Use C language to implement the least square algorithm and least square algorithm

Use C language to implement the least square algorithm and least square algorithm

Use C language to implement the least square algorithm

For more information, see http://blog.csdn.net/jdh99, :jdh.

 

Environment:

HOST: WIN8

Development Environment: MINGW

Note:

Refer to Wikipedia's least square method:

Example of a warship in the test text: predicting the width with the length of the warship

Example of simple linear model y = b0 + b1t [edit]

Randomly select 10 warships and analyze their length and width to find the relationship between their length and width. The following figure shows that the length (t) of a warship is linearly related to the width (y. The scatter chart is as follows:

The table lists the data of each warship. The subsequent step is to use the least square method to determine the linear relationship between the two variables.

No.	Length (m)	Width (m)	Ti-t	Yi-y
I	Ti	Yi	Ti *	Yi *	Ti * yi *	Ti *	Yi *
1	208	21.6	40.2	3.19	128.238	1616.04	10.1761
2	152	15.5	-15.8	-2.91	45.978	249.64	8.4681
3	113	10.4	-54.8	-8.01	438.948	3003.04	64.1601
4	227	31.0	59.2	12.59	745.328	3504.64	158.5081
5	137	13.0	-30.8	-5.41	166.628	948.64	29.2681
6	238	32.4	70.2	13.99	982.098	4928.04	195.7201
7	178	19.0	10.2	0.59	6.018	104.04	0.3481
8	104	10.4	-63.8	-8.01	511.038	4070.44	64.1601
9	191	19.0	23.2	0.59	13.688	538.24	0.3481
10	130	11.8	-37.8	-6.61	249.858	1428.84	43.6921
Sum (Σ)	1678	184.1	0.0	0.00	3287.820	20391.60	574.8490

Follow the example above.

And get the corresponding.

Then confirm b1

It can be seen that every 1 m change in the warship length, the corresponding width will change 16 cm. And obtain the constant item b0 from the following formula:

The random theory is not described here. We can see that the point fitting is very good, and the correlation between length and width is about 96.03%. Use Matlab to obtain fitting Straight

Line:

Algorithm result:

Mean_x = 167.800003, mean_y = 18.410000
A =-8.645075, B = 0.161234
The predicted width of a 39.725140 M warship is

Source code:

# Include <stdio. h> /************************************* ****** **************************************** ************************//************** **************************************** ********************* **************************************** * ********/# define LEN100 /************************** **************************************** ********************************** ************************************//** **************************************** ********** **************************************** * *****************/struct _ Data_Unit {float x; float y ;}; /*************************************** * ****************************** data fifo ******* **************************************** * ********************/struct _ Data {struct _ Data_Unit data [LEN]; int len ;}; /*************************************** * ****************************** global variables ******* **************************************** ***********************//*************** **************************************** *********************** **************************************** * *****/struct _ Data = {. len = 0 }; /*************************************** ******** **************************************** **********************//**************** **************************************** * ************** press data * parameter: x: measurement data x * y: measurement Data y ************************************* * *******************************/void push (float x, float y) {int I = 0; if (Data. len <LEN) {Data. data [Data. len]. x = x; Data. data [Data. len ++]. y = y; return;} // move Data, remove the last Data for (I = 0; I <LEN-1; I ++) {Data. data [I]. x = Data. data [I + 1]. x; Data. data [I]. y = Data. data [I + 1]. y;} Data. data [LEN]. x = x; Data. data [LEN]. y = y; Data. len = LEN ;} /*************************************** * ****************************** calculate the valuation * fit curve y = * x + B * parameters: x: x value of the number to be evaluated * return: valuation y ************************************** * ******************************/float calc (float x) {int I = 0; float mean_x = 0; float mean_y = 0; float num1 = 0; float num2 = 0; float a = 0; float B = 0; // calculate the mean of t and y for (I = 0; I <Data. len; I ++) {mean_x + = Data. data [I]. x; mean_y + = Data. data [I]. y;} mean_x/= Data. len; mean_y/= Data. len; printf ("mean_x = % f, mean_y = % f \ n", mean_x, mean_y); for (I = 0; I <Data. len; I ++) {num1 + = (Data. data [I]. x-mean_x) * (Data. data [I]. y-mean_y); num2 + = (Data. data [I]. x-mean_x) * (Data. data [I]. x-mean_x);} B = num1/num2; a = mean_y-B * mean_x; printf ("a = % f, B = % f \ n",, b); return (a + B * x);} int main () {float length [10] = {208,152,113,227,137,238,178,104,191,130}; float width [10] = {21.6, 15.5, 10.4, 31.0, 13.0, 32.4, 19.0, 10.4, 19.0}; int I = 0; for (I = 0; I <10; I ++) {push (length [I], width [I]);} printf ("the predicted width of a 300 m warship is % f m \ n", calc )); getchar (); return 0 ;}