[] add metering mode to CLI

1 files changed, 753 insertions, 0 deletions

diff --git a/contrib/libs/clapack/slaqr0.c b/contrib/libs/clapack/slaqr0.c
new file mode 100644
index 0000000000..d2dab03045
--- /dev/null
+++ b/contrib/libs/clapack/slaqr0.c
@@ -0,0 +1,753 @@
+/* slaqr0.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__13 = 13;
+static integer c__15 = 15;
+static integer c_n1 = -1;
+static integer c__12 = 12;
+static integer c__14 = 14;
+static integer c__16 = 16;
+static logical c_false = FALSE_;
+static integer c__1 = 1;
+static integer c__3 = 3;
+
+/* Subroutine */ int slaqr0_(logical *wantt, logical *wantz, integer *n, 
+	integer *ilo, integer *ihi, real *h__, integer *ldh, real *wr, real *
+	wi, integer *iloz, integer *ihiz, real *z__, integer *ldz, real *work, 
+	 integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5;
+    real r__1, r__2, r__3, r__4;
+
+    /* Local variables */
+    integer i__, k;
+    real aa, bb, cc, dd;
+    integer ld;
+    real cs;
+    integer nh, it, ks, kt;
+    real sn;
+    integer ku, kv, ls, ns;
+    real ss;
+    integer nw, inf, kdu, nho, nve, kwh, nsr, nwr, kwv, ndec, ndfl, kbot, 
+	    nmin;
+    real swap;
+    integer ktop;
+    real zdum[1]	/* was [1][1] */;
+    integer kacc22, itmax, nsmax, nwmax, kwtop;
+    extern /* Subroutine */ int slanv2_(real *, real *, real *, real *, real *
+, real *, real *, real *, real *, real *), slaqr3_(logical *, 
+	    logical *, integer *, integer *, integer *, integer *, real *, 
+	    integer *, integer *, integer *, real *, integer *, integer *, 
+	    integer *, real *, real *, real *, integer *, integer *, real *, 
+	    integer *, integer *, real *, integer *, real *, integer *), 
+	    slaqr4_(logical *, logical *, integer *, integer *, integer *, 
+	    real *, integer *, real *, real *, integer *, integer *, real *, 
+	    integer *, real *, integer *, integer *), slaqr5_(logical *, 
+	    logical *, integer *, integer *, integer *, integer *, integer *, 
+	    real *, real *, real *, integer *, integer *, integer *, real *, 
+	    integer *, real *, integer *, real *, integer *, integer *, real *
+, integer *, integer *, real *, integer *);
+    integer nibble;
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    char jbcmpz[1];
+    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 *);
+    integer nwupbd;
+    logical sorted;
+    integer lwkopt;
+
+
+/*  -- LAPACK auxiliary routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*     Purpose */
+/*     ======= */
+
+/*     SLAQR0 computes the eigenvalues of a Hessenberg matrix H */
+/*     and, optionally, the matrices T and Z from the Schur decomposition */
+/*     H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
+/*     Schur form), and Z is the orthogonal matrix of Schur vectors. */
+
+/*     Optionally Z may be postmultiplied into an input orthogonal */
+/*     matrix Q so that this routine can give the Schur factorization */
+/*     of a matrix A which has been reduced to the Hessenberg form H */
+/*     by the orthogonal matrix Q:  A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
+
+/*     Arguments */
+/*     ========= */
+
+/*     WANTT   (input) LOGICAL */
+/*          = .TRUE. : the full Schur form T is required; */
+/*          = .FALSE.: only eigenvalues are required. */
+
+/*     WANTZ   (input) LOGICAL */
+/*          = .TRUE. : the matrix of Schur vectors Z is required; */
+/*          = .FALSE.: Schur vectors are not required. */
+
+/*     N     (input) INTEGER */
+/*           The order of the matrix H.  N .GE. 0. */
+
+/*     ILO   (input) INTEGER */
+/*     IHI   (input) INTEGER */
