C语言实现householder变换（数值计算方法课程设计）

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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define N 100
struct vec
{
	float v[N];
	float beta;
};
//struct vec save;
struct vec house(float [],int n);
float two_norm(float x[],int begin,int end);
float max(float x[],int n);

int main(void)
{
	int i,j,k,n;
	float x[N];
	struct vec left;
	
	//读取需要规范化的向量x
	printf("Please enter the length of your vector:\n");
	scanf("%d",&n);
	printf("Please enter the elements of your vector:\n");
	for (i=1;i<=n;i++)
	{
		scanf("%f",&x[i]);
	}
	//检查
	for (i=1;i<=n;i++)
	{
		printf("%f",x[i]);
	}
	
	//读取数据完毕
	left=house(x,n);
	for (j=1;j<=n;j++)
	{
	    printf("%f \n",left.v[j]);
	}
	printf("%f",left.beta);
	
	return 0;
}


//householder变换的实现
struct vec house(float x[],int n)
{
	int i,j,k;
	float m,sigma,alpha;
	struct vec save;
	m=max(x,n);
	printf(" %f\n",m);
	for (i=1;i<=n;i++)
	{
		x[i]=x[i]/m;
	}
	sigma=two_norm(x,2,n);
	sigma=pow(sigma,2);
	for (j=2;j<=n;j++)
	{
		save.v[j]=x[j];
	}
	if (sigma==0)
	{
		save.beta=0.0;
	}
	else
	{
		alpha=sqrt(pow(x[1],2)+sigma);
		if (x[1]<=0)
		{
			save.v[1]=x[1]-sigma;
		}
		else 
		{
			save.v[1]=-(sigma/(x[1]+alpha));
		}
		save.beta=2*pow(save.v[1],2)/(sigma+pow(save.v[1],2));
		/*
		for (k=1;k<=n;k++)
		{
			save.v[k]=save.v[k]/save.v[1];
		}
		*/
	}
	
	return save;
} 

float two_norm(float x[],int begin,int end)
{
	int i;
	float val=0.0;
	
	for (i=begin;i<=end;i++)
	{
		val+=pow(x[i],2);
	}
	val=sqrt(val);
	
	return val;
}

float max(float x[],int n)
{
	int i,j;
	float max_val;
	max_val=x[1];
	
	for (i=1;i<=n;i++)
	{
		if (max_val<x[i])
		{
			max_val=x[i];
		}
	}
	
	return max_val;
}