sanguis::server::entities::transfer_result
sanguis::server::entities::with_ai::on_create()
{
// TODO: Improve this!
sanguis::server::ai::tree::base_unique_ptr new_ai(
create_ai_(
ai_context_
)
);
sanguis::server::ai::tree::base &ai_ref(
*new_ai
);
ai_ =
optional_ai_unique_ptr(
std::move(
new_ai
)
);
return
ai_ref.transfer();
}
/* Subroutine */ int sdrgsx_(integer *nsize, integer *ncmax, real *thresh,
integer *nin, integer *nout, real *a, integer *lda, real *b, real *ai,
real *bi, real *z__, real *q, real *alphar, real *alphai, real *beta,
real *c__, integer *ldc, real *s, real *work, integer *lwork,
integer *iwork, integer *liwork, logical *bwork, integer *info)
{
/* Format strings */
static char fmt_9999[] = "(\002 SDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002)\002)";
static char fmt_9997[] = "(\002 SDRGSX: SGET53 returned INFO=\002,i1,"
"\002 for eigenvalue \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JT"
"YPE=\002,i6,\002)\002)";
static char fmt_9996[] = "(\002 SDRGSX: S not in Schur form at eigenvalu"
"e \002,i6,\002.\002,/9x,\002N=\002,i6,\002, JTYPE=\002,i6,\002"
")\002)";
static char fmt_9995[] = "(/1x,a3,\002 -- Real Expert Generalized Schur "
"form\002,\002 problem driver\002)";
static char fmt_9993[] = "(\002 Matrix types: \002,/\002 1: A is a blo"
"ck diagonal matrix of Jordan blocks \002,\002and B is the identi"
"ty \002,/\002 matrix, \002,/\002 2: A and B are upper tri"
"angular matrices, \002,/\002 3: A and B are as type 2, but eac"
"h second diagonal \002,\002block in A_11 and \002,/\002 eac"
"h third diaongal block in A_22 are 2x2 blocks,\002,/\002 4: A "
"and B are block diagonal matrices, \002,/\002 5: (A,B) has pot"
"entially close or common \002,\002eigenvalues.\002,/)";
static char fmt_9992[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/19x,\002 a is al"
"pha, b is beta, and \002,a,\002 means \002,a,\002.)\002,/\002 1"
" = | A - Q S Z\002,a,\002 | / ( |A| n ulp ) 2 = | B - Q T "
"Z\002,a,\002 | / ( |B| n ulp )\002,/\002 3 = | I - QQ\002,a,"
"\002 | / ( n ulp ) 4 = | I - ZZ\002,a,\002 | / ( n u"
"lp )\002,/\002 5 = 1/ULP if A is not in \002,\002Schur form "
"S\002,/\002 6 = difference between (alpha,beta)\002,\002 and di"
"agonals of (S,T)\002,/\002 7 = 1/ULP if SDIM is not the correc"
"t number of \002,\002selected eigenvalues\002,/\002 8 = 1/ULP "
"if DIFEST/DIFTRU > 10*THRESH or \002,\002DIFTRU/DIFEST > 10*THRE"
"SH\002,/\002 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B"
") \002,\002when reordering fails\002,/\002 10 = 1/ULP if PLEST/"
"PLTRU > THRESH or \002,\002PLTRU/PLEST > THRESH\002,/\002 ( T"
"est 10 is only for input examples )\002,/)";
static char fmt_9991[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,e10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,f8.2)";
static char fmt_9990[] = "(\002 Matrix order=\002,i2,\002, type=\002,i2"
",\002, a=\002,e10.4,\002, order(A_11)=\002,i2,\002, result \002,"
"i2,\002 is \002,0p,e10.4)";
static char fmt_9998[] = "(\002 SDRGSX: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, Input Example #\002,i2,\002"
")\002)";
static char fmt_9994[] = "(\002Input Example\002)";
static char fmt_9989[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,0p,f8.2)";
static char fmt_9988[] = "(\002 Input example #\002,i2,\002, matrix orde"
"r=\002,i4,\002,\002,\002 result \002,i2,\002 is\002,1p,e10.3)";
/* System generated locals */
integer a_dim1, a_offset, ai_dim1, ai_offset, b_dim1, b_offset, bi_dim1,
bi_offset, c_dim1, c_offset, q_dim1, q_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10;
/* Builtin functions */
double sqrt(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void),
s_rsle(cilist *), do_lio(integer *, integer *, char *, ftnlen),
e_rsle(void);
/* Local variables */
static real temp1, temp2;
static integer i__, j;
static real abnrm;
static integer ifunc, iinfo, linfo;