+/*           It is assumed that H is already upper triangular in rows */
+/*           and columns 1:ILO-1 and IHI+1:N and, if ILO.GT.1, */
+/*           H(ILO,ILO-1) is zero. ILO and IHI are normally set by a */
+/*           previous call to SGEBAL, and then passed to SGEHRD when the */
+/*           matrix output by SGEBAL is reduced to Hessenberg form. */
+/*           Otherwise, ILO and IHI should be set to 1 and N, */
+/*           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. */
+/*           If N = 0, then ILO = 1 and IHI = 0. */
+
+/*     H     (input/output) REAL array, dimension (LDH,N) */
+/*           On entry, the upper Hessenberg matrix H. */
+/*           On exit, if INFO = 0 and WANTT is .TRUE., then H contains */
+/*           the upper quasi-triangular matrix T from the Schur */
+/*           decomposition (the Schur form); 2-by-2 diagonal blocks */
+/*           (corresponding to complex conjugate pairs of eigenvalues) */
+/*           are returned in standard form, with H(i,i) = H(i+1,i+1) */
+/*           and H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and WANTT is */
+/*           .FALSE., then the contents of H are unspecified on exit. */
+/*           (The output value of H when INFO.GT.0 is given under the */
+/*           description of INFO below.) */
+
+/*           This subroutine may explicitly set H(i,j) = 0 for i.GT.j and */
+/*           j = 1, 2, ... ILO-1 or j = IHI+1, IHI+2, ... N. */
+
+/*     LDH   (input) INTEGER */
+/*           The leading dimension of the array H. LDH .GE. max(1,N). */
+
+/*     WR    (output) REAL array, dimension (IHI) */
+/*     WI    (output) REAL array, dimension (IHI) */
+/*           The real and imaginary parts, respectively, of the computed */
+/*           eigenvalues of H(ILO:IHI,ILO:IHI) are stored in WR(ILO:IHI) */
+/*           and WI(ILO:IHI). If two eigenvalues are computed as a */
+/*           complex conjugate pair, they are stored in consecutive */
+/*           elements of WR and WI, say the i-th and (i+1)th, with */
+/*           WI(i) .GT. 0 and WI(i+1) .LT. 0. If WANTT is .TRUE., then */
+/*           the eigenvalues are stored in the same order as on the */
+/*           diagonal of the Schur form returned in H, with */
+/*           WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 diagonal */
+/*           block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
+/*           WI(i+1) = -WI(i). */
+
+/*     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. ILO; IHI .LE. IHIZ .LE. N. */
+
+/*     Z     (input/output) REAL array, dimension (LDZ,IHI) */
+/*           If WANTZ is .FALSE., then Z is not referenced. */
+/*           If WANTZ is .TRUE., then Z(ILO:IHI,ILOZ:IHIZ) is */
+/*           replaced by Z(ILO:IHI,ILOZ:IHIZ)*U where U is the */
+/*           orthogonal Schur factor of H(ILO:IHI,ILO:IHI). */
+/*           (The output value of Z when INFO.GT.0 is given under */
+/*           the description of INFO below.) */
+
+/*     LDZ   (input) INTEGER */
+/*           The leading dimension of the array Z.  if WANTZ is .TRUE. */
+/*           then LDZ.GE.MAX(1,IHIZ).  Otherwize, LDZ.GE.1. */
+
+/*     WORK  (workspace/output) REAL array, dimension LWORK */
+/*           On exit, if LWORK = -1, WORK(1) returns an estimate of */
+/*           the optimal value for LWORK. */
+
+/*     LWORK (input) INTEGER */
+/*           The dimension of the array WORK.  LWORK .GE. max(1,N) */
+/*           is sufficient, but LWORK typically as large as 6*N may */
+/*           be required for optimal performance.  A workspace query */
+/*           to determine the optimal workspace size is recommended. */
