/* Subroutine */ int zerrec_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
"ts of the error \002,\002exits ***\002)";
/* System generated locals */
integer i__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
doublecomplex a[16] /* was [4][4] */, b[16] /* was [4][4] */, c__[16]
/* was [4][4] */;
integer i__, j, m;
doublereal s[4];
doublecomplex x[4];
integer nt;
doublereal rw[24];
logical sel[4];
doublereal sep[4];
integer info, ifst, ilst;
doublecomplex work[24];
doublereal scale;
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), ztrexc_(char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, integer *,
integer *), ztrsna_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *, integer *,
integer *, doublecomplex *, integer *, doublereal *, integer *), ztrsen_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, integer *), ztrsyl_(
char *, char *, integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
/* Fortran I/O blocks */
static cilist io___18 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___19 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZERREC tests the error exits for the routines for eigen- condition */
/* estimation for DOUBLE PRECISION matrices: */
/* ZTRSYL, CTREXC, CTRSNA and CTRSEN. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
infoc_1.ok = TRUE_;
nt = 0;
/* Initialize A, B and SEL */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = i__ + (j << 2) - 5;
b[i__1].r = 0., b[i__1].i = 0.;
/* L10: */
}
/* L20: */
}
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (i__ << 2) - 5;
a[i__1].r = 1., a[i__1].i = 0.;
sel[i__ - 1] = TRUE_;
/* L30: */
}
/* Test ZTRSYL */
s_copy(srnamc_1.srnamt, "ZTRSYL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
ztrsyl_("X", "N", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsyl_("N", "X", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
ztrsyl_("N", "N", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsyl_("N", "N", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
ztrsyl_("N", "N", &c__1, &c__0, &c_n1, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ztrsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__1, b, &c__1, c__, &c__2, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
ztrsyl_("N", "N", &c__1, &c__0, &c__2, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
ztrsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__2, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test ZTREXC */
s_copy(srnamc_1.srnamt, "ZTREXC", (ftnlen)32, (ftnlen)6);
ifst = 1;
ilst = 1;
infoc_1.infot = 1;
ztrexc_("X", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ztrexc_("N", &c__0, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ilst = 2;
ztrexc_("N", &c__2, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrexc_("V", &c__2, a, &c__2, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 0;
ilst = 1;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 2;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ifst = 1;
ilst = 0;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ilst = 2;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test ZTRSNA */
s_copy(srnamc_1.srnamt, "ZTRSNA", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
ztrsna_("X", "A", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsna_("B", "X", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsna_("B", "A", sel, &c_n1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrsna_("V", "A", sel, &c__2, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__1, c__, &c__2, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
ztrsna_("B", "A", sel, &c__1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__0, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
ztrsna_("B", "S", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 16;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__2, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* Test ZTRSEN */
sel[0] = FALSE_;
s_copy(srnamc_1.srnamt, "ZTRSEN", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
ztrsen_("X", "N", sel, &c__0, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsen_("N", "X", sel, &c__0, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsen_("N", "N", sel, &c_n1, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrsen_("N", "N", sel, &c__2, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__2, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ztrsen_("N", "V", sel, &c__2, a, &c__2, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("N", "V", sel, &c__2, a, &c__2, b, &c__2, x, &m, s, sep, work, &
c__0, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("E", "V", sel, &c__3, a, &c__3, b, &c__3, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, x, &m, s, sep, work, &
c__3, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Print a summary line. */
if (infoc_1.ok) {
io___18.ciunit = infoc_1.nout;
s_wsfe(&io___18);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___19.ciunit = infoc_1.nout;
s_wsfe(&io___19);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of ZERREC */
} /* zerrec_ */
/* Subroutine */
int zgeevx_(char *balanc, char *jobvl, char *jobvr, char * sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w, doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr, integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm, doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer * lwork, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, k;
char job[1];
doublereal scl, dum[1], eps;
doublecomplex tmp;
char side[1];
doublereal anrm;
integer ierr, itau, iwrk, nout, icond;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int zscal_(integer *, doublecomplex *, doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
logical scalea;
extern doublereal dlamch_(char *);
doublereal cscale;
extern /* Subroutine */
int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), zgebak_(char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublecomplex *, integer *, integer *), zgebal_(char *, integer *, doublecomplex *, integer *, integer *, integer *, doublereal *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */
int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
logical select[1];
extern /* Subroutine */
int zdscal_(integer *, doublereal *, doublecomplex *, integer *);
doublereal bignum;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, integer *, doublereal *);
extern /* Subroutine */
int zgehrd_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *), zlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, integer *), zlacpy_(char *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, integer *);
integer minwrk, maxwrk;
