/* Subroutine */ int zgbbrd_(char *vect, integer *m, integer *n, integer *ncc,
integer *kl, integer *ku, doublecomplex *ab, integer *ldab,
doublereal *d__, doublereal *e, doublecomplex *q, integer *ldq,
doublecomplex *pt, integer *ldpt, doublecomplex *c__, integer *ldc,
doublecomplex *work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, c_dim1, c_offset, pt_dim1, pt_offset, q_dim1,
q_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
doublecomplex z__1, z__2, z__3;
/* Local variables */
integer i__, j, l;
doublecomplex t;
integer j1, j2, kb;
doublecomplex ra, rb;
doublereal rc;
integer kk, ml, nr, mu;
doublecomplex rs;
integer kb1, ml0, mu0, klm, kun, nrt, klu1, inca;
doublereal abst;
logical wantb, wantc;
integer minmn;
logical wantq;
logical wantpt;
/* -- LAPACK routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* ZGBBRD reduces a complex general m-by-n band matrix A to real upper */
/* bidiagonal form B by a unitary transformation: Q' * A * P = B. */
/* The routine computes B, and optionally forms Q or P', or computes */
/* Q'*C for a given matrix C. */
/* Arguments */
/* ========= */
/* VECT (input) CHARACTER*1 */
/* Specifies whether or not the matrices Q and P' are to be */
/* formed. */
/* = 'N': do not form Q or P'; */
/* = 'Q': form Q only; */
/* = 'P': form P' only; */
/* = 'B': form both. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* NCC (input) INTEGER */
/* The number of columns of the matrix C. NCC >= 0. */
/* KL (input) INTEGER */
/* The number of subdiagonals of the matrix A. KL >= 0. */
/* KU (input) INTEGER */
/* The number of superdiagonals of the matrix A. KU >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */
/* On entry, the m-by-n band matrix A, stored in rows 1 to */
/* KL+KU+1. The j-th column of A is stored in the j-th column of */
/* the array AB as follows: */
/* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). */
/* On exit, A is overwritten by values generated during the */
/* reduction. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array A. LDAB >= KL+KU+1. */
/* D (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The diagonal elements of the bidiagonal matrix B. */
/* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) */
/* The superdiagonal elements of the bidiagonal matrix B. */
/* Q (output) COMPLEX*16 array, dimension (LDQ,M) */
/* If VECT = 'Q' or 'B', the m-by-m unitary matrix Q. */
/* If VECT = 'N' or 'P', the array Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. */
/* LDQ >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. */
/* PT (output) COMPLEX*16 array, dimension (LDPT,N) */
/* If VECT = 'P' or 'B', the n-by-n unitary matrix P'. */
/* If VECT = 'N' or 'Q', the array PT is not referenced. */
/* LDPT (input) INTEGER */
/* The leading dimension of the array PT. */
/* LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. */
/* C (input/output) COMPLEX*16 array, dimension (LDC,NCC) */
/* On entry, an m-by-ncc matrix C. */
/* On exit, C is overwritten by Q'*C. */
/* C is not referenced if NCC = 0. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. */
/* LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. */
/* WORK (workspace) COMPLEX*16 array, dimension (max(M,N)) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (max(M,N)) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* ===================================================================== */
/* Test the input parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
pt_dim1 = *ldpt;
pt_offset = 1 + pt_dim1;
pt -= pt_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
--rwork;
/* Function Body */
wantb = lsame_(vect, "B");
wantq = lsame_(vect, "Q") || wantb;
