/*
* Invert the matrix if x = -1
* use gaussj
*/
FMatrix FMatrix::operator^( int x ) const
{
assert( x == -1 ); /* may want to extend to 2... in the future */
// check dimension
assert( XDim() == YDim() );
// convience variables
int n = XDim();
int size = n*n;
// make a copy of the matrix for nrc routine to work on
float *copy = new float[ size ];
memcpy( copy, elem, size*sizeof(float) );
float **a = convert_matrix( copy, 1, n, 1, n );
float **b = matrix( 1, n, 1, 1 );
b[1][1] = 1.0F;
for( int i = 2; i <= n; i++ )
b[i][1] = 0.0F;
gaussj( a, n, b, 1 );
FMatrix ret( n, n );
for( int iy = 0; iy < n; iy++ )
for( int ix = 0; ix < n; ix++ )
ret.Elem( iy, ix ) = copy[ iy*n + ix ];
delete [] copy;
free_matrix( b, 1, n, 1, 1 );
free_convert_matrix( a, 1, n, 1, n );
return( ret );
}
int main(void)
{
unsigned long i,j,msize,*ija;
float **a,*sa,*ax,*b;
static float ainit[NP][NP]={
3.0,0.0,1.0,0.0,0.0,
0.0,4.0,0.0,0.0,0.0,
0.0,7.0,5.0,9.0,0.0,
0.0,0.0,0.0,0.0,2.0,
0.0,0.0,0.0,6.0,5.0};
static float x[NP+1]={0.0,1.0,2.0,3.0,4.0,5.0};
ija=lvector(1,NMAX);
ax=vector(1,NP);
b=vector(1,NP);
sa=vector(1,NMAX);
a=convert_matrix(&ainit[0][0],1,NP,1,NP);
sprsin(a,NP,0.5,NMAX,sa,ija);
msize=ija[1]-2;
sprstx(sa,ija,x,b,msize);
for (i=1;i<=msize;i++)
for (ax[i]=0.0,j=1;j<=msize;j++) ax[i] += a[j][i]*x[j];
printf("\tReference\tsprstx result\n");
for (i=1;i<=msize;i++) printf("\t%5.2f\t\t%5.2f\n",ax[i],b[i]);
free_convert_matrix(a,1,NP,1,NP);
free_vector(sa,1,NMAX);
free_vector(b,1,NP);
free_vector(ax,1,NP);
free_lvector(ija,1,NMAX);
return 0;
}
int main(void)
{
int i,j;
static float c[NP][NP]=
{1.0,2.0,0.0,0.0,0.0,
-2.0,3.0,0.0,0.0,0.0,
3.0,4.0,50.0,0.0,0.0,
-4.0,5.0,-60.0,7.0,0.0,
-5.0,6.0,-70.0,8.0,-9.0};
float *wr,*wi,**a;
wr=vector(1,NP);
wi=vector(1,NP);
a=convert_matrix(&c[0][0],1,NP,1,NP);
printf("matrix:\n");
for (i=1;i<=NP;i++) {
for (j=1;j<=NP;j++) printf("%12.2f",a[i][j]);
printf("\n");
}
balanc(a,NP);
elmhes(a,NP);
hqr(a,NP,wr,wi);
printf("eigenvalues:\n");
printf("%11s %16s \n","real","imag.");
for (i=1;i<=NP;i++) printf("%15f %14f\n",wr[i],wi[i]);
free_convert_matrix(a,1,NP,1,NP);
free_vector(wi,1,NP);
free_vector(wr,1,NP);
return 0;
}
int main(void)
{
int i,j,nrot;
static float c[NP][NP]=
{5.0,4.3,3.0,2.0,1.0,0.0,-1.0,-2.0,-3.0,-4.0,
4.3,5.1,4.0,3.0,2.0,1.0,0.0,-1.0,-2.0,-3.0,
3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,-1.0,-2.0,
2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,-1.0,
1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,
0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,
-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,
-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,
-3.0,-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,
-4.0,-3.0,-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0};
float *d,**v,**e;
d=vector(1,NP);
v=matrix(1,NP,1,NP);
e=convert_matrix(&c[0][0],1,NP,1,NP);
printf("****** Finding Eigenvectors ******\n");
jacobi(e,NP,d,v,&nrot);
printf("unsorted eigenvectors:\n");
for (i=1;i<=NP;i++) {
printf("eigenvalue %3d = %12.6f\n",i,d[i]);
printf("eigenvector:\n");
for (j=1;j<=NP;j++) {
printf("%12.6f",v[j][i]);
if ((j % 5) == 0) printf("\n");
