/* Subroutine */ int dget36_(doublereal *rmax, integer *lmax, integer *ninfo,
integer *knt, integer *nin)
{
/* System generated locals */
integer i__1, i__2;
/* Builtin functions */
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
double d_sign(doublereal *, doublereal *);
/* Local variables */
integer i__, j, n;
doublereal q[100] /* was [10][10] */, t1[100] /* was [10][10] */,
t2[100] /* was [10][10] */;
integer loc;
doublereal eps, res, tmp[100] /* was [10][10] */;
integer ifst, ilst;
doublereal work[200];
integer info1, info2, ifst1, ifst2, ilst1, ilst2;
extern /* Subroutine */ int dhst01_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), dtrexc_(char *, integer *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, integer *);
integer ifstsv;
doublereal result[2];
integer ilstsv;
/* Fortran I/O blocks */
static cilist io___2 = { 0, 0, 0, 0, 0 };
static cilist io___7 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGET36 tests DTREXC, a routine for moving blocks (either 1 by 1 or */
/* 2 by 2) on the diagonal of a matrix in real Schur form. Thus, DLAEXC */
/* computes an orthogonal matrix Q such that */
/* Q' * T1 * Q = T2 */
/* and where one of the diagonal blocks of T1 (the one at row IFST) has */
/* been moved to position ILST. */
/* The test code verifies that the residual Q'*T1*Q-T2 is small, that T2 */
/* is in Schur form, and that the final position of the IFST block is */
/* ILST (within +-1). */
/* The test matrices are read from a file with logical unit number NIN. */
/* Arguments */
/* ========== */
/* RMAX (output) DOUBLE PRECISION */
/* Value of the largest test ratio. */
/* LMAX (output) INTEGER */
/* Example number where largest test ratio achieved. */
/* NINFO (output) INTEGER array, dimension (3) */
/* NINFO(J) is the number of examples where INFO=J. */
/* KNT (output) INTEGER */
/* Total number of examples tested. */
/* NIN (input) INTEGER */
/* Input logical unit number. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ninfo;
/* Function Body */
eps = dlamch_("P");
*rmax = 0.;
*lmax = 0;
*knt = 0;
ninfo[1] = 0;
ninfo[2] = 0;
ninfo[3] = 0;
/* Read input data until N=0 */
L10:
io___2.ciunit = *nin;
s_rsle(&io___2);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ifst, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ilst, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
return 0;
}
++(*knt);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___7.ciunit = *nin;
s_rsle(&io___7);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__5, &c__1, (char *)&tmp[i__ + j * 10 - 11], (ftnlen)
sizeof(doublereal));
}
e_rsle();
/* L20: */
}
dlacpy_("F", &n, &n, tmp, &c__10, t1, &c__10);
dlacpy_("F", &n, &n, tmp, &c__10, t2, &c__10);
ifstsv = ifst;
ilstsv = ilst;
ifst1 = ifst;
ilst1 = ilst;
ifst2 = ifst;
ilst2 = ilst;
res = 0.;
/* Test without accumulating Q */
dlaset_("Full", &n, &n, &c_b21, &c_b22, q, &c__10);
dtrexc_("N", &n, t1, &c__10, q, &c__10, &ifst1, &ilst1, work, &info1);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (i__ == j && q[i__ + j * 10 - 11] != 1.) {
res += 1. / eps;
}
if (i__ != j && q[i__ + j * 10 - 11] != 0.) {
res += 1. / eps;
}
/* L30: */
}
/* L40: */
}
/* Test with accumulating Q */
dlaset_("Full", &n, &n, &c_b21, &c_b22, q, &c__10);
dtrexc_("V", &n, t2, &c__10, q, &c__10, &ifst2, &ilst2, work, &info2);
/* Compare T1 with T2 */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (t1[i__ + j * 10 - 11] != t2[i__ + j * 10 - 11]) {
res += 1. / eps;
}
/* L50: */
}
/* L60: */
}
if (ifst1 != ifst2) {
res += 1. / eps;
}
if (ilst1 != ilst2) {
res += 1. / eps;
}
if (info1 != info2) {
res += 1. / eps;
}
/* Test for successful reordering of T2 */
if (info2 != 0) {
++ninfo[info2];
} else {
if ((i__1 = ifst2 - ifstsv, abs(i__1)) > 1) {
res += 1. / eps;
}
if ((i__1 = ilst2 - ilstsv, abs(i__1)) > 1) {
res += 1. / eps;
}
}
/* Test for small residual, and orthogonality of Q */
dhst01_(&n, &c__1, &n, tmp, &c__10, t2, &c__10, q, &c__10, work, &c__200,
result);
res = res + result[0] + result[1];
/* Test for T2 being in Schur form */
loc = 1;
L70:
if (t2[loc + 1 + loc * 10 - 11] != 0.) {
/* 2 by 2 block */
if (t2[loc + (loc + 1) * 10 - 11] == 0. || t2[loc + loc * 10 - 11] !=
t2[loc + 1 + (loc + 1) * 10 - 11] || d_sign(&c_b22, &t2[loc +
(loc + 1) * 10 - 11]) == d_sign(&c_b22, &t2[loc + 1 + loc *
10 - 11])) {
res += 1. / eps;
}
i__1 = n;
for (i__ = loc + 2; i__ <= i__1; ++i__) {
if (t2[i__ + loc * 10 - 11] != 0.) {
res += 1. / res;
}
if (t2[i__ + (loc + 1) * 10 - 11] != 0.) {
res += 1. / res;
}
/* L80: */
}
loc += 2;
} else {
/* 1 by 1 block */
i__1 = n;
for (i__ = loc + 1; i__ <= i__1; ++i__) {
if (t2[i__ + loc * 10 - 11] != 0.) {
res += 1. / res;
}
/* L90: */
}
++loc;
}
if (loc < n) {
goto L70;
}
if (res > *rmax) {
*rmax = res;
*lmax = *knt;
}
goto L10;
/* End of DGET36 */
} /* dget36_ */
/* Subroutine */ int dchkhs_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, doublereal *thresh, integer *nounit,
doublereal *a, integer *lda, doublereal *h__, doublereal *t1,
doublereal *t2, doublereal *u, integer *ldu, doublereal *z__,
doublereal *uz, doublereal *wr1, doublereal *wi1, doublereal *wr3,
doublereal *wi3, doublereal *evectl, doublereal *evectr, doublereal *
evecty, doublereal *evectx, doublereal *uu, doublereal *tau,
doublereal *work, integer *nwork, integer *iwork, logical *select,
doublereal *result, integer *info)
{
/* Initialized data */
static integer ktype[21] = { 1,2,3,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,9,9,9 };
static integer kmagn[21] = { 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,2,3,1,2,3 };
static integer kmode[21] = { 0,0,0,4,3,1,4,4,4,3,1,5,4,3,1,5,5,5,4,3,1 };
static integer kconds[21] = { 0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 DCHKHS: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 DCHKHS: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,9x,\002N=\002,i6,\002, JTYPE=\002,"
"i6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(\002 DCHKHS: Selected \002,a,\002 Eigenvector"
"s from \002,a,\002 do not match other eigenvectors \002,9x,\002N="
"\002,i6,\002, JTYPE=\002,i6,\002, ISEED=(\002,3(i5,\002,\002),i5,"
"\002)\002)";
/* System generated locals */
integer a_dim1, a_offset, evectl_dim1, evectl_offset, evectr_dim1,
