/* Subroutine */ int cdrgev_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, real *thresh, integer *nounit,
complex *a, integer *lda, complex *b, complex *s, complex *t, complex
*q, integer *ldq, complex *z__, complex *qe, integer *ldqe, complex *
alpha, complex *beta, complex *alpha1, complex *beta1, complex *work,
integer *lwork, real *rwork, real *result, integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 CDRGEV: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/3x,\002N=\002,i6,\002, JTYPE=\002,i6,\002, ISEED="
"(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 CDRGEV: \002,a,\002 Eigenvectors from"
" \002,a,\002 incorrectly \002,\002normalized.\002,/\002 Bits of "
"error=\002,0p,g10.3,\002,\002,3x,\002N=\002,i4,\002, JTYPE=\002,"
"i3,\002, ISEED=(\002,3(i4,\002,\002),i5,\002)\002)";
static char fmt_9997[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue"
" problem \002,\002driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see CDRGEV for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: \002,/\002 1 = max "
"| ( b A - a B )'*l | / const.,\002,/\002 2 = | |VR(i)| - 1 | / u"
"lp,\002,/\002 3 = max | ( b A - a B )*r | / const.\002,/\002 4 ="
" | |VL(i)| - 1 | / ulp,\002,/\002 5 = 0 if W same no matter if r"
" or l computed,\002,/\002 6 = 0 if l same no matter if l compute"
"d,\002,/\002 7 = 0 if r same no matter if r computed,\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i2,\002 is\002"
",1p,e10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, qe_dim1,
qe_offset, s_dim1, s_offset, t_dim1, t_offset, z_dim1, z_offset,
i__1, i__2, i__3, i__4, i__5, i__6, i__7;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Builtin functions */
double r_sign(real *, real *), c_abs(complex *);
void r_cnjg(complex *, complex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static integer iadd, ierr, nmax, i__, j, n;
static logical badnn;
extern /* Subroutine */ int cget52_(logical *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
complex *, complex *, real *, real *), cggev_(char *, char *,
integer *, complex *, integer *, complex *, integer *, complex *,
complex *, complex *, integer *, complex *, integer *, complex *,
integer *, real *, integer *);
static real rmagn[4];
static complex ctemp;
static integer nmats, jsize, nerrs, jtype, n1;
extern /* Subroutine */ int clatm4_(integer *, integer *, integer *,
integer *, logical *, real *, real *, real *, integer *, integer *
, complex *, integer *), cunm2r_(char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *);
static integer jc, nb, in;
extern /* Subroutine */ int slabad_(real *, real *);
static integer jr;
extern /* Subroutine */ int clarfg_(integer *, complex *, complex *,
integer *, complex *);
extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *);
static real safmin, safmax;
static integer ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), xerbla_(char *, integer *);
static integer minwrk, maxwrk;
static real ulpinv;
static integer mtypes, ntestt;
static real ulp;
/* Fortran I/O blocks */
static cilist io___40 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___48 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9991, 0 };
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]
#define qe_subscr(a_1,a_2) (a_2)*qe_dim1 + a_1
#define qe_ref(a_1,a_2) qe[qe_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
CDRGEV checks the nonsymmetric generalized eigenvalue problem driver
routine CGGEV.
CGGEV computes for a pair of n-by-n nonsymmetric matrices (A,B) the
generalized eigenvalues and, optionally, the left and right
eigenvectors.
A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
or a ratio alpha/beta = w, such that A - w*B is singular. It is
usually represented as the pair (alpha,beta), as there is reasonalbe
interpretation for beta=0, and even for both being zero.
A right generalized eigenvector corresponding to a generalized
eigenvalue w for a pair of matrices (A,B) is a vector r such that
(A - wB) * r = 0. A left generalized eigenvector is a vector l such
that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l.
When CDRGEV 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, a pair of matrices (A, B) will be generated
and used for testing. For each matrix pair, the following tests
will be performed and compared with the threshhold THRESH.
Results from CGGEV:
(1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of
| VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) )
where VL**H is the conjugate-transpose of VL.
(2) | |VL(i)| - 1 | / ulp and whether largest component real
VL(i) denotes the i-th column of VL.
(3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of
| (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) )
(4) | |VR(i)| - 1 | / ulp and whether largest component real
VR(i) denotes the i-th column of VR.
