inline void decomr(double fac1,MatrixReal& Jac)
{
if(calhes)
{
int ilo=1,ihi=n,lda=n,info;
int k=-1;
//find the optimum size for array work/
int nn=n;
dgehrd_(&nn,&ilo,&ihi,&Jac,&lda,tau,work,&k,&info);
k=work[0];
if(lwork<k)
{
if(work!=0) delete[] work;
lwork=k;
work=new double[lwork];
}
dgehrd_(&nn,&ilo,&ihi,&Jac,&lda,tau,work,&k,&info);
if(info!=0)
throw OdesException("odes::Matrices::Matrices, decomr: info=",
info);
calhes=false;
}
E1.equal_minus(Jac);
E1.addDiag(fac1);
int info=dech<n>(E1,ipr);
if(info!=0)
throw OdesException("odes::Matrices::Matrices, decomr (dech): ",
info);
}
/* 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 derrhs_(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)";
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
doublereal a[9] /* was [3][3] */, c__[9] /* was [3][3] */;
integer i__, j, m;
doublereal s[3], w[28];
char c2[2];
doublereal wi[3];
integer nt;
doublereal vl[9] /* was [3][3] */, vr[9] /* was [3][3] */, wr[3];
integer ihi, ilo;
logical sel[3];
doublereal tau[3];
integer info;
extern /* Subroutine */ int dgebak_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, integer *,
integer *), dgebal_(char *, integer *, doublereal
*, integer *, integer *, integer *, doublereal *, integer *), dgehrd_(integer *, integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
integer ifaill[3], ifailr[3];
extern /* Subroutine */ int dhsein_(char *, char *, char *, logical *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, integer *, integer *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int chkxer_(char *, integer *, integer *, logical
*, logical *), 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 *), dtrevc_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *), dormhr_(char *, char *, integer *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, 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 */
/* ======= */
/* DERRHS tests the error exits for DGEBAK, SGEBAL, SGEHRD, DORGHR, */
/* DORMHR, DHSEQR, SHSEIN, and DTREVC. */
/* 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__) {
a[i__ + j * 3 - 4] = 1. / (doublereal) (i__ + j);
/* L10: */
}
wi[j - 1] = (doublereal) j;
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")) {
/* DGEBAL */
s_copy(srnamc_1.srnamt, "DGEBAL", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dgebal_("/", &c__0, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("DGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgebal_("N", &c_n1, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("DGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgebal_("N", &c__2, a, &c__1, &ilo, &ihi, s, &info);
chkxer_("DGEBAL", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 3;
/* DGEBAK */
s_copy(srnamc_1.srnamt, "DGEBAK", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dgebak_("/", "R", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgebak_("N", "/", &c__0, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgebak_("N", "R", &c_n1, &c__1, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgebak_("N", "R", &c__0, &c__0, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dgebak_("N", "R", &c__0, &c__2, &c__0, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgebak_("N", "R", &c__2, &c__2, &c__1, s, &c__0, a, &c__2, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgebak_("N", "R", &c__0, &c__1, &c__1, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dgebak_("N", "R", &c__0, &c__1, &c__0, s, &c_n1, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
dgebak_("N", "R", &c__2, &c__1, &c__2, s, &c__0, a, &c__1, &info);
chkxer_("DGEBAK", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* DGEHRD */
s_copy(srnamc_1.srnamt, "DGEHRD", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dgehrd_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgehrd_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dgehrd_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgehrd_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dgehrd_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dgehrd_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__2, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dgehrd_(&c__2, &c__1, &c__2, a, &c__2, tau, w, &c__1, &info);
chkxer_("DGEHRD", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
/* DORGHR */
s_copy(srnamc_1.srnamt, "DORGHR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dorghr_(&c_n1, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorghr_(&c__0, &c__0, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dorghr_(&c__0, &c__2, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorghr_(&c__1, &c__1, &c__0, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dorghr_(&c__0, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dorghr_(&c__2, &c__1, &c__1, a, &c__1, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dorghr_(&c__3, &c__1, &c__3, a, &c__3, tau, w, &c__1, &info);
chkxer_("DORGHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 7;
/* DORMHR */
s_copy(srnamc_1.srnamt, "DORMHR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dormhr_("/", "N", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dormhr_("L", "/", &c__0, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dormhr_("L", "N", &c_n1, &c__0, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dormhr_("L", "N", &c__0, &c_n1, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormhr_("L", "N", &c__0, &c__0, &c__0, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormhr_("L", "N", &c__0, &c__0, &c__2, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormhr_("L", "N", &c__1, &c__2, &c__2, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__2, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dormhr_("R", "N", &c__2, &c__1, &c__2, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__2, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dormhr_("L", "N", &c__1, &c__1, &c__1, &c__0, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dormhr_("L", "N", &c__0, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dormhr_("R", "N", &c__1, &c__0, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dormhr_("R", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dormhr_("L", "N", &c__2, &c__1, &c__1, &c__1, a, &c__2, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dormhr_("L", "N", &c__1, &c__2, &c__1, &c__1, a, &c__1, tau, c__, &
c__1, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dormhr_("R", "N", &c__2, &c__1, &c__1, &c__1, a, &c__1, tau, c__, &
c__2, w, &c__1, &info);
chkxer_("DORMHR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 16;
/* DHSEQR */
s_copy(srnamc_1.srnamt, "DHSEQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dhseqr_("/", "N", &c__0, &c__1, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dhseqr_("E", "/", &c__0, &c__1, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dhseqr_("E", "N", &c_n1, &c__1, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dhseqr_("E", "N", &c__0, &c__0, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dhseqr_("E", "N", &c__0, &c__2, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dhseqr_("E", "N", &c__1, &c__1, &c__0, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dhseqr_("E", "N", &c__1, &c__1, &c__2, a, &c__1, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dhseqr_("E", "N", &c__2, &c__1, &c__2, a, &c__1, wr, wi, c__, &c__2,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dhseqr_("E", "V", &c__2, &c__1, &c__2, a, &c__2, wr, wi, c__, &c__1,
w, &c__1, &info);
chkxer_("DHSEQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 9;
/* DHSEIN */
s_copy(srnamc_1.srnamt, "DHSEIN", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dhsein_("/", "N", "N", sel, &c__0, a, &c__1, wr, wi, vl, &c__1, vr, &
c__1, &c__0, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dhsein_("R", "/", "N", sel, &c__0, a, &c__1, wr, wi, vl, &c__1, vr, &
c__1, &c__0, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
dhsein_("R", "N", "/", sel, &c__0, a, &c__1, wr, wi, vl, &c__1, vr, &
c__1, &c__0, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
dhsein_("R", "N", "N", sel, &c_n1, a, &c__1, wr, wi, vl, &c__1, vr, &
c__1, &c__0, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
dhsein_("R", "N", "N", sel, &c__2, a, &c__1, wr, wi, vl, &c__1, vr, &
c__2, &c__4, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dhsein_("L", "N", "N", sel, &c__2, a, &c__2, wr, wi, vl, &c__1, vr, &
c__1, &c__4, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 13;
dhsein_("R", "N", "N", sel, &c__2, a, &c__2, wr, wi, vl, &c__1, vr, &
c__1, &c__4, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
dhsein_("R", "N", "N", sel, &c__2, a, &c__2, wr, wi, vl, &c__1, vr, &
c__2, &c__1, &m, w, ifaill, ifailr, &info);
chkxer_("DHSEIN", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
nt += 8;
/* DTREVC */
s_copy(srnamc_1.srnamt, "DTREVC", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
dtrevc_("/", "A", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
dtrevc_("L", "/", sel, &c__0, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
dtrevc_("L", "A", sel, &c_n1, a, &c__1, vl, &c__1, vr, &c__1, &c__0, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
dtrevc_("L", "A", sel, &c__2, a, &c__1, vl, &c__2, vr, &c__1, &c__4, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
dtrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
dtrevc_("R", "A", sel, &c__2, a, &c__2, vl, &c__1, vr, &c__1, &c__4, &
m, w, &info);
chkxer_("DTREVC", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 11;
dtrevc_("L", "A", sel, &c__2, a, &c__2, vl, &c__2, vr, &c__1, &c__1, &
m, w, &info);
chkxer_("DTREVC", &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 DERRHS */
} /* derrhs_ */
/* Subroutine */ int dgeev_(char *jobvl, char *jobvr, integer *n, doublereal *
a, integer *lda, doublereal *wr, doublereal *wi, doublereal *vl,
integer *ldvl, doublereal *vr, integer *ldvr, doublereal *work,
integer *lwork, 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;
/* Local variables */
integer i__, k;
doublereal r__, cs, sn;
integer ihi;
doublereal scl;
integer ilo;
doublereal dum[1], eps;
integer ibal;
char side[1];
doublereal anrm;
integer ierr, itau;
integer iwrk, nout;
logical scalea;
doublereal cscale;
logical select[1];
doublereal bignum;
integer minwrk, maxwrk;
logical wantvl;
doublereal smlnum;
integer hswork;
logical lquery, wantvr;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* DGEEV computes for an N-by-N real nonsymmetric matrix A, the */
/* eigenvalues and, optionally, the left and/or right eigenvectors. */
/* 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. */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of A are computed. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* WR and WI contain the real and imaginary parts, */
/* respectively, of the computed eigenvalues. Complex */
/* conjugate pairs of eigenvalues appear consecutively */
/* with the eigenvalue having the positive imaginary part */
/* first. */
/* VL (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is real, then u(j) = VL(:,j), */
/* the j-th column of VL. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and */
/* u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is real, then v(j) = VR(:,j), */
/* the j-th column of VR. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and */
/* v(j+1) = VR(:,j) - i*VR(:,j+1). */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; if */
/* JOBVR = 'V', LDVR >= N. */
/* WORK (workspace/output) DOUBLE PRECISION 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. LWORK >= max(1,3*N), and */
/* if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*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. */
/* 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 have been computed; */
/* elements i+1:N of WR and WI contain eigenvalues which */
/* have converged. */
/* ===================================================================== */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--wr;
--wi;
vl_dim1 = *ldvl;
vl_offset = 1 + vl_dim1;
vl -= vl_offset;
vr_dim1 = *ldvr;
vr_offset = 1 + vr_dim1;
vr -= vr_offset;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvl = lsame_(jobvl, "V");
wantvr = lsame_(jobvr, "V");
if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -1;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -9;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -11;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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 << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1,
n, &c__0);
if (wantvl) {
minwrk = *n << 2;
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"DORGHR", " ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = *
n + hswork;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 2;
maxwrk = max(i__1,i__2);
} else if (wantvr) {
minwrk = *n << 2;
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"DORGHR", " ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = *
n + hswork;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 2;
maxwrk = max(i__1,i__2);
} else {
minwrk = *n * 3;
dhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
hswork = (integer) work[1];
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = *
n + hswork;
maxwrk = max(i__1,i__2);
}
maxwrk = max(maxwrk,minwrk);
}
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEEV ", &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] */
anrm = dlange_("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) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix */
/* (Workspace: need N) */
ibal = 1;
dgebal_("B", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
itau = ibal + *n;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
dgehrd_(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';
dlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate orthogonal matrix in VL */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, &ilo, &ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[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';
dlacpy_("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';
dlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate orthogonal matrix in VR */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, &ilo, &ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk],
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &
vr[vr_offset], ldvr, &work[iwrk], &i__1, info);
} else {
/* Compute eigenvalues only */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("E", "N", n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[1], &
vr[vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from DHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (Workspace: need 4*N) */
dtrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
/* (Workspace: need N) */
dgebak_("B", "L", n, &ilo, &ihi, &work[ibal], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
d__2 = vl[k + (i__ + 1) * vl_dim1];
work[iwrk + k - 1] = d__1 * d__1 + d__2 * d__2;
}
k = idamax_(n, &work[iwrk], &c__1);
dlartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1],
&cs, &sn, &r__);
drot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) *
vl_dim1 + 1], &c__1, &cs, &sn);
vl[k + (i__ + 1) * vl_dim1] = 0.;
}
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
/* (Workspace: need N) */
dgebak_("B", "R", n, &ilo, &ihi, &work[ibal], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
d__2 = vr[k + (i__ + 1) * vr_dim1];
work[iwrk + k - 1] = d__1 * d__1 + d__2 * d__2;
}
k = idamax_(n, &work[iwrk], &c__1);
dlartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
&cs, &sn, &r__);
drot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) *
vr_dim1 + 1], &c__1, &cs, &sn);
vr[k + (i__ + 1) * vr_dim1] = 0.;
}
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info +
1], &i__2, &ierr);
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*info +
1], &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1],
n, &ierr);
i__1 = ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1],
n, &ierr);
}
}
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGEEV */
} /* dgeev_ */
/* Subroutine */ int dgeev_(char *jobvl, char *jobvr, integer *n, doublereal *
a, integer *lda, doublereal *wr, doublereal *wi, doublereal *vl,
integer *ldvl, doublereal *vr, integer *ldvr, doublereal *work,
integer *lwork, 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
=======
DGEEV computes for an N-by-N real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
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.
