types.....................................2056
vslRegisterBrng ...................................................................2057
vslGetBrngProperties............................................................2058
Formats for User-Designed Generators....................................2059
Convolution and Correlation...................................................................2061
Convolution and Correlation Naming Conventions .............................2062
Convolution and Correlation Data Types ..........................................2063
Convolution and Correlation Parameters ..........................................2063
Convolution and Correlation Task Status and Error Reporting .............2065
Convolution and Correlation Task Constructors .................................2066
Contents
17
vslConvNewTask/vslCorrNewTask ...........................................2067
vslConvNewTask1D/vslCorrNewTask1D ...................................2068
vslConvNewTaskX/vslCorrNewTaskX .......................................2070
vslConvNewTaskX1D/vslCorrNewTaskX1D................................2072
Convolution and Correlation Task Editors .........................................2073
vslConvSetMode/vslCorrSetMode ...........................................2074
vslConvSetInternalPrecision/vslCorrSetInternalPrecision............2075
vslConvSetStart/vslCorrSetStart ............................................2076
vslConvSetDecimation/vslCorrSetDecimation ...........................2077
Task Execution Routines................................................................2078
vslConvExec/vslCorrExec ......................................................2079
vslConvExec1D/vslCorrExec1D...............................................2080
vslConvExecX/vslCorrExecX...................................................2082
vslConvExecX1D/vslCorrExecX1D...........................................2084
Convolution and Correlation Task Destructors...................................2085
vslConvDeleteTask/vslCorrDeleteTask......................................2086
Convolution and Correlation Task Copiers ........................................2086
vslConvCopyTask/vslCorrCopyTask .........................................2086
Convolution and Correlation Usage Examples ...................................2087
Convolution and Correlation Mathematical Notation and Definitions.....2091
Convolution and Correlation Data Allocation.....................................2092
Summary Statistics ..............................................................................2094
Summary Statistics Naming Conventions.........................................2095
Summary Statistics Data Types ......................................................2095
Summary Statistics Parameters......................................................2096
Summary Statistics Task Status and Error Reporting .........................2096
Summary Statistics Task Constructors.............................................2100
vslSSNewTask .....................................................................2100
Summary Statistics Task Editors.....................................................2102
vslSSEditTask ......................................................................2103
vslSSEditMoments................................................................2112
vslSSEditSums ....................................................................2113
vslSSEditCovCor ..................................................................2114
vslSSEditCP.........................................................................2116
vslSSEditPartialCovCor .........................................................2117
vslSSEditQuantiles ...............................................................2119
vslSSEditStreamQuantiles .....................................................2120
vslSSEditPooledCovariance ....................................................2121
vslSSEditRobustCovariance ...................................................2122
vslSSEditOutliersDetection ....................................................2124
vslSSEditMissingValues .........................................................2125
vslSSEditCorParameterization ................................................2129
Summary Statistics Task Computation Routines................................2130
vslSSCompute .....................................................................2133
Summary Statistics Task Destructor................................................2134
vslSSDeleteTask...................................................................2134
Summary Statistics Usage Examples...............................................2135
Summary Statistics Mathematical Notation and Definitions ................2136
Chapter 9: Fourier Transform Functions
FFT Functions ......................................................................................2142
FFT Interface...............................................................................2143
Computing an FFT ........................................................................2143
Configuration Settings ..................................................................2143
DFTI_PRECISION .................................................................2146
Intel
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Math Kernel Library Developer Reference
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DFTI_FORWARD_DOMAIN .....................................................2146
DFTI_DIMENSION, DFTI_LENGTHS.........................................2147
DFTI_PLACEMENT ................................................................2147
DFTI_FORWARD_SCALE, DFTI_BACKWARD_SCALE...................2148
DFTI_NUMBER_OF_USER_THREADS .......................................2148
DFTI_THREAD_LIMIT............................................................2148
DFTI_INPUT_STRIDES, DFTI_OUTPUT_STRIDES ......................2149
DFTI_NUMBER_OF_TRANSFORMS ..........................................2151
DFTI_INPUT_DISTANCE, DFTI_OUTPUT_DISTANCE ..................2151
DFTI_COMPLEX_STORAGE, DFTI_REAL_STORAGE,
DFTI_CONJUGATE_EVEN_STORAGE....................................2152
DFTI_PACKED_FORMAT ........................................................2155
DFTI_WORKSPACE...............................................................2164
DFTI_COMMIT_STATUS.........................................................2164
DFTI_ORDERING .................................................................2164
FFT Descriptor Manipulation Functions ............................................2165
DftiCreateDescriptor.............................................................2165
DftiCommitDescriptor ...........................................................2166
DftiFreeDescriptor................................................................2167
DftiCopyDescriptor ...............................................................2168
FFT Descriptor Configuration Functions............................................2169
DftiSetValue ........................................................................2169
DftiGetValue........................................................................2170
FFT Computation Functions ...........................................................2172
DftiComputeForward ............................................................2172
DftiComputeBackward ..........................................................2173
Configuring and Computing an FFT in C/C++...........................2175
