/* Subroutine */ int zchkbk_(integer *nin, integer *nout)
{
/* Format strings */
static char fmt_9999[] = "(1x,\002.. test output of ZGEBAK .. \002)";
static char fmt_9998[] = "(1x,\002value of largest test error "
" = \002,d12.3)";
static char fmt_9997[] = "(1x,\002example number where info is not zero "
" = \002,i4)";
static char fmt_9996[] = "(1x,\002example number having largest error "
" = \002,i4)";
static char fmt_9995[] = "(1x,\002number of examples where info is not 0"
" = \002,i4)";
static char fmt_9994[] = "(1x,\002total number of examples tested "
" = \002,i4)";
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2;
/* Builtin functions */
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
double d_imag(doublecomplex *);
integer s_wsfe(cilist *), e_wsfe(void), do_fio(integer *, char *, ftnlen);
/* Local variables */
static integer info, lmax[2];
static doublereal rmax, vmax;
static doublecomplex e[400] /* was [20][20] */;
static integer i__, j, n;
static doublereal scale[20], x;
static integer ninfo;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
integer *);
static doublereal safmin;
static integer ihi;
static doublecomplex ein[400] /* was [20][20] */;
static integer ilo;
static doublereal eps;
static integer knt;
/* Fortran I/O blocks */
static cilist io___7 = { 0, 0, 0, 0, 0 };
static cilist io___11 = { 0, 0, 0, 0, 0 };
static cilist io___14 = { 0, 0, 0, 0, 0 };
static cilist io___17 = { 0, 0, 0, 0, 0 };
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___23 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___24 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___25 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9994, 0 };
#define e_subscr(a_1,a_2) (a_2)*20 + a_1 - 21
#define e_ref(a_1,a_2) e[e_subscr(a_1,a_2)]
#define ein_subscr(a_1,a_2) (a_2)*20 + a_1 - 21
#define ein_ref(a_1,a_2) ein[ein_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
September 30, 1994
Purpose
=======
ZCHKBK tests ZGEBAK, a routine for backward transformation of
the computed right or left eigenvectors if the orginal matrix
was preprocessed by balance subroutine ZGEBAL.
Arguments
=========
NIN (input) INTEGER
The logical unit number for input. NIN > 0.
NOUT (input) INTEGER
The logical unit number for output. NOUT > 0.
====================================================================== */
lmax[0] = 0;
lmax[1] = 0;
ninfo = 0;
knt = 0;
rmax = 0.;
eps = dlamch_("E");
safmin = dlamch_("S");
L10:
io___7.ciunit = *nin;
s_rsle(&io___7);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ilo, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ihi, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
goto L60;
}
io___11.ciunit = *nin;
s_rsle(&io___11);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
do_lio(&c__5, &c__1, (char *)&scale[i__ - 1], (ftnlen)sizeof(
doublereal));
}
e_rsle();
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___14.ciunit = *nin;
s_rsle(&io___14);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&e_ref(i__, j), (ftnlen)sizeof(
doublecomplex));
}
e_rsle();
/* L20: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___17.ciunit = *nin;
s_rsle(&io___17);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&ein_ref(i__, j), (ftnlen)sizeof(
doublecomplex));
}
e_rsle();
/* L30: */
}
++knt;
zgebak_("B", "R", &n, &ilo, &ihi, scale, &n, e, &c__20, &info);
if (info != 0) {
++ninfo;
lmax[0] = knt;
}
vmax = 0.;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
i__3 = e_subscr(i__, j);
i__4 = ein_subscr(i__, j);
z__2.r = e[i__3].r - ein[i__4].r, z__2.i = e[i__3].i - ein[i__4]
.i;
z__1.r = z__2.r, z__1.i = z__2.i;
x = ((d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2)
)) / eps;
i__3 = e_subscr(i__, j);
if ((d__1 = e[i__3].r, abs(d__1)) + (d__2 = d_imag(&e_ref(i__, j))
, abs(d__2)) > safmin) {
i__4 = e_subscr(i__, j);
x /= (d__3 = e[i__4].r, abs(d__3)) + (d__4 = d_imag(&e_ref(
i__, j)), abs(d__4));
}
vmax = max(vmax,x);
/* L40: */
}
/* L50: */
}
if (vmax > rmax) {
lmax[1] = knt;
rmax = vmax;
}
goto L10;
L60:
io___22.ciunit = *nout;
s_wsfe(&io___22);
e_wsfe();
io___23.ciunit = *nout;
s_wsfe(&io___23);
do_fio(&c__1, (char *)&rmax, (ftnlen)sizeof(doublereal));
e_wsfe();
io___24.ciunit = *nout;
s_wsfe(&io___24);
do_fio(&c__1, (char *)&lmax[0], (ftnlen)sizeof(integer));
e_wsfe();
io___25.ciunit = *nout;
s_wsfe(&io___25);
do_fio(&c__1, (char *)&lmax[1], (ftnlen)sizeof(integer));
e_wsfe();
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, (char *)&ninfo, (ftnlen)sizeof(integer));
e_wsfe();
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, (char *)&knt, (ftnlen)sizeof(integer));
e_wsfe();
return 0;
/* End of ZCHKBK */
} /* zchkbk_ */
/* Subroutine */ int zerrhs_(char *path, integer *nunit)
{
/* Format strings */
static char fmt_9999[] = "(1x,a3,\002 routines passed the tests of the e"
"rror exits\002,\002 (\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;
doublereal d__1;
/* Local variables */
doublecomplex a[9] /* was [3][3] */, c__[9] /* was [3][3] */;
integer i__, j, m;
doublereal s[3];
doublecomplex w[9], x[3];
char c2[2];
integer nt;
doublecomplex vl[9] /* was [3][3] */, vr[9] /* was [3][3] */;
doublereal rw[3];
integer ihi, ilo;
logical sel[3];
doublecomplex tau[3];
integer info, ifaill[3];
extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