Arguments
=========
JOBVL (input) CHARACTER*1
= 'N': left eigenvectors of A are not computed;
= 'V': left eigenvectors of A are computed.
JOBVR (input) CHARACTER*1
= 'N': right eigenvectors of A are not computed;
= 'V': right eigenvectors of A are computed.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
WR (output) DOUBLE PRECISION array, dimension (N)
WI (output) DOUBLE PRECISION array, dimension (N)
WR and WI contain the real and imaginary parts,
respectively, of the computed eigenvalues. Complex
conjugate pairs of eigenvalues appear consecutively
with the eigenvalue having the positive imaginary part
first.
VL (output) DOUBLE PRECISION 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.
If the j-th eigenvalue is real, then u(j) = VL(:,j),
the j-th column of VL.
If the j-th and (j+1)-st eigenvalues form a complex
conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
u(j+1) = VL(:,j) - i*VL(:,j+1).
LDVL (input) INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = 'V', LDVL >= N.
VR (output) DOUBLE PRECISION 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.
If the j-th eigenvalue is real, then v(j) = VR(:,j),
the j-th column of VR.
If the j-th and (j+1)-st eigenvalues form a complex
conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
v(j+1) = VR(:,j) - i*VR(:,j+1).
LDVR (input) INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = 'V', LDVR >= N.
WORK (workspace/output) DOUBLE PRECISION 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(1,3*N), and
if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. For good
performance, LWORK must generally be larger.
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 have been computed;
elements i+1:N of WR and WI 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;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer ibal;
static char side[1];
static integer maxb;
static doublereal anrm;
static integer ierr, itau;
extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
doublereal *, integer *, doublereal *, doublereal *);
static integer iwrk, nout;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static integer i, k;
static doublereal r;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
extern logical lsame_(char *, char *);
extern doublereal dlapy2_(doublereal *, doublereal *);
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebak_(
char *, char *, integer *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *),
dgebal_(char *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, integer *);
static doublereal cs;
static logical scalea;
extern doublereal dlamch_(char *);
static doublereal cscale;
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *);
static doublereal sn;
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlartg_(doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *), xerbla_(char *, integer *);
static logical select[1];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static 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 *), dtrevc_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *);
static integer minwrk, maxwrk;
static logical wantvl;
static doublereal smlnum;
static integer hswork;
static logical wantvr;
static integer ihi;
static doublereal scl;
static integer ilo;
static doublereal dum[1], eps;
#define DUM(I) dum[(I)]
#define WR(I) wr[(I)-1]
#define WI(I) wi[(I)-1]
#define WORK(I) work[(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");
if (! wantvl && ! lsame_(jobvl, "N")) {
*info = -1;
} else if (! wantvr && ! lsame_(jobvr, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
} else if (*ldvl < 1 || wantvl && *ldvl < *n) {
*info = -9;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -11;
}
/* 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.
NB refers to the optimal block size for the immediately
following subroutine, as returned by ILAENV.
HSWORK refers to the workspace preferred by DHSEQR, as
calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
the worst case.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1, n, &
c__0, 6L, 1L);
if (! wantvl && ! wantvr) {
/* Computing MAX */
i__1 = 1, i__2 = *n * 3;
minwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "DHSEQR", "EN", 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, "DHSEQR", "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 = maxwrk, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = *n +
hswork;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = 1, i__2 = *n << 2;
minwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "DOR"
"GHR", " ", n, &c__1, n, &c_n1, 6L, 1L);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = ilaenv_(&c__8, "DHSEQR", "SV", 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, "DHSEQR", "SV", 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 = maxwrk, i__2 = *n + 1, i__1 = max(i__1,i__2), i__2 = *n +
hswork;
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n << 2;
maxwrk = max(i__1,i__2);
}
WORK(1) = (doublereal) maxwrk;
}
if (*lwork < minwrk) {
*info = -13;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEEV ", &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] */
anrm = dlange_("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) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &A(1,1), lda, &
ierr);
}
/* Balance the matrix
(Workspace: need N) */
ibal = 1;
dgebal_("B", n, &A(1,1), lda, &ilo, &ihi, &WORK(ibal), &ierr);
/* Reduce to upper Hessenberg form
(Workspace: need 3*N, prefer 2*N+N*NB) */
itau = ibal + *n;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
dgehrd_(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';
dlacpy_("L", n, n, &A(1,1), lda, &VL(1,1), ldvl);
/* Generate orthogonal matrix in VL
(Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, &ilo, &ihi, &VL(1,1), ldvl, &WORK(itau), &WORK(iwrk),
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL
(Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, &ilo, &ihi, &A(1,1), lda, &WR(1), &WI(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';
dlacpy_("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';
dlacpy_("L", n, n, &A(1,1), lda, &VR(1,1), ldvr);
/* Generate orthogonal matrix in VR
(Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, &ilo, &ihi, &VR(1,1), ldvr, &WORK(itau), &WORK(iwrk),
&i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR
(Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, &ilo, &ihi, &A(1,1), lda, &WR(1), &WI(1), &
VR(1,1), ldvr, &WORK(iwrk), &i__1, info);
} else {
/* Compute eigenvalues only
(Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("E", "N", n, &ilo, &ihi, &A(1,1), lda, &WR(1), &WI(1), &
VR(1,1), ldvr, &WORK(iwrk), &i__1, info);
}
/* If INFO > 0 from DHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
(Workspace: need 4*N) */
dtrevc_(side, "B", select, n, &A(1,1), lda, &VL(1,1), ldvl,
&VR(1,1), ldvr, n, &nout, &WORK(iwrk), &ierr);
}
if (wantvl) {
/* Undo balancing of left eigenvectors
(Workspace: need N) */
dgebak_("B", "L", n, &ilo, &ihi, &WORK(ibal), n, &VL(1,1), ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component real
*/
i__1 = *n;
for (i = 1; i <= *n; ++i) {
if (WI(i) == 0.) {
scl = 1. / dnrm2_(n, &VL(1,i), &c__1);
dscal_(n, &scl, &VL(1,i), &c__1);
} else if (WI(i) > 0.) {
d__1 = dnrm2_(n, &VL(1,i), &c__1);
d__2 = dnrm2_(n, &VL(1,i+1), &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &VL(1,i), &c__1);
dscal_(n, &scl, &VL(1,i+1), &c__1);
i__2 = *n;
for (k = 1; k <= *n; ++k) {
/* Computing 2nd power */
d__1 = VL(k,i);
/* Computing 2nd power */
d__2 = VL(k,i+1);
WORK(iwrk + k - 1) = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &WORK(iwrk), &c__1);
dlartg_(&VL(k,i), &VL(k,i+1), &cs,
&sn, &r);
drot_(n, &VL(1,i), &c__1, &VL(1,i+1), &c__1, &cs, &sn);
VL(k,i+1) = 0.;
}
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
(Workspace: need N) */
dgebak_("B", "R", n, &ilo, &ihi, &WORK(ibal), n, &VR(1,1), ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component real
*/
i__1 = *n;
for (i = 1; i <= *n; ++i) {
if (WI(i) == 0.) {
scl = 1. / dnrm2_(n, &VR(1,i), &c__1);
dscal_(n, &scl, &VR(1,i), &c__1);
} else if (WI(i) > 0.) {
d__1 = dnrm2_(n, &VR(1,i), &c__1);
d__2 = dnrm2_(n, &VR(1,i+1), &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &VR(1,i), &c__1);
dscal_(n, &scl, &VR(1,i+1), &c__1);
i__2 = *n;
for (k = 1; k <= *n; ++k) {
/* Computing 2nd power */
d__1 = VR(k,i);
/* Computing 2nd power */
d__2 = VR(k,i+1);
WORK(iwrk + k - 1) = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &WORK(iwrk), &c__1);
dlartg_(&VR(k,i), &VR(k,i+1), &cs,
&sn, &r);
drot_(n, &VR(1,i), &c__1, &VR(1,i+1), &c__1, &cs, &sn);
VR(k,i+1) = 0.;
}
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &WR(*info +
1), &i__2, &ierr);
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &WI(*info +
1), &i__2, &ierr);
if (*info > 0) {
i__1 = ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &WR(1),
n, &ierr);
i__1 = ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &WI(1),
n, &ierr);
}
}
WORK(1) = (doublereal) maxwrk;
return 0;
/* End of DGEEV */
} /* dgeev_ */
int dgeevx_(char *balanc, char *jobvl, char *jobvr, char *
sense, int *n, double *a, int *lda, double *wr,
double *wi, double *vl, int *ldvl, double *vr,
int *ldvr, int *ilo, int *ihi, double *scale,
double *abnrm, double *rconde, double *rcondv, double
*work, int *lwork, int *iwork, int *info)
{
/* System generated locals */
int a_dim1, a_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, i__1,
i__2, i__3;
double d__1, d__2;
/* Builtin functions */
double sqrt(double);
/* Local variables */
int i__, k;
double r__, cs, sn;
char job[1];
double scl, dum[1], eps;
char side[1];
double anrm;
int ierr, itau;
extern int drot_(int *, double *, int *,
double *, int *, double *, double *);
int iwrk, nout;
extern double dnrm2_(int *, double *, int *);
extern int dscal_(int *, double *, double *,
int *);
int icond;
extern int lsame_(char *, char *);
extern double dlapy2_(double *, double *);
extern int dlabad_(double *, double *), dgebak_(
char *, char *, int *, int *, int *, double *,
int *, double *, int *, int *),
dgebal_(char *, int *, double *, int *, int *,
int *, double *, int *);
int scalea;
extern double dlamch_(char *);
double cscale;
extern double dlange_(char *, int *, int *, double *,
int *, double *);
extern int dgehrd_(int *, int *, int *,
double *, int *, double *, double *, int *,
int *), dlascl_(char *, int *, int *, double *,
double *, int *, int *, double *, int *,
int *);
extern int idamax_(int *, double *, int *);
extern int dlacpy_(char *, int *, int *,
double *, int *, double *, int *),
dlartg_(double *, double *, double *, double *,
