--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int dlae2_(doublereal *a, doublereal *b, doublereal *c__,
+ doublereal *rt1, doublereal *rt2)
+{
+ /* System generated locals */
+ doublereal d__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ doublereal ab, df, tb, sm, rt, adf, acmn, acmx;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix */
+/* [ A B ] */
+/* [ B C ]. */
+/* On return, RT1 is the eigenvalue of larger absolute value, and RT2 */
+/* is the eigenvalue of smaller absolute value. */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) DOUBLE PRECISION */
+/* The (1,1) element of the 2-by-2 matrix. */
+
+/* B (input) DOUBLE PRECISION */
+/* The (1,2) and (2,1) elements of the 2-by-2 matrix. */
+
+/* C (input) DOUBLE PRECISION */
+/* The (2,2) element of the 2-by-2 matrix. */
+
+/* RT1 (output) DOUBLE PRECISION */
+/* The eigenvalue of larger absolute value. */
+
+/* RT2 (output) DOUBLE PRECISION */
+/* The eigenvalue of smaller absolute value. */
+
+/* Further Details */
+/* =============== */
+
+/* RT1 is accurate to a few ulps barring over/underflow. */
+
+/* RT2 may be inaccurate if there is massive cancellation in the */
+/* determinant A*C-B*B; higher precision or correctly rounded or */
+/* correctly truncated arithmetic would be needed to compute RT2 */
+/* accurately in all cases. */
+
+/* Overflow is possible only if RT1 is within a factor of 5 of overflow. */
+/* Underflow is harmless if the input data is 0 or exceeds */
+/* underflow_threshold / macheps. */
+
+/* ===================================================================== */
+
+/* .. Parameters .. */
+/* .. */
+/* .. Local Scalars .. */
+/* .. */
+/* .. Intrinsic Functions .. */
+/* .. */
+/* .. Executable Statements .. */
+
+/* Compute the eigenvalues */
+
+ sm = *a + *c__;
+ df = *a - *c__;
+ adf = abs(df);
+ tb = *b + *b;
+ ab = abs(tb);
+ if (abs(*a) > abs(*c__)) {
+ acmx = *a;
+ acmn = *c__;
+ } else {
+ acmx = *c__;
+ acmn = *a;
+ }
+ if (adf > ab) {
+/* Computing 2nd power */
+ d__1 = ab / adf;
+ rt = adf * sqrt(d__1 * d__1 + 1.);
+ } else if (adf < ab) {
+/* Computing 2nd power */
+ d__1 = adf / ab;
+ rt = ab * sqrt(d__1 * d__1 + 1.);
+ } else {
+
+/* Includes case AB=ADF=0 */
+
+ rt = ab * sqrt(2.);
+ }
+ if (sm < 0.) {
+ *rt1 = (sm - rt) * .5;
+
+/* Order of execution important. */
+/* To get fully accurate smaller eigenvalue, */
+/* next line needs to be executed in higher precision. */
+
+ *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
+ } else if (sm > 0.) {
+ *rt1 = (sm + rt) * .5;
+
+/* Order of execution important. */
+/* To get fully accurate smaller eigenvalue, */
+/* next line needs to be executed in higher precision. */
+
+ *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
+ } else {
+
+/* Includes case RT1 = RT2 = 0 */
+
+ *rt1 = rt * .5;
+ *rt2 = rt * -.5;
+ }
+ return 0;
+
+/* End of DLAE2 */
+
+} /* dlae2_ */