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|
/* lapack/complex16/zlahqr.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__2 = 2;
static integer c__1 = 1;
/*< >*/
/* 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, i__5;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
doublecomplex z__1, z__2, z__3, z__4;
/* Builtin functions */
double d_imag(doublecomplex *);
void z_sqrt(doublecomplex *, doublecomplex *), d_cnjg(doublecomplex *,
doublecomplex *);
double z_abs(doublecomplex *);
/* Local variables */
integer i__, j, k, l, m;
doublereal s;
doublecomplex t, u, v[2], x, y;
integer i1=0, i2=0;
doublecomplex t1;
doublereal t2;
doublecomplex v2;
doublereal h10;
doublecomplex h11;
doublereal h21;
doublecomplex h22;
integer nh, nz;
doublecomplex h11s;
integer itn, its;
doublereal ulp;
doublecomplex sum;
doublereal tst1;
doublecomplex temp;
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *);
doublereal rtemp, rwork[1];
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *);
extern doublereal dlamch_(char *, ftnlen);
extern /* Subroutine */ int zlarfg_(integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *);
extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
doublecomplex *);
extern doublereal zlanhs_(char *, integer *, doublecomplex *, integer *,
doublereal *, ftnlen);
doublereal smlnum;
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/*< LOGICAL WANTT, WANTZ >*/
/*< INTEGER IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N >*/
/* .. */
/* .. Array Arguments .. */
/*< COMPLEX*16 H( LDH, * ), W( * ), Z( LDZ, * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* ZLAHQR is an auxiliary routine called by ZHSEQR to update the */
/* eigenvalues and Schur decomposition already computed by ZHSEQR, 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 WANTT is .TRUE., H is upper triangular in rows */
/* and columns ILO:IHI, with any 2-by-2 diagonal blocks in */
/* standard form. If WANTT is .FALSE., the contents of H are */
/* unspecified on exit. */
/* 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 ZHSEQR, 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 */
/* > 0: if INFO = i, ZLAHQR failed to compute all the */
/* eigenvalues ILO to IHI in a total of 30*(IHI-ILO+1) */
/* iterations; elements i+1:ihi of W contain those */
/* eigenvalues which have been successfully computed. */
/* ===================================================================== */
/* .. Parameters .. */
/*< COMPLEX*16 ZERO, ONE >*/
/*< >*/
/*< DOUBLE PRECISION RZERO, HALF >*/
/*< PARAMETER ( RZERO = 0.0D+0, HALF = 0.5D+0 ) >*/
/*< DOUBLE PRECISION DAT1 >*/
/*< PARAMETER ( DAT1 = 0.75D+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, I1, I2, ITN, ITS, J, K, L, M, NH, NZ >*/
/*< DOUBLE PRECISION H10, H21, RTEMP, S, SMLNUM, T2, TST1, ULP >*/
/*< >*/
/* .. */
/* .. Local Arrays .. */
/*< DOUBLE PRECISION RWORK( 1 ) >*/
/*< COMPLEX*16 V( 2 ) >*/
/* .. */
/* .. External Functions .. */
/*< DOUBLE PRECISION DLAMCH, ZLANHS >*/
/*< COMPLEX*16 ZLADIV >*/
