/* Subroutine */ int dhseqr_(char *job, char *compz, integer *n, integer *ilo,
integer *ihi, doublereal *h__, integer *ldh, doublereal *wr,
doublereal *wi, doublereal *z__, integer *ldz, doublereal *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[2], i__3;
doublereal d__1;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer i__;
#ifdef LAPACK_DISABLE_MEMORY_HOGS
doublereal hl[1] /* was [49][49] */;
/** This function uses too much memory, so we stopped allocating the memory
* above and assert false here. */
assert(0 && "dhseqr_ was called. This function allocates too much"
" memory and has been disabled.");
#else
doublereal hl[2401] /* was [49][49] */;
#endif
integer kbot, nmin;
extern logical lsame_(char *, char *);
logical initz;
doublereal workl[49];
logical wantt, wantz;
extern /* Subroutine */ int dlaqr0_(logical *, logical *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *), dlahqr_(logical *, logical *,
integer *, integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int xerbla_(char *, 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 */
/* ======= */
/* DHSEQR computes the eigenvalues of a Hessenberg matrix H */
/* and, optionally, the matrices T and Z from the Schur decomposition */
/* H = Z T Z**T, where T is an upper quasi-triangular matrix (the */
/* Schur form), and Z is the orthogonal matrix of Schur vectors. */
/* Optionally Z may be postmultiplied into an input orthogonal */
/* 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 orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T. */
/* 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 orthogonal 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 DGEBAL, and then passed to DGEHRD */
/* when the matrix output by DGEBAL 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) DOUBLE PRECISION array, dimension (LDH,N) */
/* On entry, the upper Hessenberg matrix H. */
/* On exit, if INFO = 0 and JOB = 'S', then H contains the */
/* upper quasi-triangular matrix T from the Schur decomposition */
/* (the Schur form); 2-by-2 diagonal blocks (corresponding to */
/* complex conjugate pairs of eigenvalues) are returned in */
/* standard form, with H(i,i) = H(i+1,i+1) and */
/* H(i+1,i)*H(i,i+1).LT.0. 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 DHSEQR, 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). */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* The real and imaginary parts, respectively, of the computed */
/* eigenvalues. If two eigenvalues are computed as a complex */
/* conjugate pair, they are stored in consecutive elements of */
/* WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and */
/* WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in */
/* the same order as on the diagonal of the Schur form returned */
/* in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2 */
/* diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and */
/* WI(i+1) = -WI(i). */
/* Z (input/output) DOUBLE PRECISION 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 orthogonal 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 orthogonal matrix generated by DORGHR */
/* after the call to DGEHRD 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) DOUBLE PRECISION 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 DHSEQR does a workspace query. */
/* In this case, DHSEQR 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, DHSEQR 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 an orthogonal matrix. The final */
/* value of H is upper Hessenberg and quasi-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 orthogonal 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 orthogonal 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,'DHSEQR',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 DLAHQR vs DLAQR0 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 */
/* DLAHQR 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 */
/* . DLAHQR because of insufficient subdiagonal scratch space. */
/* . (This is a hard limit.) ==== */
/* ==== NL allocates some local workspace to help small matrices */
/* . through a rare DLAHQR 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;
--wr;
--wi;
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");
work[1] = (doublereal) max(1,*n);
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 = -11;
} else if (*lwork < max(1,*n) && ! lquery) {
*info = -13;
}
if (*info != 0) {
/* ==== Quick return in case of invalid argument. ==== */
i__1 = -(*info);
xerbla_("DHSEQR", &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 ==== */
dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[
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__1 = (doublereal) max(1,*n);
work[1] = max(d__1,work[1]);
return 0;
} else {
/* ==== copy eigenvalues isolated by DGEBAL ==== */
i__1 = *ilo - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.;
/* L10: */
}
i__1 = *n;
for (i__ = *ihi + 1; i__ <= i__1; ++i__) {
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.;
/* L20: */
}
/* ==== Initialize Z, if requested ==== */
if (initz) {
dlaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz)
;
}
/* ==== Quick return if possible ==== */
if (*ilo == *ihi) {
wr[*ilo] = h__[*ilo + *ilo * h_dim1];
wi[*ilo] = 0.;
return 0;
}
/* ==== DLAHQR/DLAQR0 crossover point ==== */
/* Writing concatenation */
i__2[0] = 1, a__1[0] = job;
i__2[1] = 1, a__1[1] = compz;
s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
nmin = ilaenv_(&c__12, "DHSEQR", ch__1, n, ilo, ihi, lwork);
nmin = max(11,nmin);
/* ==== DLAQR0 for big matrices; DLAHQR for small ones ==== */
if (*n > nmin) {
dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
&wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork,
