前言
前面介绍了各种向量-向量，矩阵-向量，矩阵-矩阵的函数简介。根据自身目前状况，主要使用实数域的操作，也就是说关注单精度float类型的s和双精度double类型的d。还有就是用的基本都是全矩阵，没有经过压缩，也不是对称、三角、带状的某一种情况。所以主要还是总结一般的乘法、加法操作。
【注】代码都以单精度float的情况书写，主要流程要记住，使用mkl_malloc申请内存，使用mkl_free释放内存。n年没用过C++了，凑合看看吧。
学MKL的肯定对编程有一定程度了解，智能提示是一个很好的工具，在VS中，输入cblas_s以后，会自动补全所有的单精度操作函数，那么根据常规经验，就能判断出它到底用于做什么以及需要的参数；比如提示axpby意思就是a*x加b*y。还有就是函数有两种，一种是有返回值，一种无返回值，怎么办，只能提示看函数的声明是void还是float或者是double类型即可。
向量-向量
加法
运算
y=a∗x+b∗y
y=a*x+b*y
代码
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B;//两个向量
int a=1, b=1;//标量
int n = 5;//向量大小
A = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
B = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
printf("The 1st vector is ");
for (int i = 0; i < n; i++){
A[i] = i;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("The 2st vector is ");
for (int i = 0; i < n; i++){
B[i] =i+1;
printf("%2.0f", B[i]);
}
printf("\\n");
//计算a*A+b*B
cblas_saxpby(n, a, A, 1, b, B, 1);
printf("The a*A+b*B is ");
for (int i = 0; i < n; i++){
printf("%2.0f", B[i]);
}
printf("\\n");
mkl_free(A);
mkl_free(B);
getchar();
return 0;
}结果
The 1st vector is 0 1 2 3 4
The 2st vector is 1 2 3 4 5
The a*A+b*B is 1 3 5 7 9乘法
运算：向量点乘
代码：
//乘法
#include<stdio.h>
#include<stdlib.h>
#include <mkl.h>
int main()
{
float *A, *B;//两个向量
int a = 1, b = 1;//标量
int n = 5;//向量大小
float res;
A = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
B = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
printf("The 1st vector is ");
for (int i = 0; i < n; i++){
A[i] = i;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("The 2st vector is ");
for (int i = 0; i < n; i++){
B[i] = i + 1;
printf("%2.0f", B[i]);
}
printf("\\n");
//乘法:对应元素乘积的加和
res=cblas_sdot(n, A, 1, B, 1);
printf("点乘结果： %2.0f",res);
printf("\\n");
mkl_free(A);
mkl_free(B);
getchar();
return 0;
}结果：
The 1st vector is 0 1 2 3 4
The 2st vector is 1 2 3 4 5
点乘结果： 40二范数
运算：二范数或者欧几里得范数，是所有元素平方和开根号
代码
//计算向量二范数
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
void main()
{
float *A;
int n = 5;
float res;
A = (float *)mkl_malloc(n*sizeof(float), 64);
printf("The original vector：\\n");
for (int i = 0; i < n; i++)
{
A[i] = i + 1;
printf("%2.0f ", A[i]);
}
printf("\\n");
res = cblas_snrm2(n, A, 1);//计算二范数
printf("The norm2 of vector is:%2.6f", res);
mkl_free(A);
getchar();
}结果：
The original vector：
1 2 3 4 5
The norm2 of vector is:7.416198旋转
运算：将空间中一个点，绕原点旋转的角度
代码：以二维坐标点
(2,0)
(2,0)绕原点旋转45°为例。代码有点问题，一释放内存就出错，具体原因是对两个向量开辟空间以后又让它们指向了别的地址，造成了开辟空间无用。所以调用Cblas函数，可以直接把指向数组的指针丢进去。暂时先这样理解吧，等把C++复习一遍再来看看分析的对不对。
//旋转，以二维空间中的一个点(2，0)绕原点旋转45°
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
#include<math.h>
#define M_PI 3.14159265358979323846
int main()
{
float *A, *B;//A是坐标点，B是旋转矩阵
float point1[] = { 2 };//旋转点x坐标
float point2[] = { 0 };//旋转点y坐标
float rotpoint[] = { cos(45.0*M_PI / 180), sin(45.0*M_PI / 180) };
//A = (float *)mkl_malloc(1 * sizeof(float), 64);
//B = (float *)mkl_malloc(1 * sizeof(float), 64);
A = point1;
B = point2;
printf("The point is (%2.0f,%2.0f)",point1[0],point2[0]);
printf("\\n");
//计算旋转后的点
cblas_srot(1, A, 1, B, 1, rotpoint[0], rotpoint[1]);
printf("The rotated is (%2.6f,%2.6f)", A[0], B[0]);
printf("\\n");
//mkl_free(A);
//mkl_free(B);
getchar();
return 0;
}
结果：还是比较正确的
The point is ( 2, 0)
The rotated is (1.414214,-1.414214)缩放
运算