logical wantvl, wntsnb;
integer hswork;
logical wntsne;
doublereal smlnum;
extern /* Subroutine */
int zhseqr_(char *, char *, integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, integer *);
logical lquery, wantvr;
extern /* Subroutine */
int ztrevc_(char *, char *, logical *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, integer *, integer *, integer *, doublecomplex *, doublereal *, integer *), ztrsna_(char *, char *, logical *, integer *, doublecomplex *, integer *, doublecomplex * , integer *, doublecomplex *, integer *, doublereal *, doublereal *, integer *, integer *, doublecomplex *, integer *, doublereal *, integer *), zunghr_(integer *, integer *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, integer *);
logical wntsnn, wntsnv;
/* -- LAPACK driver 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 .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--scale;
--rconde;
--rcondv;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
wntsnn = lsame_(sense, "N");
wntsne = lsame_(sense, "E");
wntsnv = lsame_(sense, "V");
wntsnb = lsame_(sense, "B");
if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") || lsame_(balanc, "B")))
{
*info = -1;
}
else if (! wantvl && ! lsame_(jobvl, "N"))
{
*info = -2;
}
else if (! wantvr && ! lsame_(jobvr, "N"))
{
*info = -3;
}
else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb) && ! (wantvl && wantvr))
{
*info = -4;
}
else if (*n < 0)
{
*info = -5;
}
else if (*lda < max(1,*n))
{
*info = -7;
}
else if (*ldvl < 1 || wantvl && *ldvl < *n)
{
*info = -10;
}
else if (*ldvr < 1 || wantvr && *ldvr < *n)
{
*info = -12;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to real */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by ZHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0)
{
if (*n == 0)
{
minwrk = 1;
maxwrk = 1;
}
else
{
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, & c__0);
if (wantvl)
{
zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[1], &c_n1, info);
}
else if (wantvr)
{
zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[1], &c_n1, info);
}
else
{
if (wntsnn)
{
zhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info);
}
else
{
zhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], & vr[vr_offset], ldvr, &work[1], &c_n1, info);
}
}
hswork = (integer) work[1].r;
if (! wantvl && ! wantvr)
{
minwrk = *n << 1;
if (! (wntsnn || wntsne))
{
/* Computing MAX */
i__1 = minwrk;
i__2 = *n * *n + (*n << 1); // , expr subst
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
if (! (wntsnn || wntsne))
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * *n + (*n << 1); // , expr subst
maxwrk = max(i__1,i__2);
}
}
else
{
minwrk = *n << 1;
if (! (wntsnn || wntsne))
{
/* Computing MAX */
i__1 = minwrk;
i__2 = *n * *n + (*n << 1); // , expr subst
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR", " ", n, &c__1, n, &c_n1); // , expr subst
maxwrk = max(i__1,i__2);
if (! (wntsnn || wntsne))
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n * *n + (*n << 1); // , expr subst
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n << 1; // , expr subst
maxwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,minwrk);
}
work[1].r = (doublereal) maxwrk;
work[1].i = 0.; // , expr subst
if (*lwork < minwrk && ! lquery)
{
*info = -20;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("ZGEEVX", &i__1);
return 0;
}
else if (lquery)
{
return 0;
}
/* Quick return if possible */
if (*n == 0)
{
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0. && anrm < smlnum)
{
scalea = TRUE_;
cscale = smlnum;
}
else if (anrm > bignum)
{
scalea = TRUE_;
cscale = bignum;
}
if (scalea)
{
zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & ierr);
}
/* Balance the matrix and compute ABNRM */
zgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = zlange_("1", n, n, &a[a_offset], lda, dum);
if (scalea)
{
dum[0] = *abnrm;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, & ierr);
*abnrm = dum[0];
}
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, & ierr);
if (wantvl)
{
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl) ;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], & i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[ vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr)
{
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
}
else if (wantvr)
{
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr) ;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], & i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info);
}
else
{
/* Compute eigenvalues only */
/* If condition numbers desired, compute Schur form */
if (wntsnn)
{
*(unsigned char *)job = 'E';
}
else
{
*(unsigned char *)job = 'S';
}
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[ vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0)
{
goto L50;
}
if (wantvl || wantvr)
{
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need N) */
ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], & ierr);
}
/* Compute condition numbers if desired */
/* (CWorkspace: need N*N+2*N unless SENSE = 'E') */
/* (RWorkspace: need 2*N unless SENSE = 'E') */
if (! wntsnn)
{
ztrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout, &work[iwrk], n, &rwork[1], &icond);
}
if (wantvl)
{
/* Undo balancing of left eigenvectors */
zgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl, &ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
d__1 = vl[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vl[k + i__ * vl_dim1]);
rwork[k] = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &rwork[1], &c__1);
d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
d__1 = sqrt(rwork[k]);
z__1.r = z__2.r / d__1;
z__1.i = z__2.i / d__1; // , expr subst
tmp.r = z__1.r;
tmp.i = z__1.i; // , expr subst
zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
d__1 = vl[i__3].r;
z__1.r = d__1;
z__1.i = 0.; // , expr subst
vl[i__2].r = z__1.r;
vl[i__2].i = z__1.i; // , expr subst
/* L20: */
}
}
if (wantvr)
{
/* Undo balancing of right eigenvectors */
zgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr, &ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1;
k <= i__2;
++k)
{
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
d__1 = vr[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vr[k + i__ * vr_dim1]);
rwork[k] = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &rwork[1], &c__1);
d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
d__1 = sqrt(rwork[k]);
z__1.r = z__2.r / d__1;
z__1.i = z__2.i / d__1; // , expr subst
tmp.r = z__1.r;
tmp.i = z__1.i; // , expr subst
zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
d__1 = vr[i__3].r;
z__1.r = d__1;
