From 71a3e96b49f7f770df9e44909e14379a9a75f2a1 Mon Sep 17 00:00:00 2001
From: Thomas Capricelli <orzel@freehackers.org>
Date: Mon, 9 Nov 2009 03:27:15 +0100
Subject: rename NonLinear to NonLinearOptimization

---
 .../Eigen/src/NonLinearOptimization/r1updt.h       | 175 +++++++++++++++++++++
 1 file changed, 175 insertions(+)
 create mode 100644 unsupported/Eigen/src/NonLinearOptimization/r1updt.h

(limited to 'unsupported/Eigen/src/NonLinearOptimization/r1updt.h')

diff --git a/unsupported/Eigen/src/NonLinearOptimization/r1updt.h b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
new file mode 100644
index 000000000..f2ddb189b
--- /dev/null
+++ b/unsupported/Eigen/src/NonLinearOptimization/r1updt.h
@@ -0,0 +1,175 @@
+
+    template <typename Scalar>
+void ei_r1updt(int m, int n, Scalar *s, int /* ls */, const Scalar *u, Scalar *v, Scalar *w, bool *sing)
+{
+    /* Local variables */
+    int i, j, l, jj, nm1;
+    Scalar tan__;
+    int nmj;
+    Scalar cos__, sin__, tau, temp, cotan;
+
+    /* Parameter adjustments */
+    --w;
+    --u;
+    --v;
+    --s;
+
+    /* Function Body */
+    const Scalar giant = std::numeric_limits<Scalar>::max();
+
+    /*     initialize the diagonal element pointer. */
+
+    jj = n * ((m << 1) - n + 1) / 2 - (m - n);
+
+    /*     move the nontrivial part of the last column of s into w. */
+
+    l = jj;
+    for (i = n; i <= m; ++i) {
+        w[i] = s[l];
+        ++l;
+        /* L10: */
+    }
+
+    /*     rotate the vector v into a multiple of the n-th unit vector */
+    /*     in such a way that a spike is introduced into w. */
+
+    nm1 = n - 1;
+    if (nm1 < 1) {
+        goto L70;
+    }
+    for (nmj = 1; nmj <= nm1; ++nmj) {
+        j = n - nmj;
+        jj -= m - j + 1;
+        w[j] = 0.;
+        if (v[j] == 0.) {
+            goto L50;
+        }
+
+        /*        determine a givens rotation which eliminates the */
+        /*        j-th element of v. */
+
+        if (ei_abs(v[n]) >= ei_abs(v[j]))
+            goto L20;
+        cotan = v[n] / v[j];
+        /* Computing 2nd power */
+        sin__ = Scalar(.5) / ei_sqrt(Scalar(0.25) + Scalar(0.25) * ei_abs2(cotan));
+        cos__ = sin__ * cotan;
+        tau = 1.;
+        if (ei_abs(cos__) * giant > 1.) {
+            tau = 1. / cos__;
+        }
+        goto L30;
+L20:
+        tan__ = v[j] / v[n];
+        /* Computing 2nd power */
+        cos__ = Scalar(.5) / ei_sqrt(Scalar(0.25) + Scalar(0.25) * ei_abs2(tan__));
+        sin__ = cos__ * tan__;
+        tau = sin__;
+L30:
+
+        /*        apply the transformation to v and store the information */
+        /*        necessary to recover the givens rotation. */
+
+        v[n] = sin__ * v[j] + cos__ * v[n];
+        v[j] = tau;
+
+        /*        apply the transformation to s and extend the spike in w. */
+
+        l = jj;
+        for (i = j; i <= m; ++i) {
+            temp = cos__ * s[l] - sin__ * w[i];
+            w[i] = sin__ * s[l] + cos__ * w[i];
+            s[l] = temp;
+            ++l;
+            /* L40: */
+        }
+L50:
+        /* L60: */
+        ;
+    }
+L70:
+
+    /*     add the spike from the rank 1 update to w. */
+
+    for (i = 1; i <= m; ++i) {
+        w[i] += v[n] * u[i];
+        /* L80: */
+    }
+
+    /*     eliminate the spike. */
+
+    *sing = false;
+    if (nm1 < 1) {
+        goto L140;
+    }
+    for (j = 1; j <= nm1; ++j) {
+        if (w[j] == 0.) {
+            goto L120;
+        }
+
+        /*        determine a givens rotation which eliminates the */
+        /*        j-th element of the spike. */
+
+        if (ei_abs(s[jj]) >= ei_abs(w[j]))
+            goto L90;
+        cotan = s[jj] / w[j];
+        /* Computing 2nd power */
+        sin__ = Scalar(.5) / ei_sqrt(Scalar(0.25) + Scalar(0.25) * ei_abs2(cotan));
+        cos__ = sin__ * cotan;
+        tau = 1.;
+        if (ei_abs(cos__) * giant > 1.) {
+            tau = 1. / cos__;
+        }
+        goto L100;
+L90:
+        tan__ = w[j] / s[jj];
+        /* Computing 2nd power */
+        cos__ = Scalar(.5) / ei_sqrt(Scalar(0.25) + Scalar(0.25) * ei_abs2(tan__));
+        sin__ = cos__ * tan__;
+        tau = sin__;
+L100:
+
+        /*        apply the transformation to s and reduce the spike in w. */
+
+        l = jj;
+        for (i = j; i <= m; ++i) {
+            temp = cos__ * s[l] + sin__ * w[i];
+            w[i] = -sin__ * s[l] + cos__ * w[i];
+            s[l] = temp;
+            ++l;
+            /* L110: */
+        }
+
+        /*        store the information necessary to recover the */
+        /*        givens rotation. */
+
+        w[j] = tau;
+L120:
+
+        /*        test for zero diagonal elements in the output s. */
+
+        if (s[jj] == 0.) {
+            *sing = true;
+        }
+        jj += m - j + 1;
+        /* L130: */
+    }
+L140:
+
+    /*     move w back into the last column of the output s. */
+
+    l = jj;
+    for (i = n; i <= m; ++i) {
+        s[l] = w[i];
+        ++l;
+        /* L150: */
+    }
+    if (s[jj] == 0.) {
+        *sing = true;
+    }
+    return;
+
+    /*     last card of subroutine r1updt. */
+
+} /* r1updt_ */
+
-- 
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