integer *), zgebal_(char *, integer *,
doublecomplex *, integer *, integer *, integer *, doublereal *,
integer *);
integer ifailr[3];
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), chkxer_(char *, integer *, integer *,
logical *, logical *), zhsein_(char *, char *, char *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *
, integer *, doublecomplex *, doublereal *, integer *, integer *,
integer *), zhseqr_(char *, char *,
integer *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *, integer *), ztrevc_(char *, char *,
logical *, integer *, doublecomplex *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *, integer *,
doublecomplex *, doublereal *, integer *),
zunghr_(integer *, integer *, integer *, doublecomplex *, integer
*, doublecomplex *, doublecomplex *, integer *, integer *),
zunmhr_(char *, char *, integer *, integer *, integer *, integer *
, doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, doublecomplex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___23 = { 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 */
/* ======= */
/* ZERRHS tests the error exits for ZGEBAK, CGEBAL, CGEHRD, ZUNGHR, */
/* ZUNMHR, ZHSEQR, CHSEIN, and ZTREVC. */
/* 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 Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 3; ++j) {
for (i__ = 1; i__ <= 3; ++i__) {
i__1 = i__ + j * 3 - 4;
d__1 = 1. / (doublereal) (i__ + j);
a[i__1].r = d__1, a[i__1].i = 0.;
/* L10: */
}
sel[j - 1] = TRUE_;
/* L20: */
}
infoc_1.ok = TRUE_;
nt = 0;
/* Test error exits of the nonsymmetric eigenvalue routines. */
if (lsamen_(&c__2, c2, "HS")) {
/* ZGEBAL */
s_copy(srnamc_1.srnamt, "ZGEBAL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgebal_("/", &c__0, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgebal_("N", &c_n1, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgebal_("N", &c__2, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("ZGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 3;
/* ZGEBAK */
s_copy(srnamc_1.srnamt, "ZGEBAK", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgebak_("/", "R", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgebak_("N", "/", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgebak_("N", "R", &c_n1, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgebak_("N", "R", &c__0, &c__0, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgebak_("N", "R", &c__0, &c__2, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgebak_("N", "R", &c__2, &c__2, &c__1, s, &c__0, a, &c__2, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgebak_("N", "R", &c__0, &c__1, &c__1, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgebak_("N", "R", &c__0, &c__1, &c__0, s, &c_n1, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zgebak_("N", "R", &c__2, &c__1, &c__2, s, &c__0, a, &c__1, &info);
chkxer_("ZGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* ZGEHRD */
s_copy(srnamc_1.srnamt, "ZGEHRD", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zgehrd_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgehrd_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgehrd_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgehrd_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgehrd_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgehrd_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__2, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgehrd_(&c__2, &c__1, &c__2, a, &c__2, tau, w, &c__1, &info);
chkxer_("ZGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
/* ZUNGHR */
s_copy(srnamc_1.srnamt, "ZUNGHR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zunghr_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunghr_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunghr_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunghr_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunghr_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunghr_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zunghr_(&c__3, &c__1, &c__3, a, &c__3, tau, w, &c__1, &info);
chkxer_("ZUNGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
/* ZUNMHR */
s_copy(srnamc_1.srnamt, "ZUNMHR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zunmhr_("/", "N", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zunmhr_("L", "/", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zunmhr_("L", "N", &c_n1, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zunmhr_("L", "N", &c__0, &c_n1, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmhr_("L", "N", &c__0, &c__0, &c__0, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmhr_("L", "N", &c__0, &c__0, &c__2, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmhr_("L", "N", &c__1, &c__2, &c__2, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__2, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zunmhr_("R", "N", &c__2, &c__1, &c__2, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__2, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zunmhr_("L", "N", &c__1, &c__1, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zunmhr_("L", "N", &c__0, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zunmhr_("R", "N", &c__1, &c__0, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zunmhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zunmhr_("R", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
zunmhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__2, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
zunmhr_("L", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
zunmhr_("R", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__1, &info);
chkxer_("ZUNMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 16;
/* ZHSEQR */
s_copy(srnamc_1.srnamt, "ZHSEQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zhseqr_("/", "N", &c__0, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zhseqr_("E", "/", &c__0, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zhseqr_("E", "N", &c_n1, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zhseqr_("E", "N", &c__0, &c__0, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zhseqr_("E", "N", &c__0, &c__2, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zhseqr_("E", "N", &c__1, &c__1, &c__0, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zhseqr_("E", "N", &c__1, &c__1, &c__2, a, &c__1, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zhseqr_("E", "N", &c__2, &c__1, &c__2, a, &c__1, x, c__, &c__2, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zhseqr_("E", "V", &c__2, &c__1, &c__2, a, &c__2, x, c__, &c__1, w, &
c__1, &info);
chkxer_("ZHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* ZHSEIN */
s_copy(srnamc_1.srnamt, "ZHSEIN", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
zhsein_("/", "N", "N", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&c__0, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zhsein_("R", "/", "N", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&c__0, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zhsein_("R", "N", "/", sel, &c__0, a, &c__1, x, vl, &c__1, vr, &c__1,
&c__0, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zhsein_("R", "N", "N", sel, &c_n1, a, &c__1, x, vl, &c__1, vr, &c__1,
&c__0, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zhsein_("R", "N", "N", sel, &c__2, a, &c__1, x, vl, &c__1, vr, &c__2,
&c__4, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zhsein_("L", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__1,
&c__4, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zhsein_("R", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__1,
&c__4, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
zhsein_("R", "N", "N", sel, &c__2, a, &c__2, x, vl, &c__1, vr, &c__2,
&c__1, &m, w, rw, ifaill, ifailr, &info);
chkxer_("ZHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* ZTREVC */
s_copy(srnamc_1.srnamt, "ZTREVC", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
ztrevc_("/", "A", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
ztrevc_("L", "/", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
ztrevc_("L", "A", sel, &c_n1, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
ztrevc_("L", "A", sel, &c__2, a, &c__1, vl, &c__2, vr, &c__1, &c__4, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
ztrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
ztrevc_("R", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
ztrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__2, vr, &c__1, &c__1, &
m, w, rw, &info);
chkxer_("ZTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
}
/* Print a summary line. */
if (infoc_1.ok) {
io___22.ciunit = infoc_1.nout;
s_wsfe(&io___22);
do_fio(&c__1, path, (ftnlen)3);
do_fio(&c__1, (char *)&nt, (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___23.ciunit = infoc_1.nout;
s_wsfe(&io___23);
do_fio(&c__1, path, (ftnlen)3);
e_wsfe();
}
return 0;
/* End of ZERRHS */
} /* zerrhs_ */
/* Subroutine */ int zchkbk_(integer *nin, integer *nout)
{
/* Format strings */
static char fmt_9999[] = "(1x,\002.. test output of ZGEBAK .. \002)";
static char fmt_9998[] = "(1x,\002value of largest test error "
" = \002,d12.3)";
static char fmt_9997[] = "(1x,\002example number where info is not zero "
" = \002,i4)";
static char fmt_9996[] = "(1x,\002example number having largest error "
" = \002,i4)";
static char fmt_9995[] = "(1x,\002number of examples where info is not 0"
" = \002,i4)";
static char fmt_9994[] = "(1x,\002total number of examples tested "
" = \002,i4)";
/* System generated locals */
integer i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4;
doublecomplex z__1, z__2;
/* Local variables */
doublecomplex e[400] /* was [20][20] */;
integer i__, j, n;
doublereal x;
integer ihi;
doublecomplex ein[400] /* was [20][20] */;
integer ilo;
doublereal eps;
integer knt, info, lmax[2];
doublereal rmax, vmax, scale[20];
integer ninfo;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
integer *);
doublereal safmin;
/* Fortran I/O blocks */
static cilist io___7 = { 0, 0, 0, 0, 0 };
static cilist io___11 = { 0, 0, 0, 0, 0 };
static cilist io___14 = { 0, 0, 0, 0, 0 };
static cilist io___17 = { 0, 0, 0, 0, 0 };
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___23 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___24 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___25 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9994, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZCHKBK tests ZGEBAK, a routine for backward transformation of */
/* the computed right or left eigenvectors if the orginal matrix */