z__1.i = 0.; // , expr subst
vr[i__2].r = z__1.r;
vr[i__2].i = z__1.i; // , expr subst
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea)
{
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1] , &i__2, &ierr);
if (*info == 0)
{
if ((wntsnv || wntsnb) && icond == 0)
{
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[ 1], n, &ierr);
}
}
else
{
i__1 = *ilo - 1;
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n, &ierr);
}
}
work[1].r = (doublereal) maxwrk;
work[1].i = 0.; // , expr subst
return 0;
/* End of ZGEEVX */
}
/* Subroutine */ int zerrec_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits (\002,i3,\002 tests done)\002)";
static char fmt_9998[] = "(\002 *** \002,a3,\002 routines failed the tes"
"ts of the error \002,\002exits ***\002)";
/* System generated locals */
integer i__1;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer info, ifst, ilst;
static doublecomplex work[24], a[16] /* was [4][4] */, b[16] /*
was [4][4] */, c__[16] /* was [4][4] */;
static integer i__, j, m;
static doublereal s[4], scale;
static doublecomplex x[4];
static integer nt;
static doublereal rw[24];
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), ztrexc_(char *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, integer *,
integer *), ztrsna_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *, integer *,
integer *, doublecomplex *, integer *, doublereal *, integer *), ztrsen_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, integer *), ztrsyl_(
char *, char *, integer *, integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, integer *);
static logical sel[4];
static doublereal sep[4];
/* Fortran I/O blocks */
static cilist io___18 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___19 = { 0, 0, 0, fmt_9998, 0 };
#define a_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*4 + a_1 - 5
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
ZERREC tests the error exits for the routines for eigen- condition
estimation for DOUBLE PRECISION matrices:
ZTRSYL, CTREXC, CTRSNA and CTRSEN.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
infoc_1.ok = TRUE_;
nt = 0;
/* Initialize A, B and SEL */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = a_subscr(i__, j);
a[i__1].r = 0., a[i__1].i = 0.;
i__1 = b_subscr(i__, j);
b[i__1].r = 0., b[i__1].i = 0.;
/* L10: */
}
/* L20: */
}
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = a_subscr(i__, i__);
a[i__1].r = 1., a[i__1].i = 0.;
sel[i__ - 1] = TRUE_;
/* L30: */
}
/* Test ZTRSYL */
s_copy(srnamc_1.srnamt, "ZTRSYL", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
ztrsyl_("X", "N", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsyl_("N", "X", &c__1, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
ztrsyl_("N", "N", &c__0, &c__0, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsyl_("N", "N", &c__1, &c_n1, &c__0, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
ztrsyl_("N", "N", &c__1, &c__0, &c_n1, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ztrsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__1, b, &c__1, c__, &c__2, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
ztrsyl_("N", "N", &c__1, &c__0, &c__2, a, &c__1, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
ztrsyl_("N", "N", &c__1, &c__2, &c__0, a, &c__2, b, &c__1, c__, &c__1, &
scale, &info);
chkxer_("ZTRSYL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test ZTREXC */
s_copy(srnamc_1.srnamt, "ZTREXC", (ftnlen)6, (ftnlen)6);
ifst = 1;
ilst = 1;
infoc_1.infot = 1;
ztrexc_("X", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ztrexc_("N", &c__0, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ilst = 2;
ztrexc_("N", &c__2, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrexc_("V", &c__2, a, &c__2, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 0;
ilst = 1;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
ifst = 2;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ifst = 1;
ilst = 0;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ilst = 2;
ztrexc_("V", &c__1, a, &c__1, b, &c__1, &ifst, &ilst, &info);
chkxer_("ZTREXC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Test ZTRSNA */
s_copy(srnamc_1.srnamt, "ZTRSNA", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
ztrsna_("X", "A", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsna_("B", "X", sel, &c__0, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsna_("B", "A", sel, &c_n1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrsna_("V", "A", sel, &c__2, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__1, c__, &c__2, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__1, s, sep, &
c__2, &m, work, &c__2, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
ztrsna_("B", "A", sel, &c__1, a, &c__1, b, &c__1, c__, &c__1, s, sep, &
c__0, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
ztrsna_("B", "S", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__1, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 16;
ztrsna_("B", "A", sel, &c__2, a, &c__2, b, &c__2, c__, &c__2, s, sep, &
c__2, &m, work, &c__1, rw, &info);
chkxer_("ZTRSNA", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* Test ZTRSEN */
sel[0] = FALSE_;
s_copy(srnamc_1.srnamt, "ZTRSEN", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
ztrsen_("X", "N", sel, &c__0, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrsen_("N", "X", sel, &c__0, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrsen_("N", "N", sel, &c_n1, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrsen_("N", "N", sel, &c__2, a, &c__1, b, &c__1, x, &m, s, sep, work, &
c__2, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ztrsen_("N", "V", sel, &c__2, a, &c__2, b, &c__1, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("N", "V", sel, &c__2, a, &c__2, b, &c__2, x, &m, s, sep, work, &
c__0, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("E", "V", sel, &c__3, a, &c__3, b, &c__3, x, &m, s, sep, work, &
c__1, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
ztrsen_("V", "V", sel, &c__3, a, &c__3, b, &c__3, x, &m, s, sep, work, &
c__3, &info);
chkxer_("ZTRSEN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* Print a summary line. */
if (infoc_1.ok) {
io___18.ciunit = infoc_1.nout;
s_wsfe(&io___18);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___19.ciunit = infoc_1.nout;
s_wsfe(&io___19);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of ZERREC */
} /* zerrec_ */
/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w,
doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr,
integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm,
doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer *
lwork, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, k;
char job[1];
doublereal scl, dum[1], eps;
doublecomplex tmp;
char side[1];
doublereal anrm;
integer ierr, itau, iwrk, nout, icond;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
logical scalea;
extern doublereal dlamch_(char *);
doublereal cscale;
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), zgebak_(char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublecomplex *,
integer *, integer *), zgebal_(char *, integer *,
doublecomplex *, integer *, integer *, integer *, doublereal *,
integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
logical select[1];
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
doublereal bignum;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
integer minwrk, maxwrk;
logical wantvl, wntsnb;
integer hswork;
logical wntsne;
doublereal smlnum;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
logical lquery, wantvr;
extern /* Subroutine */ int ztrevc_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *, doublecomplex *,
doublereal *, integer *), ztrsna_(char *, char *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublereal *, doublereal
*, integer *, integer *, doublecomplex *, integer *, doublereal *,
integer *), zunghr_(integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, integer *);
logical wntsnn, wntsnv;
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* Optionally also, it computes a balancing transformation to improve */
/* the conditioning of the eigenvalues and eigenvectors (ILO, IHI, */
/* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues */
/* (RCONDE), and reciprocal condition numbers for the right */
/* eigenvectors (RCONDV). */
/* The right eigenvector v(j) of A satisfies */
/* A * v(j) = lambda(j) * v(j) */
/* where lambda(j) is its eigenvalue. */
/* The left eigenvector u(j) of A satisfies */
/* u(j)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component real. */
/* Balancing a matrix means permuting the rows and columns to make it */
/* more nearly upper triangular, and applying a diagonal similarity */
/* transformation D * A * D**(-1), where D is a diagonal matrix, to */
/* make its rows and columns closer in norm and the condition numbers */
/* of its eigenvalues and eigenvectors smaller. The computed */
/* reciprocal condition numbers correspond to the balanced matrix. */
/* Permuting rows and columns will not change the condition numbers */
/* (in exact arithmetic) but diagonal scaling will. For further */
/* explanation of balancing, see section 4.10.2 of the LAPACK */
/* Users' Guide. */
/* Arguments */
/* ========= */
/* BALANC (input) CHARACTER*1 */
/* Indicates how the input matrix should be diagonally scaled */
/* and/or permuted to improve the conditioning of its */
/* eigenvalues. */
/* = 'N': Do not diagonally scale or permute; */
/* = 'P': Perform permutations to make the matrix more nearly */
/* upper triangular. Do not diagonally scale; */
/* = 'S': Diagonally scale the matrix, ie. replace A by */
/* D*A*D**(-1), where D is a diagonal matrix chosen */
/* to make the rows and columns of A more equal in */
/* norm. Do not permute; */
/* = 'B': Both diagonally scale and permute A. */
/* Computed reciprocal condition numbers will be for the matrix */
/* after balancing and/or permuting. Permuting does not change */
/* condition numbers (in exact arithmetic), but balancing does. */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVL must = 'V'. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* If SENSE = 'E' or 'B', JOBVR must = 'V'. */
/* SENSE (input) CHARACTER*1 */
/* Determines which reciprocal condition numbers are computed. */
/* = 'N': None are computed; */
/* = 'E': Computed for eigenvalues only; */
/* = 'V': Computed for right eigenvectors only; */
/* = 'B': Computed for eigenvalues and right eigenvectors. */
/* If SENSE = 'E' or 'B', both left and right eigenvectors */
/* must also be computed (JOBVL = 'V' and JOBVR = 'V'). */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. If JOBVL = 'V' or */
/* JOBVR = 'V', A contains the Schur form of the balanced */
/* version of the matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* W (output) COMPLEX*16 array, dimension (N) */
/* W contains the computed eigenvalues. */
/* VL (output) COMPLEX*16 array, dimension (LDVL,N) */
/* If JOBVL = 'V', the left eigenvectors u(j) are stored one */
/* after another in the columns of VL, in the same order */
/* as their eigenvalues. */
/* If JOBVL = 'N', VL is not referenced. */
/* u(j) = VL(:,j), the j-th column of VL. */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) COMPLEX*16 array, dimension (LDVR,N) */
/* If JOBVR = 'V', the right eigenvectors v(j) are stored one */
/* after another in the columns of VR, in the same order */
/* as their eigenvalues. */
/* If JOBVR = 'N', VR is not referenced. */
/* v(j) = VR(:,j), the j-th column of VR. */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are integer values determined when A was */
/* balanced. The balanced A(i,j) = 0 if I > J and */
/* J = 1,...,ILO-1 or I = IHI+1,...,N. */
/* SCALE (output) DOUBLE PRECISION array, dimension (N) */
/* Details of the permutations and scaling factors applied */
/* when balancing A. If P(j) is the index of the row and column */
/* interchanged with row and column j, and D(j) is the scaling */
/* factor applied to row and column j, then */
/* SCALE(J) = P(J), for J = 1,...,ILO-1 */
/* = D(J), for J = ILO,...,IHI */
/* = P(J) for J = IHI+1,...,N. */
/* The order in which the interchanges are made is N to IHI+1, */
/* then 1 to ILO-1. */
/* ABNRM (output) DOUBLE PRECISION */
/* The one-norm of the balanced matrix (the maximum */
/* of the sum of absolute values of elements of any column). */
/* RCONDE (output) DOUBLE PRECISION array, dimension (N) */
/* RCONDE(j) is the reciprocal condition number of the j-th */
/* eigenvalue. */
/* RCONDV (output) DOUBLE PRECISION array, dimension (N) */
/* RCONDV(j) is the reciprocal condition number of the j-th */
/* right eigenvector. */
/* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. If SENSE = 'N' or 'E', */
/* LWORK >= max(1,2*N), and if SENSE = 'V' or 'B', */
/* LWORK >= N*N+2*N. */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates the optimal size of the WORK array, returns */
/* this value as the first entry of the WORK array, and no error */
/* message related to LWORK is issued by XERBLA. */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, the QR algorithm failed to compute all the */
/* eigenvalues, and no eigenvectors or condition numbers */
/* have been computed; elements 1:ILO-1 and i+1:N of W */
