1 files changed, 178 insertions, 0 deletions
diff --git a/gsl-1.9/eigen/qrstep.c b/gsl-1.9/eigen/qrstep.c
new file mode 100644
index 0000000..0394677
--- /dev/null
+++ b/gsl-1.9/eigen/qrstep.c
@@ -0,0 +1,178 @@
+/* remove off-diagonal elements which are neglegible compared with the
+   neighboring diagonal elements */
+
+inline static void
+chop_small_elements (const size_t N, const double d[], double sd[])
+{
+  double d_i = d[0];
+
+  size_t i;
+
+  for (i = 0; i < N - 1; i++)
+    {
+      double sd_i = sd[i];
+      double d_ip1 = d[i + 1];
+
+      if (fabs (sd_i) < GSL_DBL_EPSILON * (fabs (d_i) + fabs (d_ip1)))
+        {
+          sd[i] = 0.0;
+        }
+      d_i = d_ip1;
+    }
+}
+
+/* Generate a Givens rotation (cos,sin) which takes v=(x,y) to (|v|,0) 
+
+   From Golub and Van Loan, "Matrix Computations", Section 5.1.8 */
+
+inline static void
+create_givens (const double a, const double b, double *c, double *s)
+{
+  if (b == 0)
+    {
+      *c = 1;
+      *s = 0;
+    }
+  else if (fabs (b) > fabs (a))
+    {
+      double t = -a / b;
+      double s1 = 1.0 / sqrt (1 + t * t);
+      *s = s1;
+      *c = s1 * t;
+    }
+  else
+    {
+      double t = -b / a;
+      double c1 = 1.0 / sqrt (1 + t * t);
+      *c = c1;
+      *s = c1 * t;
+    }
+}
+
+inline static double
+trailing_eigenvalue (const size_t n, const double d[], const double sd[])
+{
+  double ta = d[n - 2];
+  double tb = d[n - 1];
+  double tab = sd[n - 2];
+
+  double dt = (ta - tb) / 2.0;
+
+  double mu;
+
+  if (dt >= 0)
+    {
+      mu = tb - (tab * tab) / (dt + hypot (dt, tab));
+    }
+  else
+    {
+      mu = tb + (tab * tab) / ((-dt) + hypot (dt, tab));
+    }
+
+  return mu;
+}
+
+static void
+qrstep (const size_t n, double d[], double sd[], double gc[], double gs[])
+{
+  double x, z;
+  double ak, bk, zk, ap, bp, aq, bq;
+  size_t k;
+
+  double mu = trailing_eigenvalue (n, d, sd);
+
+  x = d[0] - mu;
+  z = sd[0];
+
+  ak = 0;
+  bk = 0;
+  zk = 0;
+
+  ap = d[0];
+  bp = sd[0];
+
+  aq = d[1];
+
+  if (n == 2)
+    {
+      double c, s;
+      create_givens (x, z, &c, &s);
+
+      if (gc != NULL)
+        gc[0] = c; 
+      if (gs != NULL)
+        gs[0] = s;
+
+      {
+        double ap1 = c * (c * ap - s * bp) + s * (s * aq - c * bp);
+        double bp1 = c * (s * ap + c * bp) - s * (s * bp + c * aq);
+
+        double aq1 = s * (s * ap + c * bp) + c * (s * bp + c * aq);
+
+        ak = ap1;
+        bk = bp1;
+
+        ap = aq1;
+      }
+
+      d[0] = ak;
+      sd[0] = bk;
+      d[1] = ap;
+
+      return;
+    }
+
+  bq = sd[1];
+
+  for (k = 0; k < n - 1; k++)
+    {
+      double c, s;
+      create_givens (x, z, &c, &s);
+
+      /* store Givens rotation */
+      if (gc != NULL)
+        gc[k] = c; 
+      if (gs != NULL)
+        gs[k] = s;
+
+      /* compute G' T G */
+
+      {
+        double bk1 = c * bk - s * zk;
+
+        double ap1 = c * (c * ap - s * bp) + s * (s * aq - c * bp);
+        double bp1 = c * (s * ap + c * bp) - s * (s * bp + c * aq);
+        double zp1 = -s * bq;
+
+        double aq1 = s * (s * ap + c * bp) + c * (s * bp + c * aq);
+        double bq1 = c * bq;
+
+        ak = ap1;
+        bk = bp1;
+        zk = zp1;
+
+        ap = aq1;
+        bp = bq1;
+
+        if (k < n - 2)
+          aq = d[k + 2];
+        if (k < n - 3)
+          bq = sd[k + 2];
+
+        d[k] = ak;
+
+        if (k > 0)
+          sd[k - 1] = bk1;
+
+        if (k < n - 2)
+          sd[k + 1] = bp;
+
+        x = bk;
+        z = zk;
+      }
+    }
+
+  /* k = n - 1 */
+  d[k] = ap;
+  sd[k - 1] = bk;
+}