(5) W(full) = W(partial)
W(full) denotes the eigenvalues computed when both l and r
are also computed, and W(partial) denotes the eigenvalues
computed when only W, only W and r, or only W and l are
computed.
(6) VL(full) = VL(partial)
VL(full) denotes the left eigenvectors computed when both l
and r are computed, and VL(partial) denotes the result
when only l is computed.
(7) VR(full) = VR(partial)
VR(full) denotes the right eigenvectors computed when both l
and r are also computed, and VR(partial) denotes the result
when only l is computed.
Test Matrices
---- --------
The sizes of the test matrices 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) ( 0, 0 ) (a pair of zero matrices)
(2) ( I, 0 ) (an identity and a zero matrix)
(3) ( 0, I ) (an identity and a zero matrix)
(4) ( I, I ) (a pair of identity matrices)
t t
(5) ( J , J ) (a pair of transposed Jordan blocks)
t ( I 0 )
(6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
( 0 I ) ( 0 J )
and I is a k x k identity and J a (k+1)x(k+1)
Jordan block; k=(N-1)/2
(7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
matrix with those diagonal entries.)
(8) ( I, D )
(9) ( big*D, small*I ) where "big" is near overflow and small=1/big
(10) ( small*D, big*I )
(11) ( big*I, small*D )
(12) ( small*I, big*D )
(13) ( big*D, big*I )
(14) ( small*D, small*I )
(15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
t t
(16) Q ( J , J ) Z where Q and Z are random orthogonal matrices.
(17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
with random O(1) entries above the diagonal
and diagonal entries diag(T1) =
( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
( 0, N-3, N-4,..., 1, 0, 0 )
(18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
s = machine precision.
(19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
N-5
(20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
(21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
where r1,..., r(N-4) are random.
(22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
matrices.
Arguments
=========
NSIZES (input) INTEGER
The number of sizes of matrices to use. If it is zero,
CDRGES does nothing. NSIZES >= 0.
NN (input) INTEGER array, dimension (NSIZES)
An array containing the sizes to be used for the matrices.
Zero values will be skipped. NN >= 0.
NTYPES (input) INTEGER
The number of elements in DOTYPE. If it is zero, CDRGEV
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. .
DOTYPE (input) 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.
ISEED (input/output) 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 CDRGES to continue the same random number
sequence.
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. It must be at least zero.
NOUNIT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IERR not equal to 0.)
A (input/workspace) COMPLEX array, dimension(LDA, max(NN))
Used to hold the original A matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
LDA (input) INTEGER
The leading dimension of A, B, S, and T.
It must be at least 1 and at least max( NN ).
B (input/workspace) COMPLEX array, dimension(LDA, max(NN))
Used to hold the original B matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
S (workspace) COMPLEX array, dimension (LDA, max(NN))
The Schur form matrix computed from A by CGGEV. On exit, S
contains the Schur form matrix corresponding to the matrix
in A.
T (workspace) COMPLEX array, dimension (LDA, max(NN))
The upper triangular matrix computed from B by CGGEV.
Q (workspace) COMPLEX array, dimension (LDQ, max(NN))
The (left) eigenvectors matrix computed by CGGEV.
LDQ (input) INTEGER
The leading dimension of Q and Z. It must
be at least 1 and at least max( NN ).
Z (workspace) COMPLEX array, dimension( LDQ, max(NN) )
The (right) orthogonal matrix computed by CGGEV.
QE (workspace) COMPLEX array, dimension( LDQ, max(NN) )
QE holds the computed right or left eigenvectors.
LDQE (input) INTEGER
The leading dimension of QE. LDQE >= max(1,max(NN)).
ALPHA (workspace) COMPLEX array, dimension (max(NN))
BETA (workspace) COMPLEX array, dimension (max(NN))
The generalized eigenvalues of (A,B) computed by CGGEV.
( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th
generalized eigenvalue of A and B.
ALPHA1 (workspace) COMPLEX array, dimension (max(NN))
BETA1 (workspace) COMPLEX array, dimension (max(NN))
Like ALPHAR, ALPHAI, BETA, these arrays contain the
eigenvalues of A and B, but those computed when CGGEV only
computes a partial eigendecomposition, i.e. not the
eigenvalues and left and right eigenvectors.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The number of entries in WORK. LWORK >= N*(N+1)
RWORK (workspace) REAL array, dimension (8*N)
Real workspace.
RESULT (output) REAL array, dimension (2)
The values computed by the tests described above.