evectr_offset, evectx_dim1, evectx_offset, evecty_dim1,
evecty_offset, h_dim1, h_offset, t1_dim1, t1_offset, t2_dim1,
t2_offset, u_dim1, u_offset, uu_dim1, uu_offset, uz_dim1,
uz_offset, z_dim1, z_offset, i__1, i__2, i__3, i__4;
doublereal d__1, d__2, d__3, d__4, d__5, d__6;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static doublereal cond;
static integer jcol, nmax;
static doublereal unfl, ovfl, temp1, temp2;
static integer i__, j, k, n;
static logical badnn;
extern /* Subroutine */ int dget10_(integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *),
dget22_(char *, char *, char *, integer *, doublereal *, integer *
, doublereal *, integer *, doublereal *, doublereal *, doublereal
*, doublereal *), dgemm_(char *, char *,
integer *, integer *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
static logical match;
static integer imode;
static doublereal dumma[6];
static integer iinfo, nselc;
static doublereal conds;
extern /* Subroutine */ int dhst01_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *);
static doublereal aninv, anorm;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer nmats, nselr, jsize, nerrs, itype, jtype, ntest, n1;
static doublereal rtulp;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
static integer jj, in;
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *);
static char adumma[1*1];
extern /* Subroutine */ int dlatme_(integer *, char *, integer *,
doublereal *, integer *, doublereal *, doublereal *, char *, char
*, char *, char *, doublereal *, integer *, doublereal *, integer
*, integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *), dhsein_(char
*, char *, char *, logical *, integer *, doublereal *, integer *,
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *,
integer *, integer *);
static integer idumma[1];
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
static integer ioldsd[4];
extern /* Subroutine */ int dlafts_(char *, integer *, integer *, integer
*, integer *, doublereal *, integer *, doublereal *, integer *,
integer *), dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *),
dlasum_(char *, integer *, integer *, integer *), dhseqr_(
char *, char *, integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, doublereal *, integer *,
doublereal *, integer *, integer *), dlatmr_(
integer *, integer *, char *, integer *, char *, doublereal *,
integer *, doublereal *, doublereal *, char *, char *, doublereal
*, integer *, doublereal *, doublereal *, integer *, doublereal *,
char *, integer *, integer *, integer *, doublereal *,
doublereal *, char *, doublereal *, integer *, integer *, integer
*), dlatms_(
integer *, integer *, char *, integer *, char *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *, char
*, doublereal *, integer *, doublereal *, integer *), dorghr_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dormhr_(char *, char *, integer *, integer *, integer
*, integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *),
dtrevc_(char *, char *, logical *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *, integer *, doublereal *, integer *),
xerbla_(char *, integer *);
static doublereal rtunfl, rtovfl, rtulpi, ulpinv;
static integer mtypes, ntestt, ihi, ilo;
static doublereal ulp;
/* Fortran I/O blocks */
static cilist io___36 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___39 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___58 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___59 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___60 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___61 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___62 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___63 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___64 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___65 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___66 = { 0, 0, 0, fmt_9999, 0 };
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define h___ref(a_1,a_2) h__[(a_2)*h_dim1 + a_1]
#define u_ref(a_1,a_2) u[(a_2)*u_dim1 + a_1]
#define uu_ref(a_1,a_2) uu[(a_2)*uu_dim1 + a_1]
#define evectl_ref(a_1,a_2) evectl[(a_2)*evectl_dim1 + a_1]
#define evectr_ref(a_1,a_2) evectr[(a_2)*evectr_dim1 + a_1]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1999
Purpose
=======
DCHKHS checks the nonsymmetric eigenvalue problem routines.
DGEHRD factors A as U H U' , where ' means transpose,
H is hessenberg, and U is an orthogonal matrix.
DORGHR generates the orthogonal matrix U.
DORMHR multiplies a matrix by the orthogonal matrix U.
DHSEQR factors H as Z T Z' , where Z is orthogonal and
T is "quasi-triangular", and the eigenvalue vector W.
DTREVC computes the left and right eigenvector matrices
L and R for T.
DHSEIN computes the left and right eigenvector matrices
Y and X for H, using inverse iteration.
When DCHKHS is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified. For each size ("n")
and each type of matrix, one matrix will be generated and used
to test the nonsymmetric eigenroutines. For each matrix, 14
tests will be performed:
(1) | A - U H U**T | / ( |A| n ulp )
(2) | I - UU**T | / ( n ulp )
(3) | H - Z T Z**T | / ( |H| n ulp )
(4) | I - ZZ**T | / ( n ulp )
(5) | A - UZ H (UZ)**T | / ( |A| n ulp )
(6) | I - UZ (UZ)**T | / ( n ulp )
(7) | T(Z computed) - T(Z not computed) | / ( |T| ulp )
(8) | W(Z computed) - W(Z not computed) | / ( |W| ulp )
(9) | TR - RW | / ( |T| |R| ulp )
(10) | L**H T - W**H L | / ( |T| |L| ulp )
(11) | HX - XW | / ( |H| |X| ulp )
(12) | Y**H H - W**H Y | / ( |H| |Y| ulp )
(13) | AX - XW | / ( |A| |X| ulp )
(14) | Y**H A - W**H Y | / ( |A| |Y| ulp )
The "sizes" are specified by an array NN(1:NSIZES); the value of
each element NN(j) specifies one size.
The "types" are specified by a logical array DOTYPE( 1:NTYPES );
if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
Currently, the list of possible types is:
(1) The zero matrix.
(2) The identity matrix.
(3) A (transposed) Jordan block, with 1's on the diagonal.
(4) A diagonal matrix with evenly spaced entries
1, ..., ULP and random signs.
(ULP = (first number larger than 1) - 1 )
(5) A diagonal matrix with geometrically spaced entries
1, ..., ULP and random signs.
(6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.