extern /* Subroutine */ int sget51_(integer *, integer *, real *, integer
*, real *, integer *, real *, integer *, real *, integer *, real *
, real *), sget53_(real *, integer *, real *, integer *, real *,
real *, real *, real *, integer *);
static char sense[1];
static integer nerrs, i1, ntest;
static real pltru;
extern /* Subroutine */ int slakf2_(integer *, integer *, real *, integer
*, real *, real *, real *, real *, integer *), slatm5_(integer *,
integer *, integer *, real *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *, real *,
integer *, real *, integer *, real *, integer *, real *, integer *
, integer *);
static logical ilabad;
static real thrsh2;
extern /* Subroutine */ int slabad_(real *, real *);
static integer mm, bdspac;
static real pl[2];
extern doublereal slamch_(char *), slange_(char *, integer *,
integer *, real *, integer *, real *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static real difest[2];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static real bignum;
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *);
static real weight;
extern /* Subroutine */ int sgesvd_(char *, char *, integer *, integer *,
real *, integer *, real *, real *, integer *, real *, integer *,
real *, integer *, integer *), slacpy_(char *,
integer *, integer *, real *, integer *, real *, integer *);
static real diftru;
extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *,
real *, real *, integer *), sggesx_(char *, char *, char *
, L_fp, char *, integer *, real *, integer *, real *, integer *,
integer *, real *, real *, real *, real *, integer *, real *,
integer *, real *, real *, real *, integer *, integer *, integer *
, logical *, integer *);
static integer minwrk, maxwrk;
static real smlnum;
static integer mn2, nptknt;
static real ulpinv, result[10];
static integer ntestt;
extern logical slctsx_();
static integer prtype, qba, qbb;
static real ulp;
/* Fortran I/O blocks */
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___35 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___36 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___37 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___39 = { 0, 0, 0, fmt_9991, 0 };
static cilist io___40 = { 0, 0, 0, fmt_9990, 0 };
static cilist io___42 = { 0, 0, 1, 0, 0 };
static cilist io___43 = { 0, 0, 1, 0, 0 };
static cilist io___44 = { 0, 0, 0, 0, 0 };
static cilist io___45 = { 0, 0, 0, 0, 0 };
static cilist io___46 = { 0, 0, 0, 0, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9989, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9988, 0 };
#define ai_ref(a_1,a_2) ai[(a_2)*ai_dim1 + a_1]
#define bi_ref(a_1,a_2) bi[(a_2)*bi_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
=======
SDRGSX checks the nonsymmetric generalized eigenvalue (Schur form)
problem expert driver SGGESX.
SGGESX factors A and B as Q S Z' and Q T Z', where ' means
transpose, T is upper triangular, S is in generalized Schur form
(block upper triangular, with 1x1 and 2x2 blocks on the diagonal,
the 2x2 blocks corresponding to complex conjugate pairs of
generalized eigenvalues), and Q and Z are orthogonal. It also
computes the generalized eigenvalues (alpha(1),beta(1)), ...,
(alpha(n),beta(n)). Thus, w(j) = alpha(j)/beta(j) is a root of the
characteristic equation
det( A - w(j) B ) = 0
Optionally it also reorders the eigenvalues so that a selected
cluster of eigenvalues appears in the leading diagonal block of the
Schur forms; computes a reciprocal condition number for the average
of the selected eigenvalues; and computes a reciprocal condition
number for the right and left deflating subspaces corresponding to
the selected eigenvalues.
When SDRGSX is called with NSIZE > 0, five (5) types of built-in
matrix pairs are used to test the routine SGGESX.
When SDRGSX is called with NSIZE = 0, it reads in test matrix data
to test SGGESX.
