void SVD::solve(MatDoub_I &b, MatDoub_O &x, Doub thresh = -1.)
{
int i,j,m=b.ncols();
if (b.nrows() != n || x.nrows() != n || b.ncols() != x.ncols())
throw("SVD::solve bad sizes");
VecDoub xx(n);
for (j=0;j<m;j++) {
for (i=0;i<n;i++) xx[i] = b[i][j];
solve(xx,xx,thresh);
for (i=0;i<n;i++) x[i][j] = xx[i];
}
}
QRdcmp::QRdcmp(MatDoub_I &a)
: n(a.nrows()), qt(n,n), r(a), sing(false) {
Int i,j,k;
VecDoub c(n), d(n);
Doub scale,sigma,sum,tau;
for (k=0; k<n-1; k++) {
scale=0.0;
for (i=k; i<n; i++) scale=MAX(scale,std::abs(r[i][k]));
if (scale == 0.0) {
sing=true;
c[k]=d[k]=0.0;
} else {
for (i=k; i<n; i++) r[i][k] /= scale;
for (sum=0.0,i=k; i<n; i++) sum += SQR(r[i][k]);
sigma=SIGN(sqrt(sum),r[k][k]);
r[k][k] += sigma;
c[k]=sigma*r[k][k];
d[k] = -scale*sigma;
for (j=k+1; j<n; j++) {
for (sum=0.0,i=k; i<n; i++) sum += r[i][k]*r[i][j];
tau=sum/c[k];
for (i=k; i<n; i++) r[i][j] -= tau*r[i][k];
}
}
}
d[n-1]=r[n-1][n-1];
if (d[n-1] == 0.0) sing=true;
for (i=0; i<n; i++) {
for (j=0; j<n; j++) qt[i][j]=0.0;
qt[i][i]=1.0;
}
for (k=0; k<n-1; k++) {
if (c[k] != 0.0) {
for (j=0; j<n; j++) {
sum=0.0;
for (i=k; i<n; i++)
sum += r[i][k]*qt[i][j];
sum /= c[k];
for (i=k; i<n; i++)
qt[i][j] -= sum*r[i][k];
}
}
}
for (i=0; i<n; i++) {
r[i][i]=d[i];
for (j=0; j<i; j++) r[i][j]=0.0;
}
}