wantpt = lsame_(vect, "P") || wantb;
wantc = *ncc > 0;
klu1 = *kl + *ku + 1;
*info = 0;
if (! wantq && ! wantpt && ! lsame_(vect, "N")) {
*info = -1;
} else if (*m < 0) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ncc < 0) {
*info = -4;
} else if (*kl < 0) {
*info = -5;
} else if (*ku < 0) {
*info = -6;
} else if (*ldab < klu1) {
*info = -8;
} else if (*ldq < 1 || wantq && *ldq < max(1,*m)) {
*info = -12;
} else if (*ldpt < 1 || wantpt && *ldpt < max(1,*n)) {
*info = -14;
} else if (*ldc < 1 || wantc && *ldc < max(1,*m)) {
*info = -16;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGBBRD", &i__1);
return 0;
}
/* Initialize Q and P' to the unit matrix, if needed */
if (wantq) {
zlaset_("Full", m, m, &c_b1, &c_b2, &q[q_offset], ldq);
}
if (wantpt) {
zlaset_("Full", n, n, &c_b1, &c_b2, &pt[pt_offset], ldpt);
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
minmn = min(*m,*n);
if (*kl + *ku > 1) {
/* Reduce to upper bidiagonal form if KU > 0; if KU = 0, reduce */
/* first to lower bidiagonal form and then transform to upper */
/* bidiagonal */
if (*ku > 0) {
ml0 = 1;
mu0 = 2;
} else {
ml0 = 2;
mu0 = 1;
}
/* Wherever possible, plane rotations are generated and applied in */
/* vector operations of length NR over the index set J1:J2:KLU1. */
/* The complex sines of the plane rotations are stored in WORK, */
/* and the real cosines in RWORK. */
/* Computing MIN */
i__1 = *m - 1;
klm = min(i__1,*kl);
/* Computing MIN */
i__1 = *n - 1;
kun = min(i__1,*ku);
kb = klm + kun;
kb1 = kb + 1;
inca = kb1 * *ldab;
nr = 0;
j1 = klm + 2;
j2 = 1 - kun;
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Reduce i-th column and i-th row of matrix to bidiagonal form */
ml = klm + 1;
mu = kun + 1;
i__2 = kb;
for (kk = 1; kk <= i__2; ++kk) {
j1 += kb;
j2 += kb;
/* generate plane rotations to annihilate nonzero elements */
/* which have been created below the band */
if (nr > 0) {
zlargv_(&nr, &ab[klu1 + (j1 - klm - 1) * ab_dim1], &inca,
&work[j1], &kb1, &rwork[j1], &kb1);
}
/* apply plane rotations from the left */
i__3 = kb;
for (l = 1; l <= i__3; ++l) {
if (j2 - klm + l - 1 > *n) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
zlartv_(&nrt, &ab[klu1 - l + (j1 - klm + l - 1) *
ab_dim1], &inca, &ab[klu1 - l + 1 + (j1 - klm
+ l - 1) * ab_dim1], &inca, &rwork[j1], &work[
j1], &kb1);
}
}
if (ml > ml0) {
if (ml <= *m - i__ + 1) {
/* generate plane rotation to annihilate a(i+ml-1,i) */
/* within the band, and apply rotation from the left */
zlartg_(&ab[*ku + ml - 1 + i__ * ab_dim1], &ab[*ku +
ml + i__ * ab_dim1], &rwork[i__ + ml - 1], &
work[i__ + ml - 1], &ra);
i__3 = *ku + ml - 1 + i__ * ab_dim1;
ab[i__3].r = ra.r, ab[i__3].i = ra.i;
if (i__ < *n) {
/* Computing MIN */
i__4 = *ku + ml - 2, i__5 = *n - i__;
i__3 = min(i__4,i__5);
i__6 = *ldab - 1;
i__7 = *ldab - 1;
zrot_(&i__3, &ab[*ku + ml - 2 + (i__ + 1) *
ab_dim1], &i__6, &ab[*ku + ml - 1 + (i__
+ 1) * ab_dim1], &i__7, &rwork[i__ + ml -
1], &work[i__ + ml - 1]);
}
}
++nr;
j1 -= kb1;
}
if (wantq) {
/* accumulate product of plane rotations in Q */
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4)
{
d_cnjg(&z__1, &work[j]);
zrot_(m, &q[(j - 1) * q_dim1 + 1], &c__1, &q[j *
q_dim1 + 1], &c__1, &rwork[j], &z__1);
}
}
if (wantc) {
/* apply plane rotations to C */
i__4 = j2;
i__3 = kb1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
{
zrot_(ncc, &c__[j - 1 + c_dim1], ldc, &c__[j + c_dim1]
, ldc, &rwork[j], &work[j]);
}
}
if (j2 + kun > *n) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 -= kb1;
}
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j-1,j+ku) above the band */
/* and store it in WORK(n+1:2*n) */
i__5 = j + kun;
i__6 = j;
