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MKL学习——矩阵矩阵操作

發(fā)布時(shí)間：2023/12/13 编程问答 29 豆豆

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前言

前面介紹了BLAS Level 1中向量-向量操作，以及BLAS Level 2中矩陣-向量的操作，就剩下這一篇的BLAS Level 3中的矩陣-矩陣的操作了。對(duì)稀疏矩陣的操作以后等要用再看看。對(duì)基本的矩陣和向量運(yùn)算的函數(shù)有所了解以后，就進(jìn)行常用參數(shù)分析，以及實(shí)現(xiàn)了。

所有函數(shù)概覽

函數(shù)名稱缺失部分描述

cblas_?gemm	s,d,c,z	一般矩陣的矩陣-矩陣乘法
cblas_?hemm	c,z	某個(gè)輸入矩陣是Hermitian，然后計(jì)算矩陣-矩陣乘法
cblas_?herk	c,z	Hermitian的k階更新
cblas_?herk2	c,z	Hermitian的2k階更新
cblas_?symm	s,d,c,z	某個(gè)輸入矩陣是對(duì)稱的，然后計(jì)算矩陣-矩陣乘法
cblas_?syrk	s,d,c,z	對(duì)稱矩陣的k階更新
cblas_?syr2k	s,d,c,z	對(duì)稱矩陣的2k階更新
cblas_?trmm	s,d,c,z	某個(gè)輸入矩陣是三角的，就是你矩陣-矩陣的乘法
cblas_?trsm	s,d,c,z	解三角矩陣方程

矩陣運(yùn)算

cblas_?gemm

作用 : 一般矩陣的矩陣-矩陣乘法
定義函數(shù)
void cblas_sgemm (const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT m, const MKL_INT n, const MKL_INT k, const float alpha, const float *a, const MKL_INT lda, const float *b, const MKL_INT ldb, const float beta, float *c, const MKL_INT ldc);void cblas_dgemm (const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT m, const MKL_INT n, const MKL_INT k, const double alpha, const double *a, const MKL_INT lda, const double *b, const MKL_INT ldb, const double beta, double *c, const MKL_INT ldc);void cblas_cgemm (const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT m, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);void cblas_zgemm (const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE transa, const CBLAS_TRANSPOSE transb, const MKL_INT m, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?op(A)?op(B)+β?C
其中op(x)可以是op(x)=x或者op(x)=xT或者op(x)=XH

α和β是標(biāo)量

A,B,C是矩陣: op(A)是一個(gè)m?k的矩陣，op(B)是k?n的矩陣，C是一個(gè)m?n的矩陣
輸入?yún)?shù)

Layout: 指定矩陣是行優(yōu)先(CblasRowMajor)還是列優(yōu)先(CblasColMajor)

transa: 指定對(duì)矩陣的操作op(A)，如果transa=CblasNoTrans那么op(A)=A；如果transa=CblasTrans那么op(A)=AT；如果transa=CblasConjTrans那么op(A)=AH

transb: 同上

m: 矩陣op(A)和C的行數(shù)
n: 矩陣op(B)和C的列數(shù)

k: 矩陣op(A)和op(B)的列數(shù)

alpha: 標(biāo)量

a:

transa=CblasNoTranstransa=CblasTrans或者transa=CblasConjTrans

Layout=CblasColMajor	矩陣大小lda?k
Layout=CblasRowMajor	矩陣大小lda?m

lda : 引導(dǎo)維度

transa=CblasNoTranstransa=CblasTrans或者transa=CblasConjTrans

Layout=CblasColMajor	lda至少為max(1,m)
Layout=CblasRowMajor	lda至少為max(1,k)

transa=CblasNoTranstransa=CblasTrans或者transa=CblasConjTrans

Layout=CblasColMajor	矩陣大小ldb?n
Layout=CblasRowMajor	矩陣大小ldb?k

ldb:

transa=CblasNoTranstransa=CblasTrans或者transa=CblasConjTrans

Layout=CblasColMajor	ldb至少為max(1,k)
Layout=CblasRowMajor	ldb至少為max(1,n)

beta: 標(biāo)量

c: 當(dāng)Layout=CblasColMajor時(shí)候,數(shù)組大小為lda?n；當(dāng)Layout=CblasRowMajor時(shí)候,數(shù)組大小為lda?m

ldc:當(dāng)Layout=CblasColMajor的時(shí)候，ldc必須至少為max(1,m);當(dāng)Layout=CblasRowMajor的時(shí)候，ldc必須至少為max(1,n)

