dsbgst.c

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/* dsbgst.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 doublereal c_b8 = 0.;
static doublereal c_b9 = 1.;
static integer c__1 = 1;
static doublereal c_b20 = -1.;

/* Subroutine */ int dsbgst_(char *vect, char *uplo, integer *n, integer *ka, 
        integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
        ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info)
{
    /* System generated locals */
    integer ab_dim1, ab_offset, bb_dim1, bb_offset, x_dim1, x_offset, i__1, 
            i__2, i__3, i__4;
    doublereal d__1;

    /* Local variables */
    integer i__, j, k, l, m;
    doublereal t;
    integer i0, i1, i2, j1, j2;
    doublereal ra;
    integer nr, nx, ka1, kb1;
    doublereal ra1;
    integer j1t, j2t;
    doublereal bii;
    integer kbt, nrt, inca;
    extern /* Subroutine */ int dger_(integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *), drot_(integer *, doublereal *, integer *, doublereal *
, integer *, doublereal *, doublereal *), dscal_(integer *, 
            doublereal *, doublereal *, integer *);
    extern logical lsame_(char *, char *);
    logical upper, wantx;
    extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *, 
             doublereal *, integer *, doublereal *, doublereal *, integer *), 
            dlaset_(char *, integer *, integer *, doublereal *, doublereal *, 
            doublereal *, integer *), dlartg_(doublereal *, 
            doublereal *, doublereal *, doublereal *, doublereal *), xerbla_(
            char *, integer *), dlargv_(integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, integer *);
    logical update;
    extern /* Subroutine */ int dlartv_(integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *);


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

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

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

/*  DSBGST reduces a real symmetric-definite banded generalized */
/*  eigenproblem  A*x = lambda*B*x  to standard form  C*y = lambda*y, */
/*  such that C has the same bandwidth as A. */

/*  B must have been previously factorized as S**T*S by DPBSTF, using a */
/*  split Cholesky factorization. A is overwritten by C = X**T*A*X, where */
/*  X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the */
/*  bandwidth of A. */

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

/*  VECT    (input) CHARACTER*1 */
/*          = 'N':  do not form the transformation matrix X; */
/*          = 'V':  form X. */

/*  UPLO    (input) CHARACTER*1 */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrices A and B.  N >= 0. */

/*  KA      (input) INTEGER */
/*          The number of superdiagonals of the matrix A if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KA >= 0. */

/*  KB      (input) INTEGER */
/*          The number of superdiagonals of the matrix B if UPLO = 'U', */
/*          or the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0. */

/*  AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
/*          On entry, the upper or lower triangle of the symmetric band */
/*          matrix A, stored in the first ka+1 rows of the array.  The */
/*          j-th column of A is stored in the j-th column of the array AB */
/*          as follows: */
/*          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */
/*          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka). */

/*          On exit, the transformed matrix X**T*A*X, stored in the same */
/*          format as A. */

/*  LDAB    (input) INTEGER */
/*          The leading dimension of the array AB.  LDAB >= KA+1. */

/*  BB      (input) DOUBLE PRECISION array, dimension (LDBB,N) */
/*          The banded factor S from the split Cholesky factorization of */
/*          B, as returned by DPBSTF, stored in the first KB+1 rows of */
/*          the array. */

/*  LDBB    (input) INTEGER */
/*          The leading dimension of the array BB.  LDBB >= KB+1. */

/*  X       (output) DOUBLE PRECISION array, dimension (LDX,N) */
/*          If VECT = 'V', the n-by-n matrix X. */
/*          If VECT = 'N', the array X is not referenced. */

/*  LDX     (input) INTEGER */
/*          The leading dimension of the array X. */
/*          LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. */

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (2*N) */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */

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

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

/*     Test the input parameters */

    /* Parameter adjustments */
    ab_dim1 = *ldab;
    ab_offset = 1 + ab_dim1;
    ab -= ab_offset;
    bb_dim1 = *ldbb;
    bb_offset = 1 + bb_dim1;
    bb -= bb_offset;
    x_dim1 = *ldx;
    x_offset = 1 + x_dim1;
    x -= x_offset;
    --work;

    /* Function Body */
    wantx = lsame_(vect, "V");
    upper = lsame_(uplo, "U");
    ka1 = *ka + 1;
    kb1 = *kb + 1;
    *info = 0;
    if (! wantx && ! lsame_(vect, "N")) {
        *info = -1;
    } else if (! upper && ! lsame_(uplo, "L")) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*ka < 0) {
        *info = -4;
    } else if (*kb < 0 || *kb > *ka) {
        *info = -5;
    } else if (*ldab < *ka + 1) {
        *info = -7;
    } else if (*ldbb < *kb + 1) {
        *info = -9;
    } else if (*ldx < 1 || wantx && *ldx < max(1,*n)) {
        *info = -11;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DSBGST", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
        return 0;
    }

    inca = *ldab * ka1;

/*     Initialize X to the unit matrix, if needed */

    if (wantx) {
        dlaset_("Full", n, n, &c_b8, &c_b9, &x[x_offset], ldx);
    }

/*     Set M to the splitting point m. It must be the same value as is */
/*     used in DPBSTF. The chosen value allows the arrays WORK and RWORK */
/*     to be of dimension (N). */

    m = (*n + *kb) / 2;

/*     The routine works in two phases, corresponding to the two halves */
/*     of the split Cholesky factorization of B as S**T*S where */

/*     S = ( U    ) */
/*         ( M  L ) */

/*     with U upper triangular of order m, and L lower triangular of */
/*     order n-m. S has the same bandwidth as B. */

/*     S is treated as a product of elementary matrices: */

/*     S = S(m)*S(m-1)*...*S(2)*S(1)*S(m+1)*S(m+2)*...*S(n-1)*S(n) */

/*     where S(i) is determined by the i-th row of S. */

/*     In phase 1, the index i takes the values n, n-1, ... , m+1; */
/*     in phase 2, it takes the values 1, 2, ... , m. */

/*     For each value of i, the current matrix A is updated by forming */
/*     inv(S(i))**T*A*inv(S(i)). This creates a triangular bulge outside */
/*     the band of A. The bulge is then pushed down toward the bottom of */
/*     A in phase 1, and up toward the top of A in phase 2, by applying */
/*     plane rotations. */

