几天来，我一直在研究一个 DIY linalg 求解器，并且它正在组合在一起（对你们在 stackexchange 来说不是小事） 但我目前正在经历一个 Brain Fart 并且看不出当前代码有什么问题。任何见解将不胜感激；你们真棒！
下面的代码应该是可复制粘贴的；结果应该是-15,8,2，但它当前抽出2,inf,-inf，不用说，这是不正确的。
编辑：我认为最后要修复的是 Back Substitution / Ux=x 阶段，但据我所知，这是“正确的”。我正在通过这个例子来检查我的中间工作
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#define MAT1 3
#define TINY 1e-20
#define a(i,j) a[(i)*MAT1+(j)]
void h_pivot_decomp(float *a, int *p, int *q){
int i,j,k;
int n=MAT1;
int pi,pj,tmp;
float max;
float ftmp;
for (k=0;k<n;k++){
pi=-1,pj=-1,max=0.0;
//find pivot in submatrix a(k:n,k:n)
for (i=k;i<n;i++) {
for (j=k;j<n;j++) {
if (fabs(a(i,j))>max){
max = fabs(a(i,j));
pi=i;
pj=j;
}
}
}
//Swap Row
tmp=p[k];
p[k]=p[pi];
p[pi]=tmp;
for (j=0;j<n;j++){
ftmp=a(k,j);
a(k,j)=a(pi,j);
a(pi,j)=ftmp;
}
//Swap Col
tmp=q[k];
q[k]=q[pj];
q[pj]=tmp;
for (i=0;i<n;i++){
ftmp=a(i,k);
a(i,k)=a(i,pj);
a(i,pj)=ftmp;
}
//END PIVOT
//check pivot size and decompose
if ((fabs(a(k,k))>TINY)){
for (i=k+1;i<n;i++){
//Column normalisation
ftmp=a(i,k)/=a(k,k);
for (j=k+1;j<n;j++){
//a(ik)*a(kj) subtracted from lower right submatrix elements
a(i,j)-=(ftmp*a(k,j));
}
}
}
//END DECOMPOSE
}
}
void h_solve(float *a, float *x, int *p, int *q){
//forward substitution; see Golub, Van Loan 96
//And see http://www.cs.rutgers.edu/~richter/cs510/completePivoting.pdf
int i,ii=0,ip,j,tmp;
float ftmp;
float xtmp[MAT1];
//Swap rows (x=Px)
puts("x=Px Stage");
for (i=0; i<MAT1; i++){
xtmp[i]=x[p[i]]; //value that should be here
printf("x:%.1lf,q:%d\n",xtmp[i],q[i]);
}
//Lx=x
puts("Lx=x Stage");
//I suspect this is where this is falling down, as my implementation
//uses the combined LU matrix, and this is using the non-unit diagonal
for (i=0;i<MAT1;i++){
ftmp=xtmp[i];
if (ii != 0)
for (j=ii-1;j<i;j++)
ftmp-=a(i,j)*xtmp[j];
else
if (ftmp!=0.0)
ii=i+1;
xtmp[i]=ftmp;
printf("x:%.1lf,q:%d\n",xtmp[i],q[i]);
}
puts("Ux=x");
//backward substitution
//partially taken from Sourcebook on Parallel Computing p577
//solves Uy=z
for (j=0;j<MAT1;j++){
xtmp[j]=xtmp[j]/a(j,j);
for (i=j+1;i<MAT1;i++){
xtmp[i]-=a(i,j)*xtmp[j];
}
printf("x:%.1lf,q:%d\n",xtmp[i],q[i]);
}
//Last bit
//solves x=Qy
puts("x=Qx Stage");
for (i=0;i<MAT1;i++){
x[i]=xtmp[p[i]];
printf("x:%.1lf,q:%d\n",x[i],q[i]);
}
}
void main(){
//3x3 Matrix
//float a[]={1,-2,3,2,-5,12,0,2,-10};
//float a[]={1,3,-2,3,5,6,2,4,3};
//float b[]={5,7,8};
//float a[]={1,2,3,2,-1,1,3,4,-1};
//float b[]={14,3,8};
float a[]={1,-2,1,0,2,2,-2,4,2};
float b[]={1,4,2};
int sig;
puts("Declared Stuff");
//pivot array (not used currently)
int* p_pivot = (int *)malloc(sizeof(int)*MAT1);
int* q_pivot = (int *)malloc(sizeof(int)*MAT1);
puts("Starting Stuff");
for (unsigned int i=0; i<MAT1; i++){
p_pivot[i]=i;
q_pivot[i]=i;
printf("%.1lf|",b[i]);
for (unsigned int j=0;j<MAT1; j++){
printf("%.1lf,",a(i,j));
}
printf("|%d,%d",p_pivot[i],q_pivot[i]);
puts("");
}
h_pivot_decomp(&a[0],p_pivot,q_pivot);
puts("After Pivot");
for (unsigned int i=0; i<MAT1; i++){
printf("%.1lf|",b[i]);
for (unsigned int j=0;j<MAT1; j++){
printf("%.1lf,",a(i,j));
}
printf("|%d,%d",p_pivot[i],q_pivot[i]);
puts("");
}
h_solve(&a[0],&b[0],p_pivot,q_pivot);
puts("Finished Solve");
for (unsigned int i=0; i<MAT1; i++){
printf("%.1lf|",b[i]);
for (unsigned int j=0;j<MAT1; j++){
printf("%.1lf,",a(i,j));
}
puts("");
}
}