/* zlahqr.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 integer c__1 = 1;
static integer c__2 = 2;
/* Subroutine */ int zlahqr_(logical *wantt, logical *wantz, integer *n,
integer *ilo, integer *ihi, doublecomplex *h__, integer *ldh,
doublecomplex *w, integer *iloz, integer *ihiz, doublecomplex *z__,
integer *ldz, integer *info)
{
/* System generated locals */
integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
doublecomplex z__1, z__2, z__3, z__4, z__5, z__6, z__7;
/* Builtin functions */
double d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
double z_abs(doublecomplex *);
void z_sqrt(doublecomplex *, doublecomplex *), pow_zi(doublecomplex *,
doublecomplex *, integer *);
/* Local variables */
integer i__, j, k, l, m;
doublereal s;
doublecomplex t, u, v[2], x, y;
integer i1, i2;
doublecomplex t1;
doublereal t2;
doublecomplex v2;
doublereal aa, ab, ba, bb, h10;
doublecomplex h11;
doublereal h21;
doublecomplex h22, sc;
integer nh, nz;
doublereal sx;
integer jhi;
doublecomplex h11s;
integer jlo, its;
doublereal ulp;
doublecomplex sum;
doublereal tst;
doublecomplex temp;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
doublereal rtemp;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *);
doublereal safmin, safmax;
extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
doublereal smlnum;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLAHQR is an auxiliary routine called by CHSEQR to update the */
/* eigenvalues and Schur decomposition already computed by CHSEQR, by */
/* dealing with the Hessenberg submatrix in rows and columns ILO to */
/* IHI. */
/* Arguments */
/* ========= */
/* WANTT (input) LOGICAL */
/* = .TRUE. : the full Schur form T is required; */
/* = .FALSE.: only eigenvalues are required. */
/* WANTZ (input) LOGICAL */
/* = .TRUE. : the matrix of Schur vectors Z is required; */
/* = .FALSE.: Schur vectors are not required. */
/* N (input) INTEGER */
/* The order of the matrix H. N >= 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that H is already upper triangular in rows and */
/* columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1). */
/* ZLAHQR works primarily with the Hessenberg submatrix in rows */
/* and columns ILO to IHI, but applies transformations to all of */
/* H if WANTT is .TRUE.. */
/* 1 <= ILO <= max(1,IHI); IHI <= N. */
/* H (input/output) COMPLEX*16 array, dimension (LDH,N) */
/* On entry, the upper Hessenberg matrix H. */
/* On exit, if INFO is zero and if WANTT is .TRUE., then H */
/* is upper triangular in rows and columns ILO:IHI. If INFO */
/* is zero and if WANTT is .FALSE., then the contents of H */
/* are unspecified on exit. The output state of H in case */
/* INF is positive is below under the description of INFO. */
/* LDH (input) INTEGER */
/* The leading dimension of the array H. LDH >= max(1,N). */
/* W (output) COMPLEX*16 array, dimension (N) */
/* The computed eigenvalues ILO to IHI are stored in the */
/* corresponding elements of W. If WANTT is .TRUE., the */
/* eigenvalues are stored in the same order as on the diagonal */
/* of the Schur form returned in H, with W(i) = H(i,i). */
/* ILOZ (input) INTEGER */
/* IHIZ (input) INTEGER */
/* Specify the rows of Z to which transformations must be */
/* applied if WANTZ is .TRUE.. */
/* 1 <= ILOZ <= ILO; IHI <= IHIZ <= N. */
/* Z (input/output) COMPLEX*16 array, dimension (LDZ,N) */