i__7 = (j + kun) * ab_dim1 + 1;
z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
work[i__6].i * ab[i__7].r;
work[i__5].r = z__1.r, work[i__5].i = z__1.i;
i__5 = (j + kun) * ab_dim1 + 1;
i__6 = j;
i__7 = (j + kun) * ab_dim1 + 1;
z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
ab[i__7].i;
ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
}
/* generate plane rotations to annihilate nonzero elements */
/* which have been generated above the band */
if (nr > 0) {
zlargv_(&nr, &ab[(j1 + kun - 1) * ab_dim1 + 1], &inca, &
work[j1 + kun], &kb1, &rwork[j1 + kun], &kb1);
}
/* apply plane rotations from the right */
i__4 = kb;
for (l = 1; l <= i__4; ++l) {
if (j2 + l - 1 > *m) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
zlartv_(&nrt, &ab[l + 1 + (j1 + kun - 1) * ab_dim1], &
inca, &ab[l + (j1 + kun) * ab_dim1], &inca, &
rwork[j1 + kun], &work[j1 + kun], &kb1);
}
}
if (ml == ml0 && mu > mu0) {
if (mu <= *n - i__ + 1) {
/* generate plane rotation to annihilate a(i,i+mu-1) */
/* within the band, and apply rotation from the right */
zlartg_(&ab[*ku - mu + 3 + (i__ + mu - 2) * ab_dim1],
&ab[*ku - mu + 2 + (i__ + mu - 1) * ab_dim1],
&rwork[i__ + mu - 1], &work[i__ + mu - 1], &
ra);
i__4 = *ku - mu + 3 + (i__ + mu - 2) * ab_dim1;
ab[i__4].r = ra.r, ab[i__4].i = ra.i;
/* Computing MIN */
i__3 = *kl + mu - 2, i__5 = *m - i__;
i__4 = min(i__3,i__5);
zrot_(&i__4, &ab[*ku - mu + 4 + (i__ + mu - 2) *
ab_dim1], &c__1, &ab[*ku - mu + 3 + (i__ + mu
- 1) * ab_dim1], &c__1, &rwork[i__ + mu - 1],
&work[i__ + mu - 1]);
}
++nr;
j1 -= kb1;
}
if (wantpt) {
/* accumulate product of plane rotations in P' */
i__4 = j2;
i__3 = kb1;
for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3)
{
d_cnjg(&z__1, &work[j + kun]);
zrot_(n, &pt[j + kun - 1 + pt_dim1], ldpt, &pt[j +
kun + pt_dim1], ldpt, &rwork[j + kun], &z__1);
}
}
if (j2 + kb > *m) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 -= kb1;
}
i__3 = j2;
i__4 = kb1;
for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
/* create nonzero element a(j+kl+ku,j+ku-1) below the */
/* band and store it in WORK(1:n) */
i__5 = j + kb;
i__6 = j + kun;
i__7 = klu1 + (j + kun) * ab_dim1;
z__1.r = work[i__6].r * ab[i__7].r - work[i__6].i * ab[
i__7].i, z__1.i = work[i__6].r * ab[i__7].i +
work[i__6].i * ab[i__7].r;
work[i__5].r = z__1.r, work[i__5].i = z__1.i;
i__5 = klu1 + (j + kun) * ab_dim1;
i__6 = j + kun;
i__7 = klu1 + (j + kun) * ab_dim1;
z__1.r = rwork[i__6] * ab[i__7].r, z__1.i = rwork[i__6] *
ab[i__7].i;
ab[i__5].r = z__1.r, ab[i__5].i = z__1.i;
}
if (ml > ml0) {
--ml;
} else {
--mu;
}
}
}
}
if (*ku == 0 && *kl > 0) {
/* A has been reduced to complex lower bidiagonal form */
/* Transform lower bidiagonal form to upper bidiagonal by applying */
/* plane rotations from the left, overwriting superdiagonal */
/* elements on subdiagonal elements */
/* Computing MIN */
i__2 = *m - 1;
i__1 = min(i__2,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
zlartg_(&ab[i__ * ab_dim1 + 1], &ab[i__ * ab_dim1 + 2], &rc, &rs,
&ra);
i__2 = i__ * ab_dim1 + 1;
ab[i__2].r = ra.r, ab[i__2].i = ra.i;
if (i__ < *n) {
i__2 = i__ * ab_dim1 + 2;
i__4 = (i__ + 1) * ab_dim1 + 1;
z__1.r = rs.r * ab[i__4].r - rs.i * ab[i__4].i, z__1.i = rs.r
* ab[i__4].i + rs.i * ab[i__4].r;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
i__2 = (i__ + 1) * ab_dim1 + 1;
i__4 = (i__ + 1) * ab_dim1 + 1;
z__1.r = rc * ab[i__4].r, z__1.i = rc * ab[i__4].i;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
}
if (wantq) {
d_cnjg(&z__1, &rs);
zrot_(m, &q[i__ * q_dim1 + 1], &c__1, &q[(i__ + 1) * q_dim1 +
1], &c__1, &rc, &z__1);
}
if (wantc) {
zrot_(ncc, &c__[i__ + c_dim1], ldc, &c__[i__ + 1 + c_dim1],
ldc, &rc, &rs);
}
}