Status Checking Functions.............................................................2178
DftiErrorClass ......................................................................2178
DftiErrorMessage .................................................................2179
Cluster FFT Functions............................................................................2180
Computing Cluster FFT..................................................................2181
Distributing Data among Processes.................................................2182
Cluster FFT Interface ....................................................................2183
Cluster FFT Descriptor Manipulation Functions..................................2184
DftiCreateDescriptorDM ........................................................2184
DftiCommitDescriptorDM.......................................................2185
DftiFreeDescriptorDM ...........................................................2186
Cluster FFT Computation Functions.................................................2186
DftiComputeForwardDM ........................................................2187
DftiComputeBackwardDM......................................................2188
Cluster FFT Descriptor Configuration Functions.................................2189
DftiSetValueDM ...................................................................2190
DftiGetValueDM ...................................................................2191
Error Codes .................................................................................2193
Chapter 10: PBLAS Routines
PBLAS Routines Overview ......................................................................2194
PBLAS Routine Naming Conventions........................................................2195
PBLAS Level 1 Routines .........................................................................2197
p?amax ......................................................................................2197
p?asum ......................................................................................2198
p?axpy .......................................................................................2199
p?copy........................................................................................2201
p?dot .........................................................................................2202
Contents
19
p?dotc ........................................................................................2203
p?dotu........................................................................................2204
p?nrm2.......................................................................................2205
p?scal.........................................................................................2206
p?swap .......................................................................................2207
PBLAS Level 2 Routines .........................................................................2209
p?gemv ......................................................................................2210
p?agemv.....................................................................................2212
p?ger .........................................................................................2214
p?gerc ........................................................................................2216
p?geru........................................................................................2218
p?hemv ......................................................................................2219
p?ahemv.....................................................................................2221
p?her .........................................................................................2223
p?her2........................................................................................2225
p?symv.......................................................................................2227
p?asymv .....................................................................................2228
p?syr..........................................................................................2230
p?syr2 ........................................................................................2232
p?trmv .......................................................................................2234
p?atrmv......................................................................................2236
p?trsv.........................................................................................2238
PBLAS Level 3 Routines .........................................................................2240
p?geadd......................................................................................2241
p?tradd.......................................................................................2242
p?gemm .....................................................................................2244
p?hemm .....................................................................................2246
p?herk........................................................................................2248
p?her2k ......................................................................................2250
p?symm......................................................................................2252
p?syrk ........................................................................................2255
p?syr2k ......................................................................................2257
p?tran ........................................................................................2259
p?tranu.......................................................................................2260
p?tranc .......................................................................................2261
p?trmm ......................................................................................2263
p?trsm........................................................................................2265
Chapter 11: Partial Differential Equations Support
Trigonometric Transform Routines...........................................................2268
Trigonometric Transforms Implemented...........................................2268
Sequence of Invoking TT Routines ..................................................2270
Trigonometric Transform Interface Description..................................2271
TT Routines .................................................................................2272
?_init_trig_transform............................................................2272
?_commit_trig_transform......................................................2273
?_forward_trig_transform .....................................................2275
?_backward_trig_transform...................................................2277
free_trig_transform..............................................................2279
Common Parameters of the Trigonometric Transforms .......................2279
Trigonometric Transform Implementation Details ..............................2283
Fast Poisson Solver Routines .................................................................2283
Poisson Solver Implementation ......................................................2283
Sequence of Invoking Poisson Solver Routines .................................2289
Fast Poisson Solver Interface Description.........................................2292
Intel
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Math Kernel Library Developer Reference
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