/* contain eigenvalues which have converged. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--scale;
--rconde;
--rcondv;
--work;
--rwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
wntsnn = lsame_(sense, "N");
wntsne = lsame_(sense, "E");
wntsnv = lsame_(sense, "V");
wntsnb = lsame_(sense, "B");
if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P")
|| lsame_(balanc, "B"))) {
*info = -1;
} else if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -2;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -3;
} else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
&& ! (wantvl && wantvr)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -10;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -12;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "Workspace:" describe the */
/* minimal amount of workspace needed at that point in the code, */
/* as well as the preferred amount for good performance. */
/* CWorkspace refers to complex workspace, and RWorkspace to real */
/* workspace. NB refers to the optimal block size for the */
/* immediately following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by ZHSEQR, as */
/* calculated below. HSWORK is computed assuming ILO=1 and IHI=N, */
/* the worst case.) */
if (*info == 0) {
if (*n == 0) {
minwrk = 1;
maxwrk = 1;
} else {
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &
c__0);
if (wantvl) {
zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
zhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[1], &c_n1, info);
} else {
if (wntsnn) {
zhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
} else {
zhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &w[1], &
vr[vr_offset], ldvr, &work[1], &c_n1, info);
}
}
hswork = (integer) work[1].r;
if (! wantvl && ! wantvr) {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
} else {
minwrk = *n << 1;
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
" ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 1;
maxwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,minwrk);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
if (*lwork < minwrk && ! lquery) {
*info = -20;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEEVX", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = zlange_("M", n, n, &a[a_offset], lda, dum);
scalea = FALSE_;
if (anrm > 0. && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
zgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = zlange_("1", n, n, &a[a_offset], lda, dum);
if (scalea) {
dum[0] = *abnrm;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
ierr);
*abnrm = dum[0];
}
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, ilo, ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &
ierr);
if (wantvl) {
/* Want left eigenvectors */
/* Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
zlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate unitary matrix in VL */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vl[
vl_offset], ldvl, &work[iwrk], &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors */
/* Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
zlacpy_("F", n, n, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr);
}
} else if (wantvr) {
/* Want right eigenvectors */
/* Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
zlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate unitary matrix in VR */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* If condition numbers desired, compute Schur form */
if (wntsnn) {
*(unsigned char *)job = 'E';
} else {
*(unsigned char *)job = 'S';
}
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &w[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (CWorkspace: need 2*N) */
/* (RWorkspace: need N) */
ztrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &rwork[1], &
ierr);
}
/* Compute condition numbers if desired */
/* (CWorkspace: need N*N+2*N unless SENSE = 'E') */
/* (RWorkspace: need 2*N unless SENSE = 'E') */
if (! wntsnn) {
ztrsna_(sense, "A", select, n, &a[a_offset], lda, &vl[vl_offset],
ldvl, &vr[vr_offset], ldvr, &rconde[1], &rcondv[1], n, &nout,
&work[iwrk], n, &rwork[1], &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
zgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1. / dznrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
zdscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vl_dim1;
/* Computing 2nd power */
d__1 = vl[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vl[k + i__ * vl_dim1]);
rwork[k] = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &rwork[1], &c__1);
d_cnjg(&z__2, &vl[k + i__ * vl_dim1]);
d__1 = sqrt(rwork[k]);
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &vl[i__ * vl_dim1 + 1], &c__1);
i__2 = k + i__ * vl_dim1;
i__3 = k + i__ * vl_dim1;
d__1 = vl[i__3].r;
z__1.r = d__1, z__1.i = 0.;
vl[i__2].r = z__1.r, vl[i__2].i = z__1.i;
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
zgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
scl = 1. / dznrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
zdscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
i__3 = k + i__ * vr_dim1;
/* Computing 2nd power */
d__1 = vr[i__3].r;
/* Computing 2nd power */
d__2 = d_imag(&vr[k + i__ * vr_dim1]);
rwork[k] = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &rwork[1], &c__1);
d_cnjg(&z__2, &vr[k + i__ * vr_dim1]);
d__1 = sqrt(rwork[k]);
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &vr[i__ * vr_dim1 + 1], &c__1);
i__2 = k + i__ * vr_dim1;
i__3 = k + i__ * vr_dim1;
d__1 = vr[i__3].r;
z__1.r = d__1, z__1.i = 0.;
vr[i__2].r = z__1.r, vr[i__2].i = z__1.i;
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[*info + 1]
, &i__2, &ierr);
if (*info == 0) {
if ((wntsnv || wntsnb) && icond == 0) {
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &rcondv[
1], n, &ierr);
}
} else {
i__1 = *ilo - 1;
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &w[1], n,
&ierr);
}
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZGEEVX */
} /* zgeevx_ */
/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, integer *n, doublecomplex *a, integer *lda, doublecomplex *w,
doublecomplex *vl, integer *ldvl, doublecomplex *vr, integer *ldvr,
integer *ilo, integer *ihi, doublereal *scale, doublereal *abnrm,
doublereal *rconde, doublereal *rcondv, doublecomplex *work, integer *
lwork, doublereal *rwork, integer *info)
{
/* -- LAPACK driver routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
Optionally also, it computes a balancing transformation to improve
the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
(RCONDE), and reciprocal condition numbers for the right
eigenvectors (RCONDV).