(7) Same as (4), but multiplied by SQRT( overflow threshold )
(8) Same as (4), but multiplied by SQRT( underflow threshold )
(9) A matrix of the form U' T U, where U is orthogonal and
T has evenly spaced entries 1, ..., ULP with random signs
on the diagonal and random O(1) entries in the upper
triangle.
(10) A matrix of the form U' T U, where U is orthogonal and
T has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.
(11) A matrix of the form U' T U, where U is orthogonal and
T has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal and random O(1) entries in the upper
triangle.
(12) A matrix of the form U' T U, where U is orthogonal and
T has real or complex conjugate paired eigenvalues randomly
chosen from ( ULP, 1 ) and random O(1) entries in the upper
triangle.
(13) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.
(14) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has geometrically spaced entries
1, ..., ULP with random signs on the diagonal and random
O(1) entries in the upper triangle.
(15) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP
with random signs on the diagonal and random O(1) entries
in the upper triangle.
(16) A matrix of the form X' T X, where X has condition
SQRT( ULP ) and T has real or complex conjugate paired
eigenvalues randomly chosen from ( ULP, 1 ) and random
O(1) entries in the upper triangle.
(17) Same as (16), but multiplied by SQRT( overflow threshold )
(18) Same as (16), but multiplied by SQRT( underflow threshold )
(19) Nonsymmetric matrix with random entries chosen from (-1,1).
(20) Same as (19), but multiplied by SQRT( overflow threshold )
(21) Same as (19), but multiplied by SQRT( underflow threshold )
Arguments
==========
NSIZES - INTEGER
The number of sizes of matrices to use. If it is zero,
DCHKHS does nothing. It must be at least zero.
Not modified.
NN - INTEGER array, dimension (NSIZES)
An array containing the sizes to be used for the matrices.
Zero values will be skipped. The values must be at least
zero.
Not modified.
NTYPES - INTEGER
The number of elements in DOTYPE. If it is zero, DCHKHS
does nothing. It must be at least zero. If it is MAXTYP+1
and NSIZES is 1, then an additional type, MAXTYP+1 is
defined, which is to use whatever matrix is in A. This
is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
DOTYPE(MAXTYP+1) is .TRUE. .
Not modified.
DOTYPE - LOGICAL array, dimension (NTYPES)
If DOTYPE(j) is .TRUE., then for each size in NN a
matrix of that size and of type j will be generated.
If NTYPES is smaller than the maximum number of types
defined (PARAMETER MAXTYP), then types NTYPES+1 through
MAXTYP will not be generated. If NTYPES is larger
than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
will be ignored.
Not modified.
ISEED - INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to DCHKHS to continue the same random number
sequence.
Modified.
THRESH - DOUBLE PRECISION
A test will count as "failed" if the "error", computed as
described above, exceeds THRESH. Note that the error
is scaled to be O(1), so THRESH should be a reasonably
small multiple of 1, e.g., 10 or 100. In particular,
it should not depend on the precision (single vs. double)
or the size of the matrix. It must be at least zero.
Not modified.
NOUNIT - INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.)
Not modified.
A - DOUBLE PRECISION array, dimension (LDA,max(NN))
Used to hold the matrix whose eigenvalues are to be
computed. On exit, A contains the last matrix actually
used.
Modified.
LDA - INTEGER
The leading dimension of A, H, T1 and T2. It must be at
least 1 and at least max( NN ).
Not modified.
H - DOUBLE PRECISION array, dimension (LDA,max(NN))
The upper hessenberg matrix computed by DGEHRD. On exit,
H contains the Hessenberg form of the matrix in A.
Modified.
T1 - DOUBLE PRECISION array, dimension (LDA,max(NN))
The Schur (="quasi-triangular") matrix computed by DHSEQR
if Z is computed. On exit, T1 contains the Schur form of
the matrix in A.
Modified.
T2 - DOUBLE PRECISION array, dimension (LDA,max(NN))
The Schur matrix computed by DHSEQR when Z is not computed.
This should be identical to T1.
Modified.
LDU - INTEGER
The leading dimension of U, Z, UZ and UU. It must be at
least 1 and at least max( NN ).
Not modified.
U - DOUBLE PRECISION array, dimension (LDU,max(NN))
The orthogonal matrix computed by DGEHRD.
Modified.
Z - DOUBLE PRECISION array, dimension (LDU,max(NN))
The orthogonal matrix computed by DHSEQR.
Modified.
UZ - DOUBLE PRECISION array, dimension (LDU,max(NN))
The product of U times Z.
Modified.
WR1 - DOUBLE PRECISION array, dimension (max(NN))
WI1 - DOUBLE PRECISION array, dimension (max(NN))
The real and imaginary parts of the eigenvalues of A,
as computed when Z is computed.
On exit, WR1 + WI1*i are the eigenvalues of the matrix in A.
Modified.
WR3 - DOUBLE PRECISION array, dimension (max(NN))
WI3 - DOUBLE PRECISION array, dimension (max(NN))
Like WR1, WI1, these arrays contain the eigenvalues of A,
but those computed when DHSEQR only computes the
eigenvalues, i.e., not the Schur vectors and no more of the
Schur form than is necessary for computing the
eigenvalues.
Modified.
EVECTL - DOUBLE PRECISION array, dimension (LDU,max(NN))
The (upper triangular) left eigenvector matrix for the
matrix in T1. For complex conjugate pairs, the real part
is stored in one row and the imaginary part in the next.
Modified.
EVEZTR - DOUBLE PRECISION array, dimension (LDU,max(NN))
The (upper triangular) right eigenvector matrix for the
matrix in T1. For complex conjugate pairs, the real part
is stored in one column and the imaginary part in the next.
Modified.
EVECTY - DOUBLE PRECISION array, dimension (LDU,max(NN))
The left eigenvector matrix for the
matrix in H. For complex conjugate pairs, the real part
is stored in one row and the imaginary part in the next.
Modified.
EVECTX - DOUBLE PRECISION array, dimension (LDU,max(NN))
The right eigenvector matrix for the
matrix in H. For complex conjugate pairs, the real part
is stored in one column and the imaginary part in the next.
Modified.
UU - DOUBLE PRECISION array, dimension (LDU,max(NN))
Details of the orthogonal matrix computed by DGEHRD.
Modified.
TAU - DOUBLE PRECISION array, dimension(max(NN))
Further details of the orthogonal matrix computed by DGEHRD.
Modified.
WORK - DOUBLE PRECISION array, dimension (NWORK)
Workspace.
Modified.
NWORK - INTEGER
The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2.
IWORK - INTEGER array, dimension (max(NN))
Workspace.
Modified.
SELECT - LOGICAL array, dimension (max(NN))
Workspace.
Modified.
RESULT - DOUBLE PRECISION array, dimension (14)
The values computed by the fourteen tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.