/*     There are kb*(kb+1)/2 elements in the bulge, but at most 2*kb-1 */
/*     of them are linearly independent, so annihilating a bulge requires */
/*     only 2*kb-1 plane rotations. The rotations are divided into a 1st */
/*     set of kb-1 rotations, and a 2nd set of kb rotations. */

/*     Wherever possible, rotations are generated and applied in vector */
/*     operations of length NR between the indices J1 and J2 (sometimes */
/*     replaced by modified values NRT, J1T or J2T). */

/*     The cosines and sines of the rotations are stored in the array */
/*     WORK. The cosines of the 1st set of rotations are stored in */
/*     elements n+2:n+m-kb-1 and the sines of the 1st set in elements */
/*     2:m-kb-1; the cosines of the 2nd set are stored in elements */
/*     n+m-kb+1:2*n and the sines of the second set in elements m-kb+1:n. */

/*     The bulges are not formed explicitly; nonzero elements outside the */
/*     band are created only when they are required for generating new */
/*     rotations; they are stored in the array WORK, in positions where */
/*     they are later overwritten by the sines of the rotations which */
/*     annihilate them. */

/*     **************************** Phase 1 ***************************** */

/*     The logical structure of this phase is: */

/*     UPDATE = .TRUE. */
/*     DO I = N, M + 1, -1 */
/*        use S(i) to update A and create a new bulge */
/*        apply rotations to push all bulges KA positions downward */
/*     END DO */
/*     UPDATE = .FALSE. */
/*     DO I = M + KA + 1, N - 1 */
/*        apply rotations to push all bulges KA positions downward */
/*     END DO */

/*     To avoid duplicating code, the two loops are merged. */

    update = TRUE_;
    i__ = *n + 1;
L10:
    if (update) {
        --i__;
/* Computing MIN */
        i__1 = *kb, i__2 = i__ - 1;
        kbt = min(i__1,i__2);
        i0 = i__ - 1;
/* Computing MIN */
        i__1 = *n, i__2 = i__ + *ka;
        i1 = min(i__1,i__2);
        i2 = i__ - kbt + ka1;
        if (i__ < m + 1) {
            update = FALSE_;
            ++i__;
            i0 = m;
            if (*ka == 0) {
                goto L480;
            }
            goto L10;
        }
    } else {
        i__ += *ka;
        if (i__ > *n - 1) {
            goto L480;
        }
    }

    if (upper) {

/*        Transform A, working with the upper triangle */

        if (update) {

/*           Form  inv(S(i))**T * A * inv(S(i)) */

            bii = bb[kb1 + i__ * bb_dim1];
            i__1 = i1;
            for (j = i__; j <= i__1; ++j) {
                ab[i__ - j + ka1 + j * ab_dim1] /= bii;
/* L20: */
            }
/* Computing MAX */
            i__1 = 1, i__2 = i__ - *ka;
            i__3 = i__;
            for (j = max(i__1,i__2); j <= i__3; ++j) {
                ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
/* L30: */
            }
            i__3 = i__ - 1;
            for (k = i__ - kbt; k <= i__3; ++k) {
                i__1 = k;
                for (j = i__ - kbt; j <= i__1; ++j) {
                    ab[j - k + ka1 + k * ab_dim1] = ab[j - k + ka1 + k * 
                            ab_dim1] - bb[j - i__ + kb1 + i__ * bb_dim1] * ab[
                            k - i__ + ka1 + i__ * ab_dim1] - bb[k - i__ + kb1 
                            + i__ * bb_dim1] * ab[j - i__ + ka1 + i__ * 
                            ab_dim1] + ab[ka1 + i__ * ab_dim1] * bb[j - i__ + 
                            kb1 + i__ * bb_dim1] * bb[k - i__ + kb1 + i__ * 
                            bb_dim1];
/* L40: */
                }
/* Computing MAX */
                i__1 = 1, i__2 = i__ - *ka;
                i__4 = i__ - kbt - 1;
                for (j = max(i__1,i__2); j <= i__4; ++j) {
                    ab[j - k + ka1 + k * ab_dim1] -= bb[k - i__ + kb1 + i__ * 
                            bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
/* L50: */
                }
/* L60: */
            }
            i__3 = i1;
            for (j = i__; j <= i__3; ++j) {
/* Computing MAX */
                i__4 = j - *ka, i__1 = i__ - kbt;
                i__2 = i__ - 1;
                for (k = max(i__4,i__1); k <= i__2; ++k) {
                    ab[k - j + ka1 + j * ab_dim1] -= bb[k - i__ + kb1 + i__ * 
                            bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
/* L70: */
                }
/* L80: */
            }

            if (wantx) {

/*              post-multiply X by inv(S(i)) */

                i__3 = *n - m;
                d__1 = 1. / bii;
                dscal_(&i__3, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
                if (kbt > 0) {
                    i__3 = *n - m;
                    dger_(&i__3, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
                            c__1, &bb[kb1 - kbt + i__ * bb_dim1], &c__1, &x[m 
                            + 1 + (i__ - kbt) * x_dim1], ldx);
                }
            }

/*           store a(i,i1) in RA1 for use in next loop over K */

            ra1 = ab[i__ - i1 + ka1 + i1 * ab_dim1];
        }

/*        Generate and apply vectors of rotations to chase all the */
/*        existing bulges KA positions down toward the bottom of the */
/*        band */

        i__3 = *kb - 1;
        for (k = 1; k <= i__3; ++k) {
            if (update) {

/*              Determine the rotations which would annihilate the bulge */
/*              which has in theory just been created */

                if (i__ - k + *ka < *n && i__ - k > 1) {

/*                 generate rotation to annihilate a(i,i-k+ka+1) */

                    dlartg_(&ab[k + 1 + (i__ - k + *ka) * ab_dim1], &ra1, &
                            work[*n + i__ - k + *ka - m], &work[i__ - k + *ka 
                            - m], &ra);

