slaqr2.c

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/* slaqr2.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__1 = 1;
static integer c_n1 = -1;
static real c_b12 = 0.f;
static real c_b13 = 1.f;
static logical c_true = TRUE_;

/* Subroutine */ int slaqr2_(logical *wantt, logical *wantz, integer *n, 
        integer *ktop, integer *kbot, integer *nw, real *h__, integer *ldh, 
        integer *iloz, integer *ihiz, real *z__, integer *ldz, integer *ns, 
        integer *nd, real *sr, real *si, real *v, integer *ldv, integer *nh, 
        real *t, integer *ldt, integer *nv, real *wv, integer *ldwv, real *
        work, integer *lwork)
{
    /* System generated locals */
    integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1, 
            wv_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
    real r__1, r__2, r__3, r__4, r__5, r__6;

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

    /* Local variables */
    integer i__, j, k;
    real s, aa, bb, cc, dd, cs, sn;
    integer jw;
    real evi, evk, foo;
    integer kln;
    real tau, ulp;
    integer lwk1, lwk2;
    real beta;
    integer kend, kcol, info, ifst, ilst, ltop, krow;
    logical bulge;
    extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *, 
            integer *, real *, real *, integer *, real *), sgemm_(
            char *, char *, integer *, integer *, integer *, real *, real *, 
            integer *, real *, integer *, real *, real *, integer *);
    integer infqr;
    extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *, 
            integer *);
    integer kwtop;
    extern /* Subroutine */ int slanv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *, real *), slabad_(real *, real *)
            ;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int sgehrd_(integer *, integer *, integer *, real 
            *, integer *, real *, real *, integer *, integer *);
    real safmin;
    extern /* Subroutine */ int slarfg_(integer *, real *, real *, integer *, 
            real *);
    real safmax;
    extern /* Subroutine */ int slahqr_(logical *, logical *, integer *, 
            integer *, integer *, real *, integer *, real *, real *, integer *
, integer *, real *, integer *, integer *), slacpy_(char *, 
            integer *, integer *, real *, integer *, real *, integer *), slaset_(char *, integer *, integer *, real *, real *, 
            real *, integer *);
    logical sorted;
    extern /* Subroutine */ int strexc_(char *, integer *, real *, integer *, 
            real *, integer *, integer *, integer *, real *, integer *), sormhr_(char *, char *, integer *, integer *, integer *, 
            integer *, real *, integer *, real *, real *, integer *, real *, 
            integer *, integer *);
    real smlnum;
    integer lwkopt;


/*  -- LAPACK auxiliary routine (version 3.2.1)                        -- */
/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/*  -- April 2009                                                      -- */

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

/*     This subroutine is identical to SLAQR3 except that it avoids */
/*     recursion by calling SLAHQR instead of SLAQR4. */


/*     ****************************************************************** */
/*     Aggressive early deflation: */

/*     This subroutine accepts as input an upper Hessenberg matrix */
/*     H and performs an orthogonal similarity transformation */
/*     designed to detect and deflate fully converged eigenvalues from */
/*     a trailing principal submatrix.  On output H has been over- */
/*     written by a new Hessenberg matrix that is a perturbation of */
/*     an orthogonal similarity transformation of H.  It is to be */
/*     hoped that the final version of H has many zero subdiagonal */
/*     entries. */

/*     ****************************************************************** */
/*     WANTT   (input) LOGICAL */
/*          If .TRUE., then the Hessenberg matrix H is fully updated */
/*          so that the quasi-triangular Schur factor may be */
/*          computed (in cooperation with the calling subroutine). */
/*          If .FALSE., then only enough of H is updated to preserve */
/*          the eigenvalues. */

/*     WANTZ   (input) LOGICAL */
/*          If .TRUE., then the orthogonal matrix Z is updated so */
/*          so that the orthogonal Schur factor may be computed */
/*          (in cooperation with the calling subroutine). */
/*          If .FALSE., then Z is not referenced. */

/*     N       (input) INTEGER */
/*          The order of the matrix H and (if WANTZ is .TRUE.) the */
/*          order of the orthogonal matrix Z. */

/*     KTOP    (input) INTEGER */
/*          It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
/*          KBOT and KTOP together determine an isolated block */
/*          along the diagonal of the Hessenberg matrix. */