x=a∗x
x=a*x
代码
//计算向量缩放
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
void main()
{
float *A;
int n = 5;
float scal=0.1;
A = (float *)mkl_malloc(n*sizeof(float), 64);
printf("The original vector：\\n");
for (int i = 0; i < n; i++)
{
A[i] = i + 1;
printf("%2.0f ", A[i]);
}
printf("\\n");
cblas_sscal(n, scal, A, 1);//缩放
printf("The scaled vector：\\n");
for (int i = 0; i < n; i++)
{
printf("%2.1f ", A[i]);
}
mkl_free(A);
getchar();
}结果
The original vector：
1 2 3 4 5
The scaled vector：
0.1 0.2 0.3 0.4 0.5交换
运算：交换两个向量
代码
//交换
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B;//两个向量
int a = 1, b = 1;//标量
int n = 5;//向量大小
A = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
B = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
printf("The 1st vector is ");
for (int i = 0; i < n; i++){
A[i] = i;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("The 2st vector is ");
for (int i = 0; i < n; i++){
B[i] = i + 1;
printf("%2.0f", B[i]);
}
printf("\\n");
//交换AB
cblas_sswap(n, A, 1, B, 1);
printf("The 1st swapped vctor is");
for (int i = 0; i < n; i++){
printf("%2.0f", A[i]);
}
printf("\\n");
printf("The 2st swapped vctor is");
for (int i = 0; i < n; i++){
printf("%2.0f", B[i]);
}
printf("\\n");
mkl_free(A);
mkl_free(B);
getchar();
return 0;
}结果
The 1st vector is 0 1 2 3 4
The 2st vector is 1 2 3 4 5
The 1st swapped vctor is 1 2 3 4 5
The 2st swapped vctor is 0 1 2 3 4最值
运算：求最大最小值
代码
//求最大最小值
#include<stdlib.h>
#include<stdio.h>
#include<mkl.h>
void main()
{
float *A;//向量
int n = 5;//向量大小
int max, min;
A = (float *)mkl_malloc(n * 1 * sizeof(float), 64);
printf("The 1st vector is ");
for (int i = 0; i < n; i++){
A[i] = i;
printf("%2.0f", A[i]);
}
printf("\\n");
//计算最值位置
max=cblas_isamax(n, A, 1);
min = cblas_isamin(n, A, 1);
printf("The max value is %2.0f, position is %d\\n", A[max], max + 1);
printf("The min value is %2.0f, position is %d\\n", A[min], min + 1);
mkl_free(A);
getchar();
}结果
The 1st vector is 0 1 2 3 4
The max value is 4, position is 5
The min value is 0, position is 1矩阵-向量
乘法1
运算:
y:=α∗A∗x+β∗y
y := \\alpha*A*x + \\beta*y
代码
//矩阵-向量乘积
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B,*C;//A是矩阵，B是向量,C是向量
int m = 2;//矩阵行数
int n = 5;//向量维度，矩阵列数
int a = 1, b = 1;//缩放因子
A = (float *)mkl_malloc(m*n*sizeof(float), 64);
B = (float *)mkl_malloc(n*sizeof(float), 64);
C = (float *)mkl_malloc(m*sizeof(float), 64);
//赋值,按行存储?
printf("数组为\\n");
for (int i = 0; i < m*n; i++){
if (i%n == 0 && i != 0)
printf("\\n");
A[i] = i;
printf("%2.0f",A[i]);
}
printf("\\n");
printf("向量为\\n");
for (int i = 0; i < n; i++)
{
B[i] = i + 1;
printf("%2.0f", B[i]);
}
printf("\\n");
for (int i = 0; i < m*n; i++)
C[i] = 0;
//2*5的矩阵与5*1的向量相乘
cblas_sgemv(CblasRowMajor, CblasNoTrans, m, n, a, A, n, B, 1, b, C, 1);
printf("矩阵-向量乘法结果\\n");
for (int i = 0; i < m; i++){
printf("%2.0f ", C[i]);
}
mkl_free(A);
mkl_free(B);
mkl_free(C);
getchar();
return 0;
}结果
数组为
0 1 2 3 4
5 6 7 8 9
向量为
1 2 3 4 5
矩阵-向量乘法结果
40 115乘法2
运算
A:=α∗x∗y′+A,
A := \\alpha*x*y\’+ A,
代码
//矩阵-向量乘积
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B, *C;//A是矩阵，B是向量
int m=2,n = 5;//B,C向量维度
int a = 1;//缩放因子
A = (float *)mkl_malloc(m*n*sizeof(float), 64);
B = (float *)mkl_malloc(m*sizeof(float), 64);
C = (float *)mkl_malloc(n*sizeof(float), 64);
//赋值,按行存储?