Modified.
INFO - INTEGER
If 0, then everything ran OK.
-1: NSIZES < 0
-2: Some NN(j) < 0
-3: NTYPES < 0
-6: THRESH < 0
-9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
-14: LDU < 1 or LDU < NMAX.
-28: NWORK too small.
If DLATMR, SLATMS, or SLATME returns an error code, the
absolute value of it is returned.
If 1, then DHSEQR could not find all the shifts.
If 2, then the EISPACK code (for small blocks) failed.
If >2, then 30*N iterations were not enough to find an
eigenvalue or to decompose the problem.
Modified.
-----------------------------------------------------------------------
Some Local Variables and Parameters:
---- ----- --------- --- ----------
ZERO, ONE Real 0 and 1.
MAXTYP The number of types defined.
MTEST The number of tests defined: care must be taken
that (1) the size of RESULT, (2) the number of
tests actually performed, and (3) MTEST agree.
NTEST The number of tests performed on this matrix
so far. This should be less than MTEST, and
equal to it by the last test. It will be less
if any of the routines being tested indicates
that it could not compute the matrices that
would be tested.
NMAX Largest value in NN.
NMATS The number of matrices generated so far.
NERRS The number of tests which have exceeded THRESH
so far (computed by DLAFTS).
COND, CONDS,
IMODE Values to be passed to the matrix generators.
ANORM Norm of A; passed to matrix generators.
OVFL, UNFL Overflow and underflow thresholds.
ULP, ULPINV Finest relative precision and its inverse.
RTOVFL, RTUNFL,
RTULP, RTULPI Square roots of the previous 4 values.
The following four arrays decode JTYPE:
KTYPE(j) The general type (1-10) for type "j".
KMODE(j) The MODE value to be passed to the matrix
generator for type "j".
KMAGN(j) The order of magnitude ( O(1),
O(overflow^(1/2) ), O(underflow^(1/2) )
KCONDS(j) Selects whether CONDS is to be 1 or
1/sqrt(ulp). (0 means irrelevant.)
=====================================================================
Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1 * 1;
t2 -= t2_offset;
t1_dim1 = *lda;
t1_offset = 1 + t1_dim1 * 1;
t1 -= t1_offset;
h_dim1 = *lda;
h_offset = 1 + h_dim1 * 1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
uu_dim1 = *ldu;
uu_offset = 1 + uu_dim1 * 1;
uu -= uu_offset;
evectx_dim1 = *ldu;
evectx_offset = 1 + evectx_dim1 * 1;
evectx -= evectx_offset;
evecty_dim1 = *ldu;
evecty_offset = 1 + evecty_dim1 * 1;
evecty -= evecty_offset;
evectr_dim1 = *ldu;
evectr_offset = 1 + evectr_dim1 * 1;
evectr -= evectr_offset;
evectl_dim1 = *ldu;
evectl_offset = 1 + evectl_dim1 * 1;
evectl -= evectl_offset;
uz_dim1 = *ldu;
uz_offset = 1 + uz_dim1 * 1;
uz -= uz_offset;
z_dim1 = *ldu;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
--wr1;
--wi1;
--wr3;
--wi3;
--tau;
--work;
--iwork;
--select;
--result;
/* Function Body
Check for errors */
ntestt = 0;
*info = 0;
badnn = FALSE_;
nmax = 0;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldu <= 1 || *ldu < nmax) {
*info = -14;
} else if ((nmax << 2) * nmax + 2 > *nwork) {
*info = -28;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DCHKHS", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
/* More important constants */
unfl = dlamch_("Safe minimum");
ovfl = dlamch_("Overflow");
dlabad_(&unfl, &ovfl);
ulp = dlamch_("Epsilon") * dlamch_("Base");
ulpinv = 1. / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
rtulp = sqrt(ulp);
rtulpi = 1. / rtulp;
/* Loop over sizes, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
if (n == 0) {
goto L270;
}
n1 = max(1,n);
aninv = 1. / (doublereal) n1;
if (*nsizes != 1) {
mtypes = min(21,*ntypes);
} else {
mtypes = min(22,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L260;
}
++nmats;
ntest = 0;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Initialize RESULT */
for (j = 1; j <= 14; ++j) {
result[j] = 0.;
/* L30: */
}
/* Compute "A"
Control parameters:
KMAGN KCONDS KMODE KTYPE
=1 O(1) 1 clustered 1 zero
=2 large large clustered 2 identity
=3 small exponential Jordan
=4 arithmetic diagonal, (w/ eigenvalues)
=5 random log symmetric, w/ eigenvalues
=6 random general, w/ eigenvalues
=7 random diagonal
=8 random symmetric
=9 random general
=10 random triangular */
if (mtypes > 21) {
goto L100;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.;
goto L70;
L50:
anorm = rtovfl * ulp * aninv;
goto L70;
L60:
anorm = rtunfl * n * ulpinv;
goto L70;
L70:
dlaset_("Full", lda, &n, &c_b18, &c_b18, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
/* Special Matrices */
if (itype == 1) {
/* Zero */
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
a_ref(jcol, jcol) = anorm;
/* L80: */
}
} else if (itype == 3) {
/* Jordan Block */
i__3 = n;
for (jcol = 1; jcol <= i__3; ++jcol) {
a_ref(jcol, jcol) = anorm;
if (jcol > 1) {
a_ref(jcol, jcol - 1) = 1.;
}
/* L90: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
dlatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond,
&anorm, &c__0, &c__0, "N", &a[a_offset], lda, &work[n
+ 1], &iinfo);
} else if (itype == 5) {
/* Symmetric, eigenvalues specified */
dlatms_(&n, &n, "S", &iseed[1], "S", &work[1], &imode, &cond,
&anorm, &n, &n, "N", &a[a_offset], lda, &work[n + 1],
&iinfo);
} else if (itype == 6) {
/* General, eigenvalues specified */
if (kconds[jtype - 1] == 1) {
conds = 1.;
} else if (kconds[jtype - 1] == 2) {
conds = rtulpi;
} else {
conds = 0.;
}
*(unsigned char *)&adumma[0] = ' ';
dlatme_(&n, "S", &iseed[1], &work[1], &imode, &cond, &c_b32,
adumma, "T", "T", "T", &work[n + 1], &c__4, &conds, &
n, &n, &anorm, &a[a_offset], lda, &work[(n << 1) + 1],
&iinfo);
} else if (itype == 7) {
/* Diagonal, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &c__0, &
c__0, &c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[
1], &iinfo);
} else if (itype == 8) {
/* Symmetric, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "S", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 9) {
/* General, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &n, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else if (itype == 10) {
/* Triangular, random eigenvalues */
dlatmr_(&n, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b32,
&c_b32, "T", "N", &work[n + 1], &c__1, &c_b32, &work[(
n << 1) + 1], &c__1, &c_b32, "N", idumma, &n, &c__0, &
c_b18, &anorm, "NO", &a[a_offset], lda, &iwork[1], &
iinfo);
} else {
iinfo = 1;
}
if (iinfo != 0) {
io___36.ciunit = *nounit;
s_wsfe(&io___36);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L100:
/* Call DGEHRD to compute H and U, do tests. */
dlacpy_(" ", &n, &n, &a[a_offset], lda, &h__[h_offset], lda);
ntest = 1;
ilo = 1;
ihi = n;
i__3 = *nwork - n;
dgehrd_(&n, &ilo, &ihi, &h__[h_offset], lda, &work[1], &work[n +
1], &i__3, &iinfo);
if (iinfo != 0) {
result[1] = ulpinv;
io___39.ciunit = *nounit;
s_wsfe(&io___39);
do_fio(&c__1, "DGEHRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
i__3 = n - 1;
for (j = 1; j <= i__3; ++j) {
uu_ref(j + 1, j) = 0.;
i__4 = n;
for (i__ = j + 2; i__ <= i__4; ++i__) {
u_ref(i__, j) = h___ref(i__, j);
uu_ref(i__, j) = h___ref(i__, j);
h___ref(i__, j) = 0.;
/* L110: */
}
/* L120: */
}
dcopy_(&n, &work[1], &c__1, &tau[1], &c__1);
i__3 = *nwork - n;
dorghr_(&n, &ilo, &ihi, &u[u_offset], ldu, &work[1], &work[n + 1],
&i__3, &iinfo);
ntest = 2;
dhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &h__[h_offset], lda, &
u[u_offset], ldu, &work[1], nwork, &result[1]);
/* Call DHSEQR to compute T1, T2 and Z, do tests.