+
+/*           If LWORK = -1, then SLAQR0 does a workspace query. */
+/*           In this case, SLAQR0 checks the input parameters and */
+/*           estimates the optimal workspace size for the given */
+/*           values of N, ILO and IHI.  The estimate is returned */
+/*           in WORK(1).  No error message related to LWORK is */
+/*           issued by XERBLA.  Neither H nor Z are accessed. */
+
+
+/*     INFO  (output) INTEGER */
+/*             =  0:  successful exit */
+/*           .GT. 0:  if INFO = i, SLAQR0 failed to compute all of */
+/*                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR */
+/*                and WI contain those eigenvalues which have been */
+/*                successfully computed.  (Failures are rare.) */
+
+/*                If INFO .GT. 0 and WANT is .FALSE., then on exit, */
+/*                the remaining unconverged eigenvalues are the eigen- */
+/*                values of the upper Hessenberg matrix rows and */
+/*                columns ILO through INFO of the final, output */
+/*                value of H. */
+
+/*                If INFO .GT. 0 and WANTT is .TRUE., then on exit */
+
+/*           (*)  (initial value of H)*U  = U*(final value of H) */
+
+/*                where U is an orthogonal matrix.  The final */
+/*                value of H is upper Hessenberg and quasi-triangular */
+/*                in rows and columns INFO+1 through IHI. */
+
+/*                If INFO .GT. 0 and WANTZ is .TRUE., then on exit */
+
+/*                  (final value of Z(ILO:IHI,ILOZ:IHIZ) */
+/*                   =  (initial value of Z(ILO:IHI,ILOZ:IHIZ)*U */
+
+/*                where U is the orthogonal matrix in (*) (regard- */
+/*                less of the value of WANTT.) */
+
+/*                If INFO .GT. 0 and WANTZ is .FALSE., then Z is not */
+/*                accessed. */
+
+/*     ================================================================ */
+/*     Based on contributions by */
+/*        Karen Braman and Ralph Byers, Department of Mathematics, */
+/*        University of Kansas, USA */
+
+/*     ================================================================ */
+/*     References: */
+/*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
+/*       Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
+/*       Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
+/*       929--947, 2002. */
+
+/*       K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
+/*       Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
+/*       of Matrix Analysis, volume 23, pages 948--973, 2002. */
+
+/*     ================================================================ */
+/*     .. Parameters .. */
+
+/*     ==== Matrices of order NTINY or smaller must be processed by */
+/*     .    SLAHQR because of insufficient subdiagonal scratch space. */
+/*     .    (This is a hard limit.) ==== */
+
+/*     ==== Exceptional deflation windows:  try to cure rare */
+/*     .    slow convergence by varying the size of the */
+/*     .    deflation window after KEXNW iterations. ==== */
+
+/*     ==== Exceptional shifts: try to cure rare slow convergence */
+/*     .    with ad-hoc exceptional shifts every KEXSH iterations. */
+/*     .    ==== */
+
+/*     ==== The constants WILK1 and WILK2 are used to form the */
+/*     .    exceptional shifts. ==== */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. Local Arrays .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+    /* Parameter adjustments */
+    h_dim1 = *ldh;
+    h_offset = 1 + h_dim1;
+    h__ -= h_offset;
+    --wr;