/*                 create nonzero element a(i-k,i-k+ka+1) outside the */
/*                 band and store it in WORK(i-k) */

                    t = -bb[kb1 - k + i__ * bb_dim1] * ra1;
                    work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
                            i__ - k + *ka - m] * ab[(i__ - k + *ka) * ab_dim1 
                            + 1];
                    ab[(i__ - k + *ka) * ab_dim1 + 1] = work[i__ - k + *ka - 
                            m] * t + work[*n + i__ - k + *ka - m] * ab[(i__ - 
                            k + *ka) * ab_dim1 + 1];
                    ra1 = ra;
                }
            }
/* Computing MAX */
            i__2 = 1, i__4 = k - i0 + 2;
            j2 = i__ - k - 1 + max(i__2,i__4) * ka1;
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            if (update) {
/* Computing MAX */
                i__2 = j2, i__4 = i__ + (*ka << 1) - k + 1;
                j2t = max(i__2,i__4);
            } else {
                j2t = j2;
            }
            nrt = (*n - j2t + *ka) / ka1;
            i__2 = j1;
            i__4 = ka1;
            for (j = j2t; i__4 < 0 ? j >= i__2 : j <= i__2; j += i__4) {

/*              create nonzero element a(j-ka,j+1) outside the band */
/*              and store it in WORK(j-m) */

                work[j - m] *= ab[(j + 1) * ab_dim1 + 1];
                ab[(j + 1) * ab_dim1 + 1] = work[*n + j - m] * ab[(j + 1) * 
                        ab_dim1 + 1];
/* L90: */
            }

/*           generate rotations in 1st set to annihilate elements which */
/*           have been created outside the band */

            if (nrt > 0) {
                dlargv_(&nrt, &ab[j2t * ab_dim1 + 1], &inca, &work[j2t - m], &
                        ka1, &work[*n + j2t - m], &ka1);
            }
            if (nr > 0) {

/*              apply rotations in 1st set from the right */

                i__4 = *ka - 1;
                for (l = 1; l <= i__4; ++l) {
                    dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka 
                            - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 - 
                            m], &work[j2 - m], &ka1);
/* L100: */
                }

/*              apply rotations in 1st set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) * 
                        ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
                        *n + j2 - m], &work[j2 - m], &ka1);

            }

/*           start applying rotations in 1st set from the left */

            i__4 = *kb - k + 1;
            for (l = *ka - 1; l >= i__4; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
                            ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
                            work[*n + j2 - m], &work[j2 - m], &ka1);
                }
/* L110: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 1st set */

                i__4 = j1;
                i__2 = ka1;
                for (j = j2; i__2 < 0 ? j >= i__4 : j <= i__4; j += i__2) {
                    i__1 = *n - m;
                    drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j 
                            + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j 
                            - m]);
/* L120: */
                }
            }
/* L130: */
        }

        if (update) {
            if (i2 <= *n && kbt > 0) {

/*              create nonzero element a(i-kbt,i-kbt+ka+1) outside the */
/*              band and store it in WORK(i-kbt) */

                work[i__ - kbt] = -bb[kb1 - kbt + i__ * bb_dim1] * ra1;
            }
        }

        for (k = *kb; k >= 1; --k) {
            if (update) {
/* Computing MAX */
                i__3 = 2, i__2 = k - i0 + 1;
                j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
            } else {
/* Computing MAX */
                i__3 = 1, i__2 = k - i0 + 1;
                j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
            }

/*           finish applying rotations in 2nd set from the left */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (*n - j2 + *ka + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + (j2 - l + 1) * ab_dim1], &inca, &ab[
                            l + 1 + (j2 - l + 1) * ab_dim1], &inca, &work[*n 
                            + j2 - *ka], &work[j2 - *ka], &ka1);
                }
/* L140: */
            }
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            i__3 = j2;
            i__2 = -ka1;
            for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
                work[j] = work[j - *ka];
                work[*n + j] = work[*n + j - *ka];
/* L150: */
            }
            i__2 = j1;
            i__3 = ka1;
            for (j = j2; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) {

/*              create nonzero element a(j-ka,j+1) outside the band */
/*              and store it in WORK(j) */

                work[j] *= ab[(j + 1) * ab_dim1 + 1];
                ab[(j + 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + 1) * 
                        ab_dim1 + 1];
/* L160: */
            }
            if (update) {
                if (i__ - k < *n - *ka && k <= kbt) {
                    work[i__ - k + *ka] = work[i__ - k];
                }
            }
/* L170: */
        }

        for (k = *kb; k >= 1; --k) {
/* Computing MAX */
            i__3 = 1, i__2 = k - i0 + 1;
            j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            if (nr > 0) {

/*              generate rotations in 2nd set to annihilate elements */
/*              which have been created outside the band */

                dlargv_(&nr, &ab[j2 * ab_dim1 + 1], &inca, &work[j2], &ka1, &
                        work[*n + j2], &ka1);

/*              apply rotations in 2nd set from the right */

                i__3 = *ka - 1;
                for (l = 1; l <= i__3; ++l) {
                    dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka 
                            - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2], 
                            &work[j2], &ka1);
/* L180: */
                }

/*              apply rotations in 2nd set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) * 
                        ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
                        *n + j2], &work[j2], &ka1);

            }

/*           start applying rotations in 2nd set from the left */

            i__3 = *kb - k + 1;
            for (l = *ka - 1; l >= i__3; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
                            ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
                            work[*n + j2], &work[j2], &ka1);
                }
/* L190: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 2nd set */

                i__3 = j1;
                i__2 = ka1;
                for (j = j2; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
                    i__4 = *n - m;
                    drot_(&i__4, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j 
                            + 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
/* L200: */
                }
            }
/* L210: */
        }

        i__2 = *kb - 1;
        for (k = 1; k <= i__2; ++k) {
/* Computing MAX */
            i__3 = 1, i__4 = k - i0 + 2;
            j2 = i__ - k - 1 + max(i__3,i__4) * ka1;

/*           finish applying rotations in 1st set from the left */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
                            ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
                            work[*n + j2 - m], &work[j2 - m], &ka1);
                }
/* L220: */
            }
/* L230: */
        }

        if (*kb > 1) {
            i__2 = i__ - *kb + (*ka << 1) + 1;
            for (j = *n - 1; j >= i__2; --j) {
                work[*n + j - m] = work[*n + j - *ka - m];
                work[j - m] = work[j - *ka - m];
/* L240: */
            }
        }

