add vcglib

vcglib/eigenlib/unsupported/Eigen/src/NonLinearOptimization/qrsolv.h

@@ -0,0 +1,91 @@
+namespace Eigen { 
+
+namespace internal {
+
+// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
+template <typename Scalar>
+void qrsolv(
+        Matrix< Scalar, Dynamic, Dynamic > &s,
+        // TODO : use a PermutationMatrix once lmpar is no more:
+        const VectorXi &ipvt,
+        const Matrix< Scalar, Dynamic, 1 >  &diag,
+        const Matrix< Scalar, Dynamic, 1 >  &qtb,
+        Matrix< Scalar, Dynamic, 1 >  &x,
+        Matrix< Scalar, Dynamic, 1 >  &sdiag)
+
+{
+    typedef DenseIndex Index;
+
+    /* Local variables */
+    Index i, j, k, l;
+    Scalar temp;
+    Index n = s.cols();
+    Matrix< Scalar, Dynamic, 1 >  wa(n);
+    JacobiRotation<Scalar> givens;
+
+    /* Function Body */
+    // the following will only change the lower triangular part of s, including
+    // the diagonal, though the diagonal is restored afterward
+
+    /*     copy r and (q transpose)*b to preserve input and initialize s. */
+    /*     in particular, save the diagonal elements of r in x. */
+    x = s.diagonal();
+    wa = qtb;
+
+    s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
+
+    /*     eliminate the diagonal matrix d using a givens rotation. */
+    for (j = 0; j < n; ++j) {
+
+        /*        prepare the row of d to be eliminated, locating the */
+        /*        diagonal element using p from the qr factorization. */
+        l = ipvt[j];
+        if (diag[l] == 0.)
+            break;
+        sdiag.tail(n-j).setZero();
+        sdiag[j] = diag[l];
+
+        /*        the transformations to eliminate the row of d */
+        /*        modify only a single element of (q transpose)*b */
+        /*        beyond the first n, which is initially zero. */
+        Scalar qtbpj = 0.;
+        for (k = j; k < n; ++k) {
+            /*           determine a givens rotation which eliminates the */
+            /*           appropriate element in the current row of d. */
+            givens.makeGivens(-s(k,k), sdiag[k]);
+
+            /*           compute the modified diagonal element of r and */
+            /*           the modified element of ((q transpose)*b,0). */
+            s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
+            temp = givens.c() * wa[k] + givens.s() * qtbpj;
+            qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
+            wa[k] = temp;
+
+            /*           accumulate the transformation in the row of s. */
+            for (i = k+1; i<n; ++i) {
+                temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
+                sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
+                s(i,k) = temp;
+            }
+        }
+    }
+
+    /*     solve the triangular system for z. if the system is */
+    /*     singular, then obtain a least squares solution. */
+    Index nsing;
+    for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
+
+    wa.tail(n-nsing).setZero();
+    s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
+
+    // restore
+    sdiag = s.diagonal();
+    s.diagonal() = x;
+
+    /*     permute the components of z back to components of x. */
+    for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
+}
+
+} // end namespace internal
+
+} // end namespace Eigen