For each matrix pair, the following tests will be performed and
compared with the threshhold THRESH except for the tests (7) and (9):
(1) | A - Q S Z' | / ( |A| n ulp )
(2) | B - Q T Z' | / ( |B| n ulp )
(3) | I - QQ' | / ( n ulp )
(4) | I - ZZ' | / ( n ulp )
(5) if A is in Schur form (i.e. quasi-triangular form)
(6) maximum over j of D(j) where:
if alpha(j) is real:
|alpha(j) - S(j,j)| |beta(j) - T(j,j)|
D(j) = ------------------------ + -----------------------
max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
if alpha(j) is complex:
| det( s S - w T ) |
D(j) = ---------------------------------------------------
ulp max( s norm(S), |w| norm(T) )*norm( s S - w T )
and S and T are here the 2 x 2 diagonal blocks of S and T
corresponding to the j-th and j+1-th eigenvalues.
(7) if sorting worked and SDIM is the number of eigenvalues
which were selected.
(8) the estimated value DIF does not differ from the true values of
Difu and Difl more than a factor 10*THRESH. If the estimate DIF
equals zero the corresponding true values of Difu and Difl
should be less than EPS*norm(A, B). If the true value of Difu
and Difl equal zero, the estimate DIF should be less than
EPS*norm(A, B).
(9) If INFO = N+3 is returned by SGGESX, the reordering "failed"
and we check that DIF = PL = PR = 0 and that the true value of
Difu and Difl is < EPS*norm(A, B). We count the events when
INFO=N+3.
For read-in test matrices, the above tests are run except that the
exact value for DIF (and PL) is input data. Additionally, there is
one more test run for read-in test matrices:
(10) the estimated value PL does not differ from the true value of
PLTRU more than a factor THRESH. If the estimate PL equals
zero the corresponding true value of PLTRU should be less than
EPS*norm(A, B). If the true value of PLTRU equal zero, the
estimate PL should be less than EPS*norm(A, B).
Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1)
matrix pairs are generated and tested. NSIZE should be kept small.
SVD (routine SGESVD) is used for computing the true value of DIF_u
and DIF_l when testing the built-in test problems.
Built-in Test Matrices
======================
All built-in test matrices are the 2 by 2 block of triangular
matrices
A = [ A11 A12 ] and B = [ B11 B12 ]
[ A22 ] [ B22 ]
where for different type of A11 and A22 are given as the following.
A12 and B12 are chosen so that the generalized Sylvester equation
A11*R - L*A22 = -A12
B11*R - L*B22 = -B12
have prescribed solution R and L.
Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1).
B11 = I_m, B22 = I_k
where J_k(a,b) is the k-by-k Jordan block with ``a'' on
diagonal and ``b'' on superdiagonal.
Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and
B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m
A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and
B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k
Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each
second diagonal block in A_11 and each third diagonal block
in A_22 are made as 2 by 2 blocks.
Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) )
for i=1,...,m, j=1,...,m and
A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) )
for i=m+1,...,k, j=m+1,...,k
Type 5: (A,B) and have potentially close or common eigenvalues and
very large departure from block diagonality A_11 is chosen
as the m x m leading submatrix of A_1:
| 1 b |
| -b 1 |
| 1+d b |
| -b 1+d |
A_1 = | d 1 |
| -1 d |
| -d 1 |
| -1 -d |
| 1 |
and A_22 is chosen as the k x k leading submatrix of A_2:
| -1 b |
| -b -1 |
| 1-d b |
| -b 1-d |
A_2 = | d 1+b |
| -1-b d |
| -d 1+b |
| -1+b -d |
| 1-d |
and matrix B are chosen as identity matrices (see SLATM5).
Arguments
=========
NSIZE (input) INTEGER
The maximum size of the matrices to use. NSIZE >= 0.
If NSIZE = 0, no built-in tests matrices are used, but
read-in test matrices are used to test SGGESX.
NCMAX (input) INTEGER
Maximum allowable NMAX for generating Kroneker matrix
in call to SLAKF2
THRESH (input) REAL
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. THRESH >= 0.
NIN (input) INTEGER
The FORTRAN unit number for reading in the data file of
problems to solve.
NOUT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.)
A (workspace) REAL array, dimension (LDA, NSIZE)
Used to store the matrix whose eigenvalues are to be
computed. On exit, A contains the last matrix actually used.
LDA (input) INTEGER
The leading dimension of A, B, AI, BI, Z and Q,
LDA >= max( 1, NSIZE ). For the read-in test,
LDA >= max( 1, N ), N is the size of the test matrices.
B (workspace) REAL array, dimension (LDA, NSIZE)
Used to store the matrix whose eigenvalues are to be
computed. On exit, B contains the last matrix actually used.
