slagv2.c

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/* slagv2.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 slagv2_(real *a, integer *lda, real *b, integer *ldb, 
        real *alphar, real *alphai, real *beta, real *csl, real *snl, real *
        csr, real *snr)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset;
    real r__1, r__2, r__3, r__4, r__5, r__6;

    /* Local variables */
    real r__, t, h1, h2, h3, wi, qq, rr, wr1, wr2, ulp;
    extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, 
            integer *, real *, real *), slag2_(real *, integer *, real *, 
            integer *, real *, real *, real *, real *, real *, real *);
    real anorm, bnorm, scale1, scale2;
    extern /* Subroutine */ int slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *);
    extern doublereal slapy2_(real *, real *);
    real ascale, bscale;
    extern doublereal slamch_(char *);
    real safmin;
    extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real *
);


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

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

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

/*  SLAGV2 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) REAL 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) REAL 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) REAL array, dimension (2) */
/*  ALPHAI  (output) REAL array, dimension (2) */
/*  BETA    (output) REAL 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) REAL */
/*          The cosine of the left rotation matrix. */

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

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

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

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

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

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. 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;
    --alphar;
    --alphai;
    --beta;

    /* Function Body */
    safmin = slamch_("S");
    ulp = slamch_("P");

/*     Scale A */

/* Computing MAX */
    r__5 = (r__1 = a[a_dim1 + 1], dabs(r__1)) + (r__2 = a[a_dim1 + 2], dabs(
            r__2)), r__6 = (r__3 = a[(a_dim1 << 1) + 1], dabs(r__3)) + (r__4 =
             a[(a_dim1 << 1) + 2], dabs(r__4)), r__5 = max(r__5,r__6);
    anorm = dmax(r__5,safmin);
    ascale = 1.f / anorm;
    a[a_dim1 + 1] = ascale * a[a_dim1 + 1];
    a[(a_dim1 << 1) + 1] = ascale * a[(a_dim1 << 1) + 1];
    a[a_dim1 + 2] = ascale * a[a_dim1 + 2];
    a[(a_dim1 << 1) + 2] = ascale * a[(a_dim1 << 1) + 2];

/*     Scale B */

/* Computing MAX */
    r__4 = (r__3 = b[b_dim1 + 1], dabs(r__3)), r__5 = (r__1 = b[(b_dim1 << 1) 
            + 1], dabs(r__1)) + (r__2 = b[(b_dim1 << 1) + 2], dabs(r__2)), 
            r__4 = max(r__4,r__5);
    bnorm = dmax(r__4,safmin);
    bscale = 1.f / bnorm;
    b[b_dim1 + 1] = bscale * b[b_dim1 + 1];
    b[(b_dim1 << 1) + 1] = bscale * b[(b_dim1 << 1) + 1];
    b[(b_dim1 << 1) + 2] = bscale * b[(b_dim1 << 1) + 2];

/*     Check if A can be deflated */

    if ((r__1 = a[a_dim1 + 2], dabs(r__1)) <= ulp) {
        *csl = 1.f;
        *snl = 0.f;
        *csr = 1.f;
        *snr = 0.f;
        a[a_dim1 + 2] = 0.f;
        b[b_dim1 + 2] = 0.f;

/*     Check if B is singular */

    } else if ((r__1 = b[b_dim1 + 1], dabs(r__1)) <= ulp) {
        slartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);
        *csr = 1.f;
        *snr = 0.f;
        srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
        srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
        a[a_dim1 + 2] = 0.f;
        b[b_dim1 + 1] = 0.f;
        b[b_dim1 + 2] = 0.f;

    } else if ((r__1 = b[(b_dim1 << 1) + 2], dabs(r__1)) <= ulp) {
        slartg_(&a[(a_dim1 << 1) + 2], &a[a_dim1 + 2], csr, snr, &t);
        *snr = -(*snr);
        srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1, csr, 
                 snr);
        srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1, csr, 
                 snr);
        *csl = 1.f;
        *snl = 0.f;
        a[a_dim1 + 2] = 0.f;
        b[b_dim1 + 2] = 0.f;
        b[(b_dim1 << 1) + 2] = 0.f;

    } else {

/*        B is nonsingular, first compute the eigenvalues of (A,B) */

        slag2_(&a[a_offset], lda, &b[b_offset], ldb, &safmin, &scale1, &
                scale2, &wr1, &wr2, &wi);

        if (wi == 0.f) {

/*           two real eigenvalues, compute s*A-w*B */

            h1 = scale1 * a[a_dim1 + 1] - wr1 * b[b_dim1 + 1];
            h2 = scale1 * a[(a_dim1 << 1) + 1] - wr1 * b[(b_dim1 << 1) + 1];
            h3 = scale1 * a[(a_dim1 << 1) + 2] - wr1 * b[(b_dim1 << 1) + 2];

            rr = slapy2_(&h1, &h2);
            r__1 = scale1 * a[a_dim1 + 2];
            qq = slapy2_(&r__1, &h3);

            if (rr > qq) {

/*              find right rotation matrix to zero 1,1 element of */
/*              (sA - wB) */

                slartg_(&h2, &h1, csr, snr, &t);