/*< EXTERNAL DLAMCH, ZLANHS, ZLADIV >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL ZCOPY, ZLARFG, ZSCAL >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, DBLE, DCONJG, DIMAG, MAX, MIN, SQRT >*/
/* .. */
/* .. Statement Functions .. */
/*< DOUBLE PRECISION CABS1 >*/
/* .. */
/* .. Statement Function definitions .. */
/*< CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) >*/
/* .. */
/* .. Executable Statements .. */
/*< INFO = 0 >*/
/* 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.EQ.IHI ) THEN >*/
if (*ilo == *ihi) {
/*< W( ILO ) = H( ILO, ILO ) >*/
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 >*/
return 0;
/*< END IF >*/
}
/*< NH = IHI - ILO + 1 >*/
nh = *ihi - *ilo + 1;
/*< NZ = IHIZ - ILOZ + 1 >*/
nz = *ihiz - *iloz + 1;
/* Set machine-dependent constants for the stopping criterion. */
/* If norm(H) <= sqrt(OVFL), overflow should not occur. */
/*< ULP = DLAMCH( 'Precision' ) >*/
ulp = dlamch_("Precision", (ftnlen)9);
/*< SMLNUM = DLAMCH( 'Safe minimum' ) / ULP >*/
smlnum = dlamch_("Safe minimum", (ftnlen)12) / 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 ) THEN >*/
if (*wantt) {
/*< I1 = 1 >*/
i1 = 1;
/*< I2 = N >*/
i2 = *n;
/*< END IF >*/
}
/* ITN is the total number of QR iterations allowed. */
/*< ITN = 30*NH >*/
itn = nh * 30;
/* 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 >*/
i__ = *ihi;
/*< 10 CONTINUE >*/
L10:
/*< >*/
if (i__ < *ilo) {
goto L130;
}
/* 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 >*/
l = *ilo;
/*< DO 110 ITS = 0, ITN >*/
i__1 = itn;
for (its = 0; its <= i__1; ++its) {
/* Look for a single small subdiagonal element. */
/*< DO 20 K = I, L + 1, -1 >*/
i__2 = l + 1;
for (k = i__; k >= i__2; --k) {
/*< TST1 = CABS1( H( K-1, K-1 ) ) + CABS1( H( K, K ) ) >*/
i__3 = k - 1 + (k - 1) * h_dim1;
i__4 = k + k * h_dim1;
tst1 = (d__1 = h__[i__3].r, abs(d__1)) + (d__2 = d_imag(&h__[k -
1 + (k - 1) * h_dim1]), abs(d__2)) + ((d__3 = h__[i__4].r,
abs(d__3)) + (d__4 = d_imag(&h__[k + k * h_dim1]), abs(
d__4)));
/*< >*/
if (tst1 == 0.) {
i__3 = i__ - l + 1;
tst1 = zlanhs_("1", &i__3, &h__[l + l * h_dim1], ldh, rwork, (
ftnlen)1);
}
/*< >*/
i__3 = k + (k - 1) * h_dim1;
/* Computing MAX */
d__2 = ulp * tst1;
if ((d__1 = h__[i__3].r, abs(d__1)) <= max(d__2,smlnum)) {
goto L30;
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< 30 CONTINUE >*/
L30:
/*< L = K >*/
l = k;
/*< IF( L.GT.ILO ) THEN >*/
if (l > *ilo) {
/* H(L,L-1) is negligible */
/*< H( L, L-1 ) = ZERO >*/
i__2 = l + (l - 1) * h_dim1;
h__[i__2].r = 0., h__[i__2].i = 0.;
/*< END IF >*/
}
/* Exit from loop if a submatrix of order 1 has split off. */
/*< >*/
if (l >= i__) {
goto L120;
}
/* 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( .NOT.WANTT ) THEN >*/
if (! (*wantt)) {
/*< I1 = L >*/
i1 = l;
/*< I2 = I >*/
i2 = i__;
/*< END IF >*/
}
/*< IF( ITS.EQ.10 .OR. ITS.EQ.20 ) THEN >*/
if (its == 10 || its == 20) {
/* Exceptional shift. */
/*< S = DAT1*ABS( DBLE( H( I, I-1 ) ) ) >*/
i__2 = i__ + (i__ - 1) * h_dim1;
s = (d__1 = h__[i__2].r, abs(d__1)) * .75;
/*< T = S + H( I, I ) >*/
i__2 = i__ + i__ * h_dim1;
z__1.r = s + h__[i__2].r, z__1.i = h__[i__2].i;
t.r = z__1.r, t.i = z__1.i;