/* If WANTZ is .TRUE., on entry Z must contain the current */
/* matrix Z of transformations accumulated by CHSEQR, and on */
/* exit Z has been updated; transformations are applied only to */
/* the submatrix Z(ILOZ:IHIZ,ILO:IHI). */
/* If WANTZ is .FALSE., Z is not referenced. */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. LDZ >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* .GT. 0: if INFO = i, ZLAHQR failed to compute all the */
/* eigenvalues ILO to IHI in a total of 30 iterations */
/* per eigenvalue; elements i+1:ihi of W contain */
/* those eigenvalues which have been successfully */
/* computed. */
/* If INFO .GT. 0 and WANTT is .FALSE., then on exit, */
/* the remaining unconverged eigenvalues are the */
/* eigenvalues of the upper Hessenberg matrix */
/* rows and columns ILO thorugh INFO of the final, */
/* output value of H. */
/* If INFO .GT. 0 and WANTT is .TRUE., then on exit */
/* (*) (initial value of H)*U = U*(final value of H) */
/* where U is an orthognal matrix. The final */
/* value of H is upper Hessenberg and triangular in */
/* rows and columns INFO+1 through IHI. */
/* If INFO .GT. 0 and WANTZ is .TRUE., then on exit */
/* (final value of Z) = (initial value of Z)*U */
/* where U is the orthogonal matrix in (*) */
/* (regardless of the value of WANTT.) */
/* Further Details */
/* =============== */
/* 02-96 Based on modifications by */
/* David Day, Sandia National Laboratory, USA */
/* 12-04 Further modifications by */
/* Ralph Byers, University of Kansas, USA */
/* This is a modified version of ZLAHQR from LAPACK version 3.0. */
/* It is (1) more robust against overflow and underflow and */
/* (2) adopts the more conservative Ahues & Tisseur stopping */
/* criterion (LAWN 122, 1997). */
/* ========================================================= */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
--w;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
/* Function Body */
*info = 0;
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (*ilo == *ihi) {
i__1 = *ilo;
i__2 = *ilo + *ilo * h_dim1;
w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
return 0;
}
/* ==== clear out the trash ==== */
i__1 = *ihi - 3;
for (j = *ilo; j <= i__1; ++j) {
i__2 = j + 2 + j * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
i__2 = j + 3 + j * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
/* L10: */
}
if (*ilo <= *ihi - 2) {
i__1 = *ihi + (*ihi - 2) * h_dim1;
h__[i__1].r = 0., h__[i__1].i = 0.;
}
/* ==== ensure that subdiagonal entries are real ==== */
if (*wantt) {
jlo = 1;
jhi = *n;
} else {
jlo = *ilo;
jhi = *ihi;
}
i__1 = *ihi;
for (i__ = *ilo + 1; i__ <= i__1; ++i__) {
if (d_imag(&h__[i__ + (i__ - 1) * h_dim1]) != 0.) {
/* ==== The following redundant normalization */
/* . avoids problems with both gradual and */
/* . sudden underflow in ABS(H(I,I-1)) ==== */
i__2 = i__ + (i__ - 1) * h_dim1;
i__3 = i__ + (i__ - 1) * h_dim1;
d__3 = (d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[i__
+ (i__ - 1) * h_dim1]), abs(d__2));
z__1.r = h__[i__2].r / d__3, z__1.i = h__[i__2].i / d__3;
sc.r = z__1.r, sc.i = z__1.i;
d_cnjg(&z__2, &sc);
d__1 = z_abs(&sc);
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
sc.r = z__1.r, sc.i = z__1.i;
i__2 = i__ + (i__ - 1) * h_dim1;
d__1 = z_abs(&h__[i__ + (i__ - 1) * h_dim1]);
h__[i__2].r = d__1, h__[i__2].i = 0.;