AI (workspace) REAL array, dimension (LDA, NSIZE)
Copy of A, modified by SGGESX.
BI (workspace) REAL array, dimension (LDA, NSIZE)
Copy of B, modified by SGGESX.
Z (workspace) REAL array, dimension (LDA, NSIZE)
Z holds the left Schur vectors computed by SGGESX.
Q (workspace) REAL array, dimension (LDA, NSIZE)
Q holds the right Schur vectors computed by SGGESX.
ALPHAR (workspace) REAL array, dimension (NSIZE)
ALPHAI (workspace) REAL array, dimension (NSIZE)
BETA (workspace) REAL array, dimension (NSIZE)
On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues.
C (workspace) REAL array, dimension (LDC, LDC)
Store the matrix generated by subroutine SLAKF2, this is the
matrix formed by Kronecker products used for estimating
DIF.
LDC (input) INTEGER
The leading dimension of C. LDC >= max(1, LDA*LDA/2 ).
S (workspace) REAL array, dimension (LDC)
Singular values of C
WORK (workspace) REAL array, dimension (LWORK)
LWORK (input) INTEGER
The dimension of the array WORK.
LWORK >= MAX( 5*NSIZE*NSIZE/2 - 2, 10*(NSIZE+1) )
IWORK (workspace) INTEGER array, dimension (LIWORK)
LIWORK (input) INTEGER
The dimension of the array IWORK. LIWORK >= NSIZE + 6.
BWORK (workspace) LOGICAL array, dimension (LDA)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: A routine returned an error code.
=====================================================================
Check for errors
Parameter adjustments */
q_dim1 = *lda;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
z_dim1 = *lda;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
bi_dim1 = *lda;
bi_offset = 1 + bi_dim1 * 1;
bi -= bi_offset;
ai_dim1 = *lda;
ai_offset = 1 + ai_dim1 * 1;
ai -= ai_offset;
b_dim1 = *lda;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--alphar;
--alphai;
--beta;
c_dim1 = *ldc;
c_offset = 1 + c_dim1 * 1;
c__ -= c_offset;
--s;
--work;
--iwork;
--bwork;
/* Function Body */
if (*nsize < 0) {
*info = -1;
} else if (*thresh < 0.f) {
*info = -2;
} else if (*nin <= 0) {
*info = -3;
} else if (*nout <= 0) {
*info = -4;
} else if (*lda < 1 || *lda < *nsize) {
*info = -6;
} else if (*ldc < 1 || *ldc < *nsize * *nsize / 2) {
*info = -17;
} else if (*liwork < *nsize + 6) {
*info = -21;
}
/* 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.) */
minwrk = 1;
if (*info == 0 && *lwork >= 1) {
/* MINWRK = MAX( 10*( NSIZE+1 ), 5*NSIZE*NSIZE / 2-2 )
Computing MAX */
i__1 = (*nsize + 1) * 10, i__2 = *nsize * 5 * *nsize / 2;
minwrk = max(i__1,i__2);
/* workspace for sggesx */
maxwrk = (*nsize + 1) * 9 + *nsize * ilaenv_(&c__1, "SGEQRF", " ",
nsize, &c__1, nsize, &c__0, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
i__1 = maxwrk, i__2 = (*nsize + 1) * 9 + *nsize * ilaenv_(&c__1,
"SORGQR", " ", nsize, &c__1, nsize, &c_n1, (ftnlen)6, (ftnlen)
1);
maxwrk = max(i__1,i__2);
/* workspace for sgesvd */
bdspac = *nsize * 5 * *nsize / 2;
/* Computing MAX */
i__3 = *nsize * *nsize / 2;
i__4 = *nsize * *nsize / 2;
i__1 = maxwrk, i__2 = *nsize * 3 * *nsize / 2 + *nsize * *nsize *
ilaenv_(&c__1, "SGEBRD", " ", &i__3, &i__4, &c_n1, &c_n1, (
ftnlen)6, (ftnlen)1);
maxwrk = max(i__1,i__2);
maxwrk = max(maxwrk,bdspac);
maxwrk = max(maxwrk,minwrk);
work[1] = (real) maxwrk;
}
if (*lwork < minwrk) {
*info = -19;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("SDRGSX", &i__1);
return 0;
}
/* Important constants */
ulp = slamch_("P");
ulpinv = 1.f / ulp;
smlnum = slamch_("S") / ulp;
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
thrsh2 = *thresh * 10.f;
ntestt = 0;
nerrs = 0;
/* Go to the tests for read-in matrix pairs */
ifunc = 0;
if (*nsize == 0) {
goto L70;
}
/* Test the built-in matrix pairs.