+    --wi;
+    z_dim1 = *ldz;
+    z_offset = 1 + z_dim1;
+    z__ -= z_offset;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+
+/*     ==== Quick return for N = 0: nothing to do. ==== */
+
+    if (*n == 0) {
+	work[1] = 1.f;
+	return 0;
+    }
+
+    if (*n <= 11) {
+
+/*        ==== Tiny matrices must use SLAHQR. ==== */
+
+	lwkopt = 1;
+	if (*lwork != -1) {
+	    slahqr_(wantt, wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &
+		    wi[1], iloz, ihiz, &z__[z_offset], ldz, info);
+	}
+    } else {
+
+/*        ==== Use small bulge multi-shift QR with aggressive early */
+/*        .    deflation on larger-than-tiny matrices. ==== */
+
+/*        ==== Hope for the best. ==== */
+
+	*info = 0;
+
+/*        ==== Set up job flags for ILAENV. ==== */
+
+	if (*wantt) {
+	    *(unsigned char *)jbcmpz = 'S';
+	} else {
+	    *(unsigned char *)jbcmpz = 'E';
+	}
+	if (*wantz) {
+	    *(unsigned char *)&jbcmpz[1] = 'V';
+	} else {
+	    *(unsigned char *)&jbcmpz[1] = 'N';
+	}
+
+/*        ==== NWR = recommended deflation window size.  At this */
+/*        .    point,  N .GT. NTINY = 11, so there is enough */
+/*        .    subdiagonal workspace for NWR.GE.2 as required. */
+/*        .    (In fact, there is enough subdiagonal space for */
+/*        .    NWR.GE.3.) ==== */
+
+	nwr = ilaenv_(&c__13, "SLAQR0", jbcmpz, n, ilo, ihi, lwork);
+	nwr = max(2,nwr);
+/* Computing MIN */
+	i__1 = *ihi - *ilo + 1, i__2 = (*n - 1) / 3, i__1 = min(i__1,i__2);
+	nwr = min(i__1,nwr);
+
+/*        ==== NSR = recommended number of simultaneous shifts. */
+/*        .    At this point N .GT. NTINY = 11, so there is at */
+/*        .    enough subdiagonal workspace for NSR to be even */
+/*        .    and greater than or equal to two as required. ==== */
+
+	nsr = ilaenv_(&c__15, "SLAQR0", jbcmpz, n, ilo, ihi, lwork);
+/* Computing MIN */
+	i__1 = nsr, i__2 = (*n + 6) / 9, i__1 = min(i__1,i__2), i__2 = *ihi - 
+		*ilo;
+	nsr = min(i__1,i__2);
+/* Computing MAX */
+	i__1 = 2, i__2 = nsr - nsr % 2;
+	nsr = max(i__1,i__2);
+
+/*        ==== Estimate optimal workspace ==== */
+
+/*        ==== Workspace query call to SLAQR3 ==== */
+
+	i__1 = nwr + 1;
+	slaqr3_(wantt, wantz, n, ilo, ihi, &i__1, &h__[h_offset], ldh, iloz, 
+		ihiz, &z__[z_offset], ldz, &ls, &ld, &wr[1], &wi[1], &h__[
+		h_offset], ldh, n, &h__[h_offset], ldh, n, &h__[h_offset], 
+		ldh, &work[1], &c_n1);
+
+/*        ==== Optimal workspace = MAX(SLAQR5, SLAQR3) ==== */
+
+/* Computing MAX */
+	i__1 = nsr * 3 / 2, i__2 = (integer) work[1];
+	lwkopt = max(i__1,i__2);
+
+/*        ==== Quick return in case of workspace query. ==== */
+
+	if (*lwork == -1) {
+	    work[1] = (real) lwkopt;
+	    return 0;
+	}
+
+/*        ==== SLAHQR/SLAQR0 crossover point ==== */
+
+	nmin = ilaenv_(&c__12, "SLAQR0", jbcmpz, n, ilo, ihi, lwork);
+	nmin = max(11,nmin);
+
+/*        ==== Nibble crossover point ==== */
+
+	nibble = ilaenv_(&c__14, "SLAQR0", jbcmpz, n, ilo, ihi, lwork);
+	nibble = max(0,nibble);
+
+/*        ==== Accumulate reflections during ttswp?  Use block */
+/*        .    2-by-2 structure during matrix-matrix multiply? ==== */
+
+	kacc22 = ilaenv_(&c__16, "SLAQR0", jbcmpz, n, ilo, ihi, lwork);
+	kacc22 = max(0,kacc22);
+	kacc22 = min(2,kacc22);
+
+/*        ==== NWMAX = the largest possible deflation window for */
+/*        .    which there is sufficient workspace. ==== */
+
+/* Computing MIN */
+	i__1 = (*n - 1) / 3, i__2 = *lwork / 2;
+	nwmax = min(i__1,i__2);
+	nw = nwmax;
+
+/*        ==== NSMAX = the Largest number of simultaneous shifts */
+/*        .    for which there is sufficient workspace. ==== */
+
+/* Computing MIN */