i__2 = jhi - i__ + 1;
zscal_(&i__2, &sc, &h__[i__ + i__ * h_dim1], ldh);
/* Computing MIN */
i__3 = jhi, i__4 = i__ + 1;
i__2 = min(i__3,i__4) - jlo + 1;
d_cnjg(&z__1, &sc);
zscal_(&i__2, &z__1, &h__[jlo + i__ * h_dim1], &c__1);
if (*wantz) {
i__2 = *ihiz - *iloz + 1;
d_cnjg(&z__1, &sc);
zscal_(&i__2, &z__1, &z__[*iloz + i__ * z_dim1], &c__1);
}
}
/* L20: */
}
nh = *ihi - *ilo + 1;
nz = *ihiz - *iloz + 1;
/* Set machine-dependent constants for the stopping criterion. */
safmin = dlamch_("SAFE MINIMUM");
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulp = dlamch_("PRECISION");
smlnum = safmin * ((doublereal) nh / ulp);
/* I1 and I2 are the indices of the first row and last column of H */
/* to which transformations must be applied. If eigenvalues only are */
/* being computed, I1 and I2 are set inside the main loop. */
if (*wantt) {
i1 = 1;
i2 = *n;
}
/* The main loop begins here. I is the loop index and decreases from */
/* IHI to ILO in steps of 1. Each iteration of the loop works */
/* with the active submatrix in rows and columns L to I. */
/* Eigenvalues I+1 to IHI have already converged. Either L = ILO, or */
/* H(L,L-1) is negligible so that the matrix splits. */
i__ = *ihi;
L30:
if (i__ < *ilo) {
goto L150;
}
/* Perform QR iterations on rows and columns ILO to I until a */
/* submatrix of order 1 splits off at the bottom because a */
/* subdiagonal element has become negligible. */
l = *ilo;
for (its = 0; its <= 30; ++its) {
/* Look for a single small subdiagonal element. */
i__1 = l + 1;
for (k = i__; k >= i__1; --k) {
i__2 = k + (k - 1) * h_dim1;
if ((d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[k + (k
- 1) * h_dim1]), abs(d__2)) <= smlnum) {
goto L50;
}
i__2 = k - 1 + (k - 1) * h_dim1;
i__3 = k + k * h_dim1;
tst = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[k - 1
+ (k - 1) * h_dim1]), abs(d__2)) + ((d__3 = h__[i__3].r,
abs(d__3)) + (d__4 = d_imag(&h__[k + k * h_dim1]), abs(
d__4)));
if (tst == 0.) {
if (k - 2 >= *ilo) {
i__2 = k - 1 + (k - 2) * h_dim1;
tst += (d__1 = h__[i__2].r, abs(d__1));
}
if (k + 1 <= *ihi) {
i__2 = k + 1 + k * h_dim1;
tst += (d__1 = h__[i__2].r, abs(d__1));
}
}
/* ==== The following is a conservative small subdiagonal */
/* . deflation criterion due to Ahues & Tisseur (LAWN 122, */
/* . 1997). It has better mathematical foundation and */
/* . improves accuracy in some examples. ==== */
i__2 = k + (k - 1) * h_dim1;
if ((d__1 = h__[i__2].r, abs(d__1)) <= ulp * tst) {
/* Computing MAX */
i__2 = k + (k - 1) * h_dim1;
i__3 = k - 1 + k * h_dim1;
d__5 = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[
k + (k - 1) * h_dim1]), abs(d__2)), d__6 = (d__3 =
h__[i__3].r, abs(d__3)) + (d__4 = d_imag(&h__[k - 1 +
k * h_dim1]), abs(d__4));
ab = max(d__5,d__6);
/* Computing MIN */
i__2 = k + (k - 1) * h_dim1;
i__3 = k - 1 + k * h_dim1;
d__5 = (d__1 = h__[i__2].r, abs(d__1)) + (d__2 = d_imag(&h__[
k + (k - 1) * h_dim1]), abs(d__2)), d__6 = (d__3 =
h__[i__3].r, abs(d__3)) + (d__4 = d_imag(&h__[k - 1 +
k * h_dim1]), abs(d__4));
ba = min(d__5,d__6);
i__2 = k - 1 + (k - 1) * h_dim1;
i__3 = k + k * h_dim1;
z__2.r = h__[i__2].r - h__[i__3].r, z__2.i = h__[i__2].i -
h__[i__3].i;
z__1.r = z__2.r, z__1.i = z__2.i;
/* Computing MAX */
i__4 = k + k * h_dim1;
d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[
k + k * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r,
