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/* zhseqr.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c__12 = 12;
static integer c__2 = 2;
static integer c__49 = 49;
/* Subroutine */ int zhseqr_(char *job, char *compz, integer *n, integer *ilo,
integer *ihi, doublecomplex *h__, integer *ldh, doublecomplex *w,
doublecomplex *z__, integer *ldz, doublecomplex *work, integer *lwork,
integer *info)
{
/* System generated locals */
address a__1[2];
integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__2, i__3[2];
doublereal d__1, d__2, d__3;
doublecomplex z__1;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
doublecomplex hl[2401] /* was [49][49] */;
integer kbot, nmin;
extern logical lsame_(char *, char *);
logical initz;
doublecomplex workl[49];
logical wantt, wantz;
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaqr0_(logical *, logical *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *), xerbla_(char *, integer *
);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int zlahqr_(logical *, logical *, integer *,
integer *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *),
zlacpy_(char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *), zlaset_(char *, integer *,
integer *, doublecomplex *, doublecomplex *, doublecomplex *,
integer *);
logical lquery;
/* -- LAPACK driver 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 */
/* ======= */
/* ZHSEQR computes the eigenvalues of a Hessenberg matrix H */
/* and, optionally, the matrices T and Z from the Schur decomposition */
/* H = Z T Z**H, where T is an upper triangular matrix (the */
/* Schur form), and Z is the unitary matrix of Schur vectors. */
/* Optionally Z may be postmultiplied into an input unitary */
/* matrix Q so that this routine can give the Schur factorization */
/* of a matrix A which has been reduced to the Hessenberg form H */
/* by the unitary matrix Q: A = Q*H*Q**H = (QZ)*H*(QZ)**H. */
/* Arguments */
/* ========= */
/* JOB (input) CHARACTER*1 */
/* = 'E': compute eigenvalues only; */
/* = 'S': compute eigenvalues and the Schur form T. */
/* COMPZ (input) CHARACTER*1 */
/* = 'N': no Schur vectors are computed; */
/* = 'I': Z is initialized to the unit matrix and the matrix Z */
/* of Schur vectors of H is returned; */
/* = 'V': Z must contain an unitary matrix Q on entry, and */
/* the product Q*Z is returned. */
/* N (input) INTEGER */
/* The order of the matrix H. N .GE. 0. */
/* ILO (input) INTEGER */
/* IHI (input) INTEGER */
/* It is assumed that H is already upper triangular in rows */
/* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally */
/* set by a previous call to ZGEBAL, and then passed to ZGEHRD */
/* when the matrix output by ZGEBAL is reduced to Hessenberg */
/* form. Otherwise ILO and IHI should be set to 1 and N */
/* respectively. If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N. */
/* If N = 0, then ILO = 1 and IHI = 0. */
/* H (input/output) COMPLEX*16 array, dimension (LDH,N) */
/* On entry, the upper Hessenberg matrix H. */
/* On exit, if INFO = 0 and JOB = 'S', H contains the upper */
/* triangular matrix T from the Schur decomposition (the */
/* Schur form). If INFO = 0 and JOB = 'E', the contents of */
/* H are unspecified on exit. (The output value of H when */
/* INFO.GT.0 is given under the description of INFO below.) */
/* Unlike earlier versions of ZHSEQR, this subroutine may */
/* explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1 */
/* or j = IHI+1, IHI+2, ... N. */
/* LDH (input) INTEGER */
/* The leading dimension of the array H. LDH .GE. max(1,N). */
/* W (output) COMPLEX*16 array, dimension (N) */
/* The computed eigenvalues. If JOB = 'S', 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). */
/* Z (input/output) COMPLEX*16 array, dimension (LDZ,N) */
/* If COMPZ = 'N', Z is not referenced. */
/* If COMPZ = 'I', on entry Z need not be set and on exit, */
/* if INFO = 0, Z contains the unitary matrix Z of the Schur */
/* vectors of H. If COMPZ = 'V', on entry Z must contain an */
/* N-by-N matrix Q, which is assumed to be equal to the unit */
/* matrix except for the submatrix Z(ILO:IHI,ILO:IHI). On exit, */
/* if INFO = 0, Z contains Q*Z. */
/* Normally Q is the unitary matrix generated by ZUNGHR */
/* after the call to ZGEHRD which formed the Hessenberg matrix */
/* H. (The output value of Z when INFO.GT.0 is given under */
/* the description of INFO below.) */
/* LDZ (input) INTEGER */
/* The leading dimension of the array Z. if COMPZ = 'I' or */
/* COMPZ = 'V', then LDZ.GE.MAX(1,N). Otherwize, LDZ.GE.1. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK) */