/*     KBOT    (input) INTEGER */
/*          It is assumed without a check that either */
/*          KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together */
/*          determine an isolated block along the diagonal of the */
/*          Hessenberg matrix. */

/*     NW      (input) INTEGER */
/*          Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1). */

/*     H       (input/output) REAL array, dimension (LDH,N) */
/*          On input the initial N-by-N section of H stores the */
/*          Hessenberg matrix undergoing aggressive early deflation. */
/*          On output H has been transformed by an orthogonal */
/*          similarity transformation, perturbed, and the returned */
/*          to Hessenberg form that (it is to be hoped) has some */
/*          zero subdiagonal entries. */

/*     LDH     (input) integer */
/*          Leading dimension of H just as declared in the calling */
/*          subroutine.  N .LE. LDH */

/*     ILOZ    (input) INTEGER */
/*     IHIZ    (input) INTEGER */
/*          Specify the rows of Z to which transformations must be */
/*          applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N. */

/*     Z       (input/output) REAL array, dimension (LDZ,N) */
/*          IF WANTZ is .TRUE., then on output, the orthogonal */
/*          similarity transformation mentioned above has been */
/*          accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. */
/*          If WANTZ is .FALSE., then Z is unreferenced. */

/*     LDZ     (input) integer */
/*          The leading dimension of Z just as declared in the */
/*          calling subroutine.  1 .LE. LDZ. */

/*     NS      (output) integer */
/*          The number of unconverged (ie approximate) eigenvalues */
/*          returned in SR and SI that may be used as shifts by the */
/*          calling subroutine. */

/*     ND      (output) integer */
/*          The number of converged eigenvalues uncovered by this */
/*          subroutine. */

/*     SR      (output) REAL array, dimension KBOT */
/*     SI      (output) REAL array, dimension KBOT */
/*          On output, the real and imaginary parts of approximate */
/*          eigenvalues that may be used for shifts are stored in */
/*          SR(KBOT-ND-NS+1) through SR(KBOT-ND) and */
/*          SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively. */
/*          The real and imaginary parts of converged eigenvalues */
/*          are stored in SR(KBOT-ND+1) through SR(KBOT) and */
/*          SI(KBOT-ND+1) through SI(KBOT), respectively. */

/*     V       (workspace) REAL array, dimension (LDV,NW) */
/*          An NW-by-NW work array. */

/*     LDV     (input) integer scalar */
/*          The leading dimension of V just as declared in the */
/*          calling subroutine.  NW .LE. LDV */

/*     NH      (input) integer scalar */
/*          The number of columns of T.  NH.GE.NW. */

/*     T       (workspace) REAL array, dimension (LDT,NW) */

/*     LDT     (input) integer */
/*          The leading dimension of T just as declared in the */
/*          calling subroutine.  NW .LE. LDT */

/*     NV      (input) integer */
/*          The number of rows of work array WV available for */
/*          workspace.  NV.GE.NW. */

/*     WV      (workspace) REAL array, dimension (LDWV,NW) */

/*     LDWV    (input) integer */
/*          The leading dimension of W just as declared in the */
/*          calling subroutine.  NW .LE. LDV */

/*     WORK    (workspace) REAL array, dimension LWORK. */
/*          On exit, WORK(1) is set to an estimate of the optimal value */
/*          of LWORK for the given values of N, NW, KTOP and KBOT. */

/*     LWORK   (input) integer */
/*          The dimension of the work array WORK.  LWORK = 2*NW */
/*          suffices, but greater efficiency may result from larger */
/*          values of LWORK. */

/*          If LWORK = -1, then a workspace query is assumed; SLAQR2 */
/*          only estimates the optimal workspace size for the given */
/*          values of N, NW, KTOP and KBOT.  The estimate is returned */
/*          in WORK(1).  No error message related to LWORK is issued */
/*          by XERBLA.  Neither H nor Z are accessed. */

/*     ================================================================ */
/*     Based on contributions by */
/*        Karen Braman and Ralph Byers, Department of Mathematics, */
/*        University of Kansas, USA */

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

/*     ==== Estimate optimal workspace. ==== */

    /* Parameter adjustments */
    h_dim1 = *ldh;
    h_offset = 1 + h_dim1;
    h__ -= h_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    --sr;
    --si;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    t_dim1 = *ldt;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    wv_dim1 = *ldwv;
    wv_offset = 1 + wv_dim1;
    wv -= wv_offset;
    --work;

