/** ======================================================================* NIST Guide to Available Math Software.* Fullsource for module SSYEVX.C from package CLAPACK.* Retrieved from NETLIB on Fri Mar 10 14:23:44 2000.* ======================================================================*/#include <f2c.h>/* Subroutine */ int slae2_(real *a, real *b, real *c, real *rt1, real *rt2){/*  -- LAPACK auxiliary routine (version 2.0) --          Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,          Courant Institute, Argonne National Lab, and Rice University          October 31, 1992       Purpose       =======       SLAE2  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) REAL               The (1,1) element of the 2-by-2 matrix.       B       (input) REAL               The (1,2) and (2,1) elements 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.       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.      =====================================================================          Compute the eigenvalues */    /* System generated locals */    real r__1;    /* Builtin functions */    double sqrt(doublereal);    /* Local variables */    static real acmn, acmx, ab, df, tb, sm, rt, adf;    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;/*        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;/*        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;    }    return 0;/*     End of SLAE2 */} /* slae2_ */