Loop over different functions (IFUNC) of SGGESX, types (PRTYPE)
of test matrices, different size (M+N) */
prtype = 0;
qba = 3;
qbb = 4;
weight = sqrt(ulp);
for (ifunc = 0; ifunc <= 3; ++ifunc) {
for (prtype = 1; prtype <= 5; ++prtype) {
i__1 = *nsize - 1;
for (mn_1.m = 1; mn_1.m <= i__1; ++mn_1.m) {
i__2 = *nsize - mn_1.m;
for (mn_1.n = 1; mn_1.n <= i__2; ++mn_1.n) {
weight = 1.f / weight;
mn_1.mplusn = mn_1.m + mn_1.n;
/* Generate test matrices */
mn_1.fs = TRUE_;
mn_1.k = 0;
slaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b26, &
c_b26, &ai[ai_offset], lda);
slaset_("Full", &mn_1.mplusn, &mn_1.mplusn, &c_b26, &
c_b26, &bi[bi_offset], lda);
slatm5_(&prtype, &mn_1.m, &mn_1.n, &ai[ai_offset], lda, &
ai_ref(mn_1.m + 1, mn_1.m + 1), lda, &ai_ref(1,
mn_1.m + 1), lda, &bi[bi_offset], lda, &bi_ref(
mn_1.m + 1, mn_1.m + 1), lda, &bi_ref(1, mn_1.m +
1), lda, &q[q_offset], lda, &z__[z_offset], lda, &
weight, &qba, &qbb);
/* Compute the Schur factorization and swapping the
m-by-m (1,1)-blocks with n-by-n (2,2)-blocks.
Swapping is accomplished via the function SLCTSX
which is supplied below. */
if (ifunc == 0) {
*(unsigned char *)sense = 'N';
} else if (ifunc == 1) {
*(unsigned char *)sense = 'E';
} else if (ifunc == 2) {
*(unsigned char *)sense = 'V';
} else if (ifunc == 3) {
*(unsigned char *)sense = 'B';
}
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &a[a_offset], lda);
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &b[b_offset], lda);
sggesx_("V", "V", "S", (L_fp)slctsx_, sense, &mn_1.mplusn,
&ai[ai_offset], lda, &bi[bi_offset], lda, &mm, &
alphar[1], &alphai[1], &beta[1], &q[q_offset],
lda, &z__[z_offset], lda, pl, difest, &work[1],
lwork, &iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___22.ciunit = *nout;
s_wsfe(&io___22);
do_fio(&c__1, "SGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(integer)
);
e_wsfe();
*info = linfo;
goto L30;
}
/* Compute the norm(A, B) */
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset]
, lda, &work[1], &mn_1.mplusn);
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset]
, lda, &work[mn_1.mplusn * mn_1.mplusn + 1], &
mn_1.mplusn);
i__3 = mn_1.mplusn << 1;
abnrm = slange_("Fro", &mn_1.mplusn, &i__3, &work[1], &
mn_1.mplusn, &work[1]);
/* Do tests (1) to (4) */
sget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[
ai_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], result);
sget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &z__[z_offset]
, lda, &work[1], &result[1]);
sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &q[q_offset], lda, &q[q_offset],
lda, &work[1], &result[2]);
sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[
bi_offset], lda, &z__[z_offset], lda, &z__[
z_offset], lda, &work[1], &result[3]);
ntest = 4;
/* Do tests (5) and (6): check Schur form of A and
compare eigenvalues with diagonals. */
temp1 = 0.f;
result[4] = 0.f;
result[5] = 0.f;
i__3 = mn_1.mplusn;
for (j = 1; j <= i__3; ++j) {
ilabad = FALSE_;
if (alphai[j] == 0.f) {
/* Computing MAX */
r__7 = smlnum, r__8 = (r__2 = alphar[j], dabs(
r__2)), r__7 = max(r__7,r__8), r__8 = (
r__3 = ai_ref(j, j), dabs(r__3));
/* Computing MAX */
r__9 = smlnum, r__10 = (r__5 = beta[j], dabs(r__5)
), r__9 = max(r__9,r__10), r__10 = (r__6 =
bi_ref(j, j), dabs(r__6));
temp2 = ((r__1 = alphar[j] - ai_ref(j, j), dabs(
r__1)) / dmax(r__7,r__8) + (r__4 = beta[j]
- bi_ref(j, j), dabs(r__4)) / dmax(r__9,