    /* Function Body */
/* Computing MIN */
    i__1 = *nw, i__2 = *kbot - *ktop + 1;
    jw = min(i__1,i__2);
    if (jw <= 2) {
        lwkopt = 1;
    } else {

/*        ==== Workspace query call to SGEHRD ==== */

        i__1 = jw - 1;
        sgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
                c_n1, &info);
        lwk1 = (integer) work[1];

/*        ==== Workspace query call to SORMHR ==== */

        i__1 = jw - 1;
        sormhr_("R", "N", &jw, &jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], 
                 &v[v_offset], ldv, &work[1], &c_n1, &info);
        lwk2 = (integer) work[1];

/*        ==== Optimal workspace ==== */

        lwkopt = jw + max(lwk1,lwk2);
    }

/*     ==== Quick return in case of workspace query. ==== */

    if (*lwork == -1) {
        work[1] = (real) lwkopt;
        return 0;
    }

/*     ==== Nothing to do ... */
/*     ... for an empty active block ... ==== */
    *ns = 0;
    *nd = 0;
    work[1] = 1.f;
    if (*ktop > *kbot) {
        return 0;
    }
/*     ... nor for an empty deflation window. ==== */
    if (*nw < 1) {
        return 0;
    }

/*     ==== Machine constants ==== */

    safmin = slamch_("SAFE MINIMUM");
    safmax = 1.f / safmin;
    slabad_(&safmin, &safmax);
    ulp = slamch_("PRECISION");
    smlnum = safmin * ((real) (*n) / ulp);

/*     ==== Setup deflation window ==== */

/* Computing MIN */
    i__1 = *nw, i__2 = *kbot - *ktop + 1;
    jw = min(i__1,i__2);
    kwtop = *kbot - jw + 1;
    if (kwtop == *ktop) {
        s = 0.f;
    } else {
        s = h__[kwtop + (kwtop - 1) * h_dim1];
    }

    if (*kbot == kwtop) {

/*        ==== 1-by-1 deflation window: not much to do ==== */

        sr[kwtop] = h__[kwtop + kwtop * h_dim1];
        si[kwtop] = 0.f;
        *ns = 1;
        *nd = 0;
/* Computing MAX */
        r__2 = smlnum, r__3 = ulp * (r__1 = h__[kwtop + kwtop * h_dim1], dabs(
                r__1));
        if (dabs(s) <= dmax(r__2,r__3)) {
            *ns = 0;
            *nd = 1;
            if (kwtop > *ktop) {
                h__[kwtop + (kwtop - 1) * h_dim1] = 0.f;
            }
        }
        work[1] = 1.f;
        return 0;
    }

/*     ==== Convert to spike-triangular form.  (In case of a */
/*     .    rare QR failure, this routine continues to do */
/*     .    aggressive early deflation using that part of */
/*     .    the deflation window that converged using INFQR */
/*     .    here and there to keep track.) ==== */

    slacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset], 
            ldt);
    i__1 = jw - 1;
    i__2 = *ldh + 1;
    i__3 = *ldt + 1;
    scopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
            i__3);

    slaset_("A", &jw, &jw, &c_b12, &c_b13, &v[v_offset], ldv);
    slahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop], 
            &si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);

/*     ==== STREXC needs a clean margin near the diagonal ==== */

    i__1 = jw - 3;
    for (j = 1; j <= i__1; ++j) {
        t[j + 2 + j * t_dim1] = 0.f;
        t[j + 3 + j * t_dim1] = 0.f;
/* L10: */
    }
    if (jw > 2) {
        t[jw + (jw - 2) * t_dim1] = 0.f;
    }

/*     ==== Deflation detection loop ==== */

    *ns = jw;
    ilst = infqr + 1;
L20:
    if (ilst <= *ns) {
        if (*ns == 1) {
            bulge = FALSE_;
        } else {
            bulge = t[*ns + (*ns - 1) * t_dim1] != 0.f;
        }

/*        ==== Small spike tip test for deflation ==== */

        if (! bulge) {

/*           ==== Real eigenvalue ==== */

            foo = (r__1 = t[*ns + *ns * t_dim1], dabs(r__1));
            if (foo == 0.f) {
                foo = dabs(s);
            }
/* Computing MAX */
            r__2 = smlnum, r__3 = ulp * foo;
            if ((r__1 = s * v[*ns * v_dim1 + 1], dabs(r__1)) <= dmax(r__2,
                    r__3)) {