info);
} else {
/* ==== Small matrix ==== */
dlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1],
&wi[1], ilo, ihi, &z__[z_offset], ldz, info);
if (*info > 0) {
/* ==== A rare DLAHQR failure! DLAQR0 sometimes succeeds */
/* . when DLAHQR fails. ==== */
kbot = *info;
if (*n >= 49) {
/* ==== Larger matrices have enough subdiagonal scratch */
/* . space to call DLAQR0 directly. ==== */
dlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset],
ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset],
ldz, &work[1], lwork, info);
} else {
/* ==== Tiny matrices don't have enough subdiagonal */
/* . scratch space to benefit from DLAQR0. Hence, */
/* . tiny matrices must be copied into a larger */
/* . array before calling DLAQR0. ==== */
dlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
hl[*n + 1 + *n * 49 - 50] = 0.;
i__1 = 49 - *n;
dlaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) *
49 - 49], &c__49);
dlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, &
wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz,
workl, &c__49, info);
if (wantt || *info != 0) {
dlacpy_("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__3 = *n - 2;
dlaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
}
/* ==== Ensure reported workspace size is backward-compatible with */
/* . previous LAPACK versions. ==== */
/* Computing MAX */
d__1 = (doublereal) max(1,*n);
work[1] = max(d__1,work[1]);
}
/* ==== End of DHSEQR ==== */
return 0;
} /* dhseqr_ */
/* Subroutine */
int dhseqr_(char *job, char *compz, integer *n, integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal *wr, doublereal *wi, doublereal *z__, integer *ldz, doublereal *work, integer *lwork, integer *info)
{
/* System generated locals */
integer h_dim1, h_offset, z_dim1, z_offset, i__1, i__3;
doublereal d__1;
char ch__1[2];
/* Builtin functions */
/* Subroutine */
/* Local variables */
integer i__;
doublereal hl[2401] /* was [49][49] */
;
integer kbot, nmin;
extern logical lsame_(char *, char *);
logical initz;
doublereal workl[49];
logical wantt, wantz;
extern /* Subroutine */
int dlaqr0_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), dlahqr_(logical *, logical *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
extern /* Subroutine */
int xerbla_(char *, integer *);
logical lquery;
/* -- LAPACK computational routine (version 3.4.0) -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* November 2011 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* ===================================================================== */
/* .. Parameters .. */
/* ==== Matrices of order NTINY or smaller must be processed by */
/* . DLAHQR because of insufficient subdiagonal scratch space. */
/* . (This is a hard limit.) ==== */
/* ==== NL allocates some local workspace to help small matrices */
/* . through a rare DLAHQR 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;
--wr;
--wi;
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");
work[1] = (doublereal) max(1,*n);
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 = -11;
}
else if (*lwork < max(1,*n) && ! lquery)
{
*info = -13;
}
if (*info != 0)
{
/* ==== Quick return in case of invalid argument. ==== */
i__1 = -(*info);
xerbla_("DHSEQR", &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 ==== */
dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[ 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__1 = (doublereal) max(1,*n);
work[1] = max(d__1,work[1]);
return 0;
}
else
{
/* ==== copy eigenvalues isolated by DGEBAL ==== */
i__1 = *ilo - 1;
for (i__ = 1;
i__ <= i__1;
++i__)
{
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.;
/* L10: */
}
i__1 = *n;
for (i__ = *ihi + 1;
i__ <= i__1;
++i__)
{
wr[i__] = h__[i__ + i__ * h_dim1];
wi[i__] = 0.;
/* L20: */
}
/* ==== Initialize Z, if requested ==== */
if (initz)
{
dlaset_("A", n, n, &c_b11, &c_b12, &z__[z_offset], ldz) ;
}
/* ==== Quick return if possible ==== */
if (*ilo == *ihi)
{
wr[*ilo] = h__[*ilo + *ilo * h_dim1];
wi[*ilo] = 0.;
return 0;
}
/* ==== DLAHQR/DLAQR0 crossover point ==== */
nmin = ilaenv_(&c__12, "DHSEQR", ch__1, n, ilo, ihi, lwork);
nmin = max(11,nmin);
/* ==== DLAQR0 for big matrices;
DLAHQR for small ones ==== */
if (*n > nmin)
{
dlaqr0_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
}
else
{
/* ==== Small matrix ==== */
dlahqr_(&wantt, &wantz, n, ilo, ihi, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, info);
if (*info > 0)
{
/* ==== A rare DLAHQR failure! DLAQR0 sometimes succeeds */
/* . when DLAHQR fails. ==== */
kbot = *info;
if (*n >= 49)
{
/* ==== Larger matrices have enough subdiagonal scratch */
/* . space to call DLAQR0 directly. ==== */
dlaqr0_(&wantt, &wantz, n, ilo, &kbot, &h__[h_offset], ldh, &wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, &work[1], lwork, info);
}
else
{
/* ==== Tiny matrices don't have enough subdiagonal */
/* . scratch space to benefit from DLAQR0. Hence, */
/* . tiny matrices must be copied into a larger */
/* . array before calling DLAQR0. ==== */
dlacpy_("A", n, n, &h__[h_offset], ldh, hl, &c__49);
hl[*n + 1 + *n * 49 - 50] = 0.;
i__1 = 49 - *n;
dlaset_("A", &c__49, &i__1, &c_b11, &c_b11, &hl[(*n + 1) * 49 - 49], &c__49);
dlaqr0_(&wantt, &wantz, &c__49, ilo, &kbot, hl, &c__49, & wr[1], &wi[1], ilo, ihi, &z__[z_offset], ldz, workl, &c__49, info);
if (wantt || *info != 0)
{
dlacpy_("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__3 = *n - 2;
dlaset_("L", &i__1, &i__3, &c_b11, &c_b11, &h__[h_dim1 + 3], ldh);
}
/* ==== Ensure reported workspace size is backward-compatible with */
/* . previous LAPACK versions. ==== */
/* Computing MAX */
d__1 = (doublereal) max(1,*n);
work[1] = max(d__1,work[1]);
}
/* ==== End of DHSEQR ==== */
return 0;
}