+	i__1 = (*n + 6) / 9, i__2 = (*lwork << 1) / 3;
+	nsmax = min(i__1,i__2);
+	nsmax -= nsmax % 2;
+
+/*        ==== NDFL: an iteration count restarted at deflation. ==== */
+
+	ndfl = 1;
+
+/*        ==== ITMAX = iteration limit ==== */
+
+/* Computing MAX */
+	i__1 = 10, i__2 = *ihi - *ilo + 1;
+	itmax = max(i__1,i__2) * 30;
+
+/*        ==== Last row and column in the active block ==== */
+
+	kbot = *ihi;
+
+/*        ==== Main Loop ==== */
+
+	i__1 = itmax;
+	for (it = 1; it <= i__1; ++it) {
+
+/*           ==== Done when KBOT falls below ILO ==== */
+
+	    if (kbot < *ilo) {
+		goto L90;
+	    }
+
+/*           ==== Locate active block ==== */
+
+	    i__2 = *ilo + 1;
+	    for (k = kbot; k >= i__2; --k) {
+		if (h__[k + (k - 1) * h_dim1] == 0.f) {
+		    goto L20;
+		}
+/* L10: */
+	    }
+	    k = *ilo;
+L20:
+	    ktop = k;
+
+/*           ==== Select deflation window size: */
+/*           .    Typical Case: */
+/*           .      If possible and advisable, nibble the entire */
+/*           .      active block.  If not, use size MIN(NWR,NWMAX) */
+/*           .      or MIN(NWR+1,NWMAX) depending upon which has */
+/*           .      the smaller corresponding subdiagonal entry */
+/*           .      (a heuristic). */
+/*           . */
+/*           .    Exceptional Case: */
+/*           .      If there have been no deflations in KEXNW or */
+/*           .      more iterations, then vary the deflation window */
+/*           .      size.   At first, because, larger windows are, */
+/*           .      in general, more powerful than smaller ones, */
+/*           .      rapidly increase the window to the maximum possible. */
+/*           .      Then, gradually reduce the window size. ==== */
+
+	    nh = kbot - ktop + 1;
+	    nwupbd = min(nh,nwmax);
+	    if (ndfl < 5) {
+		nw = min(nwupbd,nwr);
+	    } else {
+/* Computing MIN */
+		i__2 = nwupbd, i__3 = nw << 1;
+		nw = min(i__2,i__3);
+	    }
+	    if (nw < nwmax) {
+		if (nw >= nh - 1) {
+		    nw = nh;
+		} else {
+		    kwtop = kbot - nw + 1;
+		    if ((r__1 = h__[kwtop + (kwtop - 1) * h_dim1], dabs(r__1))
+			     > (r__2 = h__[kwtop - 1 + (kwtop - 2) * h_dim1], 
+			    dabs(r__2))) {
+			++nw;
+		    }
+		}
+	    }
+	    if (ndfl < 5) {
+		ndec = -1;
+	    } else if (ndec >= 0 || nw >= nwupbd) {
+		++ndec;
+		if (nw - ndec < 2) {
+		    ndec = 0;
+		}
+		nw -= ndec;
+	    }
+
+/*           ==== Aggressive early deflation: */
+/*           .    split workspace under the subdiagonal into */
+/*           .      - an nw-by-nw work array V in the lower */
+/*           .        left-hand-corner, */
+/*           .      - an NW-by-at-least-NW-but-more-is-better */
+/*           .        (NW-by-NHO) horizontal work array along */
+/*           .        the bottom edge, */
+/*           .      - an at-least-NW-but-more-is-better (NHV-by-NW) */
+/*           .        vertical work array along the left-hand-edge. */
+/*           .        ==== */
+
+	    kv = *n - nw + 1;
+	    kt = nw + 1;
+	    nho = *n - nw - 1 - kt + 1;
+	    kwv = nw + 2;
+	    nve = *n - nw - kwv + 1;
+
+/*           ==== Aggressive early deflation ==== */
+
+	    slaqr3_(wantt, wantz, n, &ktop, &kbot, &nw, &h__[h_offset], ldh, 
+		    iloz, ihiz, &z__[z_offset], ldz, &ls, &ld, &wr[1], &wi[1], 
+		     &h__[kv + h_dim1], ldh, &nho, &h__[kv + kt * h_dim1], 
+		    ldh, &nve, &h__[kwv + h_dim1], ldh, &work[1], lwork);
+
+/*           ==== Adjust KBOT accounting for new deflations. ==== */
+
+	    kbot -= ld;
+
+/*           ==== KS points to the shifts. ==== */
+
+	    ks = kbot - ls + 1;
+
+/*           ==== Skip an expensive QR sweep if there is a (partly */