Eigenvalues only (WR3,WI3) */
dlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
ntest = 3;
result[3] = ulpinv;
dhseqr_("E", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &wr3[1], &
wi3[1], &uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
do_fio(&c__1, "DHSEQR(E)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
if (iinfo <= n + 2) {
*info = abs(iinfo);
goto L250;
}
}
/* Eigenvalues (WR1,WI1) and Full Schur Form (T2) */
dlacpy_(" ", &n, &n, &h__[h_offset], lda, &t2[t2_offset], lda);
dhseqr_("S", "N", &n, &ilo, &ihi, &t2[t2_offset], lda, &wr1[1], &
wi1[1], &uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "DHSEQR(S)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
/* Eigenvalues (WR1,WI1), Schur Form (T1), and Schur vectors
(UZ) */
dlacpy_(" ", &n, &n, &h__[h_offset], lda, &t1[t1_offset], lda);
dlacpy_(" ", &n, &n, &u[u_offset], ldu, &uz[uz_offset], lda);
dhseqr_("S", "V", &n, &ilo, &ihi, &t1[t1_offset], lda, &wr1[1], &
wi1[1], &uz[uz_offset], ldu, &work[1], nwork, &iinfo);
if (iinfo != 0 && iinfo <= n + 2) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "DHSEQR(V)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
/* Compute Z = U' UZ */
dgemm_("T", "N", &n, &n, &n, &c_b32, &u[u_offset], ldu, &uz[
uz_offset], ldu, &c_b18, &z__[z_offset], ldu);
ntest = 8;
/* Do Tests 3: | H - Z T Z' | / ( |H| n ulp )
and 4: | I - Z Z' | / ( n ulp ) */
dhst01_(&n, &ilo, &ihi, &h__[h_offset], lda, &t1[t1_offset], lda,
&z__[z_offset], ldu, &work[1], nwork, &result[3]);
/* Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp )
and 6: | I - UZ (UZ)' | / ( n ulp ) */
dhst01_(&n, &ilo, &ihi, &a[a_offset], lda, &t1[t1_offset], lda, &
uz[uz_offset], ldu, &work[1], nwork, &result[5]);
/* Do Test 7: | T2 - T1 | / ( |T| n ulp ) */
dget10_(&n, &n, &t2[t2_offset], lda, &t1[t1_offset], lda, &work[1]
, &result[7]);
/* Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) */
temp1 = 0.;
temp2 = 0.;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX */
d__5 = temp1, d__6 = (d__1 = wr1[j], abs(d__1)) + (d__2 = wi1[
j], abs(d__2)), d__5 = max(d__5,d__6), d__6 = (d__3 =
wr3[j], abs(d__3)) + (d__4 = wi3[j], abs(d__4));
temp1 = max(d__5,d__6);
/* Computing MAX */
d__3 = temp2, d__4 = (d__1 = wr1[j] - wr3[j], abs(d__1)) + (
d__2 = wr1[j] - wr3[j], abs(d__2));
temp2 = max(d__3,d__4);
/* L130: */
}
/* Computing MAX */
d__1 = unfl, d__2 = ulp * max(temp1,temp2);
result[8] = temp2 / max(d__1,d__2);
/* Compute the Left and Right Eigenvectors of T
Compute the Right eigenvector Matrix: */
ntest = 9;
result[9] = ulpinv;
/* Select last max(N/4,1) real, max(N/4,1) complex eigenvectors */
nselc = 0;
nselr = 0;
j = n;
L140:
if (wi1[j] == 0.) {
/* Computing MAX */
i__3 = n / 4;
if (nselr < max(i__3,1)) {
++nselr;
select[j] = TRUE_;
} else {
select[j] = FALSE_;
}
--j;
} else {
/* Computing MAX */
i__3 = n / 4;
if (nselc < max(i__3,1)) {
++nselc;
select[j] = TRUE_;
select[j - 1] = FALSE_;
} else {
select[j] = FALSE_;
select[j - 1] = FALSE_;
}
j += -2;
}
if (j > 0) {
goto L140;
}
dtrevc_("Right", "All", &select[1], &n, &t1[t1_offset], lda,
dumma, ldu, &evectr[evectr_offset], ldu, &n, &in, &work[1]
, &iinfo);
if (iinfo != 0) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "DTREVC(R,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
/* Test 9: | TR - RW | / ( |T| |R| ulp ) */
dget22_("N", "N", "N", &n, &t1[t1_offset], lda, &evectr[
evectr_offset], ldu, &wr1[1], &wi1[1], &work[1], dumma);
result[9] = dumma[0];
if (dumma[1] > *thresh) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "DTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected right eigenvectors and confirm that
they agree with previous right eigenvectors */
dtrevc_("Right", "Some", &select[1], &n, &t1[t1_offset], lda,
dumma, ldu, &evectl[evectl_offset], ldu, &n, &in, &work[1]
, &iinfo);
if (iinfo != 0) {
io___52.ciunit = *nounit;
s_wsfe(&io___52);
do_fio(&c__1, "DTREVC(R,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j] && wi1[j] == 0.) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
if (evectr_ref(jj, j) != evectl_ref(jj, k)) {
match = FALSE_;
goto L180;
}
/* L150: */
}
++k;
} else if (select[j] && wi1[j] != 0.) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
if (evectr_ref(jj, j) != evectl_ref(jj, k) ||
evectr_ref(jj, j + 1) != evectl_ref(jj, k + 1)
) {
match = FALSE_;
goto L180;
}
/* L160: */
}
k += 2;
}
/* L170: */
}
L180:
if (! match) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "DTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute the Left eigenvector Matrix: */
ntest = 10;
result[10] = ulpinv;
dtrevc_("Left", "All", &select[1], &n, &t1[t1_offset], lda, &
evectl[evectl_offset], ldu, dumma, ldu, &n, &in, &work[1],
&iinfo);
if (iinfo != 0) {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
do_fio(&c__1, "DTREVC(L,A)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
/* Test 10: | LT - WL | / ( |T| |L| ulp ) */
dget22_("Trans", "N", "Conj", &n, &t1[t1_offset], lda, &evectl[
evectl_offset], ldu, &wr1[1], &wi1[1], &work[1], &dumma[2]
);
result[10] = dumma[2];
if (dumma[3] > *thresh) {
io___58.ciunit = *nounit;
s_wsfe(&io___58);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "DTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Compute selected left eigenvectors and confirm that
they agree with previous left eigenvectors */
dtrevc_("Left", "Some", &select[1], &n, &t1[t1_offset], lda, &
