dlagv2.c

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/* lapack/double/dlagv2.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__2 = 2;
static integer c__1 = 1;

/*<    >*/
/* Subroutine */ int dlagv2_(doublereal *a, integer *lda, doublereal *b, 
        integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
        beta, doublereal *csl, doublereal *snl, doublereal *csr, doublereal *
        snr)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset;
    doublereal d__1, d__2, d__3, d__4, d__5, d__6;

    /* Local variables */
    doublereal r__, t, h1, h2, h3, wi, qq, rr, wr1, wr2, ulp;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *), dlag2_(
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *);
    doublereal anorm, bnorm, scale1, scale2;
    extern /* Subroutine */ int dlasv2_(doublereal *, doublereal *, 
            doublereal *, doublereal *, doublereal *, doublereal *, 
            doublereal *, doublereal *, doublereal *);
    extern doublereal dlapy2_(doublereal *, doublereal *);
    doublereal ascale, bscale;
    extern doublereal dlamch_(char *, ftnlen);
    doublereal safmin;
    extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, 
            doublereal *, doublereal *, doublereal *);


/*  -- 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 .. */
/*<       INTEGER            LDA, LDB >*/
/*<       DOUBLE PRECISION   CSL, CSR, SNL, SNR >*/
/*     .. */
/*     .. Array Arguments .. */
/*<    >*/
/*     .. */

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

/*  DLAGV2 computes the Generalized Schur factorization of a real 2-by-2 */
/*  matrix pencil (A,B) where B is upper triangular. This routine */
/*  computes orthogonal (rotation) matrices given by CSL, SNL and CSR, */
/*  SNR such that */

/*  1) if the pencil (A,B) has two real eigenvalues (include 0/0 or 1/0 */
/*     types), then */

/*     [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ] */
/*     [  0  a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ] */

/*     [ b11 b12 ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ] */
/*     [  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ], */

/*  2) if the pencil (A,B) has a pair of complex conjugate eigenvalues, */
/*     then */

/*     [ a11 a12 ] := [  CSL  SNL ] [ a11 a12 ] [  CSR -SNR ] */
/*     [ a21 a22 ]    [ -SNL  CSL ] [ a21 a22 ] [  SNR  CSR ] */

/*     [ b11  0  ] := [  CSL  SNL ] [ b11 b12 ] [  CSR -SNR ] */
/*     [  0  b22 ]    [ -SNL  CSL ] [  0  b22 ] [  SNR  CSR ] */

/*     where b11 >= b22 > 0. */


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

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, 2) */
/*          On entry, the 2 x 2 matrix A. */
/*          On exit, A is overwritten by the ``A-part'' of the */
/*          generalized Schur form. */

/*  LDA     (input) INTEGER */
/*          THe leading dimension of the array A.  LDA >= 2. */

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB, 2) */
/*          On entry, the upper triangular 2 x 2 matrix B. */
/*          On exit, B is overwritten by the ``B-part'' of the */
/*          generalized Schur form. */

/*  LDB     (input) INTEGER */
/*          THe leading dimension of the array B.  LDB >= 2. */

/*  ALPHAR  (output) DOUBLE PRECISION array, dimension (2) */
/*  ALPHAI  (output) DOUBLE PRECISION array, dimension (2) */
/*  BETA    (output) DOUBLE PRECISION array, dimension (2) */
/*          (ALPHAR(k)+i*ALPHAI(k))/BETA(k) are the eigenvalues of the */
/*          pencil (A,B), k=1,2, i = sqrt(-1).  Note that BETA(k) may */
/*          be zero. */

/*  CSL     (output) DOUBLE PRECISION */
/*          The cosine of the left rotation matrix. */

/*  SNL     (output) DOUBLE PRECISION */
/*          The sine of the left rotation matrix. */

/*  CSR     (output) DOUBLE PRECISION */
/*          The cosine of the right rotation matrix. */

/*  SNR     (output) DOUBLE PRECISION */
/*          The sine of the right rotation matrix. */

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

/*  Based on contributions by */
/*     Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */

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

/*     .. Parameters .. */
/*<       DOUBLE PRECISION   ZERO, ONE >*/
/*<       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 ) >*/
/*     .. */
/*     .. Local Scalars .. */
/*<    >*/
/*     .. */
/*     .. External Subroutines .. */
/*<       EXTERNAL           DLAG2, DLARTG, DLASV2, DROT >*/
/*     .. */
/*     .. External Functions .. */
/*<       DOUBLE PRECISION   DLAMCH, DLAPY2 >*/
/*<       EXTERNAL           DLAMCH, DLAPY2 >*/
/*     .. */
/*     .. Intrinsic Functions .. */
/*<       INTRINSIC          ABS, MAX >*/
/*     .. */
/*     .. Executable Statements .. */

/*<       SAFMIN = DLAMCH( 'S' ) >*/
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;

    /* Function Body */
    safmin = dlamch_("S", (ftnlen)1);
/*<       ULP = DLAMCH( 'P' ) >*/
    ulp = dlamch_("P", (ftnlen)1);

/*     Scale A */

/*<    >*/
/* Computing MAX */
    d__5 = (d__1 = a[a_dim1 + 1], abs(d__1)) + (d__2 = a[a_dim1 + 2], abs(
            d__2)), d__6 = (d__3 = a[(a_dim1 << 1) + 1], abs(d__3)) + (d__4 = 
            a[(a_dim1 << 1) + 2], abs(d__4)), d__5 = max(d__5,d__6);
    anorm = max(d__5,safmin);
/*<       ASCALE = ONE / ANORM >*/
    ascale = 1. / anorm;
/*<       A( 1, 1 ) = ASCALE*A( 1, 1 ) >*/
    a[a_dim1 + 1] = ascale * a[a_dim1 + 1];
/*<       A( 1, 2 ) = ASCALE*A( 1, 2 ) >*/
    a[(a_dim1 << 1) + 1] = ascale * a[(a_dim1 << 1) + 1];
/*<       A( 2, 1 ) = ASCALE*A( 2, 1 ) >*/
    a[a_dim1 + 2] = ascale * a[a_dim1 + 2];
/*<       A( 2, 2 ) = ASCALE*A( 2, 2 ) >*/
    a[(a_dim1 << 1) + 2] = ascale * a[(a_dim1 << 1) + 2];

/*     Scale B */

/*<    >*/
/* Computing MAX */
    d__4 = (d__3 = b[b_dim1 + 1], abs(d__3)), d__5 = (d__1 = b[(b_dim1 << 1) 
            + 1], abs(d__1)) + (d__2 = b[(b_dim1 << 1) + 2], abs(d__2)), d__4 
            = max(d__4,d__5);
    bnorm = max(d__4,safmin);
/*<       BSCALE = ONE / BNORM >*/
    bscale = 1. / bnorm;
/*<       B( 1, 1 ) = BSCALE*B( 1, 1 ) >*/
    b[b_dim1 + 1] = bscale * b[b_dim1 + 1];
/*<       B( 1, 2 ) = BSCALE*B( 1, 2 ) >*/
    b[(b_dim1 << 1) + 1] = bscale * b[(b_dim1 << 1) + 1];
/*<       B( 2, 2 ) = BSCALE*B( 2, 2 ) >*/
    b[(b_dim1 << 1) + 2] = bscale * b[(b_dim1 << 1) + 2];

/*     Check if A can be deflated */

/*<       IF( ABS( A( 2, 1 ) ).LE.ULP ) THEN >*/
    if ((d__1 = a[a_dim1 + 2], abs(d__1)) <= ulp) {
/*<          CSL = ONE >*/
        *csl = 1.;
/*<          SNL = ZERO >*/
        *snl = 0.;
/*<          CSR = ONE >*/
        *csr = 1.;
/*<          SNR = ZERO >*/
        *snr = 0.;
/*<          A( 2, 1 ) = ZERO >*/
        a[a_dim1 + 2] = 0.;
/*<          B( 2, 1 ) = ZERO >*/
        b[b_dim1 + 2] = 0.;

/*     Check if B is singular */

/*<       ELSE IF( ABS( B( 1, 1 ) ).LE.ULP ) THEN >*/
    } else if ((d__1 = b[b_dim1 + 1], abs(d__1)) <= ulp) {
/*<          CALL DLARTG( A( 1, 1 ), A( 2, 1 ), CSL, SNL, R ) >*/
        dlartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
/*<          CSR = ONE >*/
        *csr = 1.;
/*<          SNR = ZERO >*/