            } else {

/*              find right rotation matrix to zero 2,1 element of */
/*              (sA - wB) */

                r__1 = scale1 * a[a_dim1 + 2];
                slartg_(&h3, &r__1, csr, snr, &t);

            }

            *snr = -(*snr);
            srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1, 
                    csr, snr);
            srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1, 
                    csr, snr);

/*           compute inf norms of A and B */

/* Computing MAX */
            r__5 = (r__1 = a[a_dim1 + 1], dabs(r__1)) + (r__2 = a[(a_dim1 << 
                    1) + 1], dabs(r__2)), r__6 = (r__3 = a[a_dim1 + 2], dabs(
                    r__3)) + (r__4 = a[(a_dim1 << 1) + 2], dabs(r__4));
            h1 = dmax(r__5,r__6);
/* Computing MAX */
            r__5 = (r__1 = b[b_dim1 + 1], dabs(r__1)) + (r__2 = b[(b_dim1 << 
                    1) + 1], dabs(r__2)), r__6 = (r__3 = b[b_dim1 + 2], dabs(
                    r__3)) + (r__4 = b[(b_dim1 << 1) + 2], dabs(r__4));
            h2 = dmax(r__5,r__6);

            if (scale1 * h1 >= dabs(wr1) * h2) {

/*              find left rotation matrix Q to zero out B(2,1) */

                slartg_(&b[b_dim1 + 1], &b[b_dim1 + 2], csl, snl, &r__);

            } else {

/*              find left rotation matrix Q to zero out A(2,1) */

                slartg_(&a[a_dim1 + 1], &a[a_dim1 + 2], csl, snl, &r__);

            }

            srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
            srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);

            a[a_dim1 + 2] = 0.f;
            b[b_dim1 + 2] = 0.f;

        } else {

/*           a pair of complex conjugate eigenvalues */
/*           first compute the SVD of the matrix B */

            slasv2_(&b[b_dim1 + 1], &b[(b_dim1 << 1) + 1], &b[(b_dim1 << 1) + 
                    2], &r__, &t, snr, csr, snl, csl);

/*           Form (A,B) := Q(A,B)Z' where Q is left rotation matrix and */
/*           Z is right rotation matrix computed from SLASV2 */

            srot_(&c__2, &a[a_dim1 + 1], lda, &a[a_dim1 + 2], lda, csl, snl);
            srot_(&c__2, &b[b_dim1 + 1], ldb, &b[b_dim1 + 2], ldb, csl, snl);
            srot_(&c__2, &a[a_dim1 + 1], &c__1, &a[(a_dim1 << 1) + 1], &c__1, 
                    csr, snr);
            srot_(&c__2, &b[b_dim1 + 1], &c__1, &b[(b_dim1 << 1) + 1], &c__1, 
                    csr, snr);

            b[b_dim1 + 2] = 0.f;
            b[(b_dim1 << 1) + 1] = 0.f;

        }

    }

/*     Unscaling */

    a[a_dim1 + 1] = anorm * a[a_dim1 + 1];
    a[a_dim1 + 2] = anorm * a[a_dim1 + 2];
    a[(a_dim1 << 1) + 1] = anorm * a[(a_dim1 << 1) + 1];
    a[(a_dim1 << 1) + 2] = anorm * a[(a_dim1 << 1) + 2];
    b[b_dim1 + 1] = bnorm * b[b_dim1 + 1];
    b[b_dim1 + 2] = bnorm * b[b_dim1 + 2];
    b[(b_dim1 << 1) + 1] = bnorm * b[(b_dim1 << 1) + 1];
    b[(b_dim1 << 1) + 2] = bnorm * b[(b_dim1 << 1) + 2];

    if (wi == 0.f) {
        alphar[1] = a[a_dim1 + 1];
        alphar[2] = a[(a_dim1 << 1) + 2];
        alphai[1] = 0.f;
        alphai[2] = 0.f;
        beta[1] = b[b_dim1 + 1];
        beta[2] = b[(b_dim1 << 1) + 2];
    } else {
        alphar[1] = anorm * wr1 / scale1 / bnorm;
        alphai[1] = anorm * wi / scale1 / bnorm;
        alphar[2] = alphar[1];
        alphai[2] = -alphai[1];
        beta[1] = 1.f;
        beta[2] = 1.f;
    }

    return 0;

/*     End of SLAGV2 */

} /* slagv2_ */