    } else {

/*        Transform A, working with the lower triangle */

        if (update) {

/*           Form  inv(S(i))**T * A * inv(S(i)) */

            bii = bb[i__ * bb_dim1 + 1];
            i__2 = i1;
            for (j = i__; j <= i__2; ++j) {
                ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
/* L250: */
            }
/* Computing MAX */
            i__2 = 1, i__3 = i__ - *ka;
            i__4 = i__;
            for (j = max(i__2,i__3); j <= i__4; ++j) {
                ab[i__ - j + 1 + j * ab_dim1] /= bii;
/* L260: */
            }
            i__4 = i__ - 1;
            for (k = i__ - kbt; k <= i__4; ++k) {
                i__2 = k;
                for (j = i__ - kbt; j <= i__2; ++j) {
                    ab[k - j + 1 + j * ab_dim1] = ab[k - j + 1 + j * ab_dim1] 
                            - bb[i__ - j + 1 + j * bb_dim1] * ab[i__ - k + 1 
                            + k * ab_dim1] - bb[i__ - k + 1 + k * bb_dim1] * 
                            ab[i__ - j + 1 + j * ab_dim1] + ab[i__ * ab_dim1 
                            + 1] * bb[i__ - j + 1 + j * bb_dim1] * bb[i__ - k 
                            + 1 + k * bb_dim1];
/* L270: */
                }
/* Computing MAX */
                i__2 = 1, i__3 = i__ - *ka;
                i__1 = i__ - kbt - 1;
                for (j = max(i__2,i__3); j <= i__1; ++j) {
                    ab[k - j + 1 + j * ab_dim1] -= bb[i__ - k + 1 + k * 
                            bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
/* L280: */
                }
/* L290: */
            }
            i__4 = i1;
            for (j = i__; j <= i__4; ++j) {
/* Computing MAX */
                i__1 = j - *ka, i__2 = i__ - kbt;
                i__3 = i__ - 1;
                for (k = max(i__1,i__2); k <= i__3; ++k) {
                    ab[j - k + 1 + k * ab_dim1] -= bb[i__ - k + 1 + k * 
                            bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
/* L300: */
                }
/* L310: */
            }

            if (wantx) {

/*              post-multiply X by inv(S(i)) */

                i__4 = *n - m;
                d__1 = 1. / bii;
                dscal_(&i__4, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
                if (kbt > 0) {
                    i__4 = *n - m;
                    i__3 = *ldbb - 1;
                    dger_(&i__4, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
                            c__1, &bb[kbt + 1 + (i__ - kbt) * bb_dim1], &i__3, 
                             &x[m + 1 + (i__ - kbt) * x_dim1], ldx);
                }
            }

/*           store a(i1,i) in RA1 for use in next loop over K */

            ra1 = ab[i1 - i__ + 1 + i__ * ab_dim1];
        }

/*        Generate and apply vectors of rotations to chase all the */
/*        existing bulges KA positions down toward the bottom of the */
/*        band */

        i__4 = *kb - 1;
        for (k = 1; k <= i__4; ++k) {
            if (update) {

/*              Determine the rotations which would annihilate the bulge */
/*              which has in theory just been created */

                if (i__ - k + *ka < *n && i__ - k > 1) {

/*                 generate rotation to annihilate a(i-k+ka+1,i) */

                    dlartg_(&ab[ka1 - k + i__ * ab_dim1], &ra1, &work[*n + 
                            i__ - k + *ka - m], &work[i__ - k + *ka - m], &ra)
                            ;

/*                 create nonzero element a(i-k+ka+1,i-k) outside the */
/*                 band and store it in WORK(i-k) */

                    t = -bb[k + 1 + (i__ - k) * bb_dim1] * ra1;
                    work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
                            i__ - k + *ka - m] * ab[ka1 + (i__ - k) * ab_dim1]
                            ;
                    ab[ka1 + (i__ - k) * ab_dim1] = work[i__ - k + *ka - m] * 
                            t + work[*n + i__ - k + *ka - m] * ab[ka1 + (i__ 
                            - k) * ab_dim1];
                    ra1 = ra;
                }
            }
/* Computing MAX */
            i__3 = 1, i__1 = k - i0 + 2;
            j2 = i__ - k - 1 + max(i__3,i__1) * ka1;
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            if (update) {
/* Computing MAX */
                i__3 = j2, i__1 = i__ + (*ka << 1) - k + 1;
                j2t = max(i__3,i__1);
            } else {
                j2t = j2;
            }
            nrt = (*n - j2t + *ka) / ka1;
            i__3 = j1;
            i__1 = ka1;
            for (j = j2t; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {

/*              create nonzero element a(j+1,j-ka) outside the band */
/*              and store it in WORK(j-m) */

                work[j - m] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
                ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j - m] * ab[ka1 
                        + (j - *ka + 1) * ab_dim1];
/* L320: */
            }

/*           generate rotations in 1st set to annihilate elements which */
/*           have been created outside the band */

            if (nrt > 0) {
                dlargv_(&nrt, &ab[ka1 + (j2t - *ka) * ab_dim1], &inca, &work[
                        j2t - m], &ka1, &work[*n + j2t - m], &ka1);
            }
            if (nr > 0) {

/*              apply rotations in 1st set from the left */

                i__1 = *ka - 1;
                for (l = 1; l <= i__1; ++l) {
                    dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
                            l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2 
                            - m], &work[j2 - m], &ka1);
/* L330: */
                }

/*              apply rotations in 1st set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 + 
                        1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2 - m], 
                        &work[j2 - m], &ka1);

            }

/*           start applying rotations in 1st set from the right */

            i__1 = *kb - k + 1;
            for (l = *ka - 1; l >= i__1; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
                            ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + 
                            j2 - m], &work[j2 - m], &ka1);
                }
/* L340: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 1st set */

                i__1 = j1;
                i__3 = ka1;
                for (j = j2; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
                    i__2 = *n - m;
                    drot_(&i__2, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j 
                            + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j 
                            - m]);
/* L350: */
                }
            }
/* L360: */
        }

        if (update) {
            if (i2 <= *n && kbt > 0) {

/*              create nonzero element a(i-kbt+ka+1,i-kbt) outside the */
/*              band and store it in WORK(i-kbt) */

                work[i__ - kbt] = -bb[kbt + 1 + (i__ - kbt) * bb_dim1] * ra1;
            }
        }

        for (k = *kb; k >= 1; --k) {
            if (update) {
/* Computing MAX */
                i__4 = 2, i__3 = k - i0 + 1;
                j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
            } else {
/* Computing MAX */
                i__4 = 1, i__3 = k - i0 + 1;
                j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
            }