evectr[evectr_offset], ldu, dumma, ldu, &n, &in, &work[1],
&iinfo);
if (iinfo != 0) {
io___59.ciunit = *nounit;
s_wsfe(&io___59);
do_fio(&c__1, "DTREVC(L,S)", (ftnlen)11);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L250;
}
k = 1;
match = TRUE_;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
if (select[j] && wi1[j] == 0.) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
if (evectl_ref(jj, j) != evectr_ref(jj, k)) {
match = FALSE_;
goto L220;
}
/* L190: */
}
++k;
} else if (select[j] && wi1[j] != 0.) {
i__4 = n;
for (jj = 1; jj <= i__4; ++jj) {
if (evectl_ref(jj, j) != evectr_ref(jj, k) ||
evectl_ref(jj, j + 1) != evectr_ref(jj, k + 1)
) {
match = FALSE_;
goto L220;
}
/* L200: */
}
k += 2;
}
/* L210: */
}
L220:
if (! match) {
io___60.ciunit = *nounit;
s_wsfe(&io___60);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "DTREVC", (ftnlen)6);
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
}
/* Call DHSEIN for Right eigenvectors of H, do test 11 */
ntest = 11;
result[11] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L230: */
}
dhsein_("Right", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &wr3[1], &wi3[1], dumma, ldu, &evectx[evectx_offset],
ldu, &n1, &in, &work[1], &iwork[1], &iwork[1], &iinfo);
if (iinfo != 0) {
io___61.ciunit = *nounit;
s_wsfe(&io___61);
do_fio(&c__1, "DHSEIN(R)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L250;
}
} else {
/* Test 11: | HX - XW | / ( |H| |X| ulp )
(from inverse iteration) */
dget22_("N", "N", "N", &n, &h__[h_offset], lda, &evectx[
evectx_offset], ldu, &wr3[1], &wi3[1], &work[1],
dumma);
if (dumma[0] < ulpinv) {
result[11] = dumma[0] * aninv;
}
if (dumma[1] > *thresh) {
io___62.ciunit = *nounit;
s_wsfe(&io___62);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "DHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call DHSEIN for Left eigenvectors of H, do test 12 */
ntest = 12;
result[12] = ulpinv;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
select[j] = TRUE_;
/* L240: */
}
dhsein_("Left", "Qr", "Ninitv", &select[1], &n, &h__[h_offset],
lda, &wr3[1], &wi3[1], &evecty[evecty_offset], ldu, dumma,
ldu, &n1, &in, &work[1], &iwork[1], &iwork[1], &iinfo);
if (iinfo != 0) {
io___63.ciunit = *nounit;
s_wsfe(&io___63);
do_fio(&c__1, "DHSEIN(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L250;
}
} else {
/* Test 12: | YH - WY | / ( |H| |Y| ulp )
(from inverse iteration) */
dget22_("C", "N", "C", &n, &h__[h_offset], lda, &evecty[
evecty_offset], ldu, &wr3[1], &wi3[1], &work[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[12] = dumma[2] * aninv;
}
if (dumma[3] > *thresh) {
io___64.ciunit = *nounit;
s_wsfe(&io___64);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "DHSEIN", (ftnlen)6);
do_fio(&c__1, (char *)&dumma[3], (ftnlen)sizeof(
doublereal));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
}
}
/* Call DORMHR for Right eigenvectors of A, do test 13 */
ntest = 13;
result[13] = ulpinv;
dormhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evectx[evectx_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___65.ciunit = *nounit;
s_wsfe(&io___65);
do_fio(&c__1, "DORMHR(R)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L250;
}
} else {
/* Test 13: | AX - XW | / ( |A| |X| ulp )
(from inverse iteration) */
dget22_("N", "N", "N", &n, &a[a_offset], lda, &evectx[
evectx_offset], ldu, &wr3[1], &wi3[1], &work[1],
dumma);
if (dumma[0] < ulpinv) {
result[13] = dumma[0] * aninv;
}
}
/* Call DORMHR for Left eigenvectors of A, do test 14 */
ntest = 14;
result[14] = ulpinv;
dormhr_("Left", "No transpose", &n, &n, &ilo, &ihi, &uu[uu_offset]
, ldu, &tau[1], &evecty[evecty_offset], ldu, &work[1],
nwork, &iinfo);
if (iinfo != 0) {
io___66.ciunit = *nounit;
s_wsfe(&io___66);
do_fio(&c__1, "DORMHR(L)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
goto L250;
}
} else {
/* Test 14: | YA - WY | / ( |A| |Y| ulp )
(from inverse iteration) */
dget22_("C", "N", "C", &n, &a[a_offset], lda, &evecty[
evecty_offset], ldu, &wr3[1], &wi3[1], &work[1], &
dumma[2]);
if (dumma[2] < ulpinv) {
result[14] = dumma[2] * aninv;
}
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L250:
ntestt += ntest;
dlafts_("DHS", &n, &n, &jtype, &ntest, &result[1], ioldsd, thresh,
nounit, &nerrs);
L260:
;
}
L270:
;
}
/* Summary */
dlasum_("DHS", nounit, &nerrs, &ntestt);
return 0;
/* End of DCHKHS */
} /* dchkhs_ */
/* Subroutine */ int dget38_(doublereal *rmax, integer *lmax, integer *ninfo,
integer *knt, integer *nin)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2;
/* Local variables */
integer i__, j, m, n;
doublereal q[400] /* was [20][20] */, s, t[400] /* was [20][20] */, v,
wi[20], wr[20], val[3], eps, sep, sin__, tol, tmp[400] /*
was [20][20] */;
integer ndim, iscl, info, kmin, itmp, ipnt[20];
doublereal vmax, qsav[400] /* was [20][20] */, tsav[400] /* was [20][
20] */, tnrm, qtmp[400] /* was [20][20] */, work[1200], stmp,
vmul, ttmp[400] /* was [20][20] */, tsav1[400] /* was [20][
20] */;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *), dhst01_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *);
doublereal sepin;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal vimin, tolin, vrmin;
integer iwork[400];
doublereal witmp[20], wrtmp[20];
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *);
integer iselec[20];
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *);
logical select[20];