r__10)) / ulp;
if (j < mn_1.mplusn) {
if (ai_ref(j + 1, j) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
if (ai_ref(j, j - 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
} else {
if (alphai[j] > 0.f) {
i1 = j;
} else {
i1 = j - 1;
}
if (i1 <= 0 || i1 >= mn_1.mplusn) {
ilabad = TRUE_;
} else if (i1 < mn_1.mplusn - 1) {
if (ai_ref(i1 + 2, i1 + 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
} else if (i1 > 1) {
if (ai_ref(i1, i1 - 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (! ilabad) {
sget53_(&ai_ref(i1, i1), lda, &bi_ref(i1, i1),
lda, &beta[j], &alphar[j], &alphai[j]
, &temp2, &iinfo);
if (iinfo >= 3) {
io___31.ciunit = *nout;
s_wsfe(&io___31);
do_fio(&c__1, (char *)&iinfo, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (
ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)
sizeof(integer));
e_wsfe();
*info = abs(iinfo);
}
} else {
temp2 = ulpinv;
}
}
temp1 = dmax(temp1,temp2);
if (ilabad) {
io___32.ciunit = *nout;
s_wsfe(&io___32);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
e_wsfe();
}
/* L10: */
}
result[5] = temp1;
ntest += 2;
/* Test (7) (if sorting worked) */
result[6] = 0.f;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
} else if (mm != mn_1.n) {
result[6] = ulpinv;
}
++ntest;
/* Test (8): compare the estimated value DIF and its
value. first, compute the exact DIF. */
result[7] = 0.f;
mn2 = mm * (mn_1.mplusn - mm) << 1;
if (ifunc >= 2 && mn2 <= *ncmax * *ncmax) {
/* Note: for either following two causes, there are
almost same number of test cases fail the test. */
i__3 = mn_1.mplusn - mm;
slakf2_(&mm, &i__3, &ai[ai_offset], lda, &ai_ref(mm +
1, mm + 1), &bi[bi_offset], &bi_ref(mm + 1,
mm + 1), &c__[c_offset], ldc);
i__3 = *lwork - 2;
sgesvd_("N", "N", &mn2, &mn2, &c__[c_offset], ldc, &s[
1], &work[1], &c__1, &work[2], &c__1, &work[3]
, &i__3, info);
diftru = s[mn2];
if (difest[1] == 0.f) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.f) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru *
thrsh2 < difest[1]) {
/* Computing MAX */
r__1 = diftru / difest[1], r__2 = difest[1] /
diftru;
result[7] = dmax(r__1,r__2);
}
++ntest;
}
/* Test (9) */
result[8] = 0.f;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.f) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.f) {
result[8] = ulpinv;
}
++ntest;
}
ntestt += ntest;
/* Print out tests which fail. */
for (j = 1; j <= 9; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail,
print a header to the data file. */
if (nerrs == 0) {
io___35.ciunit = *nout;
s_wsfe(&io___35);
do_fio(&c__1, "SGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___36.ciunit = *nout;
s_wsfe(&io___36);
e_wsfe();
/* Tests performed */
io___37.ciunit = *nout;
s_wsfe(&io___37);
do_fio(&c__1, "orthogonal", (ftnlen)10);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4f) {
io___39.ciunit = *nout;
s_wsfe(&io___39);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
real));
do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)
sizeof(real));
e_wsfe();
} else {
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)
sizeof(integer));
do_fio(&c__1, (char *)&prtype, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&weight, (ftnlen)sizeof(
real));
do_fio(&c__1, (char *)&mn_1.m, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)
sizeof(real));
e_wsfe();
}
}
/* L20: */
}
L30:
;
}
/* L40: */
}
/* L50: */
}
/* L60: */
}
goto L150;
L70:
