[] add metering mode to CLI

1 files changed, 1755 insertions, 0 deletions

diff --git a/contrib/libs/clapack/dsbgst.c b/contrib/libs/clapack/dsbgst.c
new file mode 100644
index 0000000000..24c9aad461
--- /dev/null
+++ b/contrib/libs/clapack/dsbgst.c
@@ -0,0 +1,1755 @@
+/* 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_ */