doublereal bignum;
extern /* Subroutine */ int dorghr_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dhseqr_(char *, char *, integer *, integer *, integer
*, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dtrsen_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, integer *, integer *, integer *);
doublereal septmp, smlnum, result[2];
/* Fortran I/O blocks */
static cilist io___5 = { 0, 0, 0, 0, 0 };
static cilist io___8 = { 0, 0, 0, 0, 0 };
static cilist io___11 = { 0, 0, 0, 0, 0 };
static cilist io___14 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGET38 tests DTRSEN, a routine for estimating condition numbers of a */
/* cluster of eigenvalues and/or its associated right invariant subspace */
/* The test matrices are read from a file with logical unit number NIN. */
/* Arguments */
/* ========== */
/* RMAX (output) DOUBLE PRECISION array, dimension (3) */
/* Values of the largest test ratios. */
/* RMAX(1) = largest residuals from DHST01 or comparing */
/* different calls to DTRSEN */
/* RMAX(2) = largest error in reciprocal condition */
/* numbers taking their conditioning into account */
/* RMAX(3) = largest error in reciprocal condition */
/* numbers not taking their conditioning into */
/* account (may be larger than RMAX(2)) */
/* LMAX (output) INTEGER array, dimension (3) */
/* LMAX(i) is example number where largest test ratio */
/* RMAX(i) is achieved. Also: */
/* If DGEHRD returns INFO nonzero on example i, LMAX(1)=i */
/* If DHSEQR returns INFO nonzero on example i, LMAX(2)=i */
/* If DTRSEN returns INFO nonzero on example i, LMAX(3)=i */
/* NINFO (output) INTEGER array, dimension (3) */
/* NINFO(1) = No. of times DGEHRD returned INFO nonzero */
/* NINFO(2) = No. of times DHSEQR returned INFO nonzero */
/* NINFO(3) = No. of times DTRSEN returned INFO nonzero */
/* KNT (output) INTEGER */
/* Total number of examples tested. */
/* NIN (input) INTEGER */
/* Input logical unit number. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--ninfo;
--lmax;
--rmax;
/* Function Body */
eps = dlamch_("P");
smlnum = dlamch_("S") / eps;
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* EPSIN = 2**(-24) = precision to which input data computed */
eps = max(eps,5.9605e-8);
rmax[1] = 0.;
rmax[2] = 0.;
rmax[3] = 0.;
lmax[1] = 0;
lmax[2] = 0;
lmax[3] = 0;
*knt = 0;
ninfo[1] = 0;
ninfo[2] = 0;
ninfo[3] = 0;
val[0] = sqrt(smlnum);
val[1] = 1.;
val[2] = sqrt(sqrt(bignum));
/* Read input data until N=0. Assume input eigenvalues are sorted */
/* lexicographically (increasing by real part, then decreasing by */
/* imaginary part) */
L10:
io___5.ciunit = *nin;
s_rsle(&io___5);
do_lio(&c__3, &c__1, (char *)&n, (ftnlen)sizeof(integer));
do_lio(&c__3, &c__1, (char *)&ndim, (ftnlen)sizeof(integer));
e_rsle();
if (n == 0) {
return 0;
}
io___8.ciunit = *nin;
s_rsle(&io___8);
i__1 = ndim;
for (i__ = 1; i__ <= i__1; ++i__) {
do_lio(&c__3, &c__1, (char *)&iselec[i__ - 1], (ftnlen)sizeof(integer)
);
}
e_rsle();
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___11.ciunit = *nin;
s_rsle(&io___11);
i__2 = n;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__5, &c__1, (char *)&tmp[i__ + j * 20 - 21], (ftnlen)
sizeof(doublereal));
}
e_rsle();
/* L20: */
}
io___14.ciunit = *nin;
s_rsle(&io___14);
do_lio(&c__5, &c__1, (char *)&sin__, (ftnlen)sizeof(doublereal));
do_lio(&c__5, &c__1, (char *)&sepin, (ftnlen)sizeof(doublereal));
e_rsle();
tnrm = dlange_("M", &n, &n, tmp, &c__20, work);
for (iscl = 1; iscl <= 3; ++iscl) {
/* Scale input matrix */
++(*knt);
dlacpy_("F", &n, &n, tmp, &c__20, t, &c__20);
vmul = val[iscl - 1];
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
dscal_(&n, &vmul, &t[i__ * 20 - 20], &c__1);
/* L30: */
}
if (tnrm == 0.) {
vmul = 1.;
}
dlacpy_("F", &n, &n, t, &c__20, tsav, &c__20);
/* Compute Schur form */
i__1 = 1200 - n;
dgehrd_(&n, &c__1, &n, t, &c__20, work, &work[n], &i__1, &info);
if (info != 0) {
lmax[1] = *knt;
++ninfo[1];
goto L160;
}
/* Generate orthogonal matrix */
dlacpy_("L", &n, &n, t, &c__20, q, &c__20);
i__1 = 1200 - n;
dorghr_(&n, &c__1, &n, q, &c__20, work, &work[n], &i__1, &info);
/* Compute Schur form */
dhseqr_("S", "V", &n, &c__1, &n, t, &c__20, wr, wi, q, &c__20, work, &
c__1200, &info);
if (info != 0) {
lmax[2] = *knt;
++ninfo[2];
goto L160;
}
/* Sort, select eigenvalues */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
ipnt[i__ - 1] = i__;
select[i__ - 1] = FALSE_;
/* L40: */
}
dcopy_(&n, wr, &c__1, wrtmp, &c__1);
dcopy_(&n, wi, &c__1, witmp, &c__1);
i__1 = n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
kmin = i__;
vrmin = wrtmp[i__ - 1];
vimin = witmp[i__ - 1];
i__2 = n;
for (j = i__ + 1; j <= i__2; ++j) {
if (wrtmp[j - 1] < vrmin) {
kmin = j;
vrmin = wrtmp[j - 1];
vimin = witmp[j - 1];
}
/* L50: */
}
wrtmp[kmin - 1] = wrtmp[i__ - 1];
witmp[kmin - 1] = witmp[i__ - 1];
wrtmp[i__ - 1] = vrmin;
witmp[i__ - 1] = vimin;
itmp = ipnt[i__ - 1];
ipnt[i__ - 1] = ipnt[kmin - 1];
ipnt[kmin - 1] = itmp;
/* L60: */
}
i__1 = ndim;
for (i__ = 1; i__ <= i__1; ++i__) {
select[ipnt[iselec[i__ - 1] - 1] - 1] = TRUE_;
/* L70: */
}
/* Compute condition numbers */
dlacpy_("F", &n, &n, q, &c__20, qsav, &c__20);
dlacpy_("F", &n, &n, t, &c__20, tsav1, &c__20);
dtrsen_("B", "V", select, &n, t, &c__20, q, &c__20, wrtmp, witmp, &m,
&s, &sep, work, &c__1200, iwork, &c__400, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L160;
}
septmp = sep / vmul;
