--- /dev/null
+#include "clapack.h"
+
+/* Subroutine */ int slaev2_(real *a, real *b, real *c__, real *rt1, real *
+ rt2, real *cs1, real *sn1)
+{
+ /* System generated locals */
+ real r__1;
+
+ /* Builtin functions */
+ double sqrt(doublereal);
+
+ /* Local variables */
+ real ab, df, cs, ct, tb, sm, tn, rt, adf, acs;
+ integer sgn1, sgn2;
+ real acmn, acmx;
+
+
+/* -- LAPACK auxiliary routine (version 3.1) -- */
+/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/* November 2006 */
+
+/* .. Scalar Arguments .. */
+/* .. */
+
+/* Purpose */
+/* ======= */
+
+/* SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix */
+/* [ A B ] */
+/* [ B C ]. */
+/* On return, RT1 is the eigenvalue of larger absolute value, RT2 is the */
+/* eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right */
+/* eigenvector for RT1, giving the decomposition */
+
+/* [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] */
+/* [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. */
+
+/* Arguments */
+/* ========= */
+
+/* A (input) REAL */
+/* The (1,1) element of the 2-by-2 matrix. */
+
+/* B (input) REAL */
+/* The (1,2) element and the conjugate of the (2,1) element of */
+/* the 2-by-2 matrix. */
+
+/* C (input) REAL */
+/* The (2,2) element of the 2-by-2 matrix. */
+
+/* RT1 (output) REAL */
+/* The eigenvalue of larger absolute value. */
+
+/* RT2 (output) REAL */
+/* The eigenvalue of smaller absolute value. */
+
+/* CS1 (output) REAL */
+/* SN1 (output) REAL */
+/* The vector (CS1, SN1) is a unit right eigenvector for RT1. */
+
+/* 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. */
+
+/* CS1 and SN1 are accurate to a few ulps barring over/underflow. */
+
+/* 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 = dabs(df);
+ tb = *b + *b;
+ ab = dabs(tb);
+ if (dabs(*a) > dabs(*c__)) {
+ acmx = *a;
+ acmn = *c__;
+ } else {
+ acmx = *c__;
+ acmn = *a;
+ }
+ if (adf > ab) {
+/* Computing 2nd power */
+ r__1 = ab / adf;
+ rt = adf * sqrt(r__1 * r__1 + 1.f);
+ } else if (adf < ab) {
+/* Computing 2nd power */
+ r__1 = adf / ab;
+ rt = ab * sqrt(r__1 * r__1 + 1.f);
+ } else {
+
+/* Includes case AB=ADF=0 */
+
+ rt = ab * sqrt(2.f);
+ }
+ if (sm < 0.f) {
+ *rt1 = (sm - rt) * .5f;
+ sgn1 = -1;
+
+/* 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.f) {
+ *rt1 = (sm + rt) * .5f;
+ sgn1 = 1;
+
+/* 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 * .5f;
+ *rt2 = rt * -.5f;
+ sgn1 = 1;
+ }
+
+/* Compute the eigenvector */
+
+ if (df >= 0.f) {
+ cs = df + rt;
+ sgn2 = 1;
+ } else {
+ cs = df - rt;
+ sgn2 = -1;
+ }
+ acs = dabs(cs);
+ if (acs > ab) {
+ ct = -tb / cs;
+ *sn1 = 1.f / sqrt(ct * ct + 1.f);
+ *cs1 = ct * *sn1;
+ } else {
+ if (ab == 0.f) {
+ *cs1 = 1.f;
+ *sn1 = 0.f;
+ } else {
+ tn = -cs / tb;
+ *cs1 = 1.f / sqrt(tn * tn + 1.f);
+ *sn1 = tn * *cs1;
+ }
+ }
+ if (sgn1 == sgn2) {
+ tn = *cs1;
+ *cs1 = -(*sn1);
+ *sn1 = tn;
+ }
+ return 0;
+
+/* End of SLAEV2 */
+
+} /* slaev2_ */