} else {
/* A has been reduced to complex upper bidiagonal form or is */
/* diagonal */
if (*ku > 0 && *m < *n) {
/* Annihilate a(m,m+1) by applying plane rotations from the */
/* right */
i__1 = *ku + (*m + 1) * ab_dim1;
rb.r = ab[i__1].r, rb.i = ab[i__1].i;
for (i__ = *m; i__ >= 1; --i__) {
zlartg_(&ab[*ku + 1 + i__ * ab_dim1], &rb, &rc, &rs, &ra);
i__1 = *ku + 1 + i__ * ab_dim1;
ab[i__1].r = ra.r, ab[i__1].i = ra.i;
if (i__ > 1) {
d_cnjg(&z__3, &rs);
z__2.r = -z__3.r, z__2.i = -z__3.i;
i__1 = *ku + i__ * ab_dim1;
z__1.r = z__2.r * ab[i__1].r - z__2.i * ab[i__1].i,
z__1.i = z__2.r * ab[i__1].i + z__2.i * ab[i__1]
.r;
rb.r = z__1.r, rb.i = z__1.i;
i__1 = *ku + i__ * ab_dim1;
i__2 = *ku + i__ * ab_dim1;
z__1.r = rc * ab[i__2].r, z__1.i = rc * ab[i__2].i;
ab[i__1].r = z__1.r, ab[i__1].i = z__1.i;
}
if (wantpt) {
d_cnjg(&z__1, &rs);
zrot_(n, &pt[i__ + pt_dim1], ldpt, &pt[*m + 1 + pt_dim1],
ldpt, &rc, &z__1);
}
}
}
}
/* Make diagonal and superdiagonal elements real, storing them in D */
/* and E */
i__1 = *ku + 1 + ab_dim1;
t.r = ab[i__1].r, t.i = ab[i__1].i;
i__1 = minmn;
for (i__ = 1; i__ <= i__1; ++i__) {
abst = z_abs(&t);
d__[i__] = abst;
if (abst != 0.) {
z__1.r = t.r / abst, z__1.i = t.i / abst;
t.r = z__1.r, t.i = z__1.i;
} else {
t.r = 1., t.i = 0.;
}
if (wantq) {
zscal_(m, &t, &q[i__ * q_dim1 + 1], &c__1);
}
if (wantc) {
d_cnjg(&z__1, &t);
zscal_(ncc, &z__1, &c__[i__ + c_dim1], ldc);
}
if (i__ < minmn) {
if (*ku == 0 && *kl == 0) {
e[i__] = 0.;
i__2 = (i__ + 1) * ab_dim1 + 1;
t.r = ab[i__2].r, t.i = ab[i__2].i;
} else {
if (*ku == 0) {
i__2 = i__ * ab_dim1 + 2;
d_cnjg(&z__2, &t);
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
z__2.r;
t.r = z__1.r, t.i = z__1.i;
} else {
i__2 = *ku + (i__ + 1) * ab_dim1;
d_cnjg(&z__2, &t);
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i,
z__1.i = ab[i__2].r * z__2.i + ab[i__2].i *
z__2.r;
t.r = z__1.r, t.i = z__1.i;
}
abst = z_abs(&t);
e[i__] = abst;
if (abst != 0.) {
z__1.r = t.r / abst, z__1.i = t.i / abst;
t.r = z__1.r, t.i = z__1.i;
} else {
t.r = 1., t.i = 0.;
}
if (wantpt) {
zscal_(n, &t, &pt[i__ + 1 + pt_dim1], ldpt);
}
i__2 = *ku + 1 + (i__ + 1) * ab_dim1;
d_cnjg(&z__2, &t);
z__1.r = ab[i__2].r * z__2.r - ab[i__2].i * z__2.i, z__1.i =
ab[i__2].r * z__2.i + ab[i__2].i * z__2.r;
t.r = z__1.r, t.i = z__1.i;
}
}
}
return 0;
/* End of ZGBBRD */
} /* zgbbrd_ */
/* Subroutine */ int zhbtrd_(char *vect, char *uplo, integer *n, integer *kd,
doublecomplex *ab, integer *ldab, doublereal *d__, doublereal *e,
doublecomplex *q, integer *ldq, doublecomplex *work, integer *info)
{
/* System generated locals */
integer ab_dim1, ab_offset, q_dim1, q_offset, i__1, i__2, i__3, i__4,
i__5, i__6;
doublereal d__1;
doublecomplex z__1;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *);
/* Local variables */
integer i__, j, k, l;
doublecomplex t;
integer i2, j1, j2, nq, nr, kd1, ibl, iqb, kdn, jin, nrt, kdm1, inca,
jend, lend, jinc;
doublereal abst;
integer incx, last;
doublecomplex temp;
extern /* Subroutine */ int zrot_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublecomplex *);
integer j1end, j1inc, iqend;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
logical initq, wantq, upper;
extern /* Subroutine */ int zlar2v_(integer *, doublecomplex *,
doublecomplex *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *);
integer iqaend;
extern /* Subroutine */ int xerbla_(char *, integer *), zlacgv_(
integer *, doublecomplex *, integer *), zlaset_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *), zlartg_(doublecomplex *, doublecomplex *,
doublereal *, doublecomplex *, doublecomplex *), zlargv_(integer *
, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *), zlartv_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublereal *,
doublecomplex *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZHBTRD reduces a complex Hermitian band matrix A to real symmetric */
/* tridiagonal form T by a unitary similarity transformation: */
/* Q**H * A * Q = T. */
/* Arguments */
/* ========= */
/* VECT (input) CHARACTER*1 */
/* = 'N': do not form Q; */
/* = 'V': form Q; */
/* = 'U': update a matrix X, by forming X*Q. */
/* 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 matrix A. N >= 0. */
/* KD (input) INTEGER */
/* The number of superdiagonals of the matrix A if UPLO = 'U', */
/* or the number of subdiagonals if UPLO = 'L'. KD >= 0. */
/* AB (input/output) COMPLEX*16 array, dimension (LDAB,N) */
/* On entry, the upper or lower triangle of the Hermitian band */
/* matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). */
/* On exit, the diagonal elements of AB are overwritten by the */
/* diagonal elements of the tridiagonal matrix T; if KD > 0, the */
/* elements on the first superdiagonal (if UPLO = 'U') or the */
/* first subdiagonal (if UPLO = 'L') are overwritten by the */
/* off-diagonal elements of T; the rest of AB is overwritten by */
/* values generated during the reduction. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= KD+1. */
/* D (output) DOUBLE PRECISION array, dimension (N) */
/* The diagonal elements of the tridiagonal matrix T. */
/* E (output) DOUBLE PRECISION array, dimension (N-1) */
/* The off-diagonal elements of the tridiagonal matrix T: */
/* E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. */
/* Q (input/output) COMPLEX*16 array, dimension (LDQ,N) */
/* On entry, if VECT = 'U', then Q must contain an N-by-N */
/* matrix X; if VECT = 'N' or 'V', then Q need not be set. */
/* On exit: */
/* if VECT = 'V', Q contains the N-by-N unitary matrix Q; */
/* if VECT = 'U', Q contains the product X*Q; */
/* if VECT = 'N', the array Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. */
/* LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. */
/* WORK (workspace) COMPLEX*16 array, dimension (N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* Modified by Linda Kaufman, Bell Labs. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--d__;
--e;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--work;
/* Function Body */
initq = lsame_(vect, "V");
wantq = initq || lsame_(vect, "U");
upper = lsame_(uplo, "U");
kd1 = *kd + 1;
kdm1 = *kd - 1;
incx = *ldab - 1;
iqend = 1;
*info = 0;
if (! wantq && ! lsame_(vect, "N")) {
*info = -1;
} else if (! upper && ! lsame_(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*kd < 0) {
*info = -4;
} else if (*ldab < kd1) {
*info = -6;
} else if (*ldq < max(1,*n) && wantq) {
*info = -10;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZHBTRD", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Initialize Q to the unit matrix, if needed */
if (initq) {
zlaset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
}
/* Wherever possible, plane rotations are generated and applied in */
/* vector operations of length NR over the index set J1:J2:KD1. */
/* The real cosines and complex sines of the plane rotations are */
/* stored in the arrays D and WORK. */
inca = kd1 * *ldab;
/* Computing MIN */
i__1 = *n - 1;
kdn = min(i__1,*kd);
if (upper) {
if (*kd > 1) {
/* Reduce to complex Hermitian tridiagonal form, working with */
/* the upper triangle */
nr = 0;
j1 = kdn + 2;
j2 = 1;
i__1 = kd1 + ab_dim1;
i__2 = kd1 + ab_dim1;
d__1 = ab[i__2].r;
ab[i__1].r = d__1, ab[i__1].i = 0.;
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Reduce i-th row of matrix to tridiagonal form */