abs(d__3)) + (d__4 = d_imag(&z__1), abs(d__4));
aa = max(d__5,d__6);
i__2 = k - 1 + (k - 1) * h_dim1;
i__3 = k + k * h_dim1;
z__2.r = h__[i__2].r - h__[i__3].r, z__2.i = h__[i__2].i -
h__[i__3].i;
z__1.r = z__2.r, z__1.i = z__2.i;
/* Computing MIN */
i__4 = k + k * h_dim1;
d__5 = (d__1 = h__[i__4].r, abs(d__1)) + (d__2 = d_imag(&h__[
k + k * h_dim1]), abs(d__2)), d__6 = (d__3 = z__1.r,
abs(d__3)) + (d__4 = d_imag(&z__1), abs(d__4));
bb = min(d__5,d__6);
s = aa + ab;
/* Computing MAX */
d__1 = smlnum, d__2 = ulp * (bb * (aa / s));
if (ba * (ab / s) <= max(d__1,d__2)) {
goto L50;
}
}
/* L40: */
}
L50:
l = k;
if (l > *ilo) {
/* H(L,L-1) is negligible */
i__1 = l + (l - 1) * h_dim1;
h__[i__1].r = 0., h__[i__1].i = 0.;
}
/* Exit from loop if a submatrix of order 1 has split off. */
if (l >= i__) {
goto L140;
}
/* Now the active submatrix is in rows and columns L to I. If */
/* eigenvalues only are being computed, only the active submatrix */
/* need be transformed. */
if (! (*wantt)) {
i1 = l;
i2 = i__;
}
if (its == 10) {
/* Exceptional shift. */
i__1 = l + 1 + l * h_dim1;
s = (d__1 = h__[i__1].r, abs(d__1)) * .75;
i__1 = l + l * h_dim1;
z__1.r = s + h__[i__1].r, z__1.i = h__[i__1].i;
t.r = z__1.r, t.i = z__1.i;
} else if (its == 20) {
/* Exceptional shift. */
i__1 = i__ + (i__ - 1) * h_dim1;
s = (d__1 = h__[i__1].r, abs(d__1)) * .75;
i__1 = i__ + i__ * h_dim1;
z__1.r = s + h__[i__1].r, z__1.i = h__[i__1].i;
t.r = z__1.r, t.i = z__1.i;
} else {
/* Wilkinson's shift. */
i__1 = i__ + i__ * h_dim1;
t.r = h__[i__1].r, t.i = h__[i__1].i;
z_sqrt(&z__2, &h__[i__ - 1 + i__ * h_dim1]);
z_sqrt(&z__3, &h__[i__ + (i__ - 1) * h_dim1]);
z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r *
z__3.i + z__2.i * z__3.r;
u.r = z__1.r, u.i = z__1.i;
s = (d__1 = u.r, abs(d__1)) + (d__2 = d_imag(&u), abs(d__2));
if (s != 0.) {
i__1 = i__ - 1 + (i__ - 1) * h_dim1;
z__2.r = h__[i__1].r - t.r, z__2.i = h__[i__1].i - t.i;
z__1.r = z__2.r * .5, z__1.i = z__2.i * .5;
x.r = z__1.r, x.i = z__1.i;
sx = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x), abs(d__2));
/* Computing MAX */
d__3 = s, d__4 = (d__1 = x.r, abs(d__1)) + (d__2 = d_imag(&x),
abs(d__2));
s = max(d__3,d__4);
z__5.r = x.r / s, z__5.i = x.i / s;
pow_zi(&z__4, &z__5, &c__2);
z__7.r = u.r / s, z__7.i = u.i / s;
pow_zi(&z__6, &z__7, &c__2);
z__3.r = z__4.r + z__6.r, z__3.i = z__4.i + z__6.i;
z_sqrt(&z__2, &z__3);
z__1.r = s * z__2.r, z__1.i = s * z__2.i;
y.r = z__1.r, y.i = z__1.i;
if (sx > 0.) {
z__1.r = x.r / sx, z__1.i = x.i / sx;
z__2.r = x.r / sx, z__2.i = x.i / sx;
if (z__1.r * y.r + d_imag(&z__2) * d_imag(&y) < 0.) {
z__3.r = -y.r, z__3.i = -y.i;
y.r = z__3.r, y.i = z__3.i;
}
}
z__4.r = x.r + y.r, z__4.i = x.i + y.i;
zladiv_(&z__3, &u, &z__4);
z__2.r = u.r * z__3.r - u.i * z__3.i, z__2.i = u.r * z__3.i +
u.i * z__3.r;
z__1.r = t.r - z__2.r, z__1.i = t.i - z__2.i;
t.r = z__1.r, t.i = z__1.i;
}
}
/* Look for two consecutive small subdiagonal elements. */
i__1 = l + 1;
for (m = i__ - 1; m >= i__1; --m) {
/* Determine the effect of starting the single-shift QR */
/* iteration at row M, and see if this would make H(M,M-1) */
/* negligible. */
i__2 = m + m * h_dim1;
h11.r = h__[i__2].r, h11.i = h__[i__2].i;
i__2 = m + 1 + (m + 1) * h_dim1;
h22.r = h__[i__2].r, h22.i = h__[i__2].i;
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
i__2 = m + 1 + m * h_dim1;