The values are currently limited to 1/ulp, to avoid overflow.
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. INFO is the
absolute value of the INFO value returned.
=====================================================================
Parameter adjustments */
--nn;
--dotype;
--iseed;
t_dim1 = *lda;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1 * 1;
s -= s_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;
z_dim1 = *ldq;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
qe_dim1 = *ldqe;
qe_offset = 1 + qe_dim1 * 1;
qe -= qe_offset;
--alpha;
--beta;
--alpha1;
--beta1;
--work;
--rwork;
--result;
/* Function Body
Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
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: */
}
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.f) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -9;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -14;
} else if (*ldqe <= 1 || *ldqe < nmax) {
*info = -17;
}
/* 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 = nmax * (nmax + 1);
/* Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "CGEQRF", " ", &nmax, &nmax, &c_n1, &
c_n1, (ftnlen)6, (ftnlen)1), i__1 = max(i__1,i__2), i__2 =
ilaenv_(&c__1, "CUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1, (
ftnlen)6, (ftnlen)2), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "CUNGQR", " ", &nmax, &nmax, &nmax, &c_n1, (ftnlen)6, (
ftnlen)1);
nb = max(i__1,i__2);
/* Computing MAX */
i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2
= nmax * (nmax + 1);
maxwrk = max(i__1,i__2);
work[1].r = (real) maxwrk, work[1].i = 0.f;
}
if (*lwork < minwrk) {
*info = -23;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CDRGEV", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = slamch_("Precision");
safmin = slamch_("Safe minimum");
safmin /= ulp;
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
ulpinv = 1.f / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.f;
rmagn[1] = 1.f;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (real) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L210;
}
++nmats;
/* Save ISEED in case of an error. */
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Generate test matrices A and B
Description of control parameters:
KCLASS: =1 means w/o rotation, =2 means w/ rotation,
=3 means random.
KATYPE: the "type" to be passed to CLATM4 for computing A.
KAZERO: the pattern of zeros on the diagonal for A:
=1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
=4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
=6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
non-zero entries.)
KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
=2: large, =3: small.
LASIGN: .TRUE. if the diagonal elements of A are to be
multiplied by a random magnitude 1 number.
KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
KTRIAN: =0: don't fill in the upper triangle, =1: do.
KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L100;
}
ierr = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
claset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
clatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = a_subscr(iadd, iadd);
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.f;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
claset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
clatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b28, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = b_subscr(iadd, iadd);
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.f;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations
Generate Q, Z as Householder transformations times
a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = q_subscr(jr, jc);
clarnd_(&q__1, &c__3, &iseed[1]);
q[i__5].r = q__1.r, q[i__5].i = q__1.i;
i__5 = z___subscr(jr, jc);
clarnd_(&q__1, &c__3, &iseed[1]);
z__[i__5].r = q__1.r, z__[i__5].i = q__1.i;
/* L30: */
}
i__4 = n + 1 - jc;
clarfg_(&i__4, &q_ref(jc, jc), &q_ref(jc + 1, jc), &
c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = q_subscr(jc, jc);
r__2 = q[i__5].r;
r__1 = r_sign(&c_b28, &r__2);
work[i__4].r = r__1, work[i__4].i = 0.f;
i__4 = q_subscr(jc, jc);
q[i__4].r = 1.f, q[i__4].i = 0.f;
i__4 = n + 1 - jc;
clarfg_(&i__4, &z___ref(jc, jc), &z___ref(jc + 1, jc),
&c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = z___subscr(jc, jc);
r__2 = z__[i__5].r;
r__1 = r_sign(&c_b28, &r__2);
work[i__4].r = r__1, work[i__4].i = 0.f;
i__4 = z___subscr(jc, jc);
z__[i__4].r = 1.f, z__[i__4].i = 0.f;
/* L40: */
}
clarnd_(&q__1, &c__3, &iseed[1]);
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__3 = q_subscr(n, n);
q[i__3].r = 1.f, q[i__3].i = 0.f;