}
printf("\n");
}
printf("\n****** Sorting Eigenvectors ******\n\n");
eigsrt(d,v,NP);
printf("sorted eigenvectors:\n");
for (i=1;i<=NP;i++) {
printf("eigenvalue %3d = %12.6f\n",i,d[i]);
printf("eigenvector:\n");
for (j=1;j<=NP;j++) {
printf("%12.6f",v[j][i]);
if ((j % 5) == 0) printf("\n");
}
printf("\n");
}
free_convert_matrix(e,1,NP,1,NP);
free_matrix(v,1,NP,1,NP);
free_vector(d,1,NP);
return 0;
}
int main(void)
{
int i,icase,j,*izrov,*iposv;
static float c[MP][NP]=
{0.0,1.0,1.0,3.0,-0.5,
740.0,-1.0,0.0,-2.0,0.0,
0.0,0.0,-2.0,0.0,7.0,
0.5,0.0,-1.0,1.0,-2.0,
9.0,-1.0,-1.0,-1.0,-1.0,
0.0,0.0,0.0,0.0,0.0};
float **a;
static char *txt[NM1M2+1]=
{" ","x1","x2","x3","x4","y1","y2","y3"};
izrov=ivector(1,N);
iposv=ivector(1,M);
a=convert_matrix(&c[0][0],1,MP,1,NP);
simplx(a,M,N,M1,M2,M3,&icase,izrov,iposv);
if (icase == 1)
printf("\nunbounded objective function\n");
else if (icase == -1)
printf("\nno solutions satisfy constraints given\n");
else {
printf("\n%11s"," ");
for (i=1;i<=N;i++)
if (izrov[i] <= NM1M2) printf("%10s",txt[izrov[i]]);
printf("\n");
for (i=1;i<=M+1;i++) {
if (i == 1 || iposv[i-1] <= NM1M2) {
if (i > 1)
printf("%s",txt[iposv[i-1]]);
else
printf(" ");
printf("%10.2f",a[i][1]);
for (j=2;j<=N+1;j++)
if (izrov[j-1] <= NM1M2)
printf("%10.2f",a[i][j]);
printf("\n");
}
}
}
free_convert_matrix(a,1,MP,1,NP);
free_ivector(iposv,1,M);
free_ivector(izrov,1,N);
return 0;
}
int main(void)
{
int i,j,*indx;
long idum=(-13);
float d,*x,**a,**aa;
static float ainit[NP][NP]=
{1.0,2.0,3.0,4.0,5.0,
2.0,3.0,4.0,5.0,1.0,
1.0,1.0,1.0,1.0,1.0,
4.0,5.0,1.0,2.0,3.0,
5.0,1.0,2.0,3.0,4.0};
static float b[N+1]={0.0,1.0,1.0,1.0,1.0,1.0};
indx=ivector(1,N);
x=vector(1,N);
a=convert_matrix(&ainit[0][0],1,N,1,N);
aa=matrix(1,N,1,N);
for (i=1;i<=N;i++) {
x[i]=b[i];
for (j=1;j<=N;j++)
aa[i][j]=a[i][j];
}
ludcmp(aa,N,indx,&d);
lubksb(aa,N,indx,x);
printf("\nSolution vector for the equations:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
/* now phoney up x and let mprove fix it */
for (i=1;i<=N;i++) x[i] *= (1.0+0.2*ran3(&idum));
printf("\nSolution vector with noise added:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
mprove(a,aa,N,indx,b,x);
printf("\nSolution vector recovered by mprove:\n");
for (i=1;i<=N;i++) printf("%12.6f",x[i]);
printf("\n");
free_matrix(aa,1,N,1,N);
free_convert_matrix(a,1,N,1,N);
free_vector(x,1,N);
free_ivector(indx,1,N);
return 0;
}
int main(void)
{
int i,j,k,kk,l,ll,nrot;
static float a[3][3]=
{1.0,2.0,3.0,
2.0,2.0,3.0,
3.0,3.0,3.0};
static float b[5][5]=
{-2.0,-1.0,0.0,1.0,2.0,
-1.0,-1.0,0.0,1.0,2.0,
0.0,0.0,0.0,1.0,2.0,
1.0,1.0,1.0,1.0,2.0,
2.0,2.0,2.0,2.0,2.0};
static float c[NP][NP]=
{5.0,4.3,3.0,2.0,1.0,0.0,-1.0,-2.0,-3.0,-4.0,
4.3,5.1,4.0,3.0,2.0,1.0,0.0,-1.0,-2.0,-3.0,
3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,-1.0,-2.0,
2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,-1.0,
1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,0.0,
0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,1.0,
-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,2.0,
-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,3.0,