+/*           .    heuristic) reason to expect that many eigenvalues */
+/*           .    will deflate without it.  Here, the QR sweep is */
+/*           .    skipped if many eigenvalues have just been deflated */
+/*           .    or if the remaining active block is small. */
+
+	    if (ld == 0 || ld * 100 <= nw * nibble && kbot - ktop + 1 > min(
+		    nmin,nwmax)) {
+
+/*              ==== NS = nominal number of simultaneous shifts. */
+/*              .    This may be lowered (slightly) if SLAQR3 */
+/*              .    did not provide that many shifts. ==== */
+
+/* Computing MIN */
+/* Computing MAX */
+		i__4 = 2, i__5 = kbot - ktop;
+		i__2 = min(nsmax,nsr), i__3 = max(i__4,i__5);
+		ns = min(i__2,i__3);
+		ns -= ns % 2;
+
+/*              ==== If there have been no deflations */
+/*              .    in a multiple of KEXSH iterations, */
+/*              .    then try exceptional shifts. */
+/*              .    Otherwise use shifts provided by */
+/*              .    SLAQR3 above or from the eigenvalues */
+/*              .    of a trailing principal submatrix. ==== */
+
+		if (ndfl % 6 == 0) {
+		    ks = kbot - ns + 1;
+/* Computing MAX */
+		    i__3 = ks + 1, i__4 = ktop + 2;
+		    i__2 = max(i__3,i__4);
+		    for (i__ = kbot; i__ >= i__2; i__ += -2) {
+			ss = (r__1 = h__[i__ + (i__ - 1) * h_dim1], dabs(r__1)
+				) + (r__2 = h__[i__ - 1 + (i__ - 2) * h_dim1],
+				 dabs(r__2));
+			aa = ss * .75f + h__[i__ + i__ * h_dim1];
+			bb = ss;
+			cc = ss * -.4375f;
+			dd = aa;
+			slanv2_(&aa, &bb, &cc, &dd, &wr[i__ - 1], &wi[i__ - 1]
+, &wr[i__], &wi[i__], &cs, &sn);
+/* L30: */
+		    }
+		    if (ks == ktop) {
+			wr[ks + 1] = h__[ks + 1 + (ks + 1) * h_dim1];
+			wi[ks + 1] = 0.f;
+			wr[ks] = wr[ks + 1];
+			wi[ks] = wi[ks + 1];
+		    }
+		} else {
+
+/*                 ==== Got NS/2 or fewer shifts? Use SLAQR4 or */
+/*                 .    SLAHQR on a trailing principal submatrix to */
+/*                 .    get more. (Since NS.LE.NSMAX.LE.(N+6)/9, */
+/*                 .    there is enough space below the subdiagonal */
+/*                 .    to fit an NS-by-NS scratch array.) ==== */
+
+		    if (kbot - ks + 1 <= ns / 2) {
+			ks = kbot - ns + 1;
+			kt = *n - ns + 1;
+			slacpy_("A", &ns, &ns, &h__[ks + ks * h_dim1], ldh, &
+				h__[kt + h_dim1], ldh);
+			if (ns > nmin) {
+			    slaqr4_(&c_false, &c_false, &ns, &c__1, &ns, &h__[
+				    kt + h_dim1], ldh, &wr[ks], &wi[ks], &
+				    c__1, &c__1, zdum, &c__1, &work[1], lwork, 
+				     &inf);
+			} else {
+			    slahqr_(&c_false, &c_false, &ns, &c__1, &ns, &h__[
+				    kt + h_dim1], ldh, &wr[ks], &wi[ks], &
+				    c__1, &c__1, zdum, &c__1, &inf);
+			}
+			ks += inf;
+
+/*                    ==== In case of a rare QR failure use */
+/*                    .    eigenvalues of the trailing 2-by-2 */
+/*                    .    principal submatrix.  ==== */
+
+			if (ks >= kbot) {
+			    aa = h__[kbot - 1 + (kbot - 1) * h_dim1];
+			    cc = h__[kbot + (kbot - 1) * h_dim1];
+			    bb = h__[kbot - 1 + kbot * h_dim1];
+			    dd = h__[kbot + kbot * h_dim1];
+			    slanv2_(&aa, &bb, &cc, &dd, &wr[kbot - 1], &wi[
+				    kbot - 1], &wr[kbot], &wi[kbot], &cs, &sn)
+				    ;
+			    ks = kbot - 1;
+			}
+		    }
+
+		    if (kbot - ks + 1 > ns) {
+
+/*                    ==== Sort the shifts (Helps a little) */
+/*                    .    Bubble sort keeps complex conjugate */
+/*                    .    pairs together. ==== */
+
+			sorted = FALSE_;
+			i__2 = ks + 1;
+			for (k = kbot; k >= i__2; --k) {
+			    if (sorted) {
+				goto L60;
+			    }
+			    sorted = TRUE_;
