text: #include "f2c.h"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static real c_b8 = 0.f;
  static real c_b9 = 1.f;
  static integer c__1 = 1;
  static real c_b20 = -1.f;
  
  /* Subroutine */ int ssbgst_(char *vect, char *uplo, integer *n, integer *ka, 
  	integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real *
  	x, integer *ldx, real *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;
      real r__1;
  
      /* Local variables */
      integer i__, j, k, l, m;
      real t;
      integer i0, i1, i2, j1, j2;
      real ra;
      integer nr, nx, ka1, kb1;
      real ra1;
      integer j1t, j2t;
      real bii;
      integer kbt, nrt, inca;
      extern /* Subroutine */ int sger_(integer *, integer *, real *, real *, 
  	    integer *, real *, integer *, real *, integer *), srot_(integer *, 
  	     real *, integer *, real *, integer *, real *, real *);
      extern logical lsame_(char *, char *);
      extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
      logical upper, wantx;
      extern /* Subroutine */ int slar2v_(integer *, real *, real *, real *, 
  	    integer *, real *, real *, integer *), xerbla_(char *, integer *);
      logical update;
      extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, 
  	    real *, real *, integer *), slartg_(real *, real *, real *
  , real *, real *), slargv_(integer *, real *, integer *, real *, 
  	    integer *, real *, integer *), slartv_(integer *, real *, integer 
  	    *, real *, integer *, real *, real *, integer *);
  
  
  /*  -- LAPACK routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SSBGST 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 SPBSTF, 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) REAL 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) REAL array, dimension (LDBB,N) */
  /*          The banded factor S from the split Cholesky factorization of */
  /*          B, as returned by SPBSTF, 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) REAL 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) REAL 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_("SSBGST", &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) {
  	slaset_("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 SPBSTF. 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;
  		r__1 = 1.f / bii;
  		sscal_(&i__3, &r__1, &x[m + 1 + i__ * x_dim1], &c__1);
  		if (kbt > 0) {
  		    i__3 = *n - m;
  		    sger_(&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) */
  
  		    slartg_(&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) {
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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;
  		    srot_(&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) {
  		    slartv_(&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 */
  
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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;
  		    srot_(&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) {
  		    slartv_(&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;
  		r__1 = 1.f / bii;
  		sscal_(&i__4, &r__1, &x[m + 1 + i__ * x_dim1], &c__1);
  		if (kbt > 0) {
  		    i__4 = *n - m;
  		    i__3 = *ldbb - 1;
  		    sger_(&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) */
  
  		    slartg_(&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) {
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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;
  		    srot_(&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) {
  		    slartv_(&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 */
  
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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;
  		    srot_(&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) {
  		    slartv_(&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)) */
  
  		r__1 = 1.f / bii;
  		sscal_(&nx, &r__1, &x[i__ * x_dim1 + 1], &c__1);
  		if (kbt > 0) {
  		    i__3 = *ldbb - 1;
  		    sger_(&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) */
  
  		    slartg_(&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) {
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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) {
  		    srot_(&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) {
  		    slartv_(&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 */
  
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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) {
  		    srot_(&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) {
  		    slartv_(&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)) */
  
  		r__1 = 1.f / bii;
  		sscal_(&nx, &r__1, &x[i__ * x_dim1 + 1], &c__1);
  		if (kbt > 0) {
  		    sger_(&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) */
  
  		    slartg_(&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) {
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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) {
  		    srot_(&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) {
  		    slartv_(&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 */
  
  		slargv_(&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) {
  		    slartv_(&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 */
  
  		slar2v_(&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) {
  		    slartv_(&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) {
  		    srot_(&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) {
  		    slartv_(&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 SSBGST */
  
  } /* ssbgst_ */
  