zlaev2.c

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/* zlaev2.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 zlaev2_(doublecomplex *a, doublecomplex *b, 
        doublecomplex *c__, doublereal *rt1, doublereal *rt2, doublereal *cs1, 
         doublecomplex *sn1)
{
    /* System generated locals */
    doublereal d__1, d__2, d__3;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double z_abs(doublecomplex *);
    void d_cnjg(doublecomplex *, doublecomplex *);

    /* Local variables */
    doublereal t;
    doublecomplex w;
    extern /* Subroutine */ int dlaev2_(doublereal *, doublereal *, 
            doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZLAEV2 computes the eigendecomposition of a 2-by-2 Hermitian matrix */
/*     [  A         B  ] */
/*     [  CONJG(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  CONJG(SN1) ] [    A     B ] [ CS1 -CONJG(SN1) ] = [ RT1  0  ] */
/*  [-SN1     CS1     ] [ CONJG(B) C ] [ SN1     CS1     ]   [  0  RT2 ]. */

/*  Arguments */
/*  ========= */

/*  A      (input) COMPLEX*16 */
/*         The (1,1) element of the 2-by-2 matrix. */

/*  B      (input) COMPLEX*16 */
/*         The (1,2) element and the conjugate of the (2,1) element of */
/*         the 2-by-2 matrix. */

/*  C      (input) COMPLEX*16 */
/*         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. */

/*  CS1    (output) DOUBLE PRECISION */
/*  SN1    (output) COMPLEX*16 */
/*         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 .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    if (z_abs(b) == 0.) {
        w.r = 1., w.i = 0.;
    } else {
        d_cnjg(&z__2, b);
        d__1 = z_abs(b);
        z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
        w.r = z__1.r, w.i = z__1.i;
    }
    d__1 = a->r;
    d__2 = z_abs(b);
    d__3 = c__->r;
    dlaev2_(&d__1, &d__2, &d__3, rt1, rt2, cs1, &t);
    z__1.r = t * w.r, z__1.i = t * w.i;
    sn1->r = z__1.r, sn1->i = z__1.i;
    return 0;

/*     End of ZLAEV2 */

} /* zlaev2_ */