/*< ELSE >*/
} else {
/* Wilkinson's shift. */
/*< T = H( I, I ) >*/
i__2 = i__ + i__ * h_dim1;
t.r = h__[i__2].r, t.i = h__[i__2].i;
/*< U = H( I-1, I )*DBLE( H( I, I-1 ) ) >*/
i__2 = i__ - 1 + i__ * h_dim1;
i__3 = i__ + (i__ - 1) * h_dim1;
d__1 = h__[i__3].r;
z__1.r = d__1 * h__[i__2].r, z__1.i = d__1 * h__[i__2].i;
u.r = z__1.r, u.i = z__1.i;
/*< IF( U.NE.ZERO ) THEN >*/
if (u.r != 0. || u.i != 0.) {
/*< X = HALF*( H( I-1, I-1 )-T ) >*/
i__2 = i__ - 1 + (i__ - 1) * h_dim1;
z__2.r = h__[i__2].r - t.r, z__2.i = h__[i__2].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;
/*< Y = SQRT( X*X+U ) >*/
z__3.r = x.r * x.r - x.i * x.i, z__3.i = x.r * x.i + x.i *
x.r;
z__2.r = z__3.r + u.r, z__2.i = z__3.i + u.i;
z_sqrt(&z__1, &z__2);
y.r = z__1.r, y.i = z__1.i;
/*< >*/
if (x.r * y.r + d_imag(&x) * d_imag(&y) < 0.) {
z__1.r = -y.r, z__1.i = -y.i;
y.r = z__1.r, y.i = z__1.i;
}
/*< T = T - ZLADIV( U, ( X+Y ) ) >*/
z__3.r = x.r + y.r, z__3.i = x.i + y.i;
zladiv_(&z__2, &u, &z__3);
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;
/*< END IF >*/
}
/*< END IF >*/
}
/* Look for two consecutive small subdiagonal elements. */
/*< DO 40 M = I - 1, L + 1, -1 >*/
i__2 = l + 1;
for (m = i__ - 1; m >= i__2; --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. */
/*< H11 = H( M, M ) >*/
i__3 = m + m * h_dim1;
h11.r = h__[i__3].r, h11.i = h__[i__3].i;
/*< H22 = H( M+1, M+1 ) >*/
i__3 = m + 1 + (m + 1) * h_dim1;
h22.r = h__[i__3].r, h22.i = h__[i__3].i;
/*< H11S = H11 - T >*/
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
/*< H21 = H( M+1, M ) >*/
i__3 = m + 1 + m * h_dim1;
h21 = h__[i__3].r;
/*< S = CABS1( H11S ) + ABS( H21 ) >*/
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2))
+ abs(h21);
/*< H11S = H11S / S >*/
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
/*< H21 = H21 / S >*/
h21 /= s;
/*< V( 1 ) = H11S >*/
v[0].r = h11s.r, v[0].i = h11s.i;
/*< V( 2 ) = H21 >*/
v[1].r = h21, v[1].i = 0.;
/*< H10 = H( M, M-1 ) >*/
i__3 = m + (m - 1) * h_dim1;
h10 = h__[i__3].r;
/*< TST1 = CABS1( H11S )*( CABS1( H11 )+CABS1( H22 ) ) >*/
tst1 = ((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))));
/*< >*/
if ((d__1 = h10 * h21, abs(d__1)) <= ulp * tst1) {
goto L50;
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< H11 = H( L, L ) >*/
i__2 = l + l * h_dim1;
h11.r = h__[i__2].r, h11.i = h__[i__2].i;
/*< H22 = H( L+1, L+1 ) >*/
i__2 = l + 1 + (l + 1) * h_dim1;
h22.r = h__[i__2].r, h22.i = h__[i__2].i;
/*< H11S = H11 - T >*/
z__1.r = h11.r - t.r, z__1.i = h11.i - t.i;
h11s.r = z__1.r, h11s.i = z__1.i;
/*< H21 = H( L+1, L ) >*/
i__2 = l + 1 + l * h_dim1;
h21 = h__[i__2].r;
/*< S = CABS1( H11S ) + ABS( H21 ) >*/
s = (d__1 = h11s.r, abs(d__1)) + (d__2 = d_imag(&h11s), abs(d__2)) +
abs(h21);
/*< H11S = H11S / S >*/
z__1.r = h11s.r / s, z__1.i = h11s.i / s;
h11s.r = z__1.r, h11s.i = z__1.i;
/*< H21 = H21 / S >*/
h21 /= s;
/*< V( 1 ) = H11S >*/
v[0].r = h11s.r, v[0].i = h11s.i;
/*< V( 2 ) = H21 >*/
v[1].r = h21, v[1].i = 0.;
/*< 50 CONTINUE >*/
L50:
/* Single-shift QR step */
/*< DO 100 K = M, I - 1 >*/
i__2 = i__ - 1;