printf("数组为\\n");
for (int i = 0; i < m*n; i++){
if (i%n == 0 && i != 0)
printf("\\n");
A[i] = 1;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("向量1为\\n");
for (int i = 0; i < m; i++)
{
B[i] = i + 1;
printf("%2.0f", B[i]);
}
printf("\\n");
printf("向量2为\\n");
for (int i = 0; i < n; i++)
{
C[i] = i+2;
printf("%2.0f", C[i]);
}
printf("\\n");
//5*1向量乘以1*5向量，加上5*5矩阵
cblas_sger(CblasRowMajor, m, n, a, B, 1, C, 1, A, n);
printf("向量-向量相乘+矩阵的结果\\n");
for (int i = 0; i < m*n; i++){
if (i%n == 0 && i != 0)
printf("\\n");
printf("%2.0f ", A[i]);
}
mkl_free(A);
mkl_free(B);
mkl_free(C);
getchar();
return 0;
}结果
数组为
1 1 1 1 1
1 1 1 1 1
向量1为
1 2
向量2为
2 3 4 5 6
向量-向量相乘+矩阵的结果
3 4 5 6 7
5 7 9 11 13矩阵-矩阵
乘法1
运算
C:=α∗op(A)∗op(B)+β∗C,
C := \\alpha*op(A)*op(B) + \\beta*C,
代码
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B, *C;
int m = 2, n = 3, k = 2;//A维度2*3,B维度2*3(计算时候转置),C维度2*2
int a = 1, b = 1;//缩放因子
A = (float *)mkl_malloc(m*n*sizeof(float), 64);
B = (float *)mkl_malloc(n*k*sizeof(float), 64);
C = (float *)mkl_malloc(m*k*sizeof(float), 64);
printf("矩阵1为\\n");
for (int i = 0; i < m*n; i++)
{
if (i != 0 && i%n == 0)
printf("\\n");
A[i] = i + 1;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("矩阵2为\\n");
for (int i = 0; i < n*k; i++)
{
if (i != 0 && i%k == 0)
printf("\\n");
B[i] = 1;
printf("%2.0f", B[i]);
}
printf("\\n");
printf("矩阵3为\\n");
for (int i = 0; i < m*k; i++)
{
if (i != 0 && i%k == 0)
printf("\\n");
C[i] = i;
printf("%2.0f", C[i]);
}
printf("\\n");
printf("结果矩阵\\n");
cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, k, n, a, A, n, B, k, b, C, k);//注意mkn的顺序☆
for (int i = 0; i < m*k; i++)
{
if (i != 0 && i%k == 0)
printf("\\n");
printf("%2.0f", C[i]);
}
printf("\\n");
mkl_free(A);
mkl_free(B);
mkl_free(C);
getchar();
return 0;
}结果
矩阵1为
1 2 3
4 5 6
矩阵2为
1 1
1 1
1 1
矩阵3为
0 1
2 3
结果矩阵
6 7
1718乘法2
依旧是上述的功能，此处尝试一下
#include<stdio.h>
#include<stdlib.h>
#include<mkl.h>
int main()
{
float *A, *B, *C;
int m = 2, n = 3, k = 2;//A维度2*3,B维度2*3(计算时候转置),C维度2*2
int a = 1, b = 1;//缩放因子
A = (float *)mkl_malloc(m*n*sizeof(float), 64);
B = (float *)mkl_malloc(k*n*sizeof(float), 64);
C = (float *)mkl_malloc(m*k*sizeof(float), 64);
printf("矩阵1为\\n");
for (int i = 0; i < m*n; i++)
{
if (i != 0 && i%n == 0)
printf("\\n");
A[i] = i + 1;
printf("%2.0f", A[i]);
}
printf("\\n");
printf("矩阵2为\\n");
for (int i = 0; i < k*n; i++)
{
if (i != 0 && i%n == 0)
printf("\\n");
B[i] = 1;
printf("%2.0f", B[i]);
}
printf("\\n");
printf("矩阵3为\\n");
for (int i = 0; i < m*k; i++)
{
if (i != 0 && i%k == 0)
printf("\\n");
C[i] = i;
printf("%2.0f", C[i]);
}
printf("\\n");
printf("结果矩阵\\n");
cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans, m, k, n, a, A, n, B, n, b, C, k);//注意mkn的顺序☆
for (int i = 0; i < m*k; i++)
{
if (i != 0 && i%k == 0)
printf("\\n");
printf("%2.0f", C[i]);
}
printf("\\n");
mkl_free(A);
mkl_free(B);
mkl_free(C);
getchar();
return 0;
}结果
矩阵1为
1 2 3
4 5 6
矩阵2为
1 1 1
1 1 1
矩阵3为
0 1
2 3
结果矩阵
6 7
1718注意点
最主要的是记住参数顺序，首先是矩阵
op(A)
op(A)和的C行数，
op
op代表操作，乘法2中的
op
op就是转置；然后是矩阵
op(B)
op(B)和
C
C的列数；随后才是op(A)op(A)的列数和
op(B)
op(B)的行数。对于乘法2中的第二个矩阵，也就是
B
<script type="math/tex" id="MathJax-Element-399">B</script>矩阵，虽然转置了，但是还是以不转置时候，以行存储方式的引导维度，也就是列数为输入参数。
而且丢入函数的参数，并不一定是mkl_malloc开辟的空间，也可以是其它数组，用指针指向数组地址，然后丢到函数就行了。
奉上code（vs2013）: MKL -C++基本操作
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