/* Read in data from file to check accuracy of condition estimation
Read input data until N=0 */
nptknt = 0;
L80:
io___42.ciunit = *nin;
i__1 = s_rsle(&io___42);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer))
;
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
if (mn_1.mplusn == 0) {
goto L140;
}
io___43.ciunit = *nin;
i__1 = s_rsle(&io___43);
if (i__1 != 0) {
goto L140;
}
i__1 = do_lio(&c__3, &c__1, (char *)&mn_1.n, (ftnlen)sizeof(integer));
if (i__1 != 0) {
goto L140;
}
i__1 = e_rsle();
if (i__1 != 0) {
goto L140;
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___44.ciunit = *nin;
s_rsle(&io___44);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__4, &c__1, (char *)&ai_ref(i__, j), (ftnlen)sizeof(real)
);
}
e_rsle();
/* L90: */
}
i__1 = mn_1.mplusn;
for (i__ = 1; i__ <= i__1; ++i__) {
io___45.ciunit = *nin;
s_rsle(&io___45);
i__2 = mn_1.mplusn;
for (j = 1; j <= i__2; ++j) {
do_lio(&c__4, &c__1, (char *)&bi_ref(i__, j), (ftnlen)sizeof(real)
);
}
e_rsle();
/* L100: */
}
io___46.ciunit = *nin;
s_rsle(&io___46);
do_lio(&c__4, &c__1, (char *)&pltru, (ftnlen)sizeof(real));
do_lio(&c__4, &c__1, (char *)&diftru, (ftnlen)sizeof(real));
e_rsle();
++nptknt;
mn_1.fs = TRUE_;
mn_1.k = 0;
mn_1.m = mn_1.mplusn - mn_1.n;
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &a[
a_offset], lda);
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &b[
b_offset], lda);
/* Compute the Schur factorization while swaping the
m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. */
sggesx_("V", "V", "S", (L_fp)slctsx_, "B", &mn_1.mplusn, &ai[ai_offset],
lda, &bi[bi_offset], lda, &mm, &alphar[1], &alphai[1], &beta[1], &
q[q_offset], lda, &z__[z_offset], lda, pl, difest, &work[1],
lwork, &iwork[1], liwork, &bwork[1], &linfo);
if (linfo != 0 && linfo != mn_1.mplusn + 2) {
result[0] = ulpinv;
io___48.ciunit = *nout;
s_wsfe(&io___48);
do_fio(&c__1, "SGGESX", (ftnlen)6);
do_fio(&c__1, (char *)&linfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
goto L130;
}
/* Compute the norm(A, B)
(should this be norm of (A,B) or (AI,BI)?) */
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &ai[ai_offset], lda, &work[1],
&mn_1.mplusn);
slacpy_("Full", &mn_1.mplusn, &mn_1.mplusn, &bi[bi_offset], lda, &work[
mn_1.mplusn * mn_1.mplusn + 1], &mn_1.mplusn);
i__1 = mn_1.mplusn << 1;
abnrm = slange_("Fro", &mn_1.mplusn, &i__1, &work[1], &mn_1.mplusn, &work[
1]);
/* Do tests (1) to (4) */
sget51_(&c__1, &mn_1.mplusn, &a[a_offset], lda, &ai[ai_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], result);
sget51_(&c__1, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &z__[z_offset], lda, &work[1], &result[1]);
sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &q[
q_offset], lda, &q[q_offset], lda, &work[1], &result[2]);
sget51_(&c__3, &mn_1.mplusn, &b[b_offset], lda, &bi[bi_offset], lda, &z__[
z_offset], lda, &z__[z_offset], lda, &work[1], &result[3]);
/* Do tests (5) and (6): check Schur form of A and compare
eigenvalues with diagonals. */
ntest = 6;
temp1 = 0.f;
result[4] = 0.f;
result[5] = 0.f;
i__1 = mn_1.mplusn;
for (j = 1; j <= i__1; ++j) {
ilabad = FALSE_;
if (alphai[j] == 0.f) {
/* Computing MAX */
r__7 = smlnum, r__8 = (r__2 = alphar[j], dabs(r__2)), r__7 = max(
r__7,r__8), r__8 = (r__3 = ai_ref(j, j), dabs(r__3));
/* Computing MAX */
r__9 = smlnum, r__10 = (r__5 = beta[j], dabs(r__5)), r__9 = max(
r__9,r__10), r__10 = (r__6 = bi_ref(j, j), dabs(r__6));
