BLAS库学习
首先，命名规范：
There are three levels of BLAS operations,
- Level 1
- Vector operations, e.g. y = /alpha x + y 向量操作
- Level 2
- Matrix-vector operations, e.g. y = /alpha A x + /beta y 矩阵与向量操作
- Level 3
- Matrix-matrix operations, e.g. C = /alpha A B + C 矩阵与矩阵的操作
Each routine has a name which specifies the operation, the type of matrices involved and their precisions. Some of the most common operations and their names are given below,
- DOT
- scalar product, x^T y
- AXPY
- vector sum, /alpha x + y
- MV
- matrix-vector product, A x
- SV
- matrix-vector solve, inv(A) x
- MM
- matrix-matrix product, A B
- SM
- matrix-matrix solve, inv(A) B
The type of matrices are,
- GE
- general
- GB
- general band
- SY
- symmetric
- SB
- symmetric band
- SP
- symmetric packed
- HE
- hermitian
- HB
- hermitian band
- HP
- hermitian packed
- TR
- triangular
- TB
- triangular band
- TP
- triangular packed
Each operation is defined for four precisions,
- S
- single real
- D
- double real
- C
- single complex
- Z
- double complex
Thus, for example, the name SGEMM stands for "single-precision general matrix-matrix multiply" and ZGEMM stands for "double-precision complex matrix-matrix multiply".
因此，例如，命名为SGEMM的函数意思为“单精度普通矩阵乘法”，ZGEMM为“双精度复数矩阵乘法”。
更多的，可以参考：http://www.netlib.org/blas/blasqr.pdf
下面这个例子是在csdn论坛上看到的，简单地改一下，可用GotoBlas2调用成功。
程序说明：下面的matrix.c 文件分别调用 C 代码， BLAS Level 1 函数 (ddot), BLAS Level 2 函数(dgemv) 与 BLAS Level 3的函数(DGEMM)完成矩阵计算： Yours_multiply 是 C 源代码，它直接依赖编译器生成优化代码。Ddot_Multiply，Dgemv_multiply使用Gotoblas2调用实现部分矩阵运算。Dgemm_multiply 直接调用GotoBlas2 的矩阵计算函数。
//Simple minded matrix multiply #include <stdio.h> #include <time.h> #include <stdlib.h> #include <common.h> //GotoBlas2 #include <cblas.h> //GotoBlas2 void print_arr(int N, char * name, double* array); void init_arr(int N, double* a); void Dgemm_multiply(double* a,double* b,double* c, int N); void Dgemv_multiply(double* a,double* b,double* c, int N); void Ddot_Multiply(double* a,double* b,double* c, int N); void Yours_multiply(double* a,double* b,double* c, int N); int main(int argc, char* argv[]) { clock_t start, stop; int i, j; int N; double* a; double* b; double* c; if(argc < 2) { printf("Enter matrix size N="); //please enter small number first to ensure that the //multiplication is correct! and then you may enter //a "reasonably" large number say like 500 or even 1000 scanf("%d",&N); } else { N = atoi(argv[1]); } a=(double*) malloc( sizeof(double)*N*N ); b=(double*) malloc( sizeof(double)*N*N ); c=(double*) malloc( sizeof(double)*N*N ); init_arr(N,a); init_arr(N,b); start = clock(); Yours_multiply(a,b,c,N); stop = clock(); printf("roll_your_own_multiply(). Elapsed time = %g seconds/n", ((double)(stop - start)) / CLOCKS_PER_SEC); //print simple test case of data to be sure multiplication is correct if (N < 7) { print_arr(N,"a", a); print_arr(N,"b", b); print_arr(N,"c", c); } free(a); free(b); free(c); //DDOT multiply a=(double*) malloc( sizeof(double)*N*N ); b=(double*) malloc( sizeof(double)*N*N ); c=(double*) malloc( sizeof(double)*N*N ); init_arr(N,a); init_arr(N,b); start = clock(); Ddot_Multiply(a,b,c,N); stop = clock(); printf("Ddot_Multiply(). Elapsed time = %g seconds/n", ((double)(stop - start)) / CLOCKS_PER_SEC); //print simple test case of data to be sure multiplication is correct if (N < 7) { print_arr(N,"a", a); print_arr(N,"b", b); print_arr(N,"c", c); } free(a); free(b); free(c); //DGEMV Multiply //reallcoate to force cash to be flushed a=(double*) malloc( sizeof(double)*N*N ); b=(double*) malloc( sizeof(double)*N*N ); c=(double*) malloc( sizeof(double)*N*N ); init_arr(N,a); init_arr(N,b); start = clock(); Dgemv_multiply(a,b,c,N); stop = clock(); printf("Dgemv_multiply(). Elapsed time = %g seconds/n", ((double)(stop - start)) / CLOCKS_PER_SEC); //print simple test case of data to be sure multiplication is correct if (N < 7) { print_arr(N,"a", a); print_arr(N,"b", b); print_arr(N,"c", c); } free(a); free(b); free(c); //DGEMM Multiply //reallocate to force cash to be flushed a=(double*) malloc( sizeof(double)*N*N ); b=(double*) malloc( sizeof(double)*N*N ); c=(double*) malloc( sizeof(double)*N*N ); init_arr(N,a); init_arr(N,b); start = clock(); Dgemm_multiply(a,b,c,N); stop = clock(); printf("Dgemm_multiply(). Elapsed time = %g seconds/n", ((double)(stop - start)) / CLOCKS_PER_SEC); //print simple test case of data to be sure multiplication is correct if (N < 7) { print_arr(N,"a", a); print_arr(N,"b", b); print_arr(N,"c", c); } free(a); free(b); free(c); return 0; } //Brute force way of matrix multiply void Yours_multiply(double* a,double* b,double* c, int N) { int i, j, k; for (i=0;i<N*N;i++) c[i]=0; for (i = 0; i < N; i++) { for (j=0; j<N; j++) { for (k=0; k<N; k++) { c[N*i+j] += a[N*i+k] * b[N*k+j]; } } } } //The ddot way to matrix multiply void Ddot_Multiply(double* a,double* b,double* c, int N) { int i, j; int incx = 1; int incy = N; for (i = 0; i < N; i++) { for (j=0; j<N; j++) { c[N*i+j] = cblas_ddot(N,&a[N*i],incx,&b[j],incy); } } } //DGEMV way of matrix multiply void Dgemv_multiply(double* a,double* b,double* c, int N) { int i; double alpha = 1.0, beta = 0.; int incx = 1; int incy = N; for (i = 0; i < N; i++) { cblas_dgemv(CblasRowMajor,CblasNoTrans,N,N,alpha,a,N,&b[i],N,beta,&c[i],N); } } //DGEMM way. The PREFERED way, especially for large matrices void Dgemm_multiply(double* a,double* b,double* c, int N) { int i; double alpha = 1.0, beta = 0.; int incx = 1; int incy = N; cblas_dgemm(CblasRowMajor,CblasNoTrans,CblasNoTrans,N,N,N,alpha,b,N,a,N,beta,c,N); } //initialize array with random data void init_arr(int N, double* a) { int i,j; for (i=0; i< N;i++) { for (j=0; j<N;j++) { a[i*N+j] = (i+j+1)%10; //keep all entries less than 10. pleasing to the eye! } } } //print array to std out void print_arr(int N, char * name, double* array) { int i,j; printf("/n%s/n",name); for (i=0;i<N;i++) { for (j=0;j<N;j++) { printf("%g/t",array[N*i+j]); } printf("/n"); } }