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Balancing a matrix means permuting the rows and columns to make it
more nearly upper triangular, and applying a diagonal similarity
transformation D * A * D**(-1), where D is a diagonal matrix, to
make its rows and columns closer in norm and the condition numbers
of its eigenvalues and eigenvectors smaller. The computed
reciprocal condition numbers correspond to the balanced matrix.
Permuting rows and columns will not change the condition numbers
(in exact arithmetic) but diagonal scaling will. For further
explanation of balancing, see section 4.10.2 of the LAPACK
Users' Guide.
Arguments
=========
BALANC (input) CHARACTER*1
Indicates how the input matrix should be diagonally scaled
and/or permuted to improve the conditioning of its
eigenvalues.
= 'N': Do not diagonally scale or permute;
= 'P': Perform permutations to make the matrix more nearly
upper triangular. Do not diagonally scale;
= 'S': Diagonally scale the matrix, ie. replace A by
D*A*D**(-1), where D is a diagonal matrix chosen
to make the rows and columns of A more equal in
norm. Do not permute;
= 'B': Both diagonally scale and permute A.
Computed reciprocal condition numbers will be for the matrix
after balancing and/or permuting. Permuting does not change
condition numbers (in exact arithmetic), but balancing does.
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of A are computed.
If SENSE = 'E' or 'B', JOBVL must = 'V'.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
If SENSE = 'E' or 'B', JOBVR must = 'V'.
SENSE (input) CHARACTER*1
Determines which reciprocal condition numbers are computed.
= 'N': None are computed;
= 'E': Computed for eigenvalues only;
= 'V': Computed for right eigenvectors only;
= 'B': Computed for eigenvalues and right eigenvectors.
If SENSE = 'E' or 'B', both left and right eigenvectors
must also be computed (JOBVL = 'V' and JOBVR = 'V').
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten. If JOBVL = 'V' or
JOBVR = 'V', A contains the Schur form of the balanced
version of the matrix A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues.
VL (output) COMPLEX*16 array, dimension (LDVL,N)
If JOBVL = 'V', the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = 'N', VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) COMPLEX*16 array, dimension (LDVR,N)
If JOBVR = 'V', the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = 'N', VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
ILO,IHI (output) INTEGER
ILO and IHI are integer values determined when A was
balanced. The balanced A(i,j) = 0 if I > J and
J = 1,...,ILO-1 or I = IHI+1,...,N.
SCALE (output) DOUBLE PRECISION array, dimension (N)
Details of the permutations and scaling factors applied
when balancing A. If P(j) is the index of the row and column
interchanged with row and column j, and D(j) is the scaling
factor applied to row and column j, then
SCALE(J) = P(J), for J = 1,...,ILO-1
= D(J), for J = ILO,...,IHI
= P(J) for J = IHI+1,...,N.
The order in which the interchanges are made is N to IHI+1,
then 1 to ILO-1.
ABNRM (output) DOUBLE PRECISION
The one-norm of the balanced matrix (the maximum
of the sum of absolute values of elements of any column).
RCONDE (output) DOUBLE PRECISION array, dimension (N)
RCONDE(j) is the reciprocal condition number of the j-th
eigenvalue.
RCONDV (output) DOUBLE PRECISION array, dimension (N)
RCONDV(j) is the reciprocal condition number of the j-th
right eigenvector.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. If SENSE = 'N' or 'E',
LWORK >= max(1,2*N), and if SENSE = 'V' or 'B',
LWORK >= N*N+2*N.
For good performance, LWORK must generally be larger.
RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, the QR algorithm failed to compute all the
eigenvalues, and no eigenvectors or condition numbers
have been computed; elements 1:ILO-1 and i+1:N of W
contain eigenvalues which have converged.