i__3 = n;
work[i__3].r = 0.f, work[i__3].i = 0.f;
i__3 = n * 3;
r__1 = c_abs(&ctemp);
q__1.r = ctemp.r / r__1, q__1.i = ctemp.i / r__1;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
clarnd_(&q__1, &c__3, &iseed[1]);
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__3 = z___subscr(n, n);
z__[i__3].r = 1.f, z__[i__3].i = 0.f;
i__3 = n << 1;
work[i__3].r = 0.f, work[i__3].i = 0.f;
i__3 = n << 2;
r__1 = c_abs(&ctemp);
q__1.r = ctemp.r / r__1, q__1.i = ctemp.i / r__1;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = (n << 1) + jr;
r_cnjg(&q__3, &work[n * 3 + jc]);
q__2.r = work[i__6].r * q__3.r - work[i__6].i *
q__3.i, q__2.i = work[i__6].r * q__3.i +
work[i__6].i * q__3.r;
i__7 = a_subscr(jr, jc);
q__1.r = q__2.r * a[i__7].r - q__2.i * a[i__7].i,
q__1.i = q__2.r * a[i__7].i + q__2.i * a[
i__7].r;
a[i__5].r = q__1.r, a[i__5].i = q__1.i;
i__5 = b_subscr(jr, jc);
i__6 = (n << 1) + jr;
r_cnjg(&q__3, &work[n * 3 + jc]);
q__2.r = work[i__6].r * q__3.r - work[i__6].i *
q__3.i, q__2.i = work[i__6].r * q__3.i +
work[i__6].i * q__3.r;
i__7 = b_subscr(jr, jc);
q__1.r = q__2.r * b[i__7].r - q__2.i * b[i__7].i,
q__1.i = q__2.r * b[i__7].i + q__2.i * b[
i__7].r;
b[i__5].r = q__1.r, b[i__5].i = q__1.i;
/* L50: */
}
/* L60: */
}
i__3 = n - 1;
cunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
cunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
cunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &ierr);
if (ierr != 0) {
goto L90;
}
i__3 = n - 1;
cunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &ierr);
if (ierr != 0) {
goto L90;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = kamagn[jtype - 1];
clarnd_(&q__2, &c__4, &iseed[1]);
q__1.r = rmagn[i__6] * q__2.r, q__1.i = rmagn[i__6] *
q__2.i;
a[i__5].r = q__1.r, a[i__5].i = q__1.i;
i__5 = b_subscr(jr, jc);
i__6 = kbmagn[jtype - 1];
clarnd_(&q__2, &c__4, &iseed[1]);
q__1.r = rmagn[i__6] * q__2.r, q__1.i = rmagn[i__6] *
q__2.i;
b[i__5].r = q__1.r, b[i__5].i = q__1.i;
/* L70: */
}
/* L80: */
}
}
L90:
if (ierr != 0) {
io___40.ciunit = *nounit;
s_wsfe(&io___40);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&ierr, (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(ierr);
return 0;
}
L100:
for (i__ = 1; i__ <= 7; ++i__) {
result[i__] = -1.f;
/* L110: */
}
/* Call CGGEV to compute eigenvalues and eigenvectors. */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
cggev_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &alpha[
1], &beta[1], &q[q_offset], ldq, &z__[z_offset], ldq, &
work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "CGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (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(ierr);
goto L190;
}
/* Do the tests (1) and (2) */
cget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &q[
q_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1],
&result[1]);
if (result[2] > *thresh) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "CGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[2], (ftnlen)sizeof(real));
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();
}
/* Do the tests (3) and (4) */
cget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &z__[
z_offset], ldq, &alpha[1], &beta[1], &work[1], &rwork[1],
&result[3]);
if (result[4] > *thresh) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "CGGEV1", (ftnlen)6);
do_fio(&c__1, (char *)&result[4], (ftnlen)sizeof(real));
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();
}
/* Do test (5) */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
cggev_("N", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &z__[z_offset],
ldq, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, "CGGEV2", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (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(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[5] = ulpinv;
}
/* L120: */
}
/* Do test (6): Compute eigenvalues and left eigenvectors,
and test them */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
cggev_("V", "N", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &qe[qe_offset], ldqe, &z__[z_offset]
, ldq, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___46.ciunit = *nounit;
s_wsfe(&io___46);
do_fio(&c__1, "CGGEV3", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (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(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[6] = ulpinv;
}
/* L130: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
i__5 = q_subscr(j, jc);
i__6 = qe_subscr(j, jc);
if (q[i__5].r != qe[i__6].r || q[i__5].i != qe[i__6].i) {
result[6] = ulpinv;
}
/* L140: */
}
/* L150: */
}
/* Do test (7): Compute eigenvalues and right eigenvectors,