/*           finish applying rotations in 2nd set from the right */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (*n - j2 + *ka + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + (j2 - *ka) * ab_dim1], &
                            inca, &ab[ka1 - l + (j2 - *ka + 1) * ab_dim1], &
                            inca, &work[*n + j2 - *ka], &work[j2 - *ka], &ka1)
                            ;
                }
/* L370: */
            }
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            i__4 = j2;
            i__3 = -ka1;
            for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
                work[j] = work[j - *ka];
                work[*n + j] = work[*n + j - *ka];
/* L380: */
            }
            i__3 = j1;
            i__4 = ka1;
            for (j = j2; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {

/*              create nonzero element a(j+1,j-ka) outside the band */
/*              and store it in WORK(j) */

                work[j] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
                ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j] * ab[ka1 + (
                        j - *ka + 1) * ab_dim1];
/* L390: */
            }
            if (update) {
                if (i__ - k < *n - *ka && k <= kbt) {
                    work[i__ - k + *ka] = work[i__ - k];
                }
            }
/* L400: */
        }

        for (k = *kb; k >= 1; --k) {
/* Computing MAX */
            i__4 = 1, i__3 = k - i0 + 1;
            j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
            nr = (*n - j2 + *ka) / ka1;
            j1 = j2 + (nr - 1) * ka1;
            if (nr > 0) {

/*              generate rotations in 2nd set to annihilate elements */
/*              which have been created outside the band */

                dlargv_(&nr, &ab[ka1 + (j2 - *ka) * ab_dim1], &inca, &work[j2]
, &ka1, &work[*n + j2], &ka1);

/*              apply rotations in 2nd set from the left */

                i__4 = *ka - 1;
                for (l = 1; l <= i__4; ++l) {
                    dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
                            l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2]
, &work[j2], &ka1);
/* L410: */
                }

/*              apply rotations in 2nd set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 + 
                        1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2], &
                        work[j2], &ka1);

            }

/*           start applying rotations in 2nd set from the right */

            i__4 = *kb - k + 1;
            for (l = *ka - 1; l >= i__4; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
                            ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + 
                            j2], &work[j2], &ka1);
                }
/* L420: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 2nd set */

                i__4 = j1;
                i__3 = ka1;
                for (j = j2; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
                    i__1 = *n - m;
                    drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j 
                            + 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
/* L430: */
                }
            }
/* L440: */
        }

        i__3 = *kb - 1;
        for (k = 1; k <= i__3; ++k) {
/* Computing MAX */
            i__4 = 1, i__1 = k - i0 + 2;
            j2 = i__ - k - 1 + max(i__4,i__1) * ka1;

/*           finish applying rotations in 1st set from the right */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (*n - j2 + l) / ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
                            ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + 
                            j2 - m], &work[j2 - m], &ka1);
                }
/* L450: */
            }
/* L460: */
        }

        if (*kb > 1) {
            i__3 = i__ - *kb + (*ka << 1) + 1;
            for (j = *n - 1; j >= i__3; --j) {
                work[*n + j - m] = work[*n + j - *ka - m];
                work[j - m] = work[j - *ka - m];
/* L470: */
            }
        }

    }

    goto L10;

L480:

/*     **************************** Phase 2 ***************************** */

/*     The logical structure of this phase is: */

/*     UPDATE = .TRUE. */
/*     DO I = 1, M */
/*        use S(i) to update A and create a new bulge */
/*        apply rotations to push all bulges KA positions upward */
/*     END DO */
/*     UPDATE = .FALSE. */
/*     DO I = M - KA - 1, 2, -1 */
/*        apply rotations to push all bulges KA positions upward */
/*     END DO */

/*     To avoid duplicating code, the two loops are merged. */

    update = TRUE_;
    i__ = 0;
L490:
    if (update) {
        ++i__;
/* Computing MIN */
        i__3 = *kb, i__4 = m - i__;
        kbt = min(i__3,i__4);
        i0 = i__ + 1;
/* Computing MAX */
        i__3 = 1, i__4 = i__ - *ka;
        i1 = max(i__3,i__4);
        i2 = i__ + kbt - ka1;
        if (i__ > m) {
            update = FALSE_;
            --i__;
            i0 = m + 1;
            if (*ka == 0) {
                return 0;
            }
            goto L490;
        }
    } else {
        i__ -= *ka;
        if (i__ < 2) {
            return 0;
        }
    }

    if (i__ < m - kbt) {
        nx = m;
    } else {
        nx = *n;
    }

    if (upper) {

/*        Transform A, working with the upper triangle */

        if (update) {

/*           Form  inv(S(i))**T * A * inv(S(i)) */

            bii = bb[kb1 + i__ * bb_dim1];
            i__3 = i__;
            for (j = i1; j <= i__3; ++j) {
                ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
/* L500: */
            }
/* Computing MIN */
            i__4 = *n, i__1 = i__ + *ka;
            i__3 = min(i__4,i__1);
            for (j = i__; j <= i__3; ++j) {
                ab[i__ - j + ka1 + j * ab_dim1] /= bii;
/* L510: */
            }
            i__3 = i__ + kbt;
            for (k = i__ + 1; k <= i__3; ++k) {
                i__4 = i__ + kbt;
                for (j = k; j <= i__4; ++j) {
                    ab[k - j + ka1 + j * ab_dim1] = ab[k - j + ka1 + j * 
                            ab_dim1] - bb[i__ - j + kb1 + j * bb_dim1] * ab[
                            i__ - k + ka1 + k * ab_dim1] - bb[i__ - k + kb1 + 
                            k * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1] + 
                            ab[ka1 + i__ * ab_dim1] * bb[i__ - j + kb1 + j * 
                            bb_dim1] * bb[i__ - k + kb1 + k * bb_dim1];
/* L520: */
                }
/* Computing MIN */
                i__1 = *n, i__2 = i__ + *ka;
                i__4 = min(i__1,i__2);
                for (j = i__ + kbt + 1; j <= i__4; ++j) {
                    ab[k - j + ka1 + j * ab_dim1] -= bb[i__ - k + kb1 + k * 
                            bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
/* L530: */
                }
/* L540: */
            }
            i__3 = i__;
            for (j = i1; j <= i__3; ++j) {
/* Computing MIN */
                i__1 = j + *ka, i__2 = i__ + kbt;
                i__4 = min(i__1,i__2);
                for (k = i__ + 1; k <= i__4; ++k) {
                    ab[j - k + ka1 + k * ab_dim1] -= bb[i__ - k + kb1 + k * 
                            bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
/* L550: */
                }
/* L560: */
            }

