/* ctgex2.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"

/* Table of constant values */

static integer c__2 = 2;
static integer c__1 = 1;

/* Subroutine */ int ctgex2_(logical *wantq, logical *wantz, integer *n, 
	complex *a, integer *lda, complex *b, integer *ldb, complex *q, 
	integer *ldq, complex *z__, integer *ldz, integer *j1, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, 
	    z_offset, i__1, i__2, i__3;
    real r__1;
    complex q__1, q__2, q__3;

    /* Builtin functions */
    double sqrt(doublereal), c_abs(complex *);
    void r_cnjg(complex *, complex *);

    /* Local variables */
    complex f, g;
    integer i__, m;
    complex s[4]	/* was [2][2] */, t[4]	/* was [2][2] */;
    real cq, sa, sb, cz;
    complex sq;
    real ss, ws;
    complex sz;
    real eps, sum;
    logical weak;
    complex cdum;
    extern /* Subroutine */ int crot_(integer *, complex *, integer *, 
	    complex *, integer *, real *, complex *);
    complex work[8];
    real scale;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), clartg_(complex *, 
	    complex *, real *, complex *, complex *), classq_(integer *, 
	    complex *, integer *, real *, real *);
    real thresh, smlnum;
    logical strong;


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

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

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

/*  CTGEX2 swaps adjacent diagonal 1 by 1 blocks (A11,B11) and (A22,B22) */
/*  in an upper triangular matrix pair (A, B) by an unitary equivalence */
/*  transformation. */

/*  (A, B) must be in generalized Schur canonical form, that is, A and */
/*  B are both upper triangular. */

/*  Optionally, the matrices Q and Z of generalized Schur vectors are */
/*  updated. */

/*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' */
/*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' */


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

/*  WANTQ   (input) LOGICAL */
/*          .TRUE. : update the left transformation matrix Q; */
/*          .FALSE.: do not update Q. */

/*  WANTZ   (input) LOGICAL */
/*          .TRUE. : update the right transformation matrix Z; */
/*          .FALSE.: do not update Z. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B. N >= 0. */

/*  A       (input/output) COMPLEX arrays, dimensions (LDA,N) */
/*          On entry, the matrix A in the pair (A, B). */
/*          On exit, the updated matrix A. */

/*  LDA     (input)  INTEGER */
/*          The leading dimension of the array A. LDA >= max(1,N). */

/*  B       (input/output) COMPLEX arrays, dimensions (LDB,N) */
/*          On entry, the matrix B in the pair (A, B). */
/*          On exit, the updated matrix B. */

/*  LDB     (input)  INTEGER */
/*          The leading dimension of the array B. LDB >= max(1,N). */

/*  Q       (input/output) COMPLEX array, dimension (LDZ,N) */
/*          If WANTQ = .TRUE, on entry, the unitary matrix Q. On exit, */
/*          the updated matrix Q. */
/*          Not referenced if WANTQ = .FALSE.. */

/*  LDQ     (input) INTEGER */
/*          The leading dimension of the array Q. LDQ >= 1; */
/*          If WANTQ = .TRUE., LDQ >= N. */

/*  Z       (input/output) COMPLEX array, dimension (LDZ,N) */
/*          If WANTZ = .TRUE, on entry, the unitary matrix Z. On exit, */
/*          the updated matrix Z. */
/*          Not referenced if WANTZ = .FALSE.. */

/*  LDZ     (input) INTEGER */
/*          The leading dimension of the array Z. LDZ >= 1; */
/*          If WANTZ = .TRUE., LDZ >= N. */

/*  J1      (input) INTEGER */
/*          The index to the first block (A11, B11). */

/*  INFO    (output) INTEGER */
/*           =0:  Successful exit. */
/*           =1:  The transformed matrix pair (A, B) would be too far */
/*                from generalized Schur form; the problem is ill- */
/*                conditioned. */


/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

/*  In the current code both weak and strong stability tests are */
/*  performed. The user can omit the strong stability test by changing */
/*  the internal logical parameter WANDS to .FALSE.. See ref. [2] for */
/*  details. */