/* was preprocessed by balance subroutine ZGEBAL. */
/* Arguments */
/* ========= */
/* NIN (input) INTEGER */
/* The logical unit number for input. NIN > 0. */
/* NOUT (input) INTEGER */
/* The logical unit number for output. NOUT > 0. */
/* ====================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Statement Functions .. */
/* .. */
/* .. Statement Function definitions .. */
/* .. */
/* .. Executable Statements .. */
lmax[0] = 0;
lmax[1] = 0;
ninfo = 0;
knt = 0;
rmax = 0.;
eps = dlamch_("E");
safmin = dlamch_("S");
L10:
io___7.ciunit = *nin;
s_rsle(&io___7);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ilo, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ihi, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
goto L60;
}
io___11.ciunit = *nin;
s_rsle(&io___11);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
do_lio(&c__5, &c__1, (char *)&scale[i__ - 1], (ftnlen)sizeof(
doublereal));
}
e_rsle();
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___14.ciunit = *nin;
s_rsle(&io___14);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&e[i__ + j * 20 - 21], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L20: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___17.ciunit = *nin;
s_rsle(&io___17);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__7, &c__1, (char *)&ein[i__ + j * 20 - 21], (ftnlen)
sizeof(doublecomplex));
}
e_rsle();
/* L30: */
}
++knt;
zgebak_("B", "R", &n, &ilo, &ihi, scale, &n, e, &c__20, &info);
if (info != 0) {
++ninfo;
lmax[0] = knt;
}
vmax = 0.;
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * 20 - 21;
i__4 = i__ + j * 20 - 21;
z__2.r = e[i__3].r - ein[i__4].r, z__2.i = e[i__3].i - ein[i__4]
.i;
z__1.r = z__2.r, z__1.i = z__2.i;
x = ((d__1 = z__1.r, abs(d__1)) + (d__2 = d_imag(&z__1), abs(d__2)
)) / eps;
i__3 = i__ + j * 20 - 21;
if ((d__1 = e[i__3].r, abs(d__1)) + (d__2 = d_imag(&e[i__ + j *
20 - 21]), abs(d__2)) > safmin) {
i__4 = i__ + j * 20 - 21;
x /= (d__3 = e[i__4].r, abs(d__3)) + (d__4 = d_imag(&e[i__ +
j * 20 - 21]), abs(d__4));
}
vmax = max(vmax,x);
/* L40: */
}
/* L50: */
}
if (vmax > rmax) {
lmax[1] = knt;
rmax = vmax;
}
goto L10;
L60:
io___22.ciunit = *nout;
s_wsfe(&io___22);
e_wsfe();
io___23.ciunit = *nout;
s_wsfe(&io___23);
do_fio(&c__1, (char *)&rmax, (ftnlen)sizeof(doublereal));
e_wsfe();
io___24.ciunit = *nout;
s_wsfe(&io___24);
do_fio(&c__1, (char *)&lmax[0], (ftnlen)sizeof(integer));
e_wsfe();
io___25.ciunit = *nout;
s_wsfe(&io___25);
do_fio(&c__1, (char *)&lmax[1], (ftnlen)sizeof(integer));
e_wsfe();
io___26.ciunit = *nout;
s_wsfe(&io___26);
do_fio(&c__1, (char *)&ninfo, (ftnlen)sizeof(integer));
e_wsfe();
io___27.ciunit = *nout;
s_wsfe(&io___27);
do_fio(&c__1, (char *)&knt, (ftnlen)sizeof(integer));
e_wsfe();
return 0;
/* End of ZCHKBK */
} /* zchkbk_ */
/* Subroutine */ int zgeesx_(char *jobvs, char *sort, L_fp select, char *
sense, integer *n, doublecomplex *a, integer *lda, integer *sdim,
doublecomplex *w, doublecomplex *vs, integer *ldvs, doublereal *
rconde, doublereal *rcondv, doublecomplex *work, integer *lwork,
doublereal *rwork, logical *bwork, integer *info)
{
/* -- LAPACK driver 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
=======
ZGEESX computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues, the Schur form T, and, optionally, the matrix of Schur
vectors Z. This gives the Schur factorization A = Z*T*(Z**H).
Optionally, it also orders the eigenvalues on the diagonal of the
Schur form so that selected eigenvalues are at the top left;
computes a reciprocal condition number for the average of the
selected eigenvalues (RCONDE); and computes a reciprocal condition
number for the right invariant subspace corresponding to the
selected eigenvalues (RCONDV). The leading columns of Z form an
orthonormal basis for this invariant subspace.
For further explanation of the reciprocal condition numbers RCONDE
and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
these quantities are called s and sep respectively).
A complex matrix is in Schur form if it is upper triangular.
Arguments
=========
JOBVS (input) CHARACTER*1
= 'N': Schur vectors are not computed;
= 'V': Schur vectors are computed.
SORT (input) CHARACTER*1
Specifies whether or not to order the eigenvalues on the
diagonal of the Schur form.
= 'N': Eigenvalues are not ordered;
= 'S': Eigenvalues are ordered (see SELECT).
SELECT (input) LOGICAL FUNCTION of one COMPLEX*16 argument
SELECT must be declared EXTERNAL in the calling subroutine.
If SORT = 'S', SELECT is used to select eigenvalues to order
to the top left of the Schur form.
If SORT = 'N', SELECT is not referenced.
An eigenvalue W(j) is selected if SELECT(W(j)) is true.
SENSE (input) CHARACTER*1
Determines which reciprocal condition numbers are computed.
= 'N': None are computed;
= 'E': Computed for average of selected eigenvalues only;
= 'V': Computed for selected right invariant subspace only;
= 'B': Computed for both.
If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
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 is overwritten by its Schur form T.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
SDIM (output) INTEGER
If SORT = 'N', SDIM = 0.
If SORT = 'S', SDIM = number of eigenvalues for which
SELECT is true.