h21 = h__[i__2].r;
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2))
+ abs(h21);
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
h21 /= s;
v[0].r = h11s.r, v[0].i = h11s.i;
v[1].r = h21, v[1].i = 0.;
i__2 = m + (m - 1) * h_dim1;
h10 = h__[i__2].r;
if (abs(h10) * abs(h21) <= ulp * (((d__1 = h11s.r, abs(d__1)) + (
d__2 = d_imag(&h11s), abs(d__2))) * ((d__3 = h11.r, abs(
d__3)) + (d__4 = d_imag(&h11), abs(d__4)) + ((d__5 =
h22.r, abs(d__5)) + (d__6 = d_imag(&h22), abs(d__6)))))) {
goto L70;
}
/* L60: */
}
i__1 = l + l * h_dim1;
h11.r = h__[i__1].r, h11.i = h__[i__1].i;
i__1 = l + 1 + (l + 1) * h_dim1;
h22.r = h__[i__1].r, h22.i = h__[i__1].i;
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
i__1 = l + 1 + l * h_dim1;
h21 = h__[i__1].r;
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2)) +
abs(h21);
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
h21 /= s;
v[0].r = h11s.r, v[0].i = h11s.i;
v[1].r = h21, v[1].i = 0.;
L70:
/* Single-shift QR step */
i__1 = i__ - 1;
for (k = m; k <= i__1; ++k) {
/* The first iteration of this loop determines a reflection G */
/* from the vector V and applies it from left and right to H, */
/* thus creating a nonzero bulge below the subdiagonal. */
/* Each subsequent iteration determines a reflection G to */
/* restore the Hessenberg form in the (K-1)th column, and thus */
/* chases the bulge one step toward the bottom of the active */
/* submatrix. */
/* V(2) is always real before the call to ZLARFG, and hence */
/* after the call T2 ( = T1*V(2) ) is also real. */
if (k > m) {
zcopy_(&c__2, &h__[k + (k - 1) * h_dim1], &c__1, v, &c__1);
}
zlarfg_(&c__2, v, &v[1], &c__1, &t1);
if (k > m) {
i__2 = k + (k - 1) * h_dim1;
h__[i__2].r = v[0].r, h__[i__2].i = v[0].i;
i__2 = k + 1 + (k - 1) * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
}
v2.r = v[1].r, v2.i = v[1].i;
z__1.r = t1.r * v2.r - t1.i * v2.i, z__1.i = t1.r * v2.i + t1.i *
v2.r;
t2 = z__1.r;
/* Apply G from the left to transform the rows of the matrix */
/* in columns K to I2. */
i__2 = i2;
for (j = k; j <= i__2; ++j) {
d_cnjg(&z__3, &t1);
i__3 = k + j * h_dim1;
z__2.r = z__3.r * h__[i__3].r - z__3.i * h__[i__3].i, z__2.i =
z__3.r * h__[i__3].i + z__3.i * h__[i__3].r;
i__4 = k + 1 + j * h_dim1;
z__4.r = t2 * h__[i__4].r, z__4.i = t2 * h__[i__4].i;
z__1.r = z__2.r + z__4.r, z__1.i = z__2.i + z__4.i;
sum.r = z__1.r, sum.i = z__1.i;
i__3 = k + j * h_dim1;
i__4 = k + j * h_dim1;
z__1.r = h__[i__4].r - sum.r, z__1.i = h__[i__4].i - sum.i;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
i__3 = k + 1 + j * h_dim1;
i__4 = k + 1 + j * h_dim1;
z__2.r = sum.r * v2.r - sum.i * v2.i, z__2.i = sum.r * v2.i +
sum.i * v2.r;
z__1.r = h__[i__4].r - z__2.r, z__1.i = h__[i__4].i - z__2.i;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
/* L80: */
}
/* Apply G from the right to transform the columns of the */
/* matrix in rows I1 to min(K+2,I). */
/* Computing MIN */
i__3 = k + 2;
i__2 = min(i__3,i__);
for (j = i1; j <= i__2; ++j) {
i__3 = j + k * h_dim1;
z__2.r = t1.r * h__[i__3].r - t1.i * h__[i__3].i, z__2.i =
t1.r * h__[i__3].i + t1.i * h__[i__3].r;
i__4 = j + (k + 1) * h_dim1;
z__3.r = t2 * h__[i__4].r, z__3.i = t2 * h__[i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__3 = j + k * h_dim1;
i__4 = j + k * h_dim1;
z__1.r = h__[i__4].r - sum.r, z__1.i = h__[i__4].i - sum.i;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