+			    i__3 = k - 1;
+			    for (i__ = ks; i__ <= i__3; ++i__) {
+				if ((r__1 = wr[i__], dabs(r__1)) + (r__2 = wi[
+					i__], dabs(r__2)) < (r__3 = wr[i__ + 
+					1], dabs(r__3)) + (r__4 = wi[i__ + 1],
+					 dabs(r__4))) {
+				    sorted = FALSE_;
+
+				    swap = wr[i__];
+				    wr[i__] = wr[i__ + 1];
+				    wr[i__ + 1] = swap;
+
+				    swap = wi[i__];
+				    wi[i__] = wi[i__ + 1];
+				    wi[i__ + 1] = swap;
+				}
+/* L40: */
+			    }
+/* L50: */
+			}
+L60:
+			;
+		    }
+
+/*                 ==== Shuffle shifts into pairs of real shifts */
+/*                 .    and pairs of complex conjugate shifts */
+/*                 .    assuming complex conjugate shifts are */
+/*                 .    already adjacent to one another. (Yes, */
+/*                 .    they are.)  ==== */
+
+		    i__2 = ks + 2;
+		    for (i__ = kbot; i__ >= i__2; i__ += -2) {
+			if (wi[i__] != -wi[i__ - 1]) {
+
+			    swap = wr[i__];
+			    wr[i__] = wr[i__ - 1];
+			    wr[i__ - 1] = wr[i__ - 2];
+			    wr[i__ - 2] = swap;
+
+			    swap = wi[i__];
+			    wi[i__] = wi[i__ - 1];
+			    wi[i__ - 1] = wi[i__ - 2];
+			    wi[i__ - 2] = swap;
+			}
+/* L70: */
+		    }
+		}
+
+/*              ==== If there are only two shifts and both are */
+/*              .    real, then use only one.  ==== */
+
+		if (kbot - ks + 1 == 2) {
+		    if (wi[kbot] == 0.f) {
+			if ((r__1 = wr[kbot] - h__[kbot + kbot * h_dim1], 
+				dabs(r__1)) < (r__2 = wr[kbot - 1] - h__[kbot 
+				+ kbot * h_dim1], dabs(r__2))) {
+			    wr[kbot - 1] = wr[kbot];
+			} else {
+			    wr[kbot] = wr[kbot - 1];
+			}
+		    }
+		}
+
+/*              ==== Use up to NS of the the smallest magnatiude */
+/*              .    shifts.  If there aren't NS shifts available, */
+/*              .    then use them all, possibly dropping one to */
+/*              .    make the number of shifts even. ==== */
+
+/* Computing MIN */
+		i__2 = ns, i__3 = kbot - ks + 1;
+		ns = min(i__2,i__3);
+		ns -= ns % 2;
+		ks = kbot - ns + 1;
+
+/*              ==== Small-bulge multi-shift QR sweep: */
+/*              .    split workspace under the subdiagonal into */
+/*              .    - a KDU-by-KDU work array U in the lower */
+/*              .      left-hand-corner, */
+/*              .    - a KDU-by-at-least-KDU-but-more-is-better */
+/*              .      (KDU-by-NHo) horizontal work array WH along */
+/*              .      the bottom edge, */
+/*              .    - and an at-least-KDU-but-more-is-better-by-KDU */
+/*              .      (NVE-by-KDU) vertical work WV arrow along */
+/*              .      the left-hand-edge. ==== */
+
+		kdu = ns * 3 - 3;
+		ku = *n - kdu + 1;
+		kwh = kdu + 1;
+		nho = *n - kdu - 3 - (kdu + 1) + 1;
+		kwv = kdu + 4;
+		nve = *n - kdu - kwv + 1;
+
+/*              ==== Small-bulge multi-shift QR sweep ==== */
+
+		slaqr5_(wantt, wantz, &kacc22, n, &ktop, &kbot, &ns, &wr[ks], 
+			&wi[ks], &h__[h_offset], ldh, iloz, ihiz, &z__[
+			z_offset], ldz, &work[1], &c__3, &h__[ku + h_dim1], 
+			ldh, &nve, &h__[kwv + h_dim1], ldh, &nho, &h__[ku + 
+			kwh * h_dim1], ldh);
+	    }
+
+/*           ==== Note progress (or the lack of it). ==== */
+
+	    if (ld > 0) {
+		ndfl = 1;
+	    } else {
+		++ndfl;
+	    }
+
+/*           ==== End of main loop ==== */
+/* L80: */
+	}
+
+/*        ==== Iteration limit exceeded.  Set INFO to show where */
+/*        .    the problem occurred and exit. ==== */
+
+	*info = kbot;
+L90:
+	;
+    }
+
+/*     ==== Return the optimal value of LWORK. ==== */
+
+    work[1] = (real) lwkopt;
+
+/*     ==== End of SLAQR0 ==== */
+
+    return 0;
+} /* slaqr0_ */