W (output) COMPLEX*16 array, dimension (N)
W contains the computed eigenvalues, in the same order
that they appear on the diagonal of the output Schur form T.
VS (output) COMPLEX*16 array, dimension (LDVS,N)
If JOBVS = 'V', VS contains the unitary matrix Z of Schur
vectors.
If JOBVS = 'N', VS is not referenced.
LDVS (input) INTEGER
The leading dimension of the array VS. LDVS >= 1, and if
JOBVS = 'V', LDVS >= N.
RCONDE (output) DOUBLE PRECISION
If SENSE = 'E' or 'B', RCONDE contains the reciprocal
condition number for the average of the selected eigenvalues.
Not referenced if SENSE = 'N' or 'V'.
RCONDV (output) DOUBLE PRECISION
If SENSE = 'V' or 'B', RCONDV contains the reciprocal
condition number for the selected right invariant subspace.
Not referenced if SENSE = 'N' or 'E'.
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. LWORK >= max(1,2*N).
Also, if SENSE = 'E' or 'V' or 'B', LWORK >= 2*SDIM*(N-SDIM),
where SDIM is the number of selected eigenvalues computed by
this routine. Note that 2*SDIM*(N-SDIM) <= N*N/2.
For good performance, LWORK must generally be larger.
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
BWORK (workspace) LOGICAL array, dimension (N)
Not referenced if SORT = 'N'.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: if INFO = i, and i is
<= N: the QR algorithm failed to compute all the
eigenvalues; elements 1:ILO-1 and i+1:N of W
contain those eigenvalues which have converged; if
JOBVS = 'V', VS contains the transformation which
reduces A to its partially converged Schur form.
= N+1: the eigenvalues could not be reordered because some
eigenvalues were too close to separate (the problem
is very ill-conditioned);
= N+2: after reordering, roundoff changed values of some
complex eigenvalues so that leading eigenvalues in
the Schur form no longer satisfy SELECT=.TRUE. This
could also be caused by underflow due to scaling.
=====================================================================
Test the input arguments
Parameter adjustments */
/* 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, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer ibal, maxb;
static doublereal anrm;
static integer ierr, itau, iwrk, i__, k, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
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 *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *);
static doublereal bignum;
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *);
static logical wantsb, wantse;
extern /* Subroutine */ int zlacpy_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *);
static integer minwrk, maxwrk;
static logical wantsn;
static doublereal smlnum;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *);
static integer hswork;
extern /* Subroutine */ int zunghr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
static logical wantst, wantsv, wantvs;
extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, integer *);
static integer ihi, ilo;
static doublereal dum[1], eps;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--w;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1 * 1;
vs -= vs_offset;
--work;
--rwork;
--bwork;
/* Function Body */
*info = 0;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
wantsn = lsame_(sense, "N");
wantse = lsame_(sense, "E");
wantsv = lsame_(sense, "V");
wantsb = lsame_(sense, "B");
if (! wantvs && ! lsame_(jobvs, "N")) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -2;
} else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && !
wantsn) {
*info = -4;
} else if (*n < 0) {
*info = -5;
} else if (*lda < max(1,*n)) {
*info = -7;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -11;
}
/* Compute workspace
(Note: Comments in the code beginning "Workspace:" describe the
minimal amount of real 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 SENSE = 'E', 'V' or 'B', then the amount of workspace needed
depends on SDIM, which is computed by the routine ZTRSEN later
in the code.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
if (! wantvs) {
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
maxb = max(i__1,2);
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
c_n1, (ftnlen)6, (ftnlen)2);
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,hswork);
maxwrk = max(i__1,1);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SV", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
maxb = max(i__1,2);
/* Computing MIN
Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SV", n, &c__1, n, &
c_n1, (ftnlen)6, (ftnlen)2);
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,hswork);
maxwrk = max(i__1,1);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk) {
*info = -15;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEESX", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 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] */
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);
}
/* Permute the matrix to make it more nearly triangular
(CWorkspace: none)
(RWorkspace: need N) */
ibal = 1;
zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr);
/* Reduce to upper Hessenberg form
(CWorkspace: need 2*N, prefer N+N*NB)
(RWorkspace: none) */