            if (wantx) {

/*              post-multiply X by inv(S(i)) */

                d__1 = 1. / bii;
                dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
                if (kbt > 0) {
                    i__3 = *ldbb - 1;
                    dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
                            *kb + (i__ + 1) * bb_dim1], &i__3, &x[(i__ + 1) * 
                            x_dim1 + 1], ldx);
                }
            }

/*           store a(i1,i) in RA1 for use in next loop over K */

            ra1 = ab[i1 - i__ + ka1 + i__ * ab_dim1];
        }

/*        Generate and apply vectors of rotations to chase all the */
/*        existing bulges KA positions up toward the top of the band */

        i__3 = *kb - 1;
        for (k = 1; k <= i__3; ++k) {
            if (update) {

/*              Determine the rotations which would annihilate the bulge */
/*              which has in theory just been created */

                if (i__ + k - ka1 > 0 && i__ + k < m) {

/*                 generate rotation to annihilate a(i+k-ka-1,i) */

                    dlartg_(&ab[k + 1 + i__ * ab_dim1], &ra1, &work[*n + i__ 
                            + k - *ka], &work[i__ + k - *ka], &ra);

/*                 create nonzero element a(i+k-ka-1,i+k) outside the */
/*                 band and store it in WORK(m-kb+i+k) */

                    t = -bb[kb1 - k + (i__ + k) * bb_dim1] * ra1;
                    work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t - 
                            work[i__ + k - *ka] * ab[(i__ + k) * ab_dim1 + 1];
                    ab[(i__ + k) * ab_dim1 + 1] = work[i__ + k - *ka] * t + 
                            work[*n + i__ + k - *ka] * ab[(i__ + k) * ab_dim1 
                            + 1];
                    ra1 = ra;
                }
            }
/* Computing MAX */
            i__4 = 1, i__1 = k + i0 - m + 1;
            j2 = i__ + k + 1 - max(i__4,i__1) * ka1;
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            if (update) {
/* Computing MIN */
                i__4 = j2, i__1 = i__ - (*ka << 1) + k - 1;
                j2t = min(i__4,i__1);
            } else {
                j2t = j2;
            }
            nrt = (j2t + *ka - 1) / ka1;
            i__4 = j2t;
            i__1 = ka1;
            for (j = j1; i__1 < 0 ? j >= i__4 : j <= i__4; j += i__1) {

/*              create nonzero element a(j-1,j+ka) outside the band */
/*              and store it in WORK(j) */

                work[j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
                ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + *ka 
                        - 1) * ab_dim1 + 1];
/* L570: */
            }

/*           generate rotations in 1st set to annihilate elements which */
/*           have been created outside the band */

            if (nrt > 0) {
                dlargv_(&nrt, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[j1], 
                         &ka1, &work[*n + j1], &ka1);
            }
            if (nr > 0) {

/*              apply rotations in 1st set from the left */

                i__1 = *ka - 1;
                for (l = 1; l <= i__1; ++l) {
                    dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
                            ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n 
                            + j1], &work[j1], &ka1);
/* L580: */
                }

/*              apply rotations in 1st set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) * 
                        ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n + 
                        j1], &work[j1], &ka1);

            }

/*           start applying rotations in 1st set from the right */

            i__1 = *kb - k + 1;
            for (l = *ka - 1; l >= i__1; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
                            j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
                            work[j1t], &ka1);
                }
/* L590: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 1st set */

                i__1 = j2;
                i__4 = ka1;
                for (j = j1; i__4 < 0 ? j >= i__1 : j <= i__1; j += i__4) {
                    drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 
                            + 1], &c__1, &work[*n + j], &work[j]);
/* L600: */
                }
            }
/* L610: */
        }

        if (update) {
            if (i2 > 0 && kbt > 0) {

/*              create nonzero element a(i+kbt-ka-1,i+kbt) outside the */
/*              band and store it in WORK(m-kb+i+kbt) */

                work[m - *kb + i__ + kbt] = -bb[kb1 - kbt + (i__ + kbt) * 
                        bb_dim1] * ra1;
            }
        }

        for (k = *kb; k >= 1; --k) {
            if (update) {
/* Computing MAX */
                i__3 = 2, i__4 = k + i0 - m;
                j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
            } else {
/* Computing MAX */
                i__3 = 1, i__4 = k + i0 - m;
                j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
            }

/*           finish applying rotations in 2nd set from the right */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (j2 + *ka + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + (j1t + *ka) * ab_dim1], &inca, &ab[
                            l + 1 + (j1t + *ka - 1) * ab_dim1], &inca, &work[*
                            n + m - *kb + j1t + *ka], &work[m - *kb + j1t + *
                            ka], &ka1);
                }
/* L620: */
            }
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            i__3 = j2;
            i__4 = ka1;
            for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
                work[m - *kb + j] = work[m - *kb + j + *ka];
                work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
/* L630: */
            }
            i__4 = j2;
            i__3 = ka1;
            for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {

/*              create nonzero element a(j-1,j+ka) outside the band */
/*              and store it in WORK(m-kb+j) */

                work[m - *kb + j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
                ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + m - *kb + j] * ab[
                        (j + *ka - 1) * ab_dim1 + 1];
/* L640: */
            }
            if (update) {
                if (i__ + k > ka1 && k <= kbt) {
                    work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
                }
            }
/* L650: */
        }

        for (k = *kb; k >= 1; --k) {
/* Computing MAX */
            i__3 = 1, i__4 = k + i0 - m;
            j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            if (nr > 0) {