double *), xerbla_(char *, int *);
int select[1];
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
double bignum;
extern int dorghr_(int *, int *, int *,
double *, int *, double *, double *, int *,
int *), dhseqr_(char *, char *, int *, int *, int
*, double *, int *, double *, double *,
double *, int *, double *, int *, int *), dtrevc_(char *, char *, int *, int *,
double *, int *, double *, int *, double *,
int *, int *, int *, double *, int *), dtrsna_(char *, char *, int *, int *, double
*, int *, double *, int *, double *, int *,
double *, double *, int *, int *, double *,
int *, int *, int *);
int minwrk, maxwrk;
int wantvl, wntsnb;
int hswork;
int wntsne;
double smlnum;
int lquery, wantvr, wntsnn, wntsnv;
/* -- LAPACK driver routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGEEVX computes for an N-by-N float 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 float. */
/* 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, i.e. 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) DOUBLE PRECISION 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 float Schur form of the balanced */
/* version of the input matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= MAX(1,N). */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* WR and WI contain the float and imaginary parts, */
/* respectively, of the computed eigenvalues. Complex */
/* conjugate pairs of eigenvalues will appear consecutively */
/* with the eigenvalue having the positive imaginary part */
/* first. */
/* VL (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is float, then u(j) = VL(:,j), */
/* the j-th column of VL. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and */
/* u(j+1) = VL(:,j) - i*VL(:,j+1). */
/* LDVL (input) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; if */
/* JOBVL = 'V', LDVL >= N. */
/* VR (output) DOUBLE PRECISION 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. */
/* If the j-th eigenvalue is float, then v(j) = VR(:,j), */
/* the j-th column of VR. */
/* If the j-th and (j+1)-st eigenvalues form a complex */
/* conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and */
/* v(j+1) = VR(:,j) - i*VR(:,j+1). */
/* LDVR (input) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1, and if */
/* JOBVR = 'V', LDVR >= N. */
/* ILO (output) INTEGER */
/* IHI (output) INTEGER */
/* ILO and IHI are int 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) DOUBLE PRECISION 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 JOBVL = 'V' or JOBVR = 'V', */
/* LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6). */
/* 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. */
/* IWORK (workspace) INTEGER array, dimension (2*N-2) */
/* If SENSE = 'N' or 'E', not referenced. */
/* 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 WR */
/* and WI 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;
--wr;
--wi;
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;
--iwork;
/* 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 = -11;
} else if (*ldvr < 1 || wantvr && *ldvr < *n) {
*info = -13;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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, "DGEHRD", " ", n, &c__1, n, &
c__0);
if (wantvl) {
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vl[vl_offset], ldvl, &work[1], &c_n1, info);
} else if (wantvr) {
dhseqr_("S", "V", n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[
1], &vr[vr_offset], ldvr, &work[1], &c_n1, info);
} else {
if (wntsnn) {
dhseqr_("E", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
info);
} else {
dhseqr_("S", "N", n, &c__1, n, &a[a_offset], lda, &wr[1],
&wi[1], &vr[vr_offset], ldvr, &work[1], &c_n1,
info);
}
}
hswork = (int) work[1];
if (! wantvl && ! wantvr) {
minwrk = *n << 1;
if (! wntsnn) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + *n * 6;
minwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,hswork);
if (! wntsnn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * *n + *n * 6;
maxwrk = MAX(i__1,i__2);
}
} else {
minwrk = *n * 3;
if (! wntsnn && ! wntsne) {
/* Computing MAX */
i__1 = minwrk, i__2 = *n * *n + *n * 6;
minwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,hswork);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*n - 1) * ilaenv_(&c__1, "DORGHR",
" ", 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 * 6;
maxwrk = MAX(i__1,i__2);
}
/* Computing MAX */
i__1 = maxwrk, i__2 = *n * 3;
maxwrk = MAX(i__1,i__2);
}
maxwrk = MAX(maxwrk,minwrk);
}
work[1] = (double) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -21;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEEVX", &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 = dlange_("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) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Balance the matrix and compute ABNRM */
dgebal_(balanc, n, &a[a_offset], lda, ilo, ihi, &scale[1], &ierr);
*abnrm = dlange_("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 */
/* (Workspace: need 2*N, prefer N+N*NB) */
itau = 1;
iwrk = itau + *n;
i__1 = *lwork - iwrk + 1;
dgehrd_(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';
dlacpy_("L", n, n, &a[a_offset], lda, &vl[vl_offset], ldvl)
;
/* Generate orthogonal matrix in VL */
/* (Workspace: need 2*N-1, prefer N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, ilo, ihi, &vl[vl_offset], ldvl, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VL */
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[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';
dlacpy_("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';
dlacpy_("L", n, n, &a[a_offset], lda, &vr[vr_offset], ldvr)
;
/* Generate orthogonal matrix in VR */
/* (Workspace: need 2*N-1, prefer N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(n, ilo, ihi, &vr[vr_offset], ldvr, &work[itau], &work[iwrk], &
i__1, &ierr);
/* Perform QR iteration, accumulating Schur vectors in VR */
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", "V", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[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';
}
/* (Workspace: need 1, prefer HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_(job, "N", n, ilo, ihi, &a[a_offset], lda, &wr[1], &wi[1], &vr[
vr_offset], ldvr, &work[iwrk], &i__1, info);
}
/* If INFO > 0 from DHSEQR, then quit */
if (*info > 0) {
goto L50;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors */
/* (Workspace: need 3*N) */
dtrevc_(side, "B", select, n, &a[a_offset], lda, &vl[vl_offset], ldvl,
&vr[vr_offset], ldvr, n, &nout, &work[iwrk], &ierr);
}
/* Compute condition numbers if desired */
/* (Workspace: need N*N+6*N unless SENSE = 'E') */
if (! wntsnn) {
dtrsna_(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, &iwork[1], &icond);
}
if (wantvl) {
/* Undo balancing of left eigenvectors */
dgebak_(balanc, "L", n, ilo, ihi, &scale[1], n, &vl[vl_offset], ldvl,
&ierr);
/* Normalize left eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vl[i__ * vl_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vl[i__ * vl_dim1 + 1], &c__1);
dscal_(n, &scl, &vl[(i__ + 1) * vl_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vl[k + i__ * vl_dim1];
/* Computing 2nd power */
d__2 = vl[k + (i__ + 1) * vl_dim1];
work[k] = d__1 * d__1 + d__2 * d__2;
/* L10: */
}
k = idamax_(n, &work[1], &c__1);
dlartg_(&vl[k + i__ * vl_dim1], &vl[k + (i__ + 1) * vl_dim1],
&cs, &sn, &r__);
drot_(n, &vl[i__ * vl_dim1 + 1], &c__1, &vl[(i__ + 1) *
vl_dim1 + 1], &c__1, &cs, &sn);
vl[k + (i__ + 1) * vl_dim1] = 0.;
}
/* L20: */
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors */
dgebak_(balanc, "R", n, ilo, ihi, &scale[1], n, &vr[vr_offset], ldvr,
&ierr);
/* Normalize right eigenvectors and make largest component float */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (wi[i__] == 0.) {
scl = 1. / dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
} else if (wi[i__] > 0.) {
d__1 = dnrm2_(n, &vr[i__ * vr_dim1 + 1], &c__1);
d__2 = dnrm2_(n, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
scl = 1. / dlapy2_(&d__1, &d__2);
dscal_(n, &scl, &vr[i__ * vr_dim1 + 1], &c__1);
dscal_(n, &scl, &vr[(i__ + 1) * vr_dim1 + 1], &c__1);
i__2 = *n;
for (k = 1; k <= i__2; ++k) {
/* Computing 2nd power */
d__1 = vr[k + i__ * vr_dim1];
/* Computing 2nd power */
d__2 = vr[k + (i__ + 1) * vr_dim1];
work[k] = d__1 * d__1 + d__2 * d__2;
/* L30: */
}
k = idamax_(n, &work[1], &c__1);
dlartg_(&vr[k + i__ * vr_dim1], &vr[k + (i__ + 1) * vr_dim1],
&cs, &sn, &r__);
drot_(n, &vr[i__ * vr_dim1 + 1], &c__1, &vr[(i__ + 1) *
vr_dim1 + 1], &c__1, &cs, &sn);
vr[k + (i__ + 1) * vr_dim1] = 0.;
}
/* L40: */
}
}
/* Undo scaling if necessary */
L50:
if (scalea) {
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[*info +
1], &i__2, &ierr);
i__1 = *n - *info;
/* Computing MAX */
i__3 = *n - *info;
i__2 = MAX(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[*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;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wr[1],
n, &ierr);
i__1 = *ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[1],
n, &ierr);
}
}
work[1] = (double) maxwrk;
return 0;
/* End of DGEEVX */
} /* dgeevx_ */
/* Subroutine */ int dgees_(char *jobvs, char *sort, L_fp select, integer *n,
doublereal *a, integer *lda, integer *sdim, doublereal *wr,
doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work,
integer *lwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal s;
integer i1, i2, ip, ihi, ilo;
doublereal dum[1], eps, sep;
integer ibal;
doublereal anrm;
integer idum[1], ierr, itau, iwrk, inxt, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dswap_(integer *, doublereal *, integer
*, doublereal *, integer *);
logical cursl;
extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebak_(
char *, char *, integer *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *, integer *),
dgebal_(char *, integer *, doublereal *, integer *, integer *,
integer *, doublereal *, integer *);
logical lst2sl, scalea;
extern doublereal dlamch_(char *);
doublereal cscale;
extern doublereal dlange_(char *, integer *, integer *, doublereal *,
integer *, doublereal *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dlascl_(char *, integer *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *), dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
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 *);
logical lastsl;
integer minwrk, maxwrk;
doublereal smlnum;
integer hswork;
logical wantst, lquery, wantvs;
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* .. Function Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGEES computes for an N-by-N real nonsymmetric matrix A, the */