itau = 1;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
;
/* Generate unitary matrix in VS
(CWorkspace: need 2*N-1, prefer N+(N-1)*NB)
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
&i__1, &ierr);
}
*sdim = 0;
/* Perform QR iteration, accumulating Schur vectors in VS if desired
(CWorkspace: need 1, prefer HSWORK (see comments) )
(RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[iwrk], &i__1, &ieval);
if (ieval > 0) {
*info = ieval;
}
/* Sort eigenvalues if desired */
if (wantst && *info == 0) {
if (scalea) {
zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
ierr);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&w[i__]);
/* L10: */
}
/* Reorder eigenvalues, transform Schur vectors, and compute
reciprocal condition numbers
(CWorkspace: if SENSE is not 'N', need 2*SDIM*(N-SDIM)
otherwise, need none )
(RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
ztrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &w[1], sdim, rconde, rcondv, &work[iwrk], &i__1, &
icond);
if (! wantsn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (icond == -14) {
/* Not enough complex workspace */
*info = -15;
}
}
if (wantvs) {
/* Undo balancing
(CWorkspace: none)
(RWorkspace: need N) */
zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset],
ldvs, &ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr);
i__1 = *lda + 1;
zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
if ((wantsv || wantsb) && *info == 0) {
dum[0] = *rcondv;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &c__1, &c__1, dum, &
c__1, &ierr);
*rcondv = dum[0];
}
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZGEESX */
} /* zgeesx_ */
/* 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 zgees_(char *jobvs, char *sort, L_fp select, integer *n,
doublecomplex *a, integer *lda, integer *sdim, doublecomplex *w,
doublecomplex *vs, integer *ldvs, doublecomplex *work, integer *lwork,
doublereal *rwork, logical *bwork, integer *info, ftnlen jobvs_len,
ftnlen sort_len)
{
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3, i__4;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, k;
static doublereal s;
static integer ihi, ilo;
static doublereal dum[1], eps, sep;
static integer ibal, maxb;
static doublereal anrm;
static integer ierr, itau, iwrk, icond, ieval;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
extern /* Subroutine */ int zcopy_(integer *, doublecomplex *, integer *,
doublecomplex *, integer *), dlabad_(doublereal *, doublereal *);
static logical scalea;
extern doublereal dlamch_(char *, ftnlen);
static doublereal cscale;
extern /* Subroutine */ int zgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublecomplex *, integer *,
integer *, ftnlen, ftnlen), zgebal_(char *, integer *,
doublecomplex *, integer *, integer *, integer *, doublereal *,
integer *, ftnlen), xerbla_(char *, integer *, ftnlen);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern doublereal zlange_(char *, integer *, integer *, doublecomplex *,
integer *, doublereal *, ftnlen);
static doublereal bignum;
extern /* Subroutine */ int zgehrd_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *), zlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublecomplex *,
integer *, integer *, ftnlen), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *,
ftnlen);
static integer minwrk, maxwrk;
static doublereal smlnum;
extern /* Subroutine */ int zhseqr_(char *, char *, integer *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
ftnlen, ftnlen);
static integer hswork;
extern /* Subroutine */ int zunghr_(integer *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *, integer *);
static logical wantst, lquery, wantvs;
extern /* Subroutine */ int ztrsen_(char *, char *, logical *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, integer *, ftnlen, ftnlen);
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGEES computes for an N-by-N complex nonsymmetric matrix A, the */
/* eigenvalues, the Schur form T, and, optionally, the matrix of Schur */
/* vectors Z. This gives the Schur factorization A = Z*T*(Z**H). */
/* Optionally, it also orders the eigenvalues on the diagonal of the */
/* Schur form so that selected eigenvalues are at the top left. */
/* The leading columns of Z then form an orthonormal basis for the */
/* invariant subspace corresponding to the selected eigenvalues. */
/* A complex matrix is in Schur form if it is upper triangular. */
/* Arguments */
/* ========= */
/* JOBVS (input) CHARACTER*1 */
/* = 'N': Schur vectors are not computed; */
/* = 'V': Schur vectors are computed. */
/* SORT (input) CHARACTER*1 */
/* Specifies whether or not to order the eigenvalues on the */
/* diagonal of the Schur form. */
/* = 'N': Eigenvalues are not ordered: */
/* = 'S': Eigenvalues are ordered (see SELECT). */
/* SELECT (input) LOGICAL FUNCTION of one COMPLEX*16 argument */
/* SELECT must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'S', SELECT is used to select eigenvalues to order */
/* to the top left of the Schur form. */
/* IF SORT = 'N', SELECT is not referenced. */
/* The eigenvalue W(j) is selected if SELECT(W(j)) is true. */