for (k = m; k <= i__2; ++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);
}
/*< CALL ZLARFG( 2, V( 1 ), V( 2 ), 1, T1 ) >*/
zlarfg_(&c__2, v, &v[1], &c__1, &t1);
/*< IF( K.GT.M ) THEN >*/
if (k > m) {
/*< H( K, K-1 ) = V( 1 ) >*/
i__3 = k + (k - 1) * h_dim1;
h__[i__3].r = v[0].r, h__[i__3].i = v[0].i;
/*< H( K+1, K-1 ) = ZERO >*/
i__3 = k + 1 + (k - 1) * h_dim1;
h__[i__3].r = 0., h__[i__3].i = 0.;
/*< END IF >*/
}
/*< V2 = V( 2 ) >*/
v2.r = v[1].r, v2.i = v[1].i;
/*< T2 = DBLE( T1*V2 ) >*/
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. */
/*< DO 60 J = K, I2 >*/
i__3 = i2;
for (j = k; j <= i__3; ++j) {
/*< SUM = DCONJG( T1 )*H( K, J ) + T2*H( K+1, J ) >*/
d_cnjg(&z__3, &t1);
i__4 = k + j * h_dim1;
z__2.r = z__3.r * h__[i__4].r - z__3.i * h__[i__4].i, z__2.i =
z__3.r * h__[i__4].i + z__3.i * h__[i__4].r;
i__5 = k + 1 + j * h_dim1;
z__4.r = t2 * h__[i__5].r, z__4.i = t2 * h__[i__5].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;
/*< H( K, J ) = H( K, J ) - SUM >*/
i__4 = k + j * h_dim1;
i__5 = k + j * h_dim1;
z__1.r = h__[i__5].r - sum.r, z__1.i = h__[i__5].i - sum.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/*< H( K+1, J ) = H( K+1, J ) - SUM*V2 >*/
i__4 = k + 1 + j * h_dim1;
i__5 = 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__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/*< 60 CONTINUE >*/
/* L60: */
}
/* Apply G from the right to transform the columns of the */
/* matrix in rows I1 to min(K+2,I). */
/*< DO 70 J = I1, MIN( K+2, I ) >*/
/* Computing MIN */
i__4 = k + 2;
i__3 = min(i__4,i__);
for (j = i1; j <= i__3; ++j) {
/*< SUM = T1*H( J, K ) + T2*H( J, K+1 ) >*/
i__4 = j + k * h_dim1;
z__2.r = t1.r * h__[i__4].r - t1.i * h__[i__4].i, z__2.i =
t1.r * h__[i__4].i + t1.i * h__[i__4].r;
i__5 = j + (k + 1) * h_dim1;
z__3.r = t2 * h__[i__5].r, z__3.i = t2 * h__[i__5].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;
/*< H( J, K ) = H( J, K ) - SUM >*/
i__4 = j + k * h_dim1;
i__5 = j + k * h_dim1;
z__1.r = h__[i__5].r - sum.r, z__1.i = h__[i__5].i - sum.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/*< H( J, K+1 ) = H( J, K+1 ) - SUM*DCONJG( V2 ) >*/
i__4 = j + (k + 1) * h_dim1;
i__5 = 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__5].r - z__2.r, z__1.i = h__[i__5].i - z__2.i;
h__[i__4].r = z__1.r, h__[i__4].i = z__1.i;
/*< 70 CONTINUE >*/
/* L70: */
}
/*< IF( WANTZ ) THEN >*/
if (*wantz) {
/* Accumulate transformations in the matrix Z */
/*< DO 80 J = ILOZ, IHIZ >*/
i__3 = *ihiz;
for (j = *iloz; j <= i__3; ++j) {
/*< SUM = T1*Z( J, K ) + T2*Z( J, K+1 ) >*/
i__4 = j + k * z_dim1;
z__2.r = t1.r * z__[i__4].r - t1.i * z__[i__4].i, z__2.i =
t1.r * z__[i__4].i + t1.i * z__[i__4].r;
i__5 = j + (k + 1) * z_dim1;
z__3.r = t2 * z__[i__5].r, z__3.i = t2 * z__[i__5].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;
/*< Z( J, K ) = Z( J, K ) - SUM >*/
i__4 = j + k * z_dim1;
i__5 = j + k * z_dim1;
z__1.r = z__[i__5].r - sum.r, z__1.i = z__[i__5].i -
sum.i;
z__[i__4].r = z__1.r, z__[i__4].i = z__1.i;
/*< Z( J, K+1 ) = Z( J, K+1 ) - SUM*DCONJG( V2 ) >*/
i__4 = j + (k + 1) * z_dim1;