and test them */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
cggev_("N", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &qe[qe_offset],
ldqe, &work[1], lwork, &rwork[1], &ierr);
if (ierr != 0 && ierr != n + 1) {
result[1] = ulpinv;
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "CGGEV4", (ftnlen)6);
do_fio(&c__1, (char *)&ierr, (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(ierr);
goto L190;
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = j;
i__6 = j;
i__7 = j;
if (alpha[i__4].r != alpha1[i__5].r || alpha[i__4].i !=
alpha1[i__5].i || (beta[i__6].r != beta1[i__7].r ||
beta[i__6].i != beta1[i__7].i)) {
result[7] = ulpinv;
}
/* L160: */
}
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = n;
for (jc = 1; jc <= i__4; ++jc) {
i__5 = z___subscr(j, jc);
i__6 = qe_subscr(j, jc);
if (z__[i__5].r != qe[i__6].r || z__[i__5].i != qe[i__6]
.i) {
result[7] = ulpinv;
}
/* L170: */
}
/* L180: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L190:
ntestt += 7;
/* Print out tests which fail. */
for (jr = 1; jr <= 9; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail,
print a header to the data file. */
if (nerrs == 0) {
io___48.ciunit = *nounit;
s_wsfe(&io___48);
do_fio(&c__1, "CGV", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___49.ciunit = *nounit;
s_wsfe(&io___49);
e_wsfe();
io___50.ciunit = *nounit;
s_wsfe(&io___50);
e_wsfe();
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "Orthogonal", (ftnlen)10);
e_wsfe();
/* Tests performed */
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4f) {
io___53.ciunit = *nounit;
s_wsfe(&io___53);
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));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
real));
e_wsfe();
} else {
io___54.ciunit = *nounit;
s_wsfe(&io___54);
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));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
real));
e_wsfe();
}
}
/* L200: */
}
L210:
;
}
/* L220: */
}
/* Summary */
alasvm_("CGV", nounit, &nerrs, &ntestt, &c__0);
work[1].r = (real) maxwrk, work[1].i = 0.f;
return 0;
/* End of CDRGEV */
} /* cdrgev_ */
/* Subroutine */ int cggsvp_(char *jobu, char *jobv, char *jobq, integer *m,
integer *p, integer *n, complex *a, integer *lda, complex *b, integer
*ldb, real *tola, real *tolb, integer *k, integer *l, complex *u,
integer *ldu, complex *v, integer *ldv, complex *q, integer *ldq,
integer *iwork, real *rwork, complex *tau, complex *work, integer *
info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CGGSVP computes unitary matrices U, V and Q such that
N-K-L K L
U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )
N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )
N-K-L K L
V'*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )
where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the
conjugate transpose of Z.
This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
CGGSVD.
Arguments
=========
JOBU (input) CHARACTER*1
= 'U': Unitary matrix U is computed;
= 'N': U is not computed.
JOBV (input) CHARACTER*1
= 'V': Unitary matrix V is computed;
= 'N': V is not computed.
JOBQ (input) CHARACTER*1
= 'Q': Unitary matrix Q is computed;
= 'N': Q is not computed.
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
P (input) INTEGER
The number of rows of the matrix B. P >= 0.
N (input) INTEGER
The number of columns of the matrices A and B. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,P).
TOLA (input) REAL
TOLB (input) REAL
TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.
K (output) INTEGER
L (output) INTEGER
On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A',B')'.
U (output) COMPLEX array, dimension (LDU,M)
If JOBU = 'U', U contains the unitary matrix U.
If JOBU = 'N', U is not referenced.
LDU (input) INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = 'U'; LDU >= 1 otherwise.
V (output) COMPLEX array, dimension (LDV,M)
If JOBV = 'V', V contains the unitary matrix V.
If JOBV = 'N', V is not referenced.
LDV (input) INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = 'V'; LDV >= 1 otherwise.
Q (output) COMPLEX array, dimension (LDQ,N)
If JOBQ = 'Q', Q contains the unitary matrix Q.
If JOBQ = 'N', Q is not referenced.
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = 'Q'; LDQ >= 1 otherwise.
IWORK (workspace) INTEGER array, dimension (N)
RWORK (workspace) REAL array, dimension (2*N)
TAU (workspace) COMPLEX array, dimension (N)
WORK (workspace) COMPLEX array, dimension (max(3*N,M,P))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
===============
The subroutine uses LAPACK subroutine CGEQPF for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.