/* 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 by its Schur form T. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* SDIM (output) INTEGER */
/* If SORT = 'N', SDIM = 0. */
/* If SORT = 'S', SDIM = number of eigenvalues for which */
/* SELECT is true. */
/* W (output) COMPLEX*16 array, dimension (N) */
/* W contains the computed eigenvalues, in the same order that */
/* they appear on the diagonal of the output Schur form T. */
/* VS (output) COMPLEX*16 array, dimension (LDVS,N) */
/* If JOBVS = 'V', VS contains the unitary matrix Z of Schur */
/* vectors. */
/* If JOBVS = 'N', VS is not referenced. */
/* LDVS (input) INTEGER */
/* The leading dimension of the array VS. LDVS >= 1; if */
/* JOBVS = 'V', LDVS >= N. */
/* 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. LWORK >= max(1,2*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 (N) */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* Not referenced if SORT = 'N'. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: if INFO = i, and i is */
/* <= N: the QR algorithm failed to compute all the */
/* eigenvalues; elements 1:ILO-1 and i+1:N of W */
/* contain those eigenvalues which have converged; */
/* if JOBVS = 'V', VS contains the matrix which */
/* reduces A to its partially converged Schur form. */
/* = N+1: the eigenvalues could not be reordered because */
/* some eigenvalues were too close to separate (the */
/* problem is very ill-conditioned); */
/* = N+2: after reordering, roundoff changed values of */
/* some complex eigenvalues so that leading */
/* eigenvalues in the Schur form no longer satisfy */
/* SELECT = .TRUE.. This could also be caused by */
/* underflow due to scaling. */
/* ===================================================================== */
/* .. 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;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--rwork;
--bwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvs = lsame_(jobvs, "V", (ftnlen)1, (ftnlen)1);
wantst = lsame_(sort, "S", (ftnlen)1, (ftnlen)1);
if (! wantvs && ! lsame_(jobvs, "N", (ftnlen)1, (ftnlen)1)) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N", (ftnlen)1, (ftnlen)1)) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -10;
}
/* 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 || lquery)) {
maxwrk = *n + *n * ilaenv_(&c__1, "ZGEHRD", " ", n, &c__1, n, &c__0, (
ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = 1, i__2 = *n << 1;
minwrk = max(i__1,i__2);
if (! wantvs) {
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "SN", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
maxb = max(i__1,2);
/* Computing MIN */
/* Computing MAX */
i__3 = 2, i__4 = ilaenv_(&c__4, "ZHSEQR", "SN", n, &c__1, n, &
c_n1, (ftnlen)6, (ftnlen)2);
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,hswork);
maxwrk = max(i__1,1);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "ZUNGHR",
" ", n, &c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "ZHSEQR", "EN", n, &c__1, n, &c_n1, (ftnlen)
6, (ftnlen)2);
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, (ftnlen)6, (ftnlen)2);
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,hswork);
maxwrk = max(i__1,1);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
}
if (*lwork < minwrk && ! lquery) {
*info = -12;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGEES ", &i__1, (ftnlen)6);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
*sdim = 0;
return 0;
}
/* Get machine constants */
eps = dlamch_("P", (ftnlen)1);
smlnum = dlamch_("S", (ftnlen)1);
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
smlnum = sqrt(smlnum) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = zlange_("M", n, n, &a[a_offset], lda, dum, (ftnlen)1);
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, (ftnlen)1);
}
/* Permute the matrix to make it more nearly triangular */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
ibal = 1;
zgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &rwork[ibal], &ierr, (
ftnlen)1);
/* Reduce to upper Hessenberg form */
/* (CWorkspace: need 2*N, prefer N+N*NB) */
/* (RWorkspace: none) */
itau = 1;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
zgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
zlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs, (ftnlen)1)
;
/* Generate unitary matrix in VS */
/* (CWorkspace: need 2*N-1, prefer N+(N-1)*NB) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
zunghr_(n, &ilo, &ihi, &vs[vs_offset], ldvs, &work[itau], &work[iwrk],
&i__1, &ierr);
}
*sdim = 0;
/* Perform QR iteration, accumulating Schur vectors in VS if desired */
/* (CWorkspace: need 1, prefer HSWORK (see comments) ) */
/* (RWorkspace: none) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
zhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &w[1], &vs[
vs_offset], ldvs, &work[iwrk], &i__1, &ieval, (ftnlen)1, (ftnlen)
1);
if (ieval > 0) {
*info = ieval;
}
/* Sort eigenvalues if desired */
if (wantst && *info == 0) {
if (scalea) {
zlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &w[1], n, &
ierr, (ftnlen)1);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&w[i__]);
/* L10: */
}