/*  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/*      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/*      M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/*      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */

/*  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/*      Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/*      Estimation: Theory, Algorithms and Software, Report UMINF-94.04, */
/*      Department of Computing Science, Umea University, S-901 87 Umea, */
/*      Sweden, 1994. Also as LAPACK Working Note 87. To appear in */
/*      Numerical Algorithms, 1996. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

    if (*n <= 1) {
	return 0;
    }

    m = 2;
    weak = FALSE_;
    strong = FALSE_;

/*     Make a local copy of selected block in (A, B) */

    clacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__2);
    clacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__2);

/*     Compute the threshold for testing the acceptance of swapping. */

    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    scale = 0.f;
    sum = 1.f;
    clacpy_("Full", &m, &m, s, &c__2, work, &m);
    clacpy_("Full", &m, &m, t, &c__2, &work[m * m], &m);
    i__1 = (m << 1) * m;
    classq_(&i__1, work, &c__1, &scale, &sum);
    sa = scale * sqrt(sum);
/* Computing MAX */
    r__1 = eps * 10.f * sa;
    thresh = dmax(r__1,smlnum);

/*     Compute unitary QL and RQ that swap 1-by-1 and 1-by-1 blocks */
/*     using Givens rotations and perform the swap tentatively. */

    q__2.r = s[3].r * t[0].r - s[3].i * t[0].i, q__2.i = s[3].r * t[0].i + s[
	    3].i * t[0].r;
    q__3.r = t[3].r * s[0].r - t[3].i * s[0].i, q__3.i = t[3].r * s[0].i + t[
	    3].i * s[0].r;
    q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
    f.r = q__1.r, f.i = q__1.i;
    q__2.r = s[3].r * t[2].r - s[3].i * t[2].i, q__2.i = s[3].r * t[2].i + s[
	    3].i * t[2].r;
    q__3.r = t[3].r * s[2].r - t[3].i * s[2].i, q__3.i = t[3].r * s[2].i + t[
	    3].i * s[2].r;
    q__1.r = q__2.r - q__3.r, q__1.i = q__2.i - q__3.i;
    g.r = q__1.r, g.i = q__1.i;
    sa = c_abs(&s[3]);
    sb = c_abs(&t[3]);
    clartg_(&g, &f, &cz, &sz, &cdum);
    q__1.r = -sz.r, q__1.i = -sz.i;
    sz.r = q__1.r, sz.i = q__1.i;
    r_cnjg(&q__1, &sz);
    crot_(&c__2, s, &c__1, &s[2], &c__1, &cz, &q__1);
    r_cnjg(&q__1, &sz);
    crot_(&c__2, t, &c__1, &t[2], &c__1, &cz, &q__1);
    if (sa >= sb) {
	clartg_(s, &s[1], &cq, &sq, &cdum);
    } else {
	clartg_(t, &t[1], &cq, &sq, &cdum);
    }
    crot_(&c__2, s, &c__2, &s[1], &c__2, &cq, &sq);
    crot_(&c__2, t, &c__2, &t[1], &c__2, &cq, &sq);

/*     Weak stability test: |S21| + |T21| <= O(EPS F-norm((S, T))) */

    ws = c_abs(&s[1]) + c_abs(&t[1]);
    weak = ws <= thresh;
    if (! weak) {
	goto L20;
    }

    if (TRUE_) {

/*        Strong stability test: */
/*           F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A, B))) */

