rename NonLinear to NonLinearOptimization

1 files changed, 124 insertions, 0 deletions

diff --git a/unsupported/Eigen/src/NonLinearOptimization/dogleg.h b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
new file mode 100644
index 000000000..3485c5796
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/dogleg.h
@@ -0,0 +1,124 @@
+
+template <typename Scalar>
+void ei_dogleg(
+        Matrix< Scalar, Dynamic, 1 >  &r,
+        const Matrix< Scalar, Dynamic, 1 >  &diag,
+        const Matrix< Scalar, Dynamic, 1 >  &qtb,
+        Scalar delta,
+        Matrix< Scalar, Dynamic, 1 >  &x)
+{
+    /* Local variables */
+    int i, j, k, l, jj;
+    Scalar sum, temp, alpha, bnorm;
+    Scalar gnorm, qnorm;
+    Scalar sgnorm;
+
+    /* Function Body */
+    const Scalar epsmch = epsilon<Scalar>();
+    const int n = diag.size();
+    Matrix< Scalar, Dynamic, 1 >  wa1(n), wa2(n);
+    assert(n==qtb.size());
+    assert(n==x.size());
+
+    /* first, calculate the gauss-newton direction. */
+
+    jj = n * (n + 1) / 2;
+    for (k = 0; k < n; ++k) {
+        j = n - k - 1;
+        jj -= k+1;
+        l = jj + 1;
+        sum = 0.;
+        for (i = j+1; i < n; ++i) {
+            sum += r[l] * x[i];
+            ++l;
+        }
+        temp = r[jj];
+        if (temp == 0.) {
+            l = j;
+            for (i = 0; i <= j; ++i) {
+                /* Computing MAX */
+                temp = std::max(temp,ei_abs(r[l]));
+                l = l + n - i;
+            }
+            temp = epsmch * temp;
+            if (temp == 0.)
+                temp = epsmch;
+        }
+        x[j] = (qtb[j] - sum) / temp;
+    }
+
+    /* test whether the gauss-newton direction is acceptable. */
+
+    wa1.fill(0.);
+    wa2 = diag.cwise() * x;
+    qnorm = wa2.stableNorm();
+    if (qnorm <= delta)
+        return;
+
+    /* the gauss-newton direction is not acceptable. */
+    /* next, calculate the scaled gradient direction. */
+
+    l = 0;
+    for (j = 0; j < n; ++j) {
+        temp = qtb[j];
+        for (i = j; i < n; ++i) {
+            wa1[i] += r[l] * temp;
+            ++l;
+        }
+        wa1[j] /= diag[j];
+    }
+
+    /* calculate the norm of the scaled gradient and test for */
+    /* the special case in which the scaled gradient is zero. */
+
+    gnorm = wa1.stableNorm();
+    sgnorm = 0.;
+    alpha = delta / qnorm;
+    if (gnorm == 0.)
+        goto algo_end;
+
+    /* calculate the point along the scaled gradient */
+    /* at which the quadratic is minimized. */
+
+    wa1.cwise() /= diag*gnorm;
+    l = 0;
+    for (j = 0; j < n; ++j) {
+        sum = 0.;
+        for (i = j; i < n; ++i) {
+            sum += r[l] * wa1[i];
+            ++l;
+            /* L100: */
+        }
+        wa2[j] = sum;
+        /* L110: */
+    }
+    temp = wa2.stableNorm();
+    sgnorm = gnorm / temp / temp;
+
+    /* test whether the scaled gradient direction is acceptable. */
+
+    alpha = 0.;
+    if (sgnorm >= delta)
+        goto algo_end;
+
+    /* the scaled gradient direction is not acceptable. */
+    /* finally, calculate the point along the dogleg */
+    /* at which the quadratic is minimized. */
+
+    bnorm = qtb.stableNorm();
+    temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
+    /* Computing 2nd power */
+    temp = temp - delta / qnorm * ei_abs2(sgnorm / delta) + ei_sqrt(ei_abs2(temp - delta / qnorm) + (1.-ei_abs2(delta / qnorm)) * (1.-ei_abs2(sgnorm / delta)));
+    /* Computing 2nd power */
+    alpha = delta / qnorm * (1. - ei_abs2(sgnorm / delta)) / temp;
+algo_end:
+
+    /* form appropriate convex combination of the gauss-newton */
+    /* direction and the scaled gradient direction. */
+
+    temp = (1.-alpha) * std::min(sgnorm,delta);
+    x = temp * wa1 + alpha * x;
+    return;
+
+}
+