/* eigenvalues, the real Schur form T, and, optionally, the matrix of */
/* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). */
/* Optionally, it also orders the eigenvalues on the diagonal of the */
/* real 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 matrix is in real Schur form if it is upper quasi-triangular with */
/* 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the */
/* form */
/* [ a b ] */
/* [ c a ] */
/* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */
/* 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 (external procedure) LOGICAL FUNCTION of two DOUBLE PRECISION arguments */
/* SELECT must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'S', SELECT is used to select eigenvalues to sort */
/* to the top left of the Schur form. */
/* If SORT = 'N', SELECT is not referenced. */
/* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */
/* SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex */
/* conjugate pair of eigenvalues is selected, then both complex */
/* eigenvalues are selected. */
/* Note that a selected complex eigenvalue may no longer */
/* satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */
/* ordering may change the value of complex eigenvalues */
/* (especially if the eigenvalue is ill-conditioned); in this */
/* case INFO is set to N+2 (see INFO below). */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten by its real 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 (after sorting) */
/* for which SELECT is true. (Complex conjugate */
/* pairs for which SELECT is true for either */
/* eigenvalue count as 2.) */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* WR and WI contain the real and imaginary parts, */
/* respectively, of the computed eigenvalues in the same order */
/* that they appear on the diagonal of the output Schur form T. */
/* Complex conjugate pairs of eigenvalues will appear */
/* consecutively with the eigenvalue having the positive */
/* imaginary part first. */
/* VS (output) DOUBLE PRECISION array, dimension (LDVS,N) */
/* If JOBVS = 'V', VS contains the orthogonal 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) contains the optimal LWORK. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= max(1,3*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. */
/* 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 WR and WI */
/* 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;
--wr;
--wi;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--bwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
if (! wantvs && ! lsame_(jobvs, "N")) {
*info = -1;
} else if (! wantst && ! lsame_(sort, "N")) {
*info = -2;
} else if (*n < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldvs < 1 || wantvs && *ldvs < *n) {
*info = -11;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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 << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1,
n, &c__0);
minwrk = *n * 3;
dhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1]
, &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork = (integer) work[1];
if (! wantvs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + hswork;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"DORGHR", " ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + hswork;
maxwrk = max(i__1,i__2);
}
}
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery) {
*info = -13;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEES ", &i__1);
return 0;
} else if (lquery) {
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 = dlange_("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) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (Workspace: need N) */
ibal = 1;
dgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
itau = *n + ibal;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
dgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
dlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
;
/* Generate orthogonal matrix in VS */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(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 */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[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) {
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, &
ierr);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, &
ierr);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&wr[i__], &wi[i__]);
/* L10: */
}
/* Reorder eigenvalues and transform Schur vectors */
/* (Workspace: none needed) */
i__1 = *lwork - iwrk + 1;
dtrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &wr[1], &wi[1], sdim, &s, &sep, &work[iwrk], &i__1,
idum, &c__1, &icond);
if (icond > 0) {
*info = *n + icond;
}
}
if (wantvs) {
/* Undo balancing */
/* (Workspace: need N) */
dgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs,
&ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
dlascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr);
i__1 = *lda + 1;
dcopy_(n, &a[a_offset], &i__1, &wr[1], &c__1);
if (cscale == smlnum) {
/* If scaling back towards underflow, adjust WI if an */
/* offdiagonal element of a 2-by-2 block in the Schur form */
/* underflows. */
if (ieval > 0) {
i1 = ieval + 1;
i2 = ihi - 1;
i__1 = ilo - 1;
/* Computing MAX */
i__3 = ilo - 1;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[
1], &i__2, &ierr);
} else if (wantst) {
i1 = 1;
i2 = *n - 1;
} else {
i1 = ilo;
i2 = ihi - 1;
}
inxt = i1 - 1;
i__1 = i2;
for (i__ = i1; i__ <= i__1; ++i__) {
if (i__ < inxt) {
goto L20;
}
if (wi[i__] == 0.) {
inxt = i__ + 1;
} else {
if (a[i__ + 1 + i__ * a_dim1] == 0.) {
wi[i__] = 0.;
wi[i__ + 1] = 0.;
} else if (a[i__ + 1 + i__ * a_dim1] != 0. && a[i__ + (
i__ + 1) * a_dim1] == 0.) {
wi[i__] = 0.;
wi[i__ + 1] = 0.;
if (i__ > 1) {
i__2 = i__ - 1;
dswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[(
i__ + 1) * a_dim1 + 1], &c__1);
}
if (*n > i__ + 1) {
i__2 = *n - i__ - 1;
dswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, &
a[i__ + 1 + (i__ + 2) * a_dim1], lda);
}
if (wantvs) {
dswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__
+ 1) * vs_dim1 + 1], &c__1);
}
a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ *
a_dim1];
a[i__ + 1 + i__ * a_dim1] = 0.;
}
inxt = i__ + 2;
}
L20:
;
}
}
/* Undo scaling for the imaginary part of the eigenvalues */
i__1 = *n - ieval;
/* Computing MAX */
i__3 = *n - ieval;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval +
1], &i__2, &ierr);
}
if (wantst && *info == 0) {
/* Check if reordering successful */
lastsl = TRUE_;
lst2sl = TRUE_;
*sdim = 0;
ip = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*select)(&wr[i__], &wi[i__]);
if (wi[i__] == 0.) {
if (cursl) {
++(*sdim);
}
ip = 0;
if (cursl && ! lastsl) {
*info = *n + 2;
}
} else {
if (ip == 1) {
/* Last eigenvalue of conjugate pair */
cursl = cursl || lastsl;
lastsl = cursl;
if (cursl) {
*sdim += 2;
}
ip = -1;
if (cursl && ! lst2sl) {
*info = *n + 2;
}
} else {
/* First eigenvalue of conjugate pair */
ip = 1;
}
}
lst2sl = lastsl;
lastsl = cursl;
/* L30: */
}
}
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGEES */
} /* dgees_ */
/* Subroutine */ int dlaqr2_(logical *wantt, logical *wantz, integer *n,
integer *ktop, integer *kbot, integer *nw, doublereal *h__, integer *
ldh, integer *iloz, integer *ihiz, doublereal *z__, integer *ldz,
integer *ns, integer *nd, doublereal *sr, doublereal *si, doublereal *
v, integer *ldv, integer *nh, doublereal *t, integer *ldt, integer *
nv, doublereal *wv, integer *ldwv, doublereal *work, integer *lwork)
{
/* System generated locals */
integer h_dim1, h_offset, t_dim1, t_offset, v_dim1, v_offset, wv_dim1,
wv_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);
/* Local variables */
integer i__, j, k;
doublereal s, aa, bb, cc, dd, cs, sn;
integer jw;
doublereal evi, evk, foo;
integer kln;
doublereal tau, ulp;
integer lwk1, lwk2;
doublereal beta;
integer kend, kcol, info, ifst, ilst, ltop, krow;
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *), dgemm_(char *, char *, integer *, integer *
, integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
logical bulge;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer infqr, kwtop;
extern /* Subroutine */ int dlanv2_(doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *), dlabad_(
doublereal *, doublereal *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dgehrd_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *), dlahqr_(logical *, logical *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, integer *, doublereal *, integer *,
integer *), dlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
doublereal safmin;
extern /* Subroutine */ int dlaset_(char *, integer *, integer *,
doublereal *, doublereal *, doublereal *, integer *);
doublereal safmax;
extern /* Subroutine */ int dorghr_(integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), dtrexc_(char *, integer *, doublereal *, integer *,
doublereal *, integer *, integer *, integer *, doublereal *,
integer *);
logical sorted;
doublereal smlnum;
integer lwkopt;
/* -- LAPACK auxiliary routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* This subroutine is identical to DLAQR3 except that it avoids */
/* recursion by calling DLAHQR instead of DLAQR4. */
/* ****************************************************************** */
/* Aggressive early deflation: */
/* This subroutine accepts as input an upper Hessenberg matrix */
/* H and performs an orthogonal similarity transformation */
/* designed to detect and deflate fully converged eigenvalues from */
/* a trailing principal submatrix. On output H has been over- */
/* written by a new Hessenberg matrix that is a perturbation of */
/* an orthogonal similarity transformation of H. It is to be */
/* hoped that the final version of H has many zero subdiagonal */
/* entries. */
/* ****************************************************************** */
/* WANTT (input) LOGICAL */
/* If .TRUE., then the Hessenberg matrix H is fully updated */
/* so that the quasi-triangular Schur factor may be */
/* computed (in cooperation with the calling subroutine). */
/* If .FALSE., then only enough of H is updated to preserve */
/* the eigenvalues. */
/* WANTZ (input) LOGICAL */
/* If .TRUE., then the orthogonal matrix Z is updated so */
/* so that the orthogonal Schur factor may be computed */
/* (in cooperation with the calling subroutine). */
/* If .FALSE., then Z is not referenced. */
/* N (input) INTEGER */
/* The order of the matrix H and (if WANTZ is .TRUE.) the */