輸出參數(shù): 將計(jì)算得到的矩陣寫入到c

cblas_?hemm

作用 : 當(dāng)一個(gè)輸入矩陣為Hermitian時(shí)，計(jì)算矩陣-矩陣的乘法
定義函數(shù)
void cblas_chemm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);void cblas_zhemm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?A?B+β?CC:=α?B?A+β?C
其中，α,β是標(biāo)量，A是Hermitian矩陣，B,C是m?n的矩陣

cblas_?herk

作用: Hermitian的k階更新
定義函數(shù):
void cblas_cherk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const float alpha, const void *a, const MKL_INT lda, const float beta, void *c, const MKL_INT ldc);void cblas_zherk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const double alpha, const void *a, const MKL_INT lda, const double beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?A?AH+β?CC:=α?AH?A+β?C
其中，α,β是標(biāo)量，C是n?n的Hermitian矩陣，第一個(gè)式子的A是n?k矩陣，第二個(gè)式子的A是k?n的矩陣

cblas_?herk2

作用: Hermitian矩陣的2階更新
定義函數(shù)
void cblas_cher2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const float beta, void *c, const MKL_INT ldc);void cblas_zher2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const double beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?A?BH+conjg(α)?B?AH+β?CC:=α?AH?B+conjg(α)?BH?A+β?C
其中，α,β是標(biāo)量，C是n?n是Hermitian矩陣，第一個(gè)式子中A,B是n?k矩陣，第二個(gè)式子中是k?n的矩陣

cblas_?symm

作用: 某個(gè)輸入是對(duì)稱矩陣時(shí)候，計(jì)算矩陣-矩陣的乘法
定義函數(shù)
void cblas_ssymm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const float alpha, const float *a, const MKL_INT lda, const float *b, const MKL_INT ldb, const float beta, float *c, const MKL_INT ldc);void cblas_dsymm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const double alpha, const double *a, const MKL_INT lda, const double *b, const MKL_INT ldb, const double beta, double *c, const MKL_INT ldc);void cblas_csymm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);void cblas_zsymm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?A?b+β?CC:=α?B?A+β?C
其中α,β是標(biāo)量，A是對(duì)稱陣,B,C是m?n的矩陣

cblas_?syrk

作用: 對(duì)稱矩陣的k階更新
定義函數(shù)
void cblas_ssyrk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const float alpha, const float *a, const MKL_INT lda, const float beta, float *c, const MKL_INT ldc);void cblas_dsyrk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const double alpha, const double *a, const MKL_INT lda, const double beta, double *c, const MKL_INT ldc);void cblas_csyrk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *beta, void *c, const MKL_INT ldc);void cblas_zsyrk (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *beta, void *c, const MKL_INT ldc)
運(yùn)算

C:=α?A?A′+β?CC:=α?A′?A+β?C
其中,α,β是標(biāo)量，C是n?n的對(duì)稱陣,第一個(gè)式子中A是n?n的矩陣，第二個(gè)式子中A是k?n的矩陣

cblas_?syr2k

作用: 對(duì)稱陣的二階更新
定義函數(shù)
void cblas_ssyr2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const float alpha, const float *a, const MKL_INT lda, const float *b, const MKL_INT ldb, const float beta, float *c, const MKL_INT ldc);void cblas_dsyr2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const double alpha, const double *a, const MKL_INT lda, const double *b, const MKL_INT ldb, const double beta, double *c, const MKL_INT ldc);void cblas_csyr2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);void cblas_zsyr2k (const CBLAS_LAYOUT Layout, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE trans, const MKL_INT n, const MKL_INT k, const void *alpha, const void *a, const MKL_INT lda, const void *b, const MKL_INT ldb, const void *beta, void *c, const MKL_INT ldc);
運(yùn)算

C:=α?A?B′+α?B?A′+β?CC:=α?A′?B+α?B′?A+β?C
其中,α,β是標(biāo)量，C是n?n的對(duì)稱陣，第一個(gè)式子中A,B是n?k的矩陣，第二個(gè)式子中A,B是k?n的矩陣

cblas_?trmm

作用: 某個(gè)輸入矩陣為三角陣的時(shí)候，計(jì)算矩陣-矩陣的乘法
定義函數(shù)
void cblas_strmm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const float alpha, const float *a, const MKL_INT lda, float *b, const MKL_INT ldb);void cblas_dtrmm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const double alpha, const double *a, const MKL_INT lda, double *b, const MKL_INT ldb);void cblas_ctrmm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, void *b, const MKL_INT ldb);void cblas_ztrmm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, void *b, const MKL_INT ldb);
運(yùn)算

B:=α?op(A)?BB:=α?B?op(A)
其中，α是標(biāo)量，B是m?n的矩陣，op(A)=A或者op(A)=A′或者op(A)=conjg(A′)

cblas_?trsm

作用: 解三角矩陣方程
定義函數(shù)
void cblas_strsm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const float alpha, const float *a, const MKL_INT lda, float *b, const MKL_INT ldb);void cblas_dtrsm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const double alpha, const double *a, const MKL_INT lda, double *b, const MKL_INT ldb);void cblas_ctrsm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, void *b, const MKL_INT ldb);void cblas_ztrsm (const CBLAS_LAYOUT Layout, const CBLAS_SIDE side, const CBLAS_UPLO uplo, const CBLAS_TRANSPOSE transa, const CBLAS_DIAG diag, const MKL_INT m, const MKL_INT n, const void *alpha, const void *a, const MKL_INT lda, void *b, const MKL_INT ldb);
運(yùn)算

op(A)?X=α?BX?op(A)=alpha?B
其中，α是一個(gè)標(biāo)量，X和B是一個(gè)m?n的矩陣，A是單位或者非單位，上三角或者下三角矩陣，op(A)=A或者op(A)=A′或者op(A)=conjg(A′)。把等式的解矩陣X沖寫入到B矩陣中。

后續(xù)

研究BLAS Level 1 2 3中各種矩陣相關(guān)概念。隨后是代碼實(shí)現(xiàn)

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