/* 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_ */