/* order of the orthogonal matrix Z. */
/* KTOP (input) INTEGER */
/* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0. */
/* KBOT and KTOP together determine an isolated block */
/* along the diagonal of the Hessenberg matrix. */
/* KBOT (input) INTEGER */
/* It is assumed without a check that either */
/* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together */
/* determine an isolated block along the diagonal of the */
/* Hessenberg matrix. */
/* NW (input) INTEGER */
/* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1). */
/* H (input/output) DOUBLE PRECISION array, dimension (LDH,N) */
/* On input the initial N-by-N section of H stores the */
/* Hessenberg matrix undergoing aggressive early deflation. */
/* On output H has been transformed by an orthogonal */
/* similarity transformation, perturbed, and the returned */
/* to Hessenberg form that (it is to be hoped) has some */
/* zero subdiagonal entries. */
/* LDH (input) integer */
/* Leading dimension of H just as declared in the calling */
/* subroutine. N .LE. LDH */
/* ILOZ (input) INTEGER */
/* IHIZ (input) INTEGER */
/* Specify the rows of Z to which transformations must be */
/* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N. */
/* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,IHI) */
/* IF WANTZ is .TRUE., then on output, the orthogonal */
/* similarity transformation mentioned above has been */
/* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. */
/* If WANTZ is .FALSE., then Z is unreferenced. */
/* LDZ (input) integer */
/* The leading dimension of Z just as declared in the */
/* calling subroutine. 1 .LE. LDZ. */
/* NS (output) integer */
/* The number of unconverged (ie approximate) eigenvalues */
/* returned in SR and SI that may be used as shifts by the */
/* calling subroutine. */
/* ND (output) integer */
/* The number of converged eigenvalues uncovered by this */
/* subroutine. */
/* SR (output) DOUBLE PRECISION array, dimension KBOT */
/* SI (output) DOUBLE PRECISION array, dimension KBOT */
/* On output, the real and imaginary parts of approximate */
/* eigenvalues that may be used for shifts are stored in */
/* SR(KBOT-ND-NS+1) through SR(KBOT-ND) and */
/* SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively. */
/* The real and imaginary parts of converged eigenvalues */
/* are stored in SR(KBOT-ND+1) through SR(KBOT) and */
/* SI(KBOT-ND+1) through SI(KBOT), respectively. */
/* V (workspace) DOUBLE PRECISION array, dimension (LDV,NW) */
/* An NW-by-NW work array. */
/* LDV (input) integer scalar */
/* The leading dimension of V just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* NH (input) integer scalar */
/* The number of columns of T. NH.GE.NW. */
/* T (workspace) DOUBLE PRECISION array, dimension (LDT,NW) */
/* LDT (input) integer */
/* The leading dimension of T just as declared in the */
/* calling subroutine. NW .LE. LDT */
/* NV (input) integer */
/* The number of rows of work array WV available for */
/* workspace. NV.GE.NW. */
/* WV (workspace) DOUBLE PRECISION array, dimension (LDWV,NW) */
/* LDWV (input) integer */
/* The leading dimension of W just as declared in the */
/* calling subroutine. NW .LE. LDV */
/* WORK (workspace) DOUBLE PRECISION array, dimension LWORK. */
/* On exit, WORK(1) is set to an estimate of the optimal value */
/* of LWORK for the given values of N, NW, KTOP and KBOT. */
/* LWORK (input) integer */
/* The dimension of the work array WORK. LWORK = 2*NW */
/* suffices, but greater efficiency may result from larger */
/* values of LWORK. */
/* If LWORK = -1, then a workspace query is assumed; DLAQR2 */
/* only estimates the optimal workspace size for the given */
/* values of N, NW, KTOP and KBOT. The estimate is returned */
/* in WORK(1). No error message related to LWORK is issued */
/* by XERBLA. Neither H nor Z are accessed. */
/* ================================================================ */
/* Based on contributions by */
/* Karen Braman and Ralph Byers, Department of Mathematics, */
/* University of Kansas, USA */
/* ================================================================ */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* ==== Estimate optimal workspace. ==== */
/* Parameter adjustments */
h_dim1 = *ldh;
h_offset = 1 + h_dim1;
h__ -= h_offset;
z_dim1 = *ldz;
z_offset = 1 + z_dim1;
z__ -= z_offset;
--sr;
--si;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
wv_dim1 = *ldwv;
wv_offset = 1 + wv_dim1;
wv -= wv_offset;
--work;
/* Function Body */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
if (jw <= 2) {
lwkopt = 1;
} else {
/* ==== Workspace query call to DGEHRD ==== */
i__1 = jw - 1;
dgehrd_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
c_n1, &info);
lwk1 = (integer) work[1];
/* ==== Workspace query call to DORGHR ==== */
i__1 = jw - 1;
dorghr_(&jw, &c__1, &i__1, &t[t_offset], ldt, &work[1], &work[1], &
c_n1, &info);
lwk2 = (integer) work[1];
/* ==== Optimal workspace ==== */
lwkopt = jw + max(lwk1,lwk2);
}
/* ==== Quick return in case of workspace query. ==== */
if (*lwork == -1) {
work[1] = (doublereal) lwkopt;
return 0;
}
/* ==== Nothing to do ... */
/* ... for an empty active block ... ==== */
*ns = 0;
*nd = 0;
if (*ktop > *kbot) {
return 0;
}
/* ... nor for an empty deflation window. ==== */
if (*nw < 1) {
return 0;
}
/* ==== Machine constants ==== */
safmin = dlamch_("SAFE MINIMUM");
safmax = 1. / safmin;
dlabad_(&safmin, &safmax);
ulp = dlamch_("PRECISION");
smlnum = safmin * ((doublereal) (*n) / ulp);
/* ==== Setup deflation window ==== */
/* Computing MIN */
i__1 = *nw, i__2 = *kbot - *ktop + 1;
jw = min(i__1,i__2);
kwtop = *kbot - jw + 1;
if (kwtop == *ktop) {
s = 0.;
} else {
s = h__[kwtop + (kwtop - 1) * h_dim1];
}
if (*kbot == kwtop) {
/* ==== 1-by-1 deflation window: not much to do ==== */
sr[kwtop] = h__[kwtop + kwtop * h_dim1];
si[kwtop] = 0.;
*ns = 1;
*nd = 0;
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * (d__1 = h__[kwtop + kwtop * h_dim1], abs(
d__1));
if (abs(s) <= max(d__2,d__3)) {
*ns = 0;
*nd = 1;
if (kwtop > *ktop) {
h__[kwtop + (kwtop - 1) * h_dim1] = 0.;
}
}
return 0;
}
/* ==== Convert to spike-triangular form. (In case of a */
/* . rare QR failure, this routine continues to do */
/* . aggressive early deflation using that part of */
/* . the deflation window that converged using INFQR */
/* . here and there to keep track.) ==== */
dlacpy_("U", &jw, &jw, &h__[kwtop + kwtop * h_dim1], ldh, &t[t_offset],
ldt);
i__1 = jw - 1;
i__2 = *ldh + 1;
i__3 = *ldt + 1;
dcopy_(&i__1, &h__[kwtop + 1 + kwtop * h_dim1], &i__2, &t[t_dim1 + 2], &
i__3);
dlaset_("A", &jw, &jw, &c_b10, &c_b11, &v[v_offset], ldv);
dlahqr_(&c_true, &c_true, &jw, &c__1, &jw, &t[t_offset], ldt, &sr[kwtop],
&si[kwtop], &c__1, &jw, &v[v_offset], ldv, &infqr);
/* ==== DTREXC needs a clean margin near the diagonal ==== */
i__1 = jw - 3;
for (j = 1; j <= i__1; ++j) {
t[j + 2 + j * t_dim1] = 0.;
t[j + 3 + j * t_dim1] = 0.;
/* L10: */
}
if (jw > 2) {
t[jw + (jw - 2) * t_dim1] = 0.;
}
/* ==== Deflation detection loop ==== */
*ns = jw;
ilst = infqr + 1;
L20:
if (ilst <= *ns) {
if (*ns == 1) {
bulge = FALSE_;
} else {
bulge = t[*ns + (*ns - 1) * t_dim1] != 0.;
}
/* ==== Small spike tip test for deflation ==== */
if (! bulge) {
/* ==== Real eigenvalue ==== */
foo = (d__1 = t[*ns + *ns * t_dim1], abs(d__1));
if (foo == 0.) {
foo = abs(s);
}
/* Computing MAX */
d__2 = smlnum, d__3 = ulp * foo;
if ((d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)) <= max(d__2,d__3))
{
/* ==== Deflatable ==== */
--(*ns);
} else {
/* ==== Undeflatable. Move it up out of the way. */
/* . (DTREXC can not fail in this case.) ==== */
ifst = *ns;
dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
++ilst;
}
} else {
/* ==== Complex conjugate pair ==== */
foo = (d__3 = t[*ns + *ns * t_dim1], abs(d__3)) + sqrt((d__1 = t[*
ns + (*ns - 1) * t_dim1], abs(d__1))) * sqrt((d__2 = t[*
ns - 1 + *ns * t_dim1], abs(d__2)));
if (foo == 0.) {
foo = abs(s);
}
/* Computing MAX */
d__3 = (d__1 = s * v[*ns * v_dim1 + 1], abs(d__1)), d__4 = (d__2 =
s * v[(*ns - 1) * v_dim1 + 1], abs(d__2));
/* Computing MAX */
d__5 = smlnum, d__6 = ulp * foo;
if (max(d__3,d__4) <= max(d__5,d__6)) {
/* ==== Deflatable ==== */
*ns += -2;
} else {
/* ==== Undflatable. Move them up out of the way. */
/* . Fortunately, DTREXC does the right thing with */
/* . ILST in case of a rare exchange failure. ==== */
ifst = *ns;
dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
ilst += 2;
}
}
/* ==== End deflation detection loop ==== */
goto L20;
}
/* ==== Return to Hessenberg form ==== */
if (*ns == 0) {
s = 0.;
}
if (*ns < jw) {
/* ==== sorting diagonal blocks of T improves accuracy for */
/* . graded matrices. Bubble sort deals well with */
/* . exchange failures. ==== */
sorted = FALSE_;
i__ = *ns + 1;
L30:
if (sorted) {
goto L50;
}
sorted = TRUE_;
kend = i__ - 1;
i__ = infqr + 1;
if (i__ == *ns) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
k = i__ + 1;
} else {
k = i__ + 2;
}
L40:
if (k <= kend) {
if (k == i__ + 1) {
evi = (d__1 = t[i__ + i__ * t_dim1], abs(d__1));
} else {
evi = (d__3 = t[i__ + i__ * t_dim1], abs(d__3)) + sqrt((d__1 =
t[i__ + 1 + i__ * t_dim1], abs(d__1))) * sqrt((d__2 =
t[i__ + (i__ + 1) * t_dim1], abs(d__2)));
}
if (k == kend) {
evk = (d__1 = t[k + k * t_dim1], abs(d__1));
} else if (t[k + 1 + k * t_dim1] == 0.) {
evk = (d__1 = t[k + k * t_dim1], abs(d__1));
} else {
evk = (d__3 = t[k + k * t_dim1], abs(d__3)) + sqrt((d__1 = t[
k + 1 + k * t_dim1], abs(d__1))) * sqrt((d__2 = t[k +
(k + 1) * t_dim1], abs(d__2)));
}
if (evi >= evk) {
i__ = k;
} else {
sorted = FALSE_;
ifst = i__;
ilst = k;
dtrexc_("V", &jw, &t[t_offset], ldt, &v[v_offset], ldv, &ifst,
&ilst, &work[1], &info);
if (info == 0) {
i__ = ilst;
} else {
i__ = k;
}
}
if (i__ == kend) {
k = i__ + 1;
} else if (t[i__ + 1 + i__ * t_dim1] == 0.) {
k = i__ + 1;
} else {
k = i__ + 2;
}
goto L40;
}
goto L30;
L50:
;
}
/* ==== Restore shift/eigenvalue array from T ==== */
i__ = jw;
L60:
if (i__ >= infqr + 1) {
if (i__ == infqr + 1) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.;
--i__;
} else if (t[i__ + (i__ - 1) * t_dim1] == 0.) {
sr[kwtop + i__ - 1] = t[i__ + i__ * t_dim1];
si[kwtop + i__ - 1] = 0.;
--i__;
} else {
aa = t[i__ - 1 + (i__ - 1) * t_dim1];
cc = t[i__ + (i__ - 1) * t_dim1];
bb = t[i__ - 1 + i__ * t_dim1];
dd = t[i__ + i__ * t_dim1];
dlanv2_(&aa, &bb, &cc, &dd, &sr[kwtop + i__ - 2], &si[kwtop + i__
- 2], &sr[kwtop + i__ - 1], &si[kwtop + i__ - 1], &cs, &
sn);
i__ += -2;
}
goto L60;
}
if (*ns < jw || s == 0.) {
if (*ns > 1 && s != 0.) {
/* ==== Reflect spike back into lower triangle ==== */