=====================================================================
Test the input parameters
Parameter adjustments */
/* Table of constant values */
static complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double r_imag(complex *);
/* Local variables */
static integer i__, j;
extern logical lsame_(char *, char *);
static logical wantq, wantu, wantv;
extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cgerq2_(integer *,
integer *, complex *, integer *, complex *, complex *, integer *),
cung2r_(integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *), cunm2r_(char *, char *, integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, complex *, integer *), cunmr2_(char
*, char *, integer *, integer *, integer *, complex *, integer *,
complex *, complex *, integer *, complex *, integer *), cgeqpf_(integer *, integer *, complex *, integer *,
integer *, complex *, complex *, real *, integer *), clacpy_(char
*, integer *, integer *, complex *, integer *, complex *, integer
*), claset_(char *, integer *, integer *, complex *,
complex *, complex *, integer *), xerbla_(char *, integer
*), clapmt_(logical *, integer *, integer *, complex *,
integer *, integer *);
static logical forwrd;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1
#define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)]
#define v_subscr(a_1,a_2) (a_2)*v_dim1 + a_1
#define v_ref(a_1,a_2) v[v_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--iwork;
--rwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U");
wantv = lsame_(jobv, "V");
wantq = lsame_(jobq, "Q");
forwrd = TRUE_;
*info = 0;
if (! (wantu || lsame_(jobu, "N"))) {
*info = -1;
} else if (! (wantv || lsame_(jobv, "N"))) {
*info = -2;
} else if (! (wantq || lsame_(jobq, "N"))) {
*info = -3;
} else if (*m < 0) {
*info = -4;
} else if (*p < 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < max(1,*m)) {
*info = -8;
} else if (*ldb < max(1,*p)) {
*info = -10;
} else if (*ldu < 1 || wantu && *ldu < *m) {
*info = -16;
} else if (*ldv < 1 || wantv && *ldv < *p) {
*info = -18;
} else if (*ldq < 1 || wantq && *ldq < *n) {
*info = -20;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGGSVP", &i__1);
return 0;
}
/* QR with column pivoting of B: B*P = V*( S11 S12 )
( 0 0 ) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L10: */
}
cgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], &rwork[1],
info);
/* Update A := A*P */
clapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
*l = 0;
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = b_subscr(i__, i__);
if ((r__1 = b[i__2].r, dabs(r__1)) + (r__2 = r_imag(&b_ref(i__, i__)),
dabs(r__2)) > *tolb) {
++(*l);
}
/* L20: */
}
if (wantv) {
/* Copy the details of V, and form V. */
claset_("Full", p, p, &c_b1, &c_b1, &v[v_offset], ldv);
if (*p > 1) {
i__1 = *p - 1;
clacpy_("Lower", &i__1, n, &b_ref(2, 1), ldb, &v_ref(2, 1), ldv);
}
i__1 = min(*p,*n);
cung2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
}
/* Clean up B */
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
if (*p > *l) {
i__1 = *p - *l;
claset_("Full", &i__1, n, &c_b1, &c_b1, &b_ref(*l + 1, 1), ldb);
}
if (wantq) {
/* Set Q = I and Update Q := Q*P */
claset_("Full", n, n, &c_b1, &c_b2, &q[q_offset], ldq);
clapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
}
if (*p >= *l && *n != *l) {
/* RQ factorization of ( S11 S12 ) = ( 0 S12 )*Z */
cgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
cunmr2_("Right", "Conjugate transpose", m, n, l, &b[b_offset], ldb, &
tau[1], &a[a_offset], lda, &work[1], info);
if (wantq) {
/* Update Q := Q*Z' */
cunmr2_("Right", "Conjugate transpose", n, n, l, &b[b_offset],
ldb, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up B */
i__1 = *n - *l;
claset_("Full", l, &i__1, &c_b1, &c_b1, &b[b_offset], ldb);
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
i__3 = b_subscr(i__, j);
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L50: */
}
/* L60: */
}
}
/* Let N-L L
A = ( A11 A12 ) M,
then the following does the complete QR decomposition of A11:
A11 = U*( 0 T12 )*P1'
( 0 0 ) */
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
iwork[i__] = 0;
/* L70: */
}
i__1 = *n - *l;
cgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], &rwork[
1], info);
/* Determine the effective rank of A11 */
*k = 0;
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = a_subscr(i__, i__);
if ((r__1 = a[i__2].r, dabs(r__1)) + (r__2 = r_imag(&a_ref(i__, i__)),
dabs(r__2)) > *tola) {
++(*k);
}
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
cunm2r_("Left", "Conjugate transpose", m, l, &i__1, &a[a_offset], lda, &
tau[1], &a_ref(1, *n - *l + 1), lda, &work[1], info);
if (wantu) {
/* Copy the details of U, and form U */
claset_("Full", m, m, &c_b1, &c_b1, &u[u_offset], ldu);
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
clacpy_("Lower", &i__1, &i__2, &a_ref(2, 1), lda, &u_ref(2, 1),
ldu);
}