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
static integer c__0 = 0;
static integer c__8 = 8;
static integer c_n1 = -1;
static integer c__4 = 4;
/* System generated locals */
integer a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3, i__4;
doublereal d__1, d__2;
doublecomplex z__1, z__2;
/* Builtin functions */
double sqrt(doublereal), d_imag(doublecomplex *);
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static char side[1];
static integer maxb;
static doublereal anrm;
static integer ierr, itau, iwrk, nout, i, k, icond;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zscal_(integer *, doublecomplex *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
extern doublereal dznrm2_(integer *, doublecomplex *, integer *);
static logical scalea;
extern doublereal dlamch_(char *);
static doublereal cscale;
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), zgebak_(char *, char *, integer *,
integer *, integer *, doublereal *, integer *, doublecomplex *,
integer *, integer *), zgebal_(char *, integer *,
doublecomplex *, integer *, integer *, integer *, doublereal *,
integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static logical select[1];
extern /* Subroutine */ int zdscal_(integer *, doublereal *,
doublecomplex *, integer *);
static doublereal bignum;
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
static integer minwrk, maxwrk;
static logical wantvl, wntsnb;
static integer hswork;
static logical wntsne;
static doublereal smlnum;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
static logical wantvr;
extern /* Subroutine */ int ztrevc_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, integer *, doublecomplex *,
doublereal *, integer *), ztrsna_(char *, char *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *
, integer *, doublecomplex *, integer *, doublereal *, doublereal
*, integer *, integer *, doublecomplex *, integer *, doublereal *,
integer *), zunghr_(integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, integer *);
static logical wntsnn, wntsnv;
static char job[1];
static doublereal scl, dum[1], eps;
static doublecomplex tmp;
#define DUM(I) dum[(I)]
#define W(I) w[(I)-1]
#define SCALE(I) scale[(I)-1]
#define RCONDE(I) rconde[(I)-1]
#define RCONDV(I) rcondv[(I)-1]
#define WORK(I) work[(I)-1]
#define RWORK(I) rwork[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define VL(I,J) vl[(I)-1 + ((J)-1)* ( *ldvl)]
#define VR(I,J) vr[(I)-1 + ((J)-1)* ( *ldvr)]
*info = 0;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
wntsnn = lsame_(sense, "N");
wntsne = lsame_(sense, "E");
wntsnv = lsame_(sense, "V");
wntsnb = lsame_(sense, "B");
if (! (lsame_(balanc, "N") || lsame_(balanc, "S") ||
lsame_(balanc, "P") || lsame_(balanc, "B"))) {
*info = -1;
} else if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -2;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -3;
} else if (! (wntsnn || wntsne || wntsnb || wntsnv) || (wntsne || wntsnb)
&& ! (wantvl && wantvr)) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -10;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -12;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of workspace needed at that point in the code,
as well as the preferred amount for good performance.
CWorkspace refers to complex workspace, and RWorkspace to real
workspace. NB refers to the optimal block size for the
immediately following subroutine, as returned by ILAENV.
HSWORK refers to the workspace preferred by ZHSEQR, as
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
the worst case.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0,
6L, 1L);
if (! wantvl && ! wantvr) {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, 6L, 2L);
maxb = max(i__1,2);
if (wntsnn) {
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
c_n1, 6L, 2L);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
} else {
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
c_n1, 6L, 2L);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
}
/* Computing MAX */
i__1 = k * (k + 2), i__2 = *n << 1;
hswork = max(i__1,i__2);
/* Computing MAX */
i__1 = max(maxwrk,1);
maxwrk = max(i__1,hswork);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
} else {
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + (*n << 1);
minwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, 6L, 2L);
maxb = max(i__1,2);
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "EN", n, &c__1, n, &
c_n1, 6L, 2L);
i__1 = min(maxb,*n), i__2 = max(i__3,i__4);
k = min(i__1,i__2);
/* Computing MAX */
i__1 = k * (k + 2), i__2 = *n << 1;
hswork = max(i__1,i__2);
/* Computing MAX */
i__1 = max(maxwrk,1);
maxwrk = max(i__1,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
" ", n, &c__1, n, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
if (! (wntsnn || wntsne)) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + (*n << 1);
maxwrk = max(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 1, i__1 = max(i__1,i__2);