/*              ==== Deflatable ==== */

                --(*ns);
            } else {

/*              ==== Undeflatable.   Move it up out of the way. */
/*              .    (STREXC can not fail in this case.) ==== */

                ifst = *ns;
                strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, 
                         &ilst, &work[1], &info);
                ++ilst;
            }
        } else {

/*           ==== Complex conjugate pair ==== */

            foo = (r__3 = t[*ns + *ns * t_dim1], dabs(r__3)) + sqrt((r__1 = t[
                    *ns + (*ns - 1) * t_dim1], dabs(r__1))) * sqrt((r__2 = t[*
                    ns - 1 + *ns * t_dim1], dabs(r__2)));
            if (foo == 0.f) {
                foo = dabs(s);
            }
/* Computing MAX */
            r__3 = (r__1 = s * v[*ns * v_dim1 + 1], dabs(r__1)), r__4 = (r__2 
                    = s * v[(*ns - 1) * v_dim1 + 1], dabs(r__2));
/* Computing MAX */
            r__5 = smlnum, r__6 = ulp * foo;
            if (dmax(r__3,r__4) <= dmax(r__5,r__6)) {

/*              ==== Deflatable ==== */

                *ns += -2;
            } else {

/*              ==== Undeflatable. Move them up out of the way. */
/*              .    Fortunately, STREXC does the right thing with */
/*              .    ILST in case of a rare exchange failure. ==== */

                ifst = *ns;
                strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, 
                         &ilst, &work[1], &info);
                ilst += 2;
            }
        }

/*        ==== End deflation detection loop ==== */

        goto L20;
    }

/*        ==== Return to Hessenberg form ==== */

    if (*ns == 0) {
        s = 0.f;
    }

    if (*ns < jw) {

/*        ==== sorting diagonal blocks of T improves accuracy for */
/*        .    graded matrices.  Bubble sort deals well with */
/*        .    exchange failures. ==== */

        sorted = FALSE_;
        i__ = *ns + 1;
L30:
        if (sorted) {
            goto L50;
        }
        sorted = TRUE_;

        kend = i__ - 1;
        i__ = infqr + 1;
        if (i__ == *ns) {
            k = i__ + 1;
        } else if (t[i__ + 1 + i__ * t_dim1] == 0.f) {
            k = i__ + 1;
        } else {
            k = i__ + 2;
        }
L40:
        if (k <= kend) {
            if (k == i__ + 1) {
                evi = (r__1 = t[i__ + i__ * t_dim1], dabs(r__1));
            } else {
                evi = (r__3 = t[i__ + i__ * t_dim1], dabs(r__3)) + sqrt((r__1 
                        = t[i__ + 1 + i__ * t_dim1], dabs(r__1))) * sqrt((
                        r__2 = t[i__ + (i__ + 1) * t_dim1], dabs(r__2)));
            }

            if (k == kend) {
                evk = (r__1 = t[k + k * t_dim1], dabs(r__1));
            } else if (t[k + 1 + k * t_dim1] == 0.f) {
                evk = (r__1 = t[k + k * t_dim1], dabs(r__1));
            } else {
                evk = (r__3 = t[k + k * t_dim1], dabs(r__3)) + sqrt((r__1 = t[
                        k + 1 + k * t_dim1], dabs(r__1))) * sqrt((r__2 = t[k 
                        + (k + 1) * t_dim1], dabs(r__2)));
            }

            if (evi >= evk) {
                i__ = k;
            } else {
                sorted = FALSE_;
                ifst = i__;
                ilst = k;
                strexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst, 
                         &ilst, &work[1], &info);
                if (info == 0) {
                    i__ = ilst;
                } else {
                    i__ = k;
                }
            }
            if (i__ == kend) {
                k = i__ + 1;
            } else if (t[i__ + 1 + i__ * t_dim1] == 0.f) {
                k = i__ + 1;
            } else {
                k = i__ + 2;
            }
            goto L40;
        }
        goto L30;
L50:
        ;
    }