/* On exit, if INFO = 0, WORK(1) returns an estimate of */
/* the optimal value for LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK .GE. max(1,N) */
/* is sufficient and delivers very good and sometimes */
/* optimal performance. However, LWORK as large as 11*N */
/* may be required for optimal performance. A workspace */
/* query is recommended to determine the optimal workspace */
/* size. */
/* If LWORK = -1, then ZHSEQR does a workspace query. */
/* In this case, ZHSEQR checks the input parameters and */
/* estimates the optimal workspace size for the given */
/* values of N, ILO and IHI. The estimate is returned */
/* in WORK(1). No error message related to LWORK is */
/* issued by XERBLA. Neither H nor Z are accessed. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* .LT. 0: if INFO = -i, the i-th argument had an illegal */
/* value */
/* .GT. 0: if INFO = i, ZHSEQR failed to compute all of */
/* the eigenvalues. Elements 1:ilo-1 and i+1:n of WR */
/* and WI contain those eigenvalues which have been */
/* successfully computed. (Failures are rare.) */
/* If INFO .GT. 0 and JOB = 'E', then on exit, the */
/* remaining unconverged eigenvalues are the eigen- */
/* values of the upper Hessenberg matrix rows and */
/* columns ILO through INFO of the final, output */
/* value of H. */
/* If INFO .GT. 0 and JOB = 'S', then on exit */
/* (*) (initial value of H)*U = U*(final value of H) */
/* where U is a unitary matrix. The final */
/* value of H is upper Hessenberg and triangular in */
/* rows and columns INFO+1 through IHI. */
/* If INFO .GT. 0 and COMPZ = 'V', then on exit */
/* (final value of Z) = (initial value of Z)*U */
/* where U is the unitary matrix in (*) (regard- */
/* less of the value of JOB.) */
/* If INFO .GT. 0 and COMPZ = 'I', then on exit */
/* (final value of Z) = U */
/* where U is the unitary matrix in (*) (regard- */
/* less of the value of JOB.) */
/* If INFO .GT. 0 and COMPZ = 'N', then Z is not */
/* accessed. */
/* ================================================================ */
/* Default values supplied by */
/* ILAENV(ISPEC,'ZHSEQR',JOB(:1)//COMPZ(:1),N,ILO,IHI,LWORK). */
/* It is suggested that these defaults be adjusted in order */
/* to attain best performance in each particular */
/* computational environment. */
/* ISPEC=12: The ZLAHQR vs ZLAQR0 crossover point. */
/* Default: 75. (Must be at least 11.) */
/* ISPEC=13: Recommended deflation window size. */
/* This depends on ILO, IHI and NS. NS is the */
/* number of simultaneous shifts returned */
/* by ILAENV(ISPEC=15). (See ISPEC=15 below.) */
/* The default for (IHI-ILO+1).LE.500 is NS. */
/* The default for (IHI-ILO+1).GT.500 is 3*NS/2. */
/* ISPEC=14: Nibble crossover point. (See IPARMQ for */
/* details.) Default: 14% of deflation window */
/* size. */
/* ISPEC=15: Number of simultaneous shifts in a multishift */
/* QR iteration. */
/* If IHI-ILO+1 is ... */
/* greater than ...but less ... the */
/* or equal to ... than default is */
/* 1 30 NS = 2(+) */
/* 30 60 NS = 4(+) */
/* 60 150 NS = 10(+) */
/* 150 590 NS = ** */
/* 590 3000 NS = 64 */
/* 3000 6000 NS = 128 */
/* 6000 infinity NS = 256 */
/* (+) By default some or all matrices of this order */
/* are passed to the implicit double shift routine */
/* ZLAHQR and this parameter is ignored. See */
/* ISPEC=12 above and comments in IPARMQ for */
/* details. */
/* (**) The asterisks (**) indicate an ad-hoc */
/* function of N increasing from 10 to 64. */
/* ISPEC=16: Select structured matrix multiply. */
/* If the number of simultaneous shifts (specified */
/* by ISPEC=15) is less than 14, then the default */
/* for ISPEC=16 is 0. Otherwise the default for */
/* ISPEC=16 is 2. */
/* ================================================================ */
/* Based on contributions by */
/* Karen Braman and Ralph Byers, Department of Mathematics, */
/* University of Kansas, USA */
/* ================================================================ */
/* References: */
/* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
/* Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 */
/* Performance, SIAM Journal of Matrix Analysis, volume 23, pages */
/* 929--947, 2002. */
/* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR */
/* Algorithm Part II: Aggressive Early Deflation, SIAM Journal */
/* of Matrix Analysis, volume 23, pages 948--973, 2002. */
/* ================================================================ */
/* .. Parameters .. */
/* ==== Matrices of order NTINY or smaller must be processed by */
