dtgex2.c

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/* lapack/double/dtgex2.f -- translated by f2c (version 20050501).
   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
*/

#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"

/* Table of constant values */

static integer c__16 = 16;
static doublereal c_b3 = 0.;
static integer c__0 = 0;
static integer c__1 = 1;
static integer c__4 = 4;
static integer c__2 = 2;
static doublereal c_b38 = 1.;
static doublereal c_b44 = -1.;

/*<    >*/
/* Subroutine */ int dtgex2_(logical *wantq, logical *wantz, integer *n, 
        doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
        q, integer *ldq, doublereal *z__, integer *ldz, integer *j1, integer *
        n1, integer *n2, doublereal *work, integer *lwork, 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;
    doublereal d__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    doublereal f, g;
    integer i__, m;
    doublereal s[16]    /* was [4][4] */, t[16] /* was [4][4] */, be[2], ai[2]
            , ar[2], sa, sb, li[16]     /* was [4][4] */, ir[16]        /* 
            was [4][4] */, ss, ws, eps;
    logical weak;
    doublereal ddum;
    integer idum;
    doublereal taul[4], dsum;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *);
    doublereal taur[4], scpy[16]        /* was [4][4] */, tcpy[16]      /* 
            was [4][4] */;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
            integer *);
    doublereal scale, bqra21, brqa21;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen);
    doublereal licop[16]        /* was [4][4] */;
    integer linfo;
    doublereal ircop[16]        /* was [4][4] */;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    doublereal dnorm;
    integer iwork[4];
    extern /* Subroutine */ int dlagv2_(doublereal *, integer *, doublereal *,
             integer *, doublereal *, doublereal *, doublereal *, doublereal *
            , doublereal *, doublereal *, doublereal *), dgeqr2_(integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *), dgerq2_(integer *, integer *, doublereal *, integer *,
             doublereal *, doublereal *, integer *), dorg2r_(integer *, 
            integer *, integer *, doublereal *, integer *, doublereal *, 
            doublereal *, integer *), dorgr2_(integer *, integer *, integer *,
             doublereal *, integer *, doublereal *, doublereal *, integer *), 
            dorm2r_(char *, char *, integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *, ftnlen, ftnlen), dormr2_(char *, char *, 
            integer *, integer *, integer *, doublereal *, integer *, 
            doublereal *, doublereal *, integer *, doublereal *, integer *, 
            ftnlen, ftnlen), dtgsy2_(char *, integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, doublereal *,
             integer *, integer *, integer *, ftnlen);
    extern doublereal dlamch_(char *, ftnlen);
    doublereal dscale;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *, ftnlen), 
            dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *), dlassq_(integer *, doublereal *, integer *, 
            doublereal *, doublereal *);
    logical dtrong;
    doublereal thresh, smlnum;


/*  -- LAPACK auxiliary routine (version 3.0) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/*     Courant Institute, Argonne National Lab, and Rice University */
/*     June 30, 1999 */

/*     .. Scalar Arguments .. */
/*<       LOGICAL            WANTQ, WANTZ >*/
/*<       INTEGER            INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2 >*/
/*     .. */
/*     .. Array Arguments .. */
/*<    >*/
/*     .. */

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

/*  DTGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) */
/*  of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair */
/*  (A, B) by an orthogonal equivalence transformation. */

/*  (A, B) must be in generalized real Schur canonical form (as returned */
/*  by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 */
/*  diagonal blocks. B is 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDZ,N) */
/*          On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N) */
/*          On entry, if WANTZ =.TRUE., the orthogonal 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). 1 <= J1 <= N. */

/*  N1      (input) INTEGER */
/*          The order of the first block (A11, B11). N1 = 0, 1 or 2. */

/*  N2      (input) INTEGER */
/*          The order of the second block (A22, B22). N2 = 0, 1 or 2. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK). */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. */
/*          LWORK >=  MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 ) */

/*  INFO    (output) INTEGER */
/*            =0: Successful exit */
/*            >0: If INFO = 1, the transformed matrix (A, B) would be */
/*                too far from generalized Schur form; the blocks are */
/*                not swapped and (A, B) and (Q, Z) are unchanged. */
/*                The problem of swapping is too ill-conditioned. */
/*            <0: If INFO = -16: LWORK is too small. Appropriate value */
/*                for LWORK is returned in WORK(1). */

/*  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 .. */
/*<       DOUBLE PRECISION   ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/*<       DOUBLE PRECISION   TEN >*/
/*<       PARAMETER          ( TEN = 1.0D+01 ) >*/
/*<       INTEGER            LDST >*/
/*<       PARAMETER          ( LDST = 4 ) >*/
/*<       LOGICAL            WANDS >*/
/*<       PARAMETER          ( WANDS = .TRUE. ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<       LOGICAL            DTRONG, WEAK >*/
/*<       INTEGER            I, IDUM, LINFO, M >*/
/*<    >*/
/*     .. */
/*     .. Local Arrays .. */
/*<       INTEGER            IWORK( LDST ) >*/
/*<    >*/
/*     .. */
/*     .. External Functions .. */
/*<       DOUBLE PRECISION   DLAMCH >*/
/*<       EXTERNAL           DLAMCH >*/
/*     .. */
/*     .. External Subroutines .. */
/*<    >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          ABS, MAX, SQRT >*/
/*     .. */
/*     .. Executable Statements .. */

/*<       INFO = 0 >*/
    /* 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;
    --work;

    /* Function Body */
    *info = 0;

/*     Quick return if possible */

/*<    >*/
    if (*n <= 1 || *n1 <= 0 || *n2 <= 0) {
        return 0;
    }
/*<    >*/
    if (*n1 > *n || *j1 + *n1 > *n) {
        return 0;
    }
/*<       M = N1 + N2 >*/
    m = *n1 + *n2;
/*<       IF( LWORK.LT.MAX( N*M, M*M*2 ) ) THEN >*/
/* Computing MAX */
    i__1 = *n * m, i__2 = m * m << 1;
    if (*lwork < max(i__1,i__2)) {
/*<          INFO = -16 >*/
        *info = -16;
/*<          WORK( 1 ) = MAX( N*M, M*M*2 ) >*/
/* Computing MAX */
        i__1 = *n * m, i__2 = m * m << 1;
        work[1] = (doublereal) max(i__1,i__2);
/*<          RETURN >*/
        return 0;
/*<       END IF >*/
    }

/*<       WEAK = .FALSE. >*/
    weak = FALSE_;
/*<       DTRONG = .FALSE. >*/
    dtrong = FALSE_;

/*     Make a local copy of selected block */

/*<       CALL DCOPY( LDST*LDST, ZERO, 0, LI, 1 ) >*/
    dcopy_(&c__16, &c_b3, &c__0, li, &c__1);
/*<       CALL DCOPY( LDST*LDST, ZERO, 0, IR, 1 ) >*/
    dcopy_(&c__16, &c_b3, &c__0, ir, &c__1);
/*<       CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, S, LDST ) >*/
    dlacpy_("Full", &m, &m, &a[*j1 + *j1 * a_dim1], lda, s, &c__4, (ftnlen)4);
/*<       CALL DLACPY( 'Full', M, M, B( J1, J1 ), LDB, T, LDST ) >*/
    dlacpy_("Full", &m, &m, &b[*j1 + *j1 * b_dim1], ldb, t, &c__4, (ftnlen)4);

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

/*<       EPS = DLAMCH( 'P' ) >*/