/*              generate rotations in 2nd set to annihilate elements */
/*              which have been created outside the band */

                dlargv_(&nr, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[m - *
                        kb + j1], &ka1, &work[*n + m - *kb + j1], &ka1);

/*              apply rotations in 2nd set from the left */

                i__3 = *ka - 1;
                for (l = 1; l <= i__3; ++l) {
                    dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
                            ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n 
                            + m - *kb + j1], &work[m - *kb + j1], &ka1);
/* L660: */
                }

/*              apply rotations in 2nd set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) * 
                        ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n + 
                        m - *kb + j1], &work[m - *kb + j1], &ka1);

            }

/*           start applying rotations in 2nd set from the right */

            i__3 = *kb - k + 1;
            for (l = *ka - 1; l >= i__3; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
                            j1t - 1) * ab_dim1], &inca, &work[*n + m - *kb + 
                            j1t], &work[m - *kb + j1t], &ka1);
                }
/* L670: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 2nd set */

                i__3 = j2;
                i__4 = ka1;
                for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
                    drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 
                            + 1], &c__1, &work[*n + m - *kb + j], &work[m - *
                            kb + j]);
/* L680: */
                }
            }
/* L690: */
        }

        i__4 = *kb - 1;
        for (k = 1; k <= i__4; ++k) {
/* Computing MAX */
            i__3 = 1, i__1 = k + i0 - m + 1;
            j2 = i__ + k + 1 - max(i__3,i__1) * ka1;

/*           finish applying rotations in 1st set from the right */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
                            j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
                            work[j1t], &ka1);
                }
/* L700: */
            }
/* L710: */
        }

        if (*kb > 1) {
/* Computing MIN */
            i__3 = i__ + *kb;
            i__4 = min(i__3,m) - (*ka << 1) - 1;
            for (j = 2; j <= i__4; ++j) {
                work[*n + j] = work[*n + j + *ka];
                work[j] = work[j + *ka];
/* L720: */
            }
        }

    } else {

/*        Transform A, working with the lower triangle */

        if (update) {

/*           Form  inv(S(i))**T * A * inv(S(i)) */

            bii = bb[i__ * bb_dim1 + 1];
            i__4 = i__;
            for (j = i1; j <= i__4; ++j) {
                ab[i__ - j + 1 + j * ab_dim1] /= bii;
/* L730: */
            }
/* Computing MIN */
            i__3 = *n, i__1 = i__ + *ka;
            i__4 = min(i__3,i__1);
            for (j = i__; j <= i__4; ++j) {
                ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
/* L740: */
            }
            i__4 = i__ + kbt;
            for (k = i__ + 1; k <= i__4; ++k) {
                i__3 = i__ + kbt;
                for (j = k; j <= i__3; ++j) {
                    ab[j - k + 1 + k * ab_dim1] = ab[j - k + 1 + k * ab_dim1] 
                            - bb[j - i__ + 1 + i__ * bb_dim1] * ab[k - i__ + 
                            1 + i__ * ab_dim1] - bb[k - i__ + 1 + i__ * 
                            bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1] + ab[
                            i__ * ab_dim1 + 1] * bb[j - i__ + 1 + i__ * 
                            bb_dim1] * bb[k - i__ + 1 + i__ * bb_dim1];
/* L750: */
                }
/* Computing MIN */
                i__1 = *n, i__2 = i__ + *ka;
                i__3 = min(i__1,i__2);
                for (j = i__ + kbt + 1; j <= i__3; ++j) {
                    ab[j - k + 1 + k * ab_dim1] -= bb[k - i__ + 1 + i__ * 
                            bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
/* L760: */
                }
/* L770: */
            }
            i__4 = i__;
            for (j = i1; j <= i__4; ++j) {
/* Computing MIN */
                i__1 = j + *ka, i__2 = i__ + kbt;
                i__3 = min(i__1,i__2);
                for (k = i__ + 1; k <= i__3; ++k) {
                    ab[k - j + 1 + j * ab_dim1] -= bb[k - i__ + 1 + i__ * 
                            bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
/* L780: */
                }
/* L790: */
            }

            if (wantx) {

/*              post-multiply X by inv(S(i)) */

                d__1 = 1. / bii;
                dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
                if (kbt > 0) {
                    dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
                            i__ * bb_dim1 + 2], &c__1, &x[(i__ + 1) * x_dim1 
                            + 1], ldx);
                }
            }

/*           store a(i,i1) in RA1 for use in next loop over K */

            ra1 = ab[i__ - i1 + 1 + i1 * ab_dim1];
        }

/*        Generate and apply vectors of rotations to chase all the */
/*        existing bulges KA positions up toward the top of the band */

        i__4 = *kb - 1;
        for (k = 1; k <= i__4; ++k) {
            if (update) {

/*              Determine the rotations which would annihilate the bulge */
/*              which has in theory just been created */

                if (i__ + k - ka1 > 0 && i__ + k < m) {

/*                 generate rotation to annihilate a(i,i+k-ka-1) */

                    dlartg_(&ab[ka1 - k + (i__ + k - *ka) * ab_dim1], &ra1, &
                            work[*n + i__ + k - *ka], &work[i__ + k - *ka], &
                            ra);

/*                 create nonzero element a(i+k,i+k-ka-1) outside the */
/*                 band and store it in WORK(m-kb+i+k) */

                    t = -bb[k + 1 + i__ * bb_dim1] * ra1;
                    work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t - 
                            work[i__ + k - *ka] * ab[ka1 + (i__ + k - *ka) * 
                            ab_dim1];
                    ab[ka1 + (i__ + k - *ka) * ab_dim1] = work[i__ + k - *ka] 
                            * t + work[*n + i__ + k - *ka] * ab[ka1 + (i__ + 
                            k - *ka) * ab_dim1];
                    ra1 = ra;
                }
            }
/* Computing MAX */
            i__3 = 1, i__1 = k + i0 - m + 1;
            j2 = i__ + k + 1 - max(i__3,i__1) * ka1;
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            if (update) {
/* Computing MIN */
                i__3 = j2, i__1 = i__ - (*ka << 1) + k - 1;
                j2t = min(i__3,i__1);
            } else {
                j2t = j2;
            }
            nrt = (j2t + *ka - 1) / ka1;
            i__3 = j2t;
            i__1 = ka1;
            for (j = j1; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {

/*              create nonzero element a(j+ka,j-1) outside the band */
/*              and store it in WORK(j) */

                work[j] *= ab[ka1 + (j - 1) * ab_dim1];
                ab[ka1 + (j - 1) * ab_dim1] = work[*n + j] * ab[ka1 + (j - 1) 
                        * ab_dim1];
/* L800: */
            }

/*           generate rotations in 1st set to annihilate elements which */
/*           have been created outside the band */

            if (nrt > 0) {
                dlargv_(&nrt, &ab[ka1 + j1 * ab_dim1], &inca, &work[j1], &ka1, 
                         &work[*n + j1], &ka1);
            }
            if (nr > 0) {

/*              apply rotations in 1st set from the right */

                i__1 = *ka - 1;
                for (l = 1; l <= i__1; ++l) {
                    dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2 
                            + (j1 - 1) * ab_dim1], &inca, &work[*n + j1], &
                            work[j1], &ka1);
/* L810: */
                }

/*              apply rotations in 1st set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 
                        1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + j1]
, &work[j1], &ka1);

            }

/*           start applying rotations in 1st set from the left */

            i__1 = *kb - k + 1;
            for (l = *ka - 1; l >= i__1; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], 
                             &inca, &work[*n + j1t], &work[j1t], &ka1);
                }
/* L820: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 1st set */

                i__1 = j2;
                i__3 = ka1;
                for (j = j1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
                    drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 
                            + 1], &c__1, &work[*n + j], &work[j]);
/* L830: */
                }
            }
/* L840: */
        }

        if (update) {
            if (i2 > 0 && kbt > 0) {

/*              create nonzero element a(i+kbt,i+kbt-ka-1) outside the */
/*              band and store it in WORK(m-kb+i+kbt) */

                work[m - *kb + i__ + kbt] = -bb[kbt + 1 + i__ * bb_dim1] * 
                        ra1;
            }
        }

        for (k = *kb; k >= 1; --k) {
            if (update) {
/* Computing MAX */
                i__4 = 2, i__3 = k + i0 - m;
                j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
            } else {
/* Computing MAX */
                i__4 = 1, i__3 = k + i0 - m;
                j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
            }

/*           finish applying rotations in 2nd set from the left */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (j2 + *ka + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t + l - 1) * ab_dim1], 
                            &inca, &ab[ka1 - l + (j1t + l - 1) * ab_dim1], &
                            inca, &work[*n + m - *kb + j1t + *ka], &work[m - *
                            kb + j1t + *ka], &ka1);
                }
/* L850: */
            }
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            i__4 = j2;
            i__3 = ka1;
            for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
                work[m - *kb + j] = work[m - *kb + j + *ka];
                work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
/* L860: */
            }
            i__3 = j2;
            i__4 = ka1;
            for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {

/*              create nonzero element a(j+ka,j-1) outside the band */
/*              and store it in WORK(m-kb+j) */

                work[m - *kb + j] *= ab[ka1 + (j - 1) * ab_dim1];
                ab[ka1 + (j - 1) * ab_dim1] = work[*n + m - *kb + j] * ab[ka1 
                        + (j - 1) * ab_dim1];
/* L870: */
            }
            if (update) {
                if (i__ + k > ka1 && k <= kbt) {
                    work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
                }
            }
/* L880: */
        }

        for (k = *kb; k >= 1; --k) {
/* Computing MAX */
            i__4 = 1, i__3 = k + i0 - m;
            j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
            nr = (j2 + *ka - 1) / ka1;
            j1 = j2 - (nr - 1) * ka1;
            if (nr > 0) {

/*              generate rotations in 2nd set to annihilate elements */
/*              which have been created outside the band */

                dlargv_(&nr, &ab[ka1 + j1 * ab_dim1], &inca, &work[m - *kb + 
                        j1], &ka1, &work[*n + m - *kb + j1], &ka1);

/*              apply rotations in 2nd set from the right */

                i__4 = *ka - 1;
                for (l = 1; l <= i__4; ++l) {
                    dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2 
                            + (j1 - 1) * ab_dim1], &inca, &work[*n + m - *kb 
                            + j1], &work[m - *kb + j1], &ka1);
/* L890: */
                }

/*              apply rotations in 2nd set from both sides to diagonal */
/*              blocks */

                dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 
                        1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + m 
                        - *kb + j1], &work[m - *kb + j1], &ka1);

            }

/*           start applying rotations in 2nd set from the left */

            i__4 = *kb - k + 1;
            for (l = *ka - 1; l >= i__4; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], 
                             &inca, &work[*n + m - *kb + j1t], &work[m - *kb 
                            + j1t], &ka1);
                }
/* L900: */
            }

            if (wantx) {

/*              post-multiply X by product of rotations in 2nd set */

                i__4 = j2;
                i__3 = ka1;
                for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
                    drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1 
                            + 1], &c__1, &work[*n + m - *kb + j], &work[m - *
                            kb + j]);
/* L910: */
                }
            }
/* L920: */
        }

        i__3 = *kb - 1;
        for (k = 1; k <= i__3; ++k) {
/* Computing MAX */
            i__4 = 1, i__1 = k + i0 - m + 1;
            j2 = i__ + k + 1 - max(i__4,i__1) * ka1;

/*           finish applying rotations in 1st set from the left */

            for (l = *kb - k; l >= 1; --l) {
                nrt = (j2 + l - 1) / ka1;
                j1t = j2 - (nrt - 1) * ka1;
                if (nrt > 0) {
                    dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
, &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1], 
                             &inca, &work[*n + j1t], &work[j1t], &ka1);
                }
/* L930: */
            }
/* L940: */
        }

        if (*kb > 1) {
/* Computing MIN */
            i__4 = i__ + *kb;
            i__3 = min(i__4,m) - (*ka << 1) - 1;
            for (j = 2; j <= i__3; ++j) {
                work[*n + j] = work[*n + j + *ka];
                work[j] = work[j + *ka];
/* L950: */
            }
        }

    }

    goto L490;

/*     End of DSBGST */

} /* dsbgst_ */