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
cung2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
}
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
i__1 = *n - *l;
clapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
}
/* Clean up A: set the strictly lower triangular part of
A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L90: */
}
/* L100: */
}
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
claset_("Full", &i__1, &i__2, &c_b1, &c_b1, &a_ref(*k + 1, 1), lda);
}
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
i__1 = *n - *l;
cgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
i__1 = *n - *l;
cunmr2_("Right", "Conjugate transpose", n, &i__1, k, &a[a_offset],
lda, &tau[1], &q[q_offset], ldq, &work[1], info);
}
/* Clean up A */
i__1 = *n - *l - *k;
claset_("Full", k, &i__1, &c_b1, &c_b1, &a[a_offset], lda);
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L110: */
}
/* L120: */
}
}
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
i__1 = *m - *k;
cgeqr2_(&i__1, l, &a_ref(*k + 1, *n - *l + 1), lda, &tau[1], &work[1],
info);
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
cunm2r_("Right", "No transpose", m, &i__1, &i__2, &a_ref(*k + 1, *
n - *l + 1), lda, &tau[1], &u_ref(1, *k + 1), ldu, &work[
1], info);
}
/* Clean up */
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
i__3 = a_subscr(i__, j);
a[i__3].r = 0.f, a[i__3].i = 0.f;
/* L130: */
}
/* L140: */
}
}
return 0;
/* End of CGGSVP */
} /* cggsvp_ */
/* Subroutine */ int cerrqr_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
complex a[4] /* was [2][2] */, b[2];
integer i__, j;
complex w[2], x[2], af[4] /* was [2][2] */;
integer info;
extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cung2r_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *), cunm2r_(char *, char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *), alaesm_(char *, logical *, integer
*), cgeqrf_(integer *, integer *, complex *, integer *,
complex *, complex *, integer *, integer *), cgeqrs_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *, integer *), chkxer_(char *,
integer *, integer *, logical *, logical *), cungqr_(
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *), cunmqr_(char *, char *, integer
*, integer *, integer *, complex *, integer *, complex *, complex
*, integer *, complex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 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 .. */
/* .. */
/* Purpose */
/* ======= */
/* CERRQR tests the error exits for the COMPLEX routines */
/* that use the QR decomposition of a general matrix. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
i__1 = i__ + (j << 1) - 3;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = i__ + (j << 1) - 3;
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization */
/* CGEQRF */
s_copy(srnamc_1.srnamt, "CGEQRF", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQR2 */
s_copy(srnamc_1.srnamt, "CGEQR2", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQRS */
s_copy(srnamc_1.srnamt, "CGEQRS", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGQR */
s_copy(srnamc_1.srnamt, "CUNGQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cungqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cungqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNG2R */
s_copy(srnamc_1.srnamt, "CUNG2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cung2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cung2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMQR */
s_copy(srnamc_1.srnamt, "CUNMQR", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunmqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNM2R */
s_copy(srnamc_1.srnamt, "CUNM2R", (ftnlen)32, (ftnlen)6);
infoc_1.infot = 1;
cunm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRQR */
} /* cerrqr_ */
/* Subroutine */ int cgeqpf_(integer *m, integer *n, complex *a, integer *lda,
integer *jpvt, complex *tau, complex *work, real *rwork, integer *
info)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
This routine is deprecated and has been replaced by routine CGEQP3.
CGEQPF computes a QR factorization with column pivoting of a
complex M-by-N matrix A: A*P = Q*R.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the upper triangle of the array contains the
min(M,N)-by-N upper triangular matrix R; the elements
below the diagonal, together with the array TAU,
represent the unitary matrix Q as a product of
min(m,n) elementary reflectors.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
JPVT (input/output) INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace) COMPLEX array, dimension (N)
RWORK (workspace) REAL array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(n)
Each H(i) has the form
H = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
The matrix P is represented in jpvt as follows: If
jpvt(j) = i
then the jth column of P is the ith canonical unit vector.