dcopy_(ns, &v[v_offset], ldv, &work[1], &c__1);
beta = work[1];
dlarfg_(ns, &beta, &work[2], &c__1, &tau);
work[1] = 1.;
i__1 = jw - 2;
i__2 = jw - 2;
dlaset_("L", &i__1, &i__2, &c_b10, &c_b10, &t[t_dim1 + 3], ldt);
dlarf_("L", ns, &jw, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
dlarf_("R", ns, ns, &work[1], &c__1, &tau, &t[t_offset], ldt, &
work[jw + 1]);
dlarf_("R", &jw, ns, &work[1], &c__1, &tau, &v[v_offset], ldv, &
work[jw + 1]);
i__1 = *lwork - jw;
dgehrd_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
}
/* ==== Copy updated reduced window into place ==== */
if (kwtop > 1) {
h__[kwtop + (kwtop - 1) * h_dim1] = s * v[v_dim1 + 1];
}
dlacpy_("U", &jw, &jw, &t[t_offset], ldt, &h__[kwtop + kwtop * h_dim1]
, ldh);
i__1 = jw - 1;
i__2 = *ldt + 1;
i__3 = *ldh + 1;
dcopy_(&i__1, &t[t_dim1 + 2], &i__2, &h__[kwtop + 1 + kwtop * h_dim1],
&i__3);
/* ==== Accumulate orthogonal matrix in order update */
/* . H and Z, if requested. (A modified version */
/* . of DORGHR that accumulates block Householder */
/* . transformations into V directly might be */
/* . marginally more efficient than the following.) ==== */
if (*ns > 1 && s != 0.) {
i__1 = *lwork - jw;
dorghr_(&jw, &c__1, ns, &t[t_offset], ldt, &work[1], &work[jw + 1]
, &i__1, &info);
dgemm_("N", "N", &jw, ns, ns, &c_b11, &v[v_offset], ldv, &t[
t_offset], ldt, &c_b10, &wv[wv_offset], ldwv);
dlacpy_("A", &jw, ns, &wv[wv_offset], ldwv, &v[v_offset], ldv);
}
/* ==== Update vertical slab in H ==== */
if (*wantt) {
ltop = 1;
} else {
ltop = *ktop;
}
i__1 = kwtop - 1;
i__2 = *nv;
for (krow = ltop; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = kwtop - krow;
kln = min(i__3,i__4);
dgemm_("N", "N", &kln, &jw, &jw, &c_b11, &h__[krow + kwtop *
h_dim1], ldh, &v[v_offset], ldv, &c_b10, &wv[wv_offset],
ldwv);
dlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &h__[krow + kwtop *
h_dim1], ldh);
/* L70: */
}
/* ==== Update horizontal slab in H ==== */
if (*wantt) {
i__2 = *n;
i__1 = *nh;
for (kcol = *kbot + 1; i__1 < 0 ? kcol >= i__2 : kcol <= i__2;
kcol += i__1) {
/* Computing MIN */
i__3 = *nh, i__4 = *n - kcol + 1;
kln = min(i__3,i__4);
dgemm_("C", "N", &jw, &kln, &jw, &c_b11, &v[v_offset], ldv, &
h__[kwtop + kcol * h_dim1], ldh, &c_b10, &t[t_offset],
ldt);
dlacpy_("A", &jw, &kln, &t[t_offset], ldt, &h__[kwtop + kcol *
h_dim1], ldh);
/* L80: */
}
}
/* ==== Update vertical slab in Z ==== */
if (*wantz) {
i__1 = *ihiz;
i__2 = *nv;
for (krow = *iloz; i__2 < 0 ? krow >= i__1 : krow <= i__1; krow +=
i__2) {
/* Computing MIN */
i__3 = *nv, i__4 = *ihiz - krow + 1;
kln = min(i__3,i__4);
dgemm_("N", "N", &kln, &jw, &jw, &c_b11, &z__[krow + kwtop *
z_dim1], ldz, &v[v_offset], ldv, &c_b10, &wv[
wv_offset], ldwv);
dlacpy_("A", &kln, &jw, &wv[wv_offset], ldwv, &z__[krow +
kwtop * z_dim1], ldz);
/* L90: */
}
}
}
/* ==== Return the number of deflations ... ==== */
*nd = jw - *ns;
/* ==== ... and the number of shifts. (Subtracting */
/* . INFQR from the spike length takes care */
/* . of the case of a rare QR failure while */
/* . calculating eigenvalues of the deflation */
/* . window.) ==== */
*ns -= infqr;
/* ==== Return optimal workspace. ==== */
work[1] = (doublereal) lwkopt;
/* ==== End of DLAQR2 ==== */
return 0;
} /* dlaqr2_ */
/* Subroutine */ int dgeesx_(char *jobvs, char *sort, L_fp select, char *
sense, integer *n, doublereal *a, integer *lda, integer *sdim,
doublereal *wr, doublereal *wi, doublereal *vs, integer *ldvs,
doublereal *rconde, doublereal *rcondv, doublereal *work, integer *
lwork, integer *iwork, integer *liwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, i1, i2, ip, ihi, ilo;
doublereal dum[1], eps;
integer ibal;
doublereal anrm;
integer ierr, itau, iwrk, lwrk, inxt, icond, ieval;
logical cursl;
integer liwrk;
logical lst2sl, scalea;
doublereal cscale;
doublereal bignum;
logical wantsb;
logical wantse, lastsl;
integer minwrk, maxwrk;
logical wantsn;
doublereal smlnum;
integer hswork;
logical wantst, lquery, wantsv, wantvs;
/* -- LAPACK driver routine (version 3.2) -- */
/* November 2006 */
/* Purpose */
/* ======= */
/* DGEESX computes for an N-by-N real nonsymmetric matrix A, the */
/* eigenvalues, the real Schur form T, and, optionally, the matrix of */
/* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T). */
/* Optionally, it also orders the eigenvalues on the diagonal of the */
/* real 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 real matrix is in real Schur form if it is upper quasi-triangular */
/* with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in */
/* the form */
/* [ a b ] */
/* [ c a ] */
/* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc). */
/* 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 (external procedure) LOGICAL FUNCTION of two DOUBLE PRECISION arguments */
/* SELECT must be declared EXTERNAL in the calling subroutine. */
/* If SORT = 'S', SELECT is used to select eigenvalues to sort */
/* to the top left of the Schur form. */
/* If SORT = 'N', SELECT is not referenced. */
/* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if */
/* SELECT(WR(j),WI(j)) is true; i.e., if either one of a */
/* complex conjugate pair of eigenvalues is selected, then both */
/* are. Note that a selected complex eigenvalue may no longer */
/* satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since */
/* ordering may change the value of complex eigenvalues */
/* (especially if the eigenvalue is ill-conditioned); in this */
/* case INFO may be set to N+3 (see INFO below). */
/* 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) DOUBLE PRECISION array, dimension (LDA, N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A is overwritten by its real 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 (after sorting) */
/* for which SELECT is true. (Complex conjugate */
/* pairs for which SELECT is true for either */
/* eigenvalue count as 2.) */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION array, dimension (N) */
/* WR and WI contain the real and imaginary parts, respectively, */
/* of the computed eigenvalues, in the same order that they */
/* appear on the diagonal of the output Schur form T. Complex */
/* conjugate pairs of eigenvalues appear consecutively with the */
/* eigenvalue having the positive imaginary part first. */
/* VS (output) DOUBLE PRECISION array, dimension (LDVS,N) */
/* If JOBVS = 'V', VS contains the orthogonal 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) DOUBLE PRECISION 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. LWORK >= max(1,3*N). */
/* Also, if SENSE = 'E' or 'V' or 'B', */
/* LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of */
/* selected eigenvalues computed by this routine. Note that */
/* N+2*SDIM*(N-SDIM) <= N+N*N/2. Note also that an error is only */
/* returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or */
/* 'B' this may not be large enough. */
/* For good performance, LWORK must generally be larger. */
/* If LWORK = -1, then a workspace query is assumed; the routine */
/* only calculates upper bounds on the optimal sizes of the */
/* arrays WORK and IWORK, returns these values as the first */
/* entries of the WORK and IWORK arrays, and no error messages */
/* related to LWORK or LIWORK are issued by XERBLA. */
/* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */
/* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
/* LIWORK (input) INTEGER */
/* The dimension of the array IWORK. */
/* LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM). */
/* Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is */
/* only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this */
/* may not be large enough. */
/* If LIWORK = -1, then a workspace query is assumed; the */
/* routine only calculates upper bounds on the optimal sizes of */
/* the arrays WORK and IWORK, returns these values as the first */
/* entries of the WORK and IWORK arrays, and no error messages */
/* related to LWORK or LIWORK are issued by XERBLA. */
/* 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 WR and WI */
/* 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 */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--wr;
--wi;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--iwork;
--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");
lquery = *lwork == -1 || *liwork == -1;
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 = -12;
}
/* Compute workspace */
/* (Note: Comments in the code beginning "RWorkspace:" describe the */
/* minimal amount of real workspace needed at that point in the */
/* code, as well as the preferred amount for good performance. */
/* IWorkspace refers to integer workspace. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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 DTRSEN later */
/* in the code.) */
if (*info == 0) {
liwrk = 1;
if (*n == 0) {
minwrk = 1;
lwrk = 1;
} else {
maxwrk = (*n << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1,
n, &c__0);
minwrk = *n * 3;
dhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1]
, &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork = (integer) work[1];
if (! wantvs) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + hswork;
maxwrk = max(i__1,i__2);
} else {
/* Computing MAX */
i__1 = maxwrk, i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1,
"DORGHR", " ", n, &c__1, n, &c_n1);
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + hswork;
maxwrk = max(i__1,i__2);
}
lwrk = maxwrk;
if (! wantsn) {
/* Computing MAX */
i__1 = lwrk, i__2 = *n + *n * *n / 2;
lwrk = max(i__1,i__2);
}
if (wantsv || wantsb) {
liwrk = *n * *n / 4;
}
}
iwork[1] = liwrk;
work[1] = (doublereal) lwrk;
if (*lwork < minwrk && ! lquery) {
*info = -16;
} else if (*liwork < 1 && ! lquery) {
*info = -18;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEESX", &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 = dlange_("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) {
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, &
ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (RWorkspace: need N) */
ibal = 1;
dgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (RWorkspace: need 3*N, prefer 2*N+N*NB) */
itau = *n + ibal;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
dgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1,
&ierr);
if (wantvs) {
/* Copy Householder vectors to VS */
dlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs)
;
/* Generate orthogonal matrix in VS */
/* (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(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 */