/*     ==== Restore shift/eigenvalue array from T ==== */

    i__ = jw;
L60:
    if (i__ >= infqr + 1) {
        if (i__ == infqr + 1) {
            sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
            si[kwtop + i__ - 1] = 0.f;
            --i__;
        } else if (t[i__ + (i__ - 1) * t_dim1] == 0.f) {
            sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
            si[kwtop + i__ - 1] = 0.f;
            --i__;
        } else {
            aa = t[i__ - 1 + (i__ - 1) * t_dim1];
            cc = t[i__ + (i__ - 1) * t_dim1];
            bb = t[i__ - 1 + i__ * t_dim1];
            dd = t[i__ + i__ * t_dim1];
            slanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__ 
                    - 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, &
                    sn);
            i__ += -2;
        }
        goto L60;
    }

    if (*ns < jw || s == 0.f) {
        if (*ns > 1 && s != 0.f) {

/*           ==== Reflect spike back into lower triangle ==== */

            scopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
            beta = work[1];
            slarfg_(ns, &beta, &work[2], &c__1, &tau);
            work[1] = 1.f;

            i__1 = jw - 2;
            i__2 = jw - 2;
            slaset_("L", &i__1, &i__2, &c_b12, &c_b12, &t[t_dim1 + 3], ldt);

            slarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, &
                    work[jw + 1]);
            slarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
                    work[jw + 1]);
            slarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
                    work[jw + 1]);

            i__1 = *lwork - jw;
            sgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
        }

/*        ==== Copy updated reduced window into place ==== */

        if (kwtop > 1) {
            h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
        }
        slacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
        i__1 = jw - 1;
        i__2 = *ldt + 1;
        i__3 = *ldh + 1;
        scopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1], 
                 &i__3);

/*        ==== Accumulate orthogonal matrix in order update */
/*        .    H and Z, if requested.  ==== */

        if (*ns > 1 && s != 0.f) {
            i__1 = *lwork - jw;
            sormhr_("R", "N", &jw, ns, &c__1, ns, &t[t_offset], ldt, &work[1], 
                     &v[v_offset], ldv, &work[jw + 1], &i__1, &info);
        }

/*        ==== Update vertical slab in H ==== */

        if (*wantt) {
            ltop = 1;
        } else {
            ltop = *ktop;
        }
        i__1 = kwtop - 1;
        i__2 = *nv;
        for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow += 
                i__2) {
/* Computing MIN */
            i__3 = *nv, i__4 = kwtop - krow;
            kln = min(i__3,i__4);
            sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &h__[krow + kwtop * 
                    h_dim1], ldh, &v[v_offset], ldv, &c_b12, &wv[wv_offset], 
                    ldwv);
            slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop * 
                    h_dim1], ldh);
/* L70: */
        }

/*        ==== Update horizontal slab in H ==== */

        if (*wantt) {
            i__2 = *n;
            i__1 = *nh;
            for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2; 
                    kcol += i__1) {
/* Computing MIN */
                i__3 = *nh, i__4 = *n - kcol + 1;
                kln = min(i__3,i__4);
                sgemm_("C", "N", &jw, &kln, &jw, &c_b13, &v[v_offset], ldv, &
                        h__[kwtop + kcol * h_dim1], ldh, &c_b12, &t[t_offset], 
                         ldt);
                slacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
                         h_dim1], ldh);
/* L80: */
            }
        }

/*        ==== Update vertical slab in Z ==== */

        if (*wantz) {
            i__1 = *ihiz;
            i__2 = *nv;
            for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
                     i__2) {
/* Computing MIN */
                i__3 = *nv, i__4 = *ihiz - krow + 1;
                kln = min(i__3,i__4);
                sgemm_("N", "N", &kln, &jw, &jw, &c_b13, &z__[krow + kwtop * 
                        z_dim1], ldz, &v[v_offset], ldv, &c_b12, &wv[
                        wv_offset], ldwv);
                slacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow + 
                        kwtop * z_dim1], ldz);
/* L90: */
            }
        }
    }

/*     ==== Return the number of deflations ... ==== */

    *nd = jw - *ns;

/*     ==== ... and the number of shifts. (Subtracting */
/*     .    INFQR from the spike length takes care */
/*     .    of the case of a rare QR failure while */
/*     .    calculating eigenvalues of the deflation */
/*     .    window.)  ==== */

    *ns -= infqr;

/*      ==== Return optimal workspace. ==== */

    work[1] = (real) lwkopt;

/*     ==== End of SLAQR2 ==== */

    return 0;
} /* slaqr2_ */