/* . ZLAHQR because of insufficient subdiagonal scratch space. */
/* . (This is a hard limit.) ==== */
/* ==== NL allocates some local workspace to help small matrices */
/* . through a rare ZLAHQR failure. NL .GT. NTINY = 11 is */
/* . required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom- */
/* . mended. (The default value of NMIN is 75.) Using NL = 49 */
/* . allows up to six simultaneous shifts and a 16-by-16 */
/* . deflation window. ==== */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* ==== Decode and check the input parameters. ==== */
/* 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;
--work;
/* Function Body */
wantt = lsame_(job, "S");
initz = lsame_(compz, "I");
wantz = initz || lsame_(compz, "V");
d__1 = (doublereal) max(1,*n);
z__1.r = d__1, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
lquery = *lwork == -1;
*info = 0;
if (! lsame_(job, "E") && ! wantt) {
*info = -1;
} else if (! lsame_(compz, "N") && ! wantz) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*ilo < 1 || *ilo > max(1,*n)) {
*info = -4;
} else if (*ihi < min(*ilo,*n) || *ihi > *n) {
*info = -5;
} else if (*ldh < max(1,*n)) {
*info = -7;
} else if (*ldz < 1 || wantz && *ldz < max(1,*n)) {
*info = -10;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -12;
}
if (*info != 0) {
/* ==== Quick return in case of invalid argument. ==== */
i__1 = -(*info);
xerbla_("ZHSEQR", &i__1);
return 0;
} else if (*n == 0) {
/* ==== Quick return in case N = 0; nothing to do. ==== */
return 0;
} else if (lquery) {
/* ==== Quick return in case of a workspace query ==== */
zlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1], ilo,
ihi, &z__[z_offset], ldz, &work[1], lwork, info);
/* ==== Ensure reported workspace size is backward-compatible with */
/* . previous LAPACK versions. ==== */
/* Computing MAX */
d__2 = work[1].r, d__3 = (doublereal) max(1,*n);
d__1 = max(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
return 0;
} else {
/* ==== copy eigenvalues isolated by ZGEBAL ==== */
if (*ilo > 1) {
i__1 = *ilo - 1;
i__2 = *ldh + 1;
zcopy_(&i__1, &h__[h_offset], &i__2, &w[1], &c__1);
}
if (*ihi < *n) {
i__1 = *n - *ihi;
i__2 = *ldh + 1;
zcopy_(&i__1, &h__[*ihi + 1 + (*ihi + 1) * h_dim1], &i__2, &w[*
ihi + 1], &c__1);
}
/* ==== Initialize Z, if requested ==== */
if (initz) {
zlaset_("A", n, n, &c_b1, &c_b2, &z__[z_offset], ldz);
}
/* ==== Quick return if possible ==== */
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;
}
/* ==== ZLAHQR/ZLAQR0 crossover point ==== */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = job;
i__3[1] = 1, a__1[1] = compz;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
nmin = ilaenv_(&c__12, "ZHSEQR", ch__1, n, ilo, ihi, lwork);
nmin = max(11,nmin);
/* ==== ZLAQR0 for big matrices; ZLAHQR for small ones ==== */
if (*n > nmin) {
zlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1],
ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
} else {
/* ==== Small matrix ==== */
zlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &w[1],
ilo, ihi, &z__[z_offset], ldz, info);
if (*info > 0) {
/* ==== A rare ZLAHQR failure! ZLAQR0 sometimes succeeds */
/* . when ZLAHQR fails. ==== */
kbot = *info;
if (*n >= 49) {
/* ==== Larger matrices have enough subdiagonal scratch */
/* . space to call ZLAQR0 directly. ==== */
zlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset],
ldh, &w[1], ilo, ihi, &z__[z_offset], ldz, &work[
1], lwork, info);
} else {
/* ==== Tiny matrices don't have enough subdiagonal */
/* . scratch space to benefit from ZLAQR0. Hence, */
/* . tiny matrices must be copied into a larger */
/* . array before calling ZLAQR0. ==== */
zlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
i__1 = *n + 1 + *n * 49 - 50;
hl[i__1].r = 0., hl[i__1].i = 0.;
i__1 = 49 - *n;
zlaset_("A", &c__49, &i__1, &c_b1, &c_b1, &hl[(*n + 1) *
49 - 49], &c__49);
zlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, &
w[1], ilo, ihi, &z__[z_offset], ldz, workl, &
c__49, info);
if (wantt || *info != 0) {
zlacpy_("A", n, n, hl, &c__49, &h__[h_offset], ldh);
}
}
}
}
/* ==== Clear out the trash, if necessary. ==== */
if ((wantt || *info != 0) && *n > 2) {
i__1 = *n - 2;
i__2 = *n - 2;
zlaset_("L", &i__1, &i__2, &c_b1, &c_b1, &h__[h_dim1 + 3], ldh);
}
/* ==== Ensure reported workspace size is backward-compatible with */
/* . previous LAPACK versions. ==== */
/* Computing MAX */
d__2 = (doublereal) max(1,*n), d__3 = work[1].r;
d__1 = max(d__2,d__3);
z__1.r = d__1, z__1.i = 0.;
work[1].r = z__1.r, work[1].i = z__1.i;
}
/* ==== End of ZHSEQR ==== */
return 0;
} /* zhseqr_ */
|