/* (RWorkspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[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) {
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, &
ierr);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, &
ierr);
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
bwork[i__] = (*select)(&wr[i__], &wi[i__]);
}
/* Reorder eigenvalues, transform Schur vectors, and compute */
/* reciprocal condition numbers */
/* (RWorkspace: if SENSE is not 'N', need N+2*SDIM*(N-SDIM) */
/* otherwise, need N ) */
/* (IWorkspace: if SENSE is 'V' or 'B', need SDIM*(N-SDIM) */
/* otherwise, need 0 ) */
i__1 = *lwork - iwrk + 1;
dtrsen_(sense, jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset],
ldvs, &wr[1], &wi[1], sdim, rconde, rcondv, &work[iwrk], &
i__1, &iwork[1], liwork, &icond);
if (! wantsn) {
/* Computing MAX */
i__1 = maxwrk, i__2 = *n + (*sdim << 1) * (*n - *sdim);
maxwrk = max(i__1,i__2);
}
if (icond == -15) {
/* Not enough real workspace */
*info = -16;
} else if (icond == -17) {
/* Not enough integer workspace */
*info = -18;
} else if (icond > 0) {
/* DTRSEN failed to reorder or to restore standard Schur form */
*info = icond + *n;
}
}
if (wantvs) {
/* Undo balancing */
/* (RWorkspace: need N) */
dgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs,
&ierr);
}
if (scalea) {
/* Undo scaling for the Schur form of A */
dlascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, &
ierr);
i__1 = *lda + 1;
dcopy_(n, &a[a_offset], &i__1, &wr[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];
}
if (cscale == smlnum) {
/* If scaling back towards underflow, adjust WI if an */
/* offdiagonal element of a 2-by-2 block in the Schur form */
/* underflows. */
if (ieval > 0) {
i1 = ieval + 1;
i2 = ihi - 1;
i__1 = ilo - 1;
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[
1], n, &ierr);
} else if (wantst) {
i1 = 1;
i2 = *n - 1;
} else {
i1 = ilo;
i2 = ihi - 1;
}
inxt = i1 - 1;
i__1 = i2;
for (i__ = i1; i__ <= i__1; ++i__) {
if (i__ < inxt) {
goto L20;
}
if (wi[i__] == 0.) {
inxt = i__ + 1;
} else {
if (a[i__ + 1 + i__ * a_dim1] == 0.) {
wi[i__] = 0.;
wi[i__ + 1] = 0.;
} else if (a[i__ + 1 + i__ * a_dim1] != 0. && a[i__ + (
i__ + 1) * a_dim1] == 0.) {
wi[i__] = 0.;
wi[i__ + 1] = 0.;
if (i__ > 1) {
i__2 = i__ - 1;
dswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[(
i__ + 1) * a_dim1 + 1], &c__1);
}
if (*n > i__ + 1) {
i__2 = *n - i__ - 1;
dswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, &
a[i__ + 1 + (i__ + 2) * a_dim1], lda);
}
dswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__ + 1)
* vs_dim1 + 1], &c__1);
a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ *
a_dim1];
a[i__ + 1 + i__ * a_dim1] = 0.;
}
inxt = i__ + 2;
}
L20:
;
}
}
i__1 = *n - ieval;
/* Computing MAX */
i__3 = *n - ieval;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval +
1], &i__2, &ierr);
}
if (wantst && *info == 0) {
/* Check if reordering successful */
lastsl = TRUE_;
lst2sl = TRUE_;
*sdim = 0;
ip = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
cursl = (*select)(&wr[i__], &wi[i__]);
if (wi[i__] == 0.) {
if (cursl) {
++(*sdim);
}
ip = 0;
if (cursl && ! lastsl) {
*info = *n + 2;
}
} else {
if (ip == 1) {
/* Last eigenvalue of conjugate pair */
cursl = cursl || lastsl;
lastsl = cursl;
if (cursl) {
*sdim += 2;
}
ip = -1;
if (cursl && ! lst2sl) {
*info = *n + 2;
}
} else {
/* First eigenvalue of conjugate pair */
ip = 1;
}
}
lst2sl = lastsl;
lastsl = cursl;
}
}
work[1] = (doublereal) maxwrk;
if (wantsv || wantsb) {
/* Computing MAX */
i__1 = 1, i__2 = *sdim * (*n - *sdim);
iwork[1] = max(i__1,i__2);
} else {
iwork[1] = 1;
}
return 0;
/* End of DGEESX */
} /* dgeesx_ */
/* 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_ */
/* Subroutine */ int dget37_(doublereal *rmax, integer *lmax, integer *ninfo,
integer *knt, integer *nin)
{
/* System generated locals */
integer i__1, i__2;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
integer s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
integer i__, j, m, n;
doublereal s[20], t[400] /* was [20][20] */, v, le[400] /* was [20][
20] */, re[400] /* was [20][20] */, wi[20], wr[20], val[3],
dum[1], eps, sep[20], sin__[20], tol, tmp[400] /* was [20][
20] */;
integer ifnd, icmp, iscl, info, lcmp[3], kmin;
doublereal wiin[20], vmax, tnrm, wrin[20], work[1200], vmul, stmp[20];
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
doublereal sepin[20];
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
doublereal vimin, tolin, vrmin;
integer iwork[40];
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 *), dlacpy_(char *, integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
logical select[20];
doublereal bignum;
extern /* Subroutine */ int dhseqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *), dtrevc_(char *, char *, logical *, integer *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *, integer *, integer *, doublereal *, integer *), dtrsna_(char *, char *, logical *, integer *, doublereal
*, integer *, doublereal *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *, integer *);
doublereal septmp[20], smlnum;
/* 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 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGET37 tests DTRSNA, a routine for estimating condition numbers of */
/* eigenvalues and/or right eigenvectors of a matrix. */
/* The test matrices are read from a file with logical unit number NIN. */
/* Arguments */
/* ========== */
/* RMAX (output) DOUBLE PRECISION array, dimension (3) */
/* Value of the largest test ratio. */
/* RMAX(1) = largest ratio comparing different calls to DTRSNA */
/* 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 DTRSNA 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 DTRSNA 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(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));
e_rsle();
if (n == 0) {
return 0;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___8.ciunit = *nin;
s_rsle(&io___8);
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: */
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
io___11.ciunit = *nin;
s_rsle(&io___11);
do_lio(&c__5, &c__1, (char *)&wrin[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&wiin[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&sin__[i__ - 1], (ftnlen)sizeof(
doublereal));
do_lio(&c__5, &c__1, (char *)&sepin[i__ - 1], (ftnlen)sizeof(
doublereal));
e_rsle();
/* L30: */
}
tnrm = dlange_("M", &n, &n, tmp, &c__20, work);
/* Begin test */
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);
/* L40: */
}
if (tnrm == 0.) {
vmul = 1.;
}
/* Compute eigenvalues and eigenvectors */
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 L240;
}
i__1 = n - 2;
for (j = 1; j <= i__1; ++j) {
i__2 = n;
for (i__ = j + 2; i__ <= i__2; ++i__) {
t[i__ + j * 20 - 21] = 0.;
/* L50: */
}
/* L60: */
}
/* Compute Schur form */
dhseqr_("S", "N", &n, &c__1, &n, t, &c__20, wr, wi, dum, &c__1, work,
&c__1200, &info);
if (info != 0) {
lmax[2] = *knt;
++ninfo[2];
goto L240;
}
/* Compute eigenvectors */
dtrevc_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20,
&n, &m, work, &info);
/* Compute condition numbers */
dtrsna_("Both", "All", select, &n, t, &c__20, le, &c__20, re, &c__20,
s, sep, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
/* Sort eigenvalues and condition numbers lexicographically */
/* to compare with inputs */
dcopy_(&n, wr, &c__1, wrtmp, &c__1);
dcopy_(&n, wi, &c__1, witmp, &c__1);
dcopy_(&n, s, &c__1, stmp, &c__1);
dcopy_(&n, sep, &c__1, septmp, &c__1);
d__1 = 1. / vmul;
dscal_(&n, &d__1, septmp, &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];
}
/* L70: */
}
wrtmp[kmin - 1] = wrtmp[i__ - 1];
witmp[kmin - 1] = witmp[i__ - 1];
wrtmp[i__ - 1] = vrmin;
witmp[i__ - 1] = vimin;
vrmin = stmp[kmin - 1];
stmp[kmin - 1] = stmp[i__ - 1];
stmp[i__ - 1] = vrmin;
vrmin = septmp[kmin - 1];
septmp[kmin - 1] = septmp[i__ - 1];
septmp[i__ - 1] = vrmin;
/* L80: */
}
/* Compare condition numbers for eigenvalues */
/* taking their condition numbers into account */
/* Computing MAX */
d__1 = (doublereal) n * 2. * eps * tnrm;
v = max(d__1,smlnum);
if (tnrm == 0.) {
v = 1.;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > septmp[i__ - 1]) {
tol = 1.;
} else {
tol = v / septmp[i__ - 1];
}
if (v > sepin[i__ - 1]) {
tolin = 1.;
} else {
tolin = v / sepin[i__ - 1];
}
/* 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__[i__ - 1] - tolin) > stmp[i__ - 1] + tol) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] - tolin > stmp[i__ - 1] + tol) {
vmax = (sin__[i__ - 1] - tolin) / (stmp[i__ - 1] + tol);
} else if (sin__[i__ - 1] + tolin < eps * (stmp[i__ - 1] - tol)) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] + tolin < stmp[i__ - 1] - tol) {
vmax = (stmp[i__ - 1] - tol) / (sin__[i__ - 1] + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* L90: */
}
/* Compare condition numbers for eigenvectors */
/* taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (v > septmp[i__ - 1] * stmp[i__ - 1]) {
tol = septmp[i__ - 1];
} else {
tol = v / stmp[i__ - 1];
}
if (v > sepin[i__ - 1] * sin__[i__ - 1]) {
tolin = sepin[i__ - 1];
} else {
tolin = v / sin__[i__ - 1];
}
/* 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[i__ - 1] - tolin) > septmp[i__ - 1] + tol) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] - tolin > septmp[i__ - 1] + tol) {
vmax = (sepin[i__ - 1] - tolin) / (septmp[i__ - 1] + tol);
} else if (sepin[i__ - 1] + tolin < eps * (septmp[i__ - 1] - tol))
{
vmax = 1. / eps;
} else if (sepin[i__ - 1] + tolin < septmp[i__ - 1] - tol) {
vmax = (septmp[i__ - 1] - tol) / (sepin[i__ - 1] + tolin);
} else {
vmax = 1.;
}
if (vmax > rmax[2]) {
rmax[2] = vmax;
if (ninfo[2] == 0) {
lmax[2] = *knt;
}
}
/* L100: */
}
/* Compare condition numbers for eigenvalues */
/* without taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (sin__[i__ - 1] <= (doublereal) (n << 1) * eps && stmp[i__ - 1]
<= (doublereal) (n << 1) * eps) {
vmax = 1.;
} else if (eps * sin__[i__ - 1] > stmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] > stmp[i__ - 1]) {
vmax = sin__[i__ - 1] / stmp[i__ - 1];
} else if (sin__[i__ - 1] < eps * stmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sin__[i__ - 1] < stmp[i__ - 1]) {
vmax = stmp[i__ - 1] / sin__[i__ - 1];
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* L110: */
}
/* Compare condition numbers for eigenvectors */
/* without taking their condition numbers into account */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (sepin[i__ - 1] <= v && septmp[i__ - 1] <= v) {
vmax = 1.;
} else if (eps * sepin[i__ - 1] > septmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] > septmp[i__ - 1]) {