for (k = kdn + 1; k >= 2; --k) {
j1 += kdn;
j2 += kdn;
if (nr > 0) {
/* generate plane rotations to annihilate nonzero */
/* elements which have been created outside the band */
zlargv_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &inca, &
work[j1], &kd1, &d__[j1], &kd1);
/* apply rotations from the right */
/* Dependent on the the number of diagonals either */
/* ZLARTV or ZROT is used */
if (nr >= (*kd << 1) - 1) {
i__2 = *kd - 1;
for (l = 1; l <= i__2; ++l) {
zlartv_(&nr, &ab[l + 1 + (j1 - 1) * ab_dim1],
&inca, &ab[l + j1 * ab_dim1], &inca, &
d__[j1], &work[j1], &kd1);
/* L10: */
}
} else {
jend = j1 + (nr - 1) * kd1;
i__2 = jend;
i__3 = kd1;
for (jinc = j1; i__3 < 0 ? jinc >= i__2 : jinc <=
i__2; jinc += i__3) {
zrot_(&kdm1, &ab[(jinc - 1) * ab_dim1 + 2], &
c__1, &ab[jinc * ab_dim1 + 1], &c__1,
&d__[jinc], &work[jinc]);
/* L20: */
}
}
}
if (k > 2) {
if (k <= *n - i__ + 1) {
/* generate plane rotation to annihilate a(i,i+k-1) */
/* within the band */
zlartg_(&ab[*kd - k + 3 + (i__ + k - 2) * ab_dim1]
, &ab[*kd - k + 2 + (i__ + k - 1) *
ab_dim1], &d__[i__ + k - 1], &work[i__ +
k - 1], &temp);
i__3 = *kd - k + 3 + (i__ + k - 2) * ab_dim1;
ab[i__3].r = temp.r, ab[i__3].i = temp.i;
/* apply rotation from the right */
i__3 = k - 3;
zrot_(&i__3, &ab[*kd - k + 4 + (i__ + k - 2) *
ab_dim1], &c__1, &ab[*kd - k + 3 + (i__ +
k - 1) * ab_dim1], &c__1, &d__[i__ + k -
1], &work[i__ + k - 1]);
}
++nr;
j1 = j1 - kdn - 1;
}
/* apply plane rotations from both sides to diagonal */
/* blocks */
if (nr > 0) {
zlar2v_(&nr, &ab[kd1 + (j1 - 1) * ab_dim1], &ab[kd1 +
j1 * ab_dim1], &ab[*kd + j1 * ab_dim1], &inca,
&d__[j1], &work[j1], &kd1);
}
/* apply plane rotations from the left */
if (nr > 0) {
zlacgv_(&nr, &work[j1], &kd1);
if ((*kd << 1) - 1 < nr) {
/* Dependent on the the number of diagonals either */
/* ZLARTV or ZROT is used */
i__3 = *kd - 1;
for (l = 1; l <= i__3; ++l) {
if (j2 + l > *n) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
zlartv_(&nrt, &ab[*kd - l + (j1 + l) *
ab_dim1], &inca, &ab[*kd - l + 1
+ (j1 + l) * ab_dim1], &inca, &
d__[j1], &work[j1], &kd1);
}
/* L30: */
}
} else {
j1end = j1 + kd1 * (nr - 2);
if (j1end >= j1) {
i__3 = j1end;
i__2 = kd1;
for (jin = j1; i__2 < 0 ? jin >= i__3 : jin <=
i__3; jin += i__2) {
i__4 = *kd - 1;
zrot_(&i__4, &ab[*kd - 1 + (jin + 1) *
ab_dim1], &incx, &ab[*kd + (jin +
1) * ab_dim1], &incx, &d__[jin], &
work[jin]);
/* L40: */
}
}
/* Computing MIN */
i__2 = kdm1, i__3 = *n - j2;
lend = min(i__2,i__3);
last = j1end + kd1;
if (lend > 0) {
zrot_(&lend, &ab[*kd - 1 + (last + 1) *
ab_dim1], &incx, &ab[*kd + (last + 1)
* ab_dim1], &incx, &d__[last], &work[
last]);
}
}
}
if (wantq) {
/* accumulate product of plane rotations in Q */
if (initq) {
/* take advantage of the fact that Q was */
/* initially the Identity matrix */
iqend = max(iqend,j2);
/* Computing MAX */
i__2 = 0, i__3 = k - 3;
i2 = max(i__2,i__3);
iqaend = i__ * *kd + 1;
if (k == 2) {
iqaend += *kd;
}
iqaend = min(iqaend,iqend);
i__2 = j2;
i__3 = kd1;
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
+= i__3) {
ibl = i__ - i2 / kdm1;
++i2;
/* Computing MAX */
i__4 = 1, i__5 = j - ibl;
iqb = max(i__4,i__5);
nq = iqaend + 1 - iqb;
/* Computing MIN */
i__4 = iqaend + *kd;
iqaend = min(i__4,iqend);
d_cnjg(&z__1, &work[j]);
zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
&q[iqb + j * q_dim1], &c__1, &d__[j],
&z__1);
/* L50: */
}
} else {
i__3 = j2;
i__2 = kd1;
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
+= i__2) {
d_cnjg(&z__1, &work[j]);
zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
j * q_dim1 + 1], &c__1, &d__[j], &
z__1);
/* L60: */
}
}
}
if (j2 + kdn > *n) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 = j2 - kdn - 1;