i__3 = j + (k + 1) * h_dim1;
i__4 = j + (k + 1) * h_dim1;
d_cnjg(&z__3, &v2);
z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r *
z__3.i + sum.i * z__3.r;
z__1.r = h__[i__4].r - z__2.r, z__1.i = h__[i__4].i - z__2.i;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
/* L90: */
}
if (*wantz) {
/* Accumulate transformations in the matrix Z */
i__2 = *ihiz;
for (j = *iloz; j <= i__2; ++j) {
i__3 = j + k * z_dim1;
z__2.r = t1.r * z__[i__3].r - t1.i * z__[i__3].i, z__2.i =
t1.r * z__[i__3].i + t1.i * z__[i__3].r;
i__4 = j + (k + 1) * z_dim1;
z__3.r = t2 * z__[i__4].r, z__3.i = t2 * z__[i__4].i;
z__1.r = z__2.r + z__3.r, z__1.i = z__2.i + z__3.i;
sum.r = z__1.r, sum.i = z__1.i;
i__3 = j + k * z_dim1;
i__4 = j + k * z_dim1;
z__1.r = z__[i__4].r - sum.r, z__1.i = z__[i__4].i -
sum.i;
z__[i__3].r = z__1.r, z__[i__3].i = z__1.i;
i__3 = j + (k + 1) * z_dim1;
i__4 = j + (k + 1) * z_dim1;
d_cnjg(&z__3, &v2);
z__2.r = sum.r * z__3.r - sum.i * z__3.i, z__2.i = sum.r *
z__3.i + sum.i * z__3.r;
z__1.r = z__[i__4].r - z__2.r, z__1.i = z__[i__4].i -
z__2.i;
z__[i__3].r = z__1.r, z__[i__3].i = z__1.i;
/* L100: */
}
}
if (k == m && m > l) {
/* If the QR step was started at row M > L because two */
/* consecutive small subdiagonals were found, then extra */
/* scaling must be performed to ensure that H(M,M-1) remains */
/* real. */
z__1.r = 1. - t1.r, z__1.i = 0. - t1.i;
temp.r = z__1.r, temp.i = z__1.i;
d__1 = z_abs(&temp);
z__1.r = temp.r / d__1, z__1.i = temp.i / d__1;
temp.r = z__1.r, temp.i = z__1.i;
i__2 = m + 1 + m * h_dim1;
i__3 = m + 1 + m * h_dim1;
d_cnjg(&z__2, &temp);
z__1.r = h__[i__3].r * z__2.r - h__[i__3].i * z__2.i, z__1.i =
h__[i__3].r * z__2.i + h__[i__3].i * z__2.r;
h__[i__2].r = z__1.r, h__[i__2].i = z__1.i;
if (m + 2 <= i__) {
i__2 = m + 2 + (m + 1) * h_dim1;
i__3 = m + 2 + (m + 1) * h_dim1;
z__1.r = h__[i__3].r * temp.r - h__[i__3].i * temp.i,
z__1.i = h__[i__3].r * temp.i + h__[i__3].i *
temp.r;
h__[i__2].r = z__1.r, h__[i__2].i = z__1.i;
}
i__2 = i__;
for (j = m; j <= i__2; ++j) {
if (j != m + 1) {
if (i2 > j) {
i__3 = i2 - j;
zscal_(&i__3, &temp, &h__[j + (j + 1) * h_dim1],
ldh);
}
i__3 = j - i1;
d_cnjg(&z__1, &temp);
zscal_(&i__3, &z__1, &h__[i1 + j * h_dim1], &c__1);
if (*wantz) {
d_cnjg(&z__1, &temp);
zscal_(&nz, &z__1, &z__[*iloz + j * z_dim1], &
c__1);
}
}
/* L110: */
}
}
/* L120: */
}
/* Ensure that H(I,I-1) is real. */
i__1 = i__ + (i__ - 1) * h_dim1;
temp.r = h__[i__1].r, temp.i = h__[i__1].i;
if (d_imag(&temp) != 0.) {
rtemp = z_abs(&temp);
i__1 = i__ + (i__ - 1) * h_dim1;
h__[i__1].r = rtemp, h__[i__1].i = 0.;
z__1.r = temp.r / rtemp, z__1.i = temp.i / rtemp;
temp.r = z__1.r, temp.i = z__1.i;
if (i2 > i__) {
i__1 = i2 - i__;
d_cnjg(&z__1, &temp);
zscal_(&i__1, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
}
i__1 = i__ - i1;
zscal_(&i__1, &temp, &h__[i1 + i__ * h_dim1], &c__1);
if (*wantz) {
zscal_(&nz, &temp, &z__[*iloz + i__ * z_dim1], &c__1);
}
}
/* L130: */
}
/* Failure to converge in remaining number of iterations */
*info = i__;
return 0;
L140:
/* H(I,I-1) is negligible: one eigenvalue has converged. */
i__1 = i__;
i__2 = i__ + i__ * h_dim1;
w[i__1].r = h__[i__2].r, w[i__1].i = h__[i__2].i;
/* return to start of the main loop with new value of I. */
i__ = l - 1;
goto L30;
L150:
return 0;
/* End of ZLAHQR */
} /* zlahqr_ */