vmax = sepin[i__ - 1] / septmp[i__ - 1];
} else if (sepin[i__ - 1] < eps * septmp[i__ - 1]) {
vmax = 1. / eps;
} else if (sepin[i__ - 1] < septmp[i__ - 1]) {
vmax = septmp[i__ - 1] / sepin[i__ - 1];
} else {
vmax = 1.;
}
if (vmax > rmax[3]) {
rmax[3] = vmax;
if (ninfo[3] == 0) {
lmax[3] = *knt;
}
}
/* L120: */
}
/* Compute eigenvalue condition numbers only and compare */
vmax = 0.;
dum[0] = -1.;
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "All", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L130: */
}
/* Compute eigenvector condition numbers only and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "All", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
/* L140: */
}
/* Compute all condition numbers using SELECT and compare */
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
select[i__ - 1] = TRUE_;
/* L150: */
}
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
/* L160: */
}
/* Compute eigenvalue condition numbers using SELECT and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != s[i__ - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L170: */
}
/* Compute eigenvector condition numbers using SELECT and compare */
dcopy_(&n, dum, &c__0, stmp, &c__1);
dcopy_(&n, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[i__ - 1]) {
vmax = 1. / eps;
}
/* L180: */
}
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
/* Select first real and first complex eigenvalue */
if (wi[0] == 0.) {
lcmp[0] = 1;
ifnd = 0;
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
if (ifnd == 1 || wi[i__ - 1] == 0.) {
select[i__ - 1] = FALSE_;
} else {
ifnd = 1;
lcmp[1] = i__;
lcmp[2] = i__ + 1;
dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[20], &c__1);
dcopy_(&n, &re[(i__ + 1) * 20 - 20], &c__1, &re[40], &
c__1);
dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[20], &c__1);
dcopy_(&n, &le[(i__ + 1) * 20 - 20], &c__1, &le[40], &
c__1);
}
/* L190: */
}
if (ifnd == 0) {
icmp = 1;
} else {
icmp = 3;
}
} else {
lcmp[0] = 1;
lcmp[1] = 2;
ifnd = 0;
i__1 = n;
for (i__ = 3; i__ <= i__1; ++i__) {
if (ifnd == 1 || wi[i__ - 1] != 0.) {
select[i__ - 1] = FALSE_;
} else {
lcmp[2] = i__;
ifnd = 1;
dcopy_(&n, &re[i__ * 20 - 20], &c__1, &re[40], &c__1);
dcopy_(&n, &le[i__ * 20 - 20], &c__1, &le[40], &c__1);
}
/* L200: */
}
if (ifnd == 0) {
icmp = 2;
} else {
icmp = 3;
}
}
/* Compute all selected condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Bothcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (septmp[i__ - 1] != sep[j - 1]) {
vmax = 1. / eps;
}
if (stmp[i__ - 1] != s[j - 1]) {
vmax = 1. / eps;
}
/* L210: */
}
/* Compute selected eigenvalue condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Eigcond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (stmp[i__ - 1] != s[j - 1]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
/* L220: */
}
/* Compute selected eigenvector condition numbers */
dcopy_(&icmp, dum, &c__0, stmp, &c__1);
dcopy_(&icmp, dum, &c__0, septmp, &c__1);
dtrsna_("Veccond", "Some", select, &n, t, &c__20, le, &c__20, re, &
c__20, stmp, septmp, &n, &m, work, &n, iwork, &info);
if (info != 0) {
lmax[3] = *knt;
++ninfo[3];
goto L240;
}
i__1 = icmp;
for (i__ = 1; i__ <= i__1; ++i__) {
j = lcmp[i__ - 1];
if (stmp[i__ - 1] != dum[0]) {
vmax = 1. / eps;
}
if (septmp[i__ - 1] != sep[j - 1]) {
vmax = 1. / eps;
}
/* L230: */
}
if (vmax > rmax[1]) {
rmax[1] = vmax;
if (ninfo[1] == 0) {
lmax[1] = *knt;
}
}
L240:
;
}
goto L10;
/* End of DGET37 */
} /* dget37_ */
/* Subroutine */
int dgees_(char *jobvs, char *sort, L_fp select, integer *n, doublereal *a, integer *lda, integer *sdim, doublereal *wr, doublereal *wi, doublereal *vs, integer *ldvs, doublereal *work, integer *lwork, logical *bwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, vs_dim1, vs_offset, i__1, i__2, i__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal s;
integer i1, i2, ip, ihi, ilo;
doublereal dum[1], eps, sep;
integer ibal;
doublereal anrm;
integer idum[1], ierr, itau, iwrk, inxt, icond, ieval;
extern logical lsame_(char *, char *);
extern /* Subroutine */
int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *);
logical cursl;
extern /* Subroutine */
int dlabad_(doublereal *, doublereal *), dgebak_( char *, char *, integer *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *), dgebal_(char *, integer *, doublereal *, integer *, integer *, integer *, doublereal *, integer *);
logical lst2sl, scalea;
extern doublereal dlamch_(char *);
doublereal cscale;
extern doublereal dlange_(char *, integer *, integer *, doublereal *, integer *, doublereal *);
extern /* Subroutine */
int dgehrd_(integer *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
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 *);
logical lastsl;
integer minwrk, maxwrk;
doublereal smlnum;
integer hswork;
logical wantst, lquery, wantvs;
/* -- 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 .. */
/* .. */
/* .. Function 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;
--wr;
--wi;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--work;
--bwork;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
wantvs = lsame_(jobvs, "V");
wantst = lsame_(sort, "S");
if (! wantvs && ! lsame_(jobvs, "N"))
{
*info = -1;
}
else if (! wantst && ! lsame_(sort, "N"))
{
*info = -2;
}
else if (*n < 0)
{
*info = -4;
}
else if (*lda < max(1,*n))
{
*info = -6;
}
else if (*ldvs < 1 || wantvs && *ldvs < *n)
{
*info = -11;
}
/* 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. */
/* NB refers to the optimal block size for the immediately */
/* following subroutine, as returned by ILAENV. */
/* HSWORK refers to the workspace preferred by DHSEQR, 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 << 1) + *n * ilaenv_(&c__1, "DGEHRD", " ", n, &c__1, n, &c__0);
minwrk = *n * 3;
dhseqr_("S", jobvs, n, &c__1, n, &a[a_offset], lda, &wr[1], &wi[1] , &vs[vs_offset], ldvs, &work[1], &c_n1, &ieval);
hswork = (integer) work[1];
if (! wantvs)
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + hswork; // , expr subst
maxwrk = max(i__1,i__2);
}
else
{
/* Computing MAX */
i__1 = maxwrk;
i__2 = (*n << 1) + (*n - 1) * ilaenv_(&c__1, "DORGHR", " ", n, &c__1, n, &c_n1); // , expr subst
maxwrk = max(i__1,i__2);
/* Computing MAX */
i__1 = maxwrk;
i__2 = *n + hswork; // , expr subst
maxwrk = max(i__1,i__2);
}
}
work[1] = (doublereal) maxwrk;
if (*lwork < minwrk && ! lquery)
{
*info = -13;
}
}
if (*info != 0)
{
i__1 = -(*info);
xerbla_("DGEES ", &i__1);
return 0;
}
else if (lquery)
{
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 = dlange_("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)
{
dlascl_("G", &c__0, &c__0, &anrm, &cscale, n, n, &a[a_offset], lda, & ierr);
}
/* Permute the matrix to make it more nearly triangular */
/* (Workspace: need N) */
ibal = 1;
dgebal_("P", n, &a[a_offset], lda, &ilo, &ihi, &work[ibal], &ierr);
/* Reduce to upper Hessenberg form */
/* (Workspace: need 3*N, prefer 2*N+N*NB) */
itau = *n + ibal;
iwrk = *n + itau;
i__1 = *lwork - iwrk + 1;
dgehrd_(n, &ilo, &ihi, &a[a_offset], lda, &work[itau], &work[iwrk], &i__1, &ierr);
if (wantvs)
{
/* Copy Householder vectors to VS */
dlacpy_("L", n, n, &a[a_offset], lda, &vs[vs_offset], ldvs) ;
/* Generate orthogonal matrix in VS */
/* (Workspace: need 3*N-1, prefer 2*N+(N-1)*NB) */
i__1 = *lwork - iwrk + 1;
dorghr_(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 */
/* (Workspace: need N+1, prefer N+HSWORK (see comments) ) */
iwrk = itau;
i__1 = *lwork - iwrk + 1;
dhseqr_("S", jobvs, n, &ilo, &ihi, &a[a_offset], lda, &wr[1], &wi[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)
{
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wr[1], n, & ierr);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, n, &c__1, &wi[1], n, & ierr);
}
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
bwork[i__] = (*select)(&wr[i__], &wi[i__]);
/* L10: */
}
/* Reorder eigenvalues and transform Schur vectors */
/* (Workspace: none needed) */
i__1 = *lwork - iwrk + 1;
dtrsen_("N", jobvs, &bwork[1], n, &a[a_offset], lda, &vs[vs_offset], ldvs, &wr[1], &wi[1], sdim, &s, &sep, &work[iwrk], &i__1, idum, &c__1, &icond);
if (icond > 0)
{
*info = *n + icond;
}
}
if (wantvs)
{
/* Undo balancing */
/* (Workspace: need N) */
dgebak_("P", "R", n, &ilo, &ihi, &work[ibal], n, &vs[vs_offset], ldvs, &ierr);
}
if (scalea)
{
/* Undo scaling for the Schur form of A */
dlascl_("H", &c__0, &c__0, &cscale, &anrm, n, n, &a[a_offset], lda, & ierr);
i__1 = *lda + 1;
dcopy_(n, &a[a_offset], &i__1, &wr[1], &c__1);
if (cscale == smlnum)
{
/* If scaling back towards underflow, adjust WI if an */
/* offdiagonal element of a 2-by-2 block in the Schur form */
/* underflows. */
if (ieval > 0)
{
i1 = ieval + 1;
i2 = ihi - 1;
i__1 = ilo - 1;
/* Computing MAX */
i__3 = ilo - 1;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ 1], &i__2, &ierr);
}
else if (wantst)
{
i1 = 1;
i2 = *n - 1;
}
else
{
i1 = ilo;
i2 = ihi - 1;
}
inxt = i1 - 1;
i__1 = i2;
for (i__ = i1;
i__ <= i__1;
++i__)
{
if (i__ < inxt)
{
goto L20;
}
if (wi[i__] == 0.)
{
inxt = i__ + 1;
}
else
{
if (a[i__ + 1 + i__ * a_dim1] == 0.)
{
wi[i__] = 0.;
wi[i__ + 1] = 0.;
}
else if (a[i__ + 1 + i__ * a_dim1] != 0. && a[i__ + ( i__ + 1) * a_dim1] == 0.)
{
wi[i__] = 0.;
wi[i__ + 1] = 0.;
if (i__ > 1)
{
i__2 = i__ - 1;
dswap_(&i__2, &a[i__ * a_dim1 + 1], &c__1, &a[( i__ + 1) * a_dim1 + 1], &c__1);
}
if (*n > i__ + 1)
{
i__2 = *n - i__ - 1;
dswap_(&i__2, &a[i__ + (i__ + 2) * a_dim1], lda, & a[i__ + 1 + (i__ + 2) * a_dim1], lda);
}
if (wantvs)
{
dswap_(n, &vs[i__ * vs_dim1 + 1], &c__1, &vs[(i__ + 1) * vs_dim1 + 1], &c__1);
}
a[i__ + (i__ + 1) * a_dim1] = a[i__ + 1 + i__ * a_dim1];
a[i__ + 1 + i__ * a_dim1] = 0.;
}
inxt = i__ + 2;
}
L20:
;
}
}
/* Undo scaling for the imaginary part of the eigenvalues */
i__1 = *n - ieval;
/* Computing MAX */
i__3 = *n - ieval;
i__2 = max(i__3,1);
dlascl_("G", &c__0, &c__0, &cscale, &anrm, &i__1, &c__1, &wi[ieval + 1], &i__2, &ierr);
}
if (wantst && *info == 0)
{
/* Check if reordering successful */
lastsl = TRUE_;
lst2sl = TRUE_;
*sdim = 0;
ip = 0;
i__1 = *n;
for (i__ = 1;
i__ <= i__1;
++i__)
{
cursl = (*select)(&wr[i__], &wi[i__]);
if (wi[i__] == 0.)
{
if (cursl)
{
++(*sdim);
}
ip = 0;
if (cursl && ! lastsl)
{
*info = *n + 2;
}
}
else
{
if (ip == 1)
{
/* Last eigenvalue of conjugate pair */
cursl = cursl || lastsl;
lastsl = cursl;
if (cursl)
{
*sdim += 2;
}
ip = -1;
if (cursl && ! lst2sl)
{
*info = *n + 2;
}
}
else
{
/* First eigenvalue of conjugate pair */
ip = 1;
}
}
lst2sl = lastsl;
lastsl = cursl;
/* L30: */
}
}
work[1] = (doublereal) maxwrk;
return 0;
/* End of DGEES */
}