stmp = s;
/* Compute residuals */
dhst01_(&n, &c__1, &n, tsav, &c__20, t, &c__20, q, &c__20, work, &
c__1200, result);
vmax = max(result[0],result[1]);
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
/* Compare condition number for eigenvalue cluster */
/* taking its condition number into account */
/* Computing MAX */
d__1 = (doublereal) n * 2. * eps * tnrm;
v = max(d__1,smlnum);
if (tnrm == 0.) {
v = 1.;
}
if (v > septmp) {
tol = 1.;
} else {
tol = v / septmp;
}
if (v > sepin) {
tolin = 1.;
} else {
tolin = v / sepin;
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (sin__ - tolin) > stmp + tol) {
vmax = 1. / eps;
} else if (sin__ - tolin > stmp + tol) {
vmax = (sin__ - tolin) / (stmp + tol);
} else if (sin__ + tolin < eps * (stmp - tol)) {
vmax = 1. / eps;
} else if (sin__ + tolin < stmp - tol) {
vmax = (stmp - tol) / (sin__ + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* Compare condition numbers for invariant subspace */
/* taking its condition number into account */
if (v > septmp * stmp) {
tol = septmp;
} else {
tol = v / stmp;
}
if (v > sepin * sin__) {
tolin = sepin;
} else {
tolin = v / sin__;
}
/* Computing MAX */
d__1 = tol, d__2 = smlnum / eps;
tol = max(d__1,d__2);
/* Computing MAX */
d__1 = tolin, d__2 = smlnum / eps;
tolin = max(d__1,d__2);
if (eps * (sepin - tolin) > septmp + tol) {
vmax = 1. / eps;
} else if (sepin - tolin > septmp + tol) {
vmax = (sepin - tolin) / (septmp + tol);
} else if (sepin + tolin < eps * (septmp - tol)) {
vmax = 1. / eps;
} else if (sepin + tolin < septmp - tol) {
vmax = (septmp - tol) / (sepin + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* Compare condition number for eigenvalue cluster */
/* without taking its condition number into account */
if (sin__ <= (doublereal) (n << 1) * eps && stmp <= (doublereal) (n <<
1) * eps) {
vmax = 1.;
} else if (eps * sin__ > stmp) {
vmax = 1. / eps;
} else if (sin__ > stmp) {
vmax = sin__ / stmp;
} else if (sin__ < eps * stmp) {
vmax = 1. / eps;
} else if (sin__ < stmp) {
vmax = stmp / sin__;
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* Compare condition numbers for invariant subspace */
/* without taking its condition number into account */
if (sepin <= v && septmp <= v) {
vmax = 1.;
} else if (eps * sepin > septmp) {
vmax = 1. / eps;
} else if (sepin > septmp) {
vmax = sepin / septmp;
} else if (sepin < eps * septmp) {
vmax = 1. / eps;
} else if (sepin < septmp) {
vmax = septmp / sepin;
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* Compute eigenvalue condition number only and compare */
/* Update Q */
vmax = 0.;
dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20);
dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20);
septmp = -1.;
stmp = -1.;
dtrsen_("E", "V", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp,
witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, &
info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L160;
}
if (s != stmp) {
vmax = 1. / eps;
}
if (-1. != septmp) {
vmax = 1. / eps;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
if (qtmp[i__ + j * 20 - 21] != q[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
/* L80: */
}
/* L90: */
}
/* Compute invariant subspace condition number only and compare */
/* Update Q */
dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20);
dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20);
septmp = -1.;
stmp = -1.;
dtrsen_("V", "V", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp,
witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, &
info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L160;
}
if (-1. != stmp) {
vmax = 1. / eps;
}
if (sep != septmp) {
vmax = 1. / eps;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
if (qtmp[i__ + j * 20 - 21] != q[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
/* L100: */
}
/* L110: */
}
/* Compute eigenvalue condition number only and compare */
/* Do not update Q */
dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20);
dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20);
septmp = -1.;
stmp = -1.;
dtrsen_("E", "N", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp,
witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, &
info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L160;
}
if (s != stmp) {
vmax = 1. / eps;
}
if (-1. != septmp) {
vmax = 1. / eps;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
if (qtmp[i__ + j * 20 - 21] != qsav[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
/* L120: */
}
/* L130: */
}
/* Compute invariant subspace condition number only and compare */
/* Do not update Q */
dlacpy_("F", &n, &n, tsav1, &c__20, ttmp, &c__20);
dlacpy_("F", &n, &n, qsav, &c__20, qtmp, &c__20);
septmp = -1.;
stmp = -1.;
dtrsen_("V", "N", select, &n, ttmp, &c__20, qtmp, &c__20, wrtmp,
witmp, &m, &stmp, &septmp, work, &c__1200, iwork, &c__400, &
info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L160;
}
if (-1. != stmp) {
vmax = 1. / eps;
}
if (sep != septmp) {
vmax = 1. / eps;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = n;
for (j = 1; j <= i__2; ++j) {
if (ttmp[i__ + j * 20 - 21] != t[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
if (qtmp[i__ + j * 20 - 21] != qsav[i__ + j * 20 - 21]) {
vmax = 1. / eps;
}
/* L140: */
}
/* L150: */
}
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
L160:
;
}
goto L10;
/* End of DGET38 */
} /* dget38_ */