i__5 = 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__5].r - z__2.r, z__1.i = z__[i__5].i -
z__2.i;
z__[i__4].r = z__1.r, z__[i__4].i = z__1.i;
/*< 80 CONTINUE >*/
/* L80: */
}
/*< END IF >*/
}
/*< IF( K.EQ.M .AND. M.GT.L ) THEN >*/
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. */
/*< TEMP = ONE - T1 >*/
z__1.r = 1. - t1.r, z__1.i = 0. - t1.i;
temp.r = z__1.r, temp.i = z__1.i;
/*< TEMP = TEMP / ABS( TEMP ) >*/
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;
/*< H( M+1, M ) = H( M+1, M )*DCONJG( TEMP ) >*/
i__3 = m + 1 + m * h_dim1;
i__4 = m + 1 + m * h_dim1;
d_cnjg(&z__2, &temp);
z__1.r = h__[i__4].r * z__2.r - h__[i__4].i * z__2.i, z__1.i =
h__[i__4].r * z__2.i + h__[i__4].i * z__2.r;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
/*< >*/
if (m + 2 <= i__) {
i__3 = m + 2 + (m + 1) * h_dim1;
i__4 = m + 2 + (m + 1) * h_dim1;
z__1.r = h__[i__4].r * temp.r - h__[i__4].i * temp.i,
z__1.i = h__[i__4].r * temp.i + h__[i__4].i *
temp.r;
h__[i__3].r = z__1.r, h__[i__3].i = z__1.i;
}
/*< DO 90 J = M, I >*/
i__3 = i__;
for (j = m; j <= i__3; ++j) {
/*< IF( J.NE.M+1 ) THEN >*/
if (j != m + 1) {
/*< >*/
if (i2 > j) {
i__4 = i2 - j;
zscal_(&i__4, &temp, &h__[j + (j + 1) * h_dim1],
ldh);
}
/*< CALL ZSCAL( J-I1, DCONJG( TEMP ), H( I1, J ), 1 ) >*/
i__4 = j - i1;
d_cnjg(&z__1, &temp);
zscal_(&i__4, &z__1, &h__[i1 + j * h_dim1], &c__1);
/*< IF( WANTZ ) THEN >*/
if (*wantz) {
/*< >*/
d_cnjg(&z__1, &temp);
zscal_(&nz, &z__1, &z__[*iloz + j * z_dim1], &
c__1);
/*< END IF >*/
}
/*< END IF >*/
}
/*< 90 CONTINUE >*/
/* L90: */
}
/*< END IF >*/
}
/*< 100 CONTINUE >*/
/* L100: */
}
/* Ensure that H(I,I-1) is real. */
/*< TEMP = H( I, I-1 ) >*/
i__2 = i__ + (i__ - 1) * h_dim1;
temp.r = h__[i__2].r, temp.i = h__[i__2].i;
/*< IF( DIMAG( TEMP ).NE.RZERO ) THEN >*/
if (d_imag(&temp) != 0.) {
/*< RTEMP = ABS( TEMP ) >*/
rtemp = z_abs(&temp);
/*< H( I, I-1 ) = RTEMP >*/
i__2 = i__ + (i__ - 1) * h_dim1;
h__[i__2].r = rtemp, h__[i__2].i = 0.;
/*< TEMP = TEMP / RTEMP >*/
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__2 = i2 - i__;
d_cnjg(&z__1, &temp);
zscal_(&i__2, &z__1, &h__[i__ + (i__ + 1) * h_dim1], ldh);
}
/*< CALL ZSCAL( I-I1, TEMP, H( I1, I ), 1 ) >*/
i__2 = i__ - i1;
zscal_(&i__2, &temp, &h__[i1 + i__ * h_dim1], &c__1);
/*< IF( WANTZ ) THEN >*/
if (*wantz) {
/*< CALL ZSCAL( NZ, TEMP, Z( ILOZ, I ), 1 ) >*/
zscal_(&nz, &temp, &z__[*iloz + i__ * z_dim1], &c__1);
/*< END IF >*/
}
/*< END IF >*/
}
/*< 110 CONTINUE >*/
/* L110: */
}
/* Failure to converge in remaining number of iterations */
/*< INFO = I >*/
*info = i__;
/*< RETURN >*/
return 0;
/*< 120 CONTINUE >*/
L120:
/* H(I,I-1) is negligible: one eigenvalue has converged. */
/*< W( I ) = H( I, I ) >*/
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;
/* Decrement number of remaining iterations, and return to start of */
/* the main loop with new value of I. */
/*< ITN = ITN - ITS >*/
itn -= its;
/*< I = L - 1 >*/
i__ = l - 1;
/*< GO TO 10 >*/
goto L10;
/*< 130 CONTINUE >*/
L130:
/*< RETURN >*/
return 0;
/* End of ZLAHQR */
/*< END >*/
} /* zlahqr_ */
#ifdef __cplusplus
}
#endif
|