/* Reorder eigenvalues and transform Schur vectors */
/* (CWorkspace: none) */
/* (RWorkspace: none) */
i__1 = *lwork - iwrk + 1;
ztrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &w[1], sdim, &s, &sep, &work[iwrk], &i__1, &icond, (
ftnlen)1, (ftnlen)1);
}
if (wantvs) {
/* Undo balancing */
/* (CWorkspace: none) */
/* (RWorkspace: need N) */
zgebak_("P", "R", n, &ilo, &ihi, &rwork[ibal], n, &vs[vs_offset],
ldvs, &ierr, (ftnlen)1, (ftnlen)1);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
zlascl_("U", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr, (ftnlen)1);
i__1 = *lda + 1;
zcopy_(n, &a[a_offset], &i__1, &w[1], &c__1);
}
work[1].r = (doublereal) maxwrk, work[1].i = 0.;
return 0;
/* End of ZGEES */
} /* zgees_ */
/* 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_ */
int main(void)
{
/* Local scalars */
char job, job_i;
char side, side_i;
lapack_int n, n_i;
lapack_int ilo, ilo_i;
lapack_int ihi, ihi_i;
lapack_int m, m_i;
lapack_int ldv, ldv_i;
lapack_int ldv_r;
lapack_int info, info_i;
lapack_int i;
int failed;
/* Local arrays */
double *scale = NULL, *scale_i = NULL;
lapack_complex_double *v = NULL, *v_i = NULL;
lapack_complex_double *v_save = NULL;
lapack_complex_double *v_r = NULL;
/* Iniitialize the scalar parameters */
init_scalars_zgebak( &job, &side, &n, &ilo, &ihi, &m, &ldv );
ldv_r = m+2;
job_i = job;
side_i = side;
n_i = n;
ilo_i = ilo;
ihi_i = ihi;
m_i = m;
ldv_i = ldv;
/* Allocate memory for the LAPACK routine arrays */
scale = (double *)LAPACKE_malloc( n * sizeof(double) );
v = (lapack_complex_double *)
LAPACKE_malloc( ldv*m * sizeof(lapack_complex_double) );
/* Allocate memory for the C interface function arrays */
scale_i = (double *)LAPACKE_malloc( n * sizeof(double) );
v_i = (lapack_complex_double *)
LAPACKE_malloc( ldv*m * sizeof(lapack_complex_double) );
/* Allocate memory for the backup arrays */
v_save = (lapack_complex_double *)
LAPACKE_malloc( ldv*m * sizeof(lapack_complex_double) );
/* Allocate memory for the row-major arrays */
v_r = (lapack_complex_double *)
LAPACKE_malloc( n*(m+2) * sizeof(lapack_complex_double) );
/* Initialize input arrays */
init_scale( n, scale );
init_v( ldv*m, v );
/* Backup the ouptut arrays */
for( i = 0; i < ldv*m; i++ ) {
v_save[i] = v[i];
}
/* Call the LAPACK routine */
zgebak_( &job, &side, &n, &ilo, &ihi, scale, &m, v, &ldv, &info );
/* Initialize input data, call the column-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < n; i++ ) {
scale_i[i] = scale[i];
}
for( i = 0; i < ldv*m; i++ ) {
v_i[i] = v_save[i];
}
info_i = LAPACKE_zgebak_work( LAPACK_COL_MAJOR, job_i, side_i, n_i, ilo_i,
ihi_i, scale_i, m_i, v_i, ldv_i );
failed = compare_zgebak( v, v_i, info, info_i, ldv, m );
if( failed == 0 ) {
printf( "PASSED: column-major middle-level interface to zgebak\n" );
} else {
printf( "FAILED: column-major middle-level interface to zgebak\n" );
}
/* Initialize input data, call the column-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < n; i++ ) {
scale_i[i] = scale[i];
}
for( i = 0; i < ldv*m; i++ ) {
v_i[i] = v_save[i];
}
info_i = LAPACKE_zgebak( LAPACK_COL_MAJOR, job_i, side_i, n_i, ilo_i, ihi_i,
scale_i, m_i, v_i, ldv_i );
failed = compare_zgebak( v, v_i, info, info_i, ldv, m );
if( failed == 0 ) {
printf( "PASSED: column-major high-level interface to zgebak\n" );
} else {
printf( "FAILED: column-major high-level interface to zgebak\n" );
}
/* Initialize input data, call the row-major middle-level
* interface to LAPACK routine and check the results */
for( i = 0; i < n; i++ ) {
scale_i[i] = scale[i];
}
for( i = 0; i < ldv*m; i++ ) {
v_i[i] = v_save[i];
}
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, m, v_i, ldv, v_r, m+2 );
info_i = LAPACKE_zgebak_work( LAPACK_ROW_MAJOR, job_i, side_i, n_i, ilo_i,
ihi_i, scale_i, m_i, v_r, ldv_r );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, m, v_r, m+2, v_i, ldv );
failed = compare_zgebak( v, v_i, info, info_i, ldv, m );
if( failed == 0 ) {
printf( "PASSED: row-major middle-level interface to zgebak\n" );
} else {
printf( "FAILED: row-major middle-level interface to zgebak\n" );
}
/* Initialize input data, call the row-major high-level
* interface to LAPACK routine and check the results */
for( i = 0; i < n; i++ ) {
scale_i[i] = scale[i];
}
for( i = 0; i < ldv*m; i++ ) {
v_i[i] = v_save[i];
}
/* Init row_major arrays */
LAPACKE_zge_trans( LAPACK_COL_MAJOR, n, m, v_i, ldv, v_r, m+2 );
info_i = LAPACKE_zgebak( LAPACK_ROW_MAJOR, job_i, side_i, n_i, ilo_i, ihi_i,
scale_i, m_i, v_r, ldv_r );
LAPACKE_zge_trans( LAPACK_ROW_MAJOR, n, m, v_r, m+2, v_i, ldv );
failed = compare_zgebak( v, v_i, info, info_i, ldv, m );
if( failed == 0 ) {
printf( "PASSED: row-major high-level interface to zgebak\n" );
} else {
printf( "FAILED: row-major high-level interface to zgebak\n" );
}
/* Release memory */
if( scale != NULL ) {
LAPACKE_free( scale );
}
if( scale_i != NULL ) {
LAPACKE_free( scale_i );
}
if( v != NULL ) {
LAPACKE_free( v );
}
if( v_i != NULL ) {
LAPACKE_free( v_i );
}
if( v_r != NULL ) {
LAPACKE_free( v_r );
}
if( v_save != NULL ) {
LAPACKE_free( v_save );
}
return 0;
}
/* 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_ */
