向量化简的算法
这种理解方式:
(h(x1)-y1)* x1
把(h(x1)-y1)看成标量,x1看成矢量:
1 * [1 2 3]
(h(x1)-y1)* x1
+(h(x2)-y2)* x2
[1 2] * [1 2 3; 4 5 6] 分解后 [1 2] * [1;4] [1 2] * [2;5] [1 2] * [3;6]
假设:(h(x1)-y1)=1 (h(x2)-y2)=2 x1 = [1 2 3] x2 = [4 5 6]
另一种理解比较复杂:
(
h
(
x
n
)
−
y
)
∗
x
1
=
[
1
,
2
,
3
,
4
,
5
,
6
,
7
]
∗
[
11
,
12
,
13
,
14
,
15
,
16
,
17
]
T
(h(x_n)-y)* x_1 = [1,2,3,4,5,6,7] * [11,12,13,14,15,16,17] ^T
(h(xn)−y)∗x1=[1,2,3,4,5,6,7]∗[11,12,13,14,15,16,17]T
(
h
(
x
n
)
−
y
)
∗
x
2
=
[
1
,
2
,
3
,
4
,
5
,
6
,
7
]
∗
[
21
,
22
,
23
,
24
,
25
,
26
,
27
]
T
(h(x_n)-y)* x_2 = [1,2,3,4,5,6,7] * [21,22,23,24,25,26,27] ^T
(h(xn)−y)∗x2=[1,2,3,4,5,6,7]∗[21,22,23,24,25,26,27]T
合起来就是:
(
h
(
x
n
)
−
y
)
∗
x
n
=
[
1
,
2
,
3
,
4
,
5
,
6
,
7
]
∗
[
11
,
12
,
13
,
14
,
15
,
16
,
17
;
21
,
22
,
23
,
24
,
25
,
26
,
27
]
T
(h(x_n)-y)* x_n = [1,2,3,4,5,6,7] * [11,12,13,14,15,16,17;21,22,23,24,25,26,27] ^T
(h(xn)−y)∗xn=[1,2,3,4,5,6,7]∗[11,12,13,14,15,16,17;21,22,23,24,25,26,27]T
(h(xn)-y) = [1 2 3 4 5 6 7]
x1 = [11 12 13 14 15 16 17]
x2 =[21 22 23 24 25 26 27]
花间前的笨方法比较耗时。
https://blog.****.net/xujie126/article/details/100772693