-3.0,-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0,4.0,
-4.0,-3.0,-2.0,-1.0,0.0,1.0,2.0,3.0,4.0,5.0};
float *d,*r,**v,**e;
static int num[4]={0,3,5,10};
d=vector(1,NP);
r=vector(1,NP);
v=matrix(1,NP,1,NP);
for (i=1;i<=NMAT;i++) {
if (i == 1) e=convert_matrix(&a[0][0],1,num[i],1,num[i]);
else if (i == 2) e=convert_matrix(&b[0][0],1,num[i],1,num[i]);
else if (i == 3) e=convert_matrix(&c[0][0],1,num[i],1,num[i]);
jacobi(e,num[i],d,v,&nrot);
printf("matrix number %2d\n",i);
printf("number of JACOBI rotations: %3d\n",nrot);
printf("eigenvalues: \n");
for (j=1;j<=num[i];j++) {
printf("%12.6f",d[j]);
if ((j % 5) == 0) printf("\n");
}
printf("\neigenvectors:\n");
for (j=1;j<=num[i];j++) {
printf("%9s %3d \n","number",j);
for (k=1;k<=num[i];k++) {
printf("%12.6f",v[k][j]);
if ((k % 5) == 0) printf("\n");
}
printf("\n");
}
/* eigenvector test */
printf("eigenvector test\n");
for (j=1;j<=num[i];j++) {
for (l=1;l<=num[i];l++) {
r[l]=0.0;
for (k=1;k<=num[i];k++) {
if (k > l) {
kk=l;
ll=k;
} else {
kk=k;
ll=l;
}
r[l] += (e[ll][kk]*v[k][j]);
}
}
printf("vector number %3d\n",j);
printf("%11s %14s %10s\n",
"vector","mtrx*vec.","ratio");
for (l=1;l<=num[i];l++)
printf("%12.6f %12.6f %12.6f\n",
v[l][j],r[l],r[l]/v[l][j]);
}
printf("press RETURN to continue...\n");
(void) getchar();
free_convert_matrix(e,1,num[i],1,num[i]);
}
free_matrix(v,1,NP,1,NP);
free_vector(r,1,NP);
free_vector(d,1,NP);
return 0;
}
int main(void)
{
unsigned long i,j,k,*ija,*ijb,*ijbt,*ijc;
float *sa,*sb,*sbt,*sc,**a,**b,**c,**ab;
static float ainit[NP][NP]={
1.0,0.5,0.0,0.0,0.0,
0.5,2.0,0.5,0.0,0.0,
0.0,0.5,3.0,0.5,0.0,
0.0,0.0,0.5,4.0,0.5,
0.0,0.0,0.0,0.5,5.0};
static float binit[NP][NP]={
1.0,1.0,0.0,0.0,0.0,
1.0,2.0,1.0,0.0,0.0,
0.0,1.0,3.0,1.0,0.0,
0.0,0.0,1.0,4.0,1.0,
0.0,0.0,0.0,1.0,5.0};
ija=lvector(1,NMAX);
ijb=lvector(1,NMAX);
ijbt=lvector(1,NMAX);
ijc=lvector(1,NMAX);
sa=vector(1,NMAX);
sb=vector(1,NMAX);
sbt=vector(1,NMAX);
sc=vector(1,NMAX);
c=matrix(1,NP,1,NP);
ab=matrix(1,NP,1,NP);
a=convert_matrix(&ainit[0][0],1,NP,1,NP);
b=convert_matrix(&binit[0][0],1,NP,1,NP);
sprsin(a,NP,0.5,NMAX,sa,ija);
sprsin(b,NP,0.5,NMAX,sb,ijb);
sprstp(sb,ijb,sbt,ijbt);
/* specify tridiagonal output, using fact that a is tridiagonal */
for (i=1;i<=ija[ija[1]-1]-1;i++) ijc[i]=ija[i];
sprspm(sa,ija,sbt,ijbt,sc,ijc);
for (i=1;i<=NP;i++) {
for (j=1;j<=NP;j++) {
ab[i][j]=0.0;
for (k=1;k<=NP;k++) {
ab[i][j]=ab[i][j]+a[i][k]*b[k][j];
}
}
}
printf("Reference matrix:\n");
for (i=1;i<=NP;i++) {
for (j=1;j<=NP;j++) printf("%5.2f\t",ab[i][j]);
printf("\n");
}
printf("sprspm matrix (should show only tridiagonals):\n");
for (i=1;i<=NP;i++) for (j=1;j<=NP;j++) c[i][j]=0.0;
for (i=1;i<=NP;i++) {
c[i][i]=sc[i];
for (j=ijc[i];j<=ijc[i+1]-1;j++) c[i][ijc[j]]=sc[j];
}
for (i=1;i<=NP;i++) {
for (j=1;j<=NP;j++) printf("%5.2f\t",c[i][j]);
printf("\n");
}
free_convert_matrix(b,1,NP,1,NP);
free_convert_matrix(a,1,NP,1,NP);
free_matrix(ab,1,NP,1,NP);
free_matrix(c,1,NP,1,NP);
free_vector(sc,1,NMAX);
free_vector(sbt,1,NMAX);
free_vector(sb,1,NMAX);
free_vector(sa,1,NMAX);
free_lvector(ijc,1,NMAX);
free_lvector(ijbt,1,NMAX);
free_lvector(ijb,1,NMAX);
free_lvector(ija,1,NMAX);
return 0;
}