	clacpy_("Full", &m, &m, s, &c__2, work, &m);
	clacpy_("Full", &m, &m, t, &c__2, &work[m * m], &m);
	r_cnjg(&q__2, &sz);
	q__1.r = -q__2.r, q__1.i = -q__2.i;
	crot_(&c__2, work, &c__1, &work[2], &c__1, &cz, &q__1);
	r_cnjg(&q__2, &sz);
	q__1.r = -q__2.r, q__1.i = -q__2.i;
	crot_(&c__2, &work[4], &c__1, &work[6], &c__1, &cz, &q__1);
	q__1.r = -sq.r, q__1.i = -sq.i;
	crot_(&c__2, work, &c__2, &work[1], &c__2, &cq, &q__1);
	q__1.r = -sq.r, q__1.i = -sq.i;
	crot_(&c__2, &work[4], &c__2, &work[5], &c__2, &cq, &q__1);
	for (i__ = 1; i__ <= 2; ++i__) {
	    i__1 = i__ - 1;
	    i__2 = i__ - 1;
	    i__3 = *j1 + i__ - 1 + *j1 * a_dim1;
	    q__1.r = work[i__2].r - a[i__3].r, q__1.i = work[i__2].i - a[i__3]
		    .i;
	    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
	    i__1 = i__ + 1;
	    i__2 = i__ + 1;
	    i__3 = *j1 + i__ - 1 + (*j1 + 1) * a_dim1;
	    q__1.r = work[i__2].r - a[i__3].r, q__1.i = work[i__2].i - a[i__3]
		    .i;
	    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
	    i__1 = i__ + 3;
	    i__2 = i__ + 3;
	    i__3 = *j1 + i__ - 1 + *j1 * b_dim1;
	    q__1.r = work[i__2].r - b[i__3].r, q__1.i = work[i__2].i - b[i__3]
		    .i;
	    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
	    i__1 = i__ + 5;
	    i__2 = i__ + 5;
	    i__3 = *j1 + i__ - 1 + (*j1 + 1) * b_dim1;
	    q__1.r = work[i__2].r - b[i__3].r, q__1.i = work[i__2].i - b[i__3]
		    .i;
	    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
/* L10: */
	}
	scale = 0.f;
	sum = 1.f;
	i__1 = (m << 1) * m;
	classq_(&i__1, work, &c__1, &scale, &sum);
	ss = scale * sqrt(sum);
	strong = ss <= thresh;
	if (! strong) {
	    goto L20;
	}
    }

/*     If the swap is accepted ("weakly" and "strongly"), apply the */
/*     equivalence transformations to the original matrix pair (A,B) */

    i__1 = *j1 + 1;
    r_cnjg(&q__1, &sz);
    crot_(&i__1, &a[*j1 * a_dim1 + 1], &c__1, &a[(*j1 + 1) * a_dim1 + 1], &
	    c__1, &cz, &q__1);
    i__1 = *j1 + 1;
    r_cnjg(&q__1, &sz);
    crot_(&i__1, &b[*j1 * b_dim1 + 1], &c__1, &b[(*j1 + 1) * b_dim1 + 1], &
	    c__1, &cz, &q__1);
    i__1 = *n - *j1 + 1;
    crot_(&i__1, &a[*j1 + *j1 * a_dim1], lda, &a[*j1 + 1 + *j1 * a_dim1], lda, 
	     &cq, &sq);
    i__1 = *n - *j1 + 1;
    crot_(&i__1, &b[*j1 + *j1 * b_dim1], ldb, &b[*j1 + 1 + *j1 * b_dim1], ldb, 
	     &cq, &sq);

/*     Set  N1 by N2 (2,1) blocks to 0 */

    i__1 = *j1 + 1 + *j1 * a_dim1;
    a[i__1].r = 0.f, a[i__1].i = 0.f;
    i__1 = *j1 + 1 + *j1 * b_dim1;
    b[i__1].r = 0.f, b[i__1].i = 0.f;

/*     Accumulate transformations into Q and Z if requested. */

    if (*wantz) {
	r_cnjg(&q__1, &sz);
	crot_(n, &z__[*j1 * z_dim1 + 1], &c__1, &z__[(*j1 + 1) * z_dim1 + 1], 
		&c__1, &cz, &q__1);
    }
    if (*wantq) {
	r_cnjg(&q__1, &sq);
	crot_(n, &q[*j1 * q_dim1 + 1], &c__1, &q[(*j1 + 1) * q_dim1 + 1], &
		c__1, &cq, &q__1);
    }

/*     Exit with INFO = 0 if swap was successfully performed. */

    return 0;

/*     Exit with INFO = 1 if swap was rejected. */

L20:
    *info = 1;
    return 0;

/*     End of CTGEX2 */

} /* ctgex2_ */