temp2 = ((r__1 = alphar[j] - ai_ref(j, j), dabs(r__1)) / dmax(
r__7,r__8) + (r__4 = beta[j] - bi_ref(j, j), dabs(r__4)) /
dmax(r__9,r__10)) / ulp;
if (j < mn_1.mplusn) {
if (ai_ref(j + 1, j) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (j > 1) {
if (ai_ref(j, j - 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
} else {
if (alphai[j] > 0.f) {
i1 = j;
} else {
i1 = j - 1;
}
if (i1 <= 0 || i1 >= mn_1.mplusn) {
ilabad = TRUE_;
} else if (i1 < mn_1.mplusn - 1) {
if (ai_ref(i1 + 2, i1 + 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
} else if (i1 > 1) {
if (ai_ref(i1, i1 - 1) != 0.f) {
ilabad = TRUE_;
result[4] = ulpinv;
}
}
if (! ilabad) {
sget53_(&ai_ref(i1, i1), lda, &bi_ref(i1, i1), lda, &beta[j],
&alphar[j], &alphai[j], &temp2, &iinfo);
if (iinfo >= 3) {
io___49.ciunit = *nout;
s_wsfe(&io___49);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
}
} else {
temp2 = ulpinv;
}
}
temp1 = dmax(temp1,temp2);
if (ilabad) {
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
e_wsfe();
}
/* L110: */
}
result[5] = temp1;
/* Test (7) (if sorting worked) <--------- need to be checked. */
ntest = 7;
result[6] = 0.f;
if (linfo == mn_1.mplusn + 3) {
result[6] = ulpinv;
}
/* Test (8): compare the estimated value of DIF and its true value. */
ntest = 8;
result[7] = 0.f;
if (difest[1] == 0.f) {
if (diftru > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru == 0.f) {
if (difest[1] > abnrm * ulp) {
result[7] = ulpinv;
}
} else if (diftru > thrsh2 * difest[1] || diftru * thrsh2 < difest[1]) {
/* Computing MAX */
r__1 = diftru / difest[1], r__2 = difest[1] / diftru;
result[7] = dmax(r__1,r__2);
}
/* Test (9) */
ntest = 9;
result[8] = 0.f;
if (linfo == mn_1.mplusn + 2) {
if (diftru > abnrm * ulp) {
result[8] = ulpinv;
}
if (ifunc > 1 && difest[1] != 0.f) {
result[8] = ulpinv;
}
if (ifunc == 1 && pl[0] != 0.f) {
result[8] = ulpinv;
}
}
/* Test (10): compare the estimated value of PL and it true value. */
ntest = 10;
result[9] = 0.f;
if (pl[0] == 0.f) {
if (pltru > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru == 0.f) {
if (pl[0] > abnrm * ulp) {
result[9] = ulpinv;
}
} else if (pltru > *thresh * pl[0] || pltru * *thresh < pl[0]) {
result[9] = ulpinv;
}
ntestt += ntest;
/* Print out tests which fail. */
i__1 = ntest;
for (j = 1; j <= i__1; ++j) {
if (result[j - 1] >= *thresh) {
/* If this is the first test to fail,
print a header to the data file. */
if (nerrs == 0) {
io___51.ciunit = *nout;
s_wsfe(&io___51);
do_fio(&c__1, "SGX", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___52.ciunit = *nout;
s_wsfe(&io___52);
e_wsfe();
/* Tests performed */
io___53.ciunit = *nout;
s_wsfe(&io___53);
do_fio(&c__1, "orthogonal", (ftnlen)10);
do_fio(&c__1, "'", (ftnlen)1);
do_fio(&c__1, "transpose", (ftnlen)9);
for (i__ = 1; i__ <= 4; ++i__) {
do_fio(&c__1, "'", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[j - 1] < 1e4f) {
io___54.ciunit = *nout;
s_wsfe(&io___54);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(real));
e_wsfe();
} else {
io___55.ciunit = *nout;
s_wsfe(&io___55);
do_fio(&c__1, (char *)&nptknt, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&mn_1.mplusn, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(real));
e_wsfe();
}
}
/* L120: */
}
L130:
goto L80;
L140:
L150:
/* Summary */
alasvm_("SGX", nout, &nerrs, &ntestt, &c__0);
work[1] = (real) maxwrk;
return 0;
/* End of SDRGSX */
} /* sdrgsx_ */