maxwrk = max(i__1,1);
}
WORK(1).r = (doublereal) maxwrk, WORK(1).i = 0.;
}
if (*lwork < minwrk) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEEVX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Get machine constants */
eps = dlamch_("P");
smlnum = dlamch_("S");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
icond = 0;
anrm = zlange_("M", n, n, &A(1,1), lda, dum);
scalea = FALSE_;
if (anrm > 0. && anrm < smlnum) {
scalea = TRUE_;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = TRUE_;
cscale = bignum;
}
if (scalea) {
zlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &A(1,1), lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
zgebal_(balanc, n, &A(1,1), lda, ilo, ihi, &SCALE(1), &ierr);
*abnrm = zlange_("1", n, n, &A(1,1), lda, dum);
if (scalea) {
DUM(0) = *abnrm;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &c__1, &
ierr);
*abnrm = DUM(0);
}
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, ilo, ihi, &A(1,1), lda, &WORK(itau), &WORK(iwrk), &i__1, &
ierr);
if (wantvl) {
/* Want left eigenvectors
Copy Householder vectors to VL */
*(unsigned char *)side = 'L';
zlacpy_("L", n, n, &A(1,1), lda, &VL(1,1), ldvl);
/* Generate unitary matrix in VL
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &VL(1,1), ldvl, &WORK(itau), &WORK(iwrk), &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &A(1,1), lda, &W(1), &VL(1,1), ldvl, &WORK(iwrk), &i__1, info);
if (wantvr) {
/* Want left and right eigenvectors
Copy Schur vectors to VR */
*(unsigned char *)side = 'B';
zlacpy_("F", n, n, &VL(1,1), ldvl, &VR(1,1), ldvr)
;
}
} else if (wantvr) {
/* Want right eigenvectors
Copy Householder vectors to VR */
*(unsigned char *)side = 'R';
zlacpy_("L", n, n, &A(1,1), lda, &VR(1,1), ldvr);
/* Generate unitary matrix in VR
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, ilo, ihi, &VR(1,1), ldvr, &WORK(itau), &WORK(iwrk), &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", "V", n, ilo, ihi, &A(1,1), lda, &W(1), &VR(1,1), ldvr, &WORK(iwrk), &i__1, info);
} else {
/* Compute eigenvalues only
If condition numbers desired, compute Schur form */
if (wntsnn) {
*(unsigned char *)job = 'E';
} else {
*(unsigned char *)job = 'S';
}
/* (CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_(job, "N", n, ilo, ihi, &A(1,1), lda, &W(1), &VR(1,1), ldvr, &WORK(iwrk), &i__1, info);
}
/* If INFO > 0 from ZHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
(CWorkspace: need 2*N)
(RWorkspace: need N) */
ztrevc_(side, "B", select, n, &A(1,1), lda, &VL(1,1), ldvl,
&VR(1,1), ldvr, n, &nout, &WORK(iwrk), &RWORK(1), &
ierr);
}
/* Compute condition numbers if desired
(CWorkspace: need N*N+2*N unless SENSE = 'E')
(RWorkspace: need 2*N unless SENSE = 'E') */
if (! wntsnn) {
ztrsna_(sense, "A", select, n, &A(1,1), lda, &VL(1,1),
ldvl, &VR(1,1), ldvr, &RCONDE(1), &RCONDV(1), n, &nout,
&WORK(iwrk), n, &RWORK(1), &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
zgebak_(balanc, "L", n, ilo, ihi, &SCALE(1), n, &VL(1,1), ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real
*/
i__1 = *n;
for (i = 1; i <= *n; ++i) {
scl = 1. / dznrm2_(n, &VL(1,i), &c__1);
zdscal_(n, &scl, &VL(1,i), &c__1);
i__2 = *n;
for (k = 1; k <= *n; ++k) {
i__3 = k + i * vl_dim1;
/* Computing 2nd power */
d__1 = VL(k,i).r;
/* Computing 2nd power */
d__2 = d_imag(&VL(k,i));
RWORK(k) = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &RWORK(1), &c__1);
d_cnjg(&z__2, &VL(k,i));
d__1 = sqrt(RWORK(k));
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &VL(1,i), &c__1);
i__2 = k + i * vl_dim1;
i__3 = k + i * vl_dim1;
d__1 = VL(k,i).r;
z__1.r = d__1, z__1.i = 0.;
VL(k,i).r = z__1.r, VL(k,i).i = z__1.i;
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
zgebak_(balanc, "R", n, ilo, ihi, &SCALE(1), n, &VR(1,1), ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real
*/
i__1 = *n;
for (i = 1; i <= *n; ++i) {
scl = 1. / dznrm2_(n, &VR(1,i), &c__1);
zdscal_(n, &scl, &VR(1,i), &c__1);
i__2 = *n;
for (k = 1; k <= *n; ++k) {
i__3 = k + i * vr_dim1;
/* Computing 2nd power */
d__1 = VR(k,i).r;
/* Computing 2nd power */
d__2 = d_imag(&VR(k,i));
RWORK(k) = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &RWORK(1), &c__1);
d_cnjg(&z__2, &VR(k,i));
d__1 = sqrt(RWORK(k));
z__1.r = z__2.r / d__1, z__1.i = z__2.i / d__1;
tmp.r = z__1.r, tmp.i = z__1.i;
zscal_(n, &tmp, &VR(1,i), &c__1);
i__2 = k + i * vr_dim1;
i__3 = k + i * vr_dim1;
d__1 = VR(k,i).r;
z__1.r = d__1, z__1.i = 0.;
VR(k,i).r = z__1.r, VR(k,i).i = z__1.i;
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &W(*info + 1)
, &i__2, &ierr);
if (*info == 0) {
if ((wntsnv || wntsnb) && icond == 0) {
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &RCONDV(
1), n, &ierr);
}
} else {
i__1 = *ilo - 1;
zlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &W(1), n,
&ierr);
}
}
WORK(1).r = (doublereal) maxwrk, WORK(1).i = 0.;
return 0;
/* End of ZGEEVX */
} /* zgeevx_ */
