slaev2.c

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/* slaev2.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.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 3.2) -- */
/*     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_ */