}
i__2 = j2;
i__3 = kd1;
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3)
{
/* create nonzero element a(j-1,j+kd) outside the band */
/* and store it in WORK */
i__4 = j + *kd;
i__5 = j;
i__6 = (j + *kd) * ab_dim1 + 1;
z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i *
ab[i__6].i, z__1.i = work[i__5].r * ab[i__6]
.i + work[i__5].i * ab[i__6].r;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
i__4 = (j + *kd) * ab_dim1 + 1;
i__5 = j;
i__6 = (j + *kd) * ab_dim1 + 1;
z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] *
ab[i__6].i;
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
/* L70: */
}
/* L80: */
}
/* L90: */
}
}
if (*kd > 0) {
/* make off-diagonal elements real and copy them to E */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__3 = *kd + (i__ + 1) * ab_dim1;
t.r = ab[i__3].r, t.i = ab[i__3].i;
abst = z_abs(&t);
i__3 = *kd + (i__ + 1) * ab_dim1;
ab[i__3].r = abst, ab[i__3].i = 0.;
e[i__] = abst;
if (abst != 0.) {
z__1.r = t.r / abst, z__1.i = t.i / abst;
t.r = z__1.r, t.i = z__1.i;
} else {
t.r = 1., t.i = 0.;
}
if (i__ < *n - 1) {
i__3 = *kd + (i__ + 2) * ab_dim1;
i__2 = *kd + (i__ + 2) * ab_dim1;
z__1.r = ab[i__2].r * t.r - ab[i__2].i * t.i, z__1.i = ab[
i__2].r * t.i + ab[i__2].i * t.r;
ab[i__3].r = z__1.r, ab[i__3].i = z__1.i;
}
if (wantq) {
d_cnjg(&z__1, &t);
zscal_(n, &z__1, &q[(i__ + 1) * q_dim1 + 1], &c__1);
}
/* L100: */
}
} else {
/* set E to zero if original matrix was diagonal */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = 0.;
/* L110: */
}
}
/* copy diagonal elements to D */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__3 = i__;
i__2 = kd1 + i__ * ab_dim1;
d__[i__3] = ab[i__2].r;
/* L120: */
}
} else {
if (*kd > 1) {
/* Reduce to complex Hermitian tridiagonal form, working with */
/* the lower triangle */
nr = 0;
j1 = kdn + 2;
j2 = 1;
i__1 = ab_dim1 + 1;
i__3 = ab_dim1 + 1;
d__1 = ab[i__3].r;
ab[i__1].r = d__1, ab[i__1].i = 0.;
i__1 = *n - 2;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Reduce i-th column of matrix to tridiagonal form */
for (k = kdn + 1; k >= 2; --k) {
j1 += kdn;
j2 += kdn;
if (nr > 0) {
/* generate plane rotations to annihilate nonzero */
/* elements which have been created outside the band */
zlargv_(&nr, &ab[kd1 + (j1 - kd1) * ab_dim1], &inca, &
work[j1], &kd1, &d__[j1], &kd1);
/* apply plane rotations from one side */
/* Dependent on the the number of diagonals either */
/* ZLARTV or ZROT is used */
if (nr > (*kd << 1) - 1) {
i__3 = *kd - 1;
for (l = 1; l <= i__3; ++l) {
zlartv_(&nr, &ab[kd1 - l + (j1 - kd1 + l) *
ab_dim1], &inca, &ab[kd1 - l + 1 + (
j1 - kd1 + l) * ab_dim1], &inca, &d__[
j1], &work[j1], &kd1);
/* L130: */
}
} else {
jend = j1 + kd1 * (nr - 1);
i__3 = jend;
i__2 = kd1;
for (jinc = j1; i__2 < 0 ? jinc >= i__3 : jinc <=
i__3; jinc += i__2) {
zrot_(&kdm1, &ab[*kd + (jinc - *kd) * ab_dim1]
, &incx, &ab[kd1 + (jinc - *kd) *
ab_dim1], &incx, &d__[jinc], &work[
jinc]);
/* L140: */
}
}
}
if (k > 2) {
if (k <= *n - i__ + 1) {
/* generate plane rotation to annihilate a(i+k-1,i) */
/* within the band */
zlartg_(&ab[k - 1 + i__ * ab_dim1], &ab[k + i__ *
ab_dim1], &d__[i__ + k - 1], &work[i__ +
k - 1], &temp);
i__2 = k - 1 + i__ * ab_dim1;
ab[i__2].r = temp.r, ab[i__2].i = temp.i;
/* apply rotation from the left */
i__2 = k - 3;
i__3 = *ldab - 1;
i__4 = *ldab - 1;
zrot_(&i__2, &ab[k - 2 + (i__ + 1) * ab_dim1], &
i__3, &ab[k - 1 + (i__ + 1) * ab_dim1], &
i__4, &d__[i__ + k - 1], &work[i__ + k -
1]);
}
++nr;
j1 = j1 - kdn - 1;
}
/* apply plane rotations from both sides to diagonal */
/* blocks */
if (nr > 0) {
zlar2v_(&nr, &ab[(j1 - 1) * ab_dim1 + 1], &ab[j1 *
ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 + 2], &
inca, &d__[j1], &work[j1], &kd1);
}
/* apply plane rotations from the right */
/* Dependent on the the number of diagonals either */
/* ZLARTV or ZROT is used */
if (nr > 0) {
zlacgv_(&nr, &work[j1], &kd1);
if (nr > (*kd << 1) - 1) {
i__2 = *kd - 1;
for (l = 1; l <= i__2; ++l) {
if (j2 + l > *n) {
nrt = nr - 1;
} else {
nrt = nr;
}
if (nrt > 0) {
zlartv_(&nrt, &ab[l + 2 + (j1 - 1) *
ab_dim1], &inca, &ab[l + 1 + j1 *
ab_dim1], &inca, &d__[j1], &work[
j1], &kd1);
}
/* L150: */
}
} else {
j1end = j1 + kd1 * (nr - 2);
if (j1end >= j1) {
i__2 = j1end;
i__3 = kd1;
for (j1inc = j1; i__3 < 0 ? j1inc >= i__2 :
j1inc <= i__2; j1inc += i__3) {
zrot_(&kdm1, &ab[(j1inc - 1) * ab_dim1 +
3], &c__1, &ab[j1inc * ab_dim1 +
2], &c__1, &d__[j1inc], &work[
j1inc]);
/* L160: */
}
}
/* Computing MIN */
i__3 = kdm1, i__2 = *n - j2;
lend = min(i__3,i__2);
last = j1end + kd1;
if (lend > 0) {
zrot_(&lend, &ab[(last - 1) * ab_dim1 + 3], &
c__1, &ab[last * ab_dim1 + 2], &c__1,
&d__[last], &work[last]);
}
}
}
if (wantq) {
/* accumulate product of plane rotations in Q */
if (initq) {
/* take advantage of the fact that Q was */
/* initially the Identity matrix */
iqend = max(iqend,j2);
/* Computing MAX */
i__3 = 0, i__2 = k - 3;
i2 = max(i__3,i__2);
iqaend = i__ * *kd + 1;
if (k == 2) {
iqaend += *kd;
}
iqaend = min(iqaend,iqend);
i__3 = j2;
i__2 = kd1;
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j
+= i__2) {
ibl = i__ - i2 / kdm1;
++i2;
/* Computing MAX */
i__4 = 1, i__5 = j - ibl;
iqb = max(i__4,i__5);
nq = iqaend + 1 - iqb;
/* Computing MIN */
i__4 = iqaend + *kd;
iqaend = min(i__4,iqend);
zrot_(&nq, &q[iqb + (j - 1) * q_dim1], &c__1,
&q[iqb + j * q_dim1], &c__1, &d__[j],
&work[j]);
/* L170: */
}
} else {
i__2 = j2;
i__3 = kd1;
for (j = j1; i__3 < 0 ? j >= i__2 : j <= i__2; j
+= i__3) {
zrot_(n, &q[(j - 1) * q_dim1 + 1], &c__1, &q[
j * q_dim1 + 1], &c__1, &d__[j], &
work[j]);
/* L180: */
}
}
}
if (j2 + kdn > *n) {
/* adjust J2 to keep within the bounds of the matrix */
--nr;
j2 = j2 - kdn - 1;
}
i__3 = j2;
i__2 = kd1;
for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2)
{
/* create nonzero element a(j+kd,j-1) outside the */
/* band and store it in WORK */
i__4 = j + *kd;
i__5 = j;
i__6 = kd1 + j * ab_dim1;
z__1.r = work[i__5].r * ab[i__6].r - work[i__5].i *
ab[i__6].i, z__1.i = work[i__5].r * ab[i__6]
.i + work[i__5].i * ab[i__6].r;
work[i__4].r = z__1.r, work[i__4].i = z__1.i;
i__4 = kd1 + j * ab_dim1;
i__5 = j;
i__6 = kd1 + j * ab_dim1;
z__1.r = d__[i__5] * ab[i__6].r, z__1.i = d__[i__5] *
ab[i__6].i;
ab[i__4].r = z__1.r, ab[i__4].i = z__1.i;
/* L190: */
}
/* L200: */
}
/* L210: */
}
}
if (*kd > 0) {
/* make off-diagonal elements real and copy them to E */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ * ab_dim1 + 2;
t.r = ab[i__2].r, t.i = ab[i__2].i;
abst = z_abs(&t);
i__2 = i__ * ab_dim1 + 2;
ab[i__2].r = abst, ab[i__2].i = 0.;
e[i__] = abst;
if (abst != 0.) {
z__1.r = t.r / abst, z__1.i = t.i / abst;
t.r = z__1.r, t.i = z__1.i;
} else {
t.r = 1., t.i = 0.;
}
if (i__ < *n - 1) {
i__2 = (i__ + 1) * ab_dim1 + 2;
i__3 = (i__ + 1) * ab_dim1 + 2;
z__1.r = ab[i__3].r * t.r - ab[i__3].i * t.i, z__1.i = ab[
i__3].r * t.i + ab[i__3].i * t.r;
ab[i__2].r = z__1.r, ab[i__2].i = z__1.i;
}
if (wantq) {
zscal_(n, &t, &q[(i__ + 1) * q_dim1 + 1], &c__1);
}
/* L220: */
}
} else {
/* set E to zero if original matrix was diagonal */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
e[i__] = 0.;
/* L230: */
}
}
/* copy diagonal elements to D */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__ * ab_dim1 + 1;
d__[i__2] = ab[i__3].r;
/* L240: */
}
}
return 0;
/* End of ZHBTRD */
} /* zhbtrd_ */