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1;
complex q__1;
/* Builtin functions */
void r_cnjg(complex *, complex *);
double c_abs(complex *), sqrt(doublereal);
/* Local variables */
static real temp, temp2;
static integer i__, j;
extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex *
, integer *, complex *, complex *, integer *, complex *),
cswap_(integer *, complex *, integer *, complex *, integer *);
static integer itemp;
extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *);
extern doublereal scnrm2_(integer *, complex *, integer *);
extern /* Subroutine */ int cunm2r_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *);
static integer ma, mn;
extern /* Subroutine */ int clarfg_(integer *, complex *, complex *,
integer *, complex *), xerbla_(char *, integer *);
extern integer isamax_(integer *, real *, integer *);
static complex aii;
static integer pvt;
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--jpvt;
--tau;
--work;
--rwork;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGEQPF", &i__1);
return 0;
}
mn = min(*m,*n);
/* Move initial columns up front */
itemp = 1;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (jpvt[i__] != 0) {
if (i__ != itemp) {
cswap_(m, &a_ref(1, i__), &c__1, &a_ref(1, itemp), &c__1);
jpvt[i__] = jpvt[itemp];
jpvt[itemp] = i__;
} else {
jpvt[i__] = i__;
}
++itemp;
} else {
jpvt[i__] = i__;
}
/* L10: */
}
--itemp;
/* Compute the QR factorization and update remaining columns */
if (itemp > 0) {
ma = min(itemp,*m);
cgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
if (ma < *n) {
i__1 = *n - ma;
cunm2r_("Left", "Conjugate transpose", m, &i__1, &ma, &a[a_offset]
, lda, &tau[1], &a_ref(1, ma + 1), lda, &work[1], info);
}
}
if (itemp < mn) {
/* Initialize partial column norms. The first n elements of
work store the exact column norms. */
i__1 = *n;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
i__2 = *m - itemp;
rwork[i__] = scnrm2_(&i__2, &a_ref(itemp + 1, i__), &c__1);
rwork[*n + i__] = rwork[i__];
/* L20: */
}
/* Compute factorization */
i__1 = mn;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
/* Determine ith pivot column and swap if necessary */
i__2 = *n - i__ + 1;
pvt = i__ - 1 + isamax_(&i__2, &rwork[i__], &c__1);
if (pvt != i__) {
cswap_(m, &a_ref(1, pvt), &c__1, &a_ref(1, i__), &c__1);
itemp = jpvt[pvt];
jpvt[pvt] = jpvt[i__];
jpvt[i__] = itemp;
rwork[pvt] = rwork[i__];
rwork[*n + pvt] = rwork[*n + i__];
}
/* Generate elementary reflector H(i) */
i__2 = a_subscr(i__, i__);
aii.r = a[i__2].r, aii.i = a[i__2].i;
/* Computing MIN */
i__2 = i__ + 1;
i__3 = *m - i__ + 1;
clarfg_(&i__3, &aii, &a_ref(min(i__2,*m), i__), &c__1, &tau[i__]);
i__2 = a_subscr(i__, i__);
a[i__2].r = aii.r, a[i__2].i = aii.i;
if (i__ < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
i__2 = a_subscr(i__, i__);
aii.r = a[i__2].r, aii.i = a[i__2].i;
i__2 = a_subscr(i__, i__);
a[i__2].r = 1.f, a[i__2].i = 0.f;
i__2 = *m - i__ + 1;
i__3 = *n - i__;
r_cnjg(&q__1, &tau[i__]);
clarf_("Left", &i__2, &i__3, &a_ref(i__, i__), &c__1, &q__1, &
a_ref(i__, i__ + 1), lda, &work[1]);
i__2 = a_subscr(i__, i__);
a[i__2].r = aii.r, a[i__2].i = aii.i;
}
/* Update partial column norms */
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (rwork[j] != 0.f) {
/* Computing 2nd power */
r__1 = c_abs(&a_ref(i__, j)) / rwork[j];
temp = 1.f - r__1 * r__1;
temp = dmax(temp,0.f);
/* Computing 2nd power */
r__1 = rwork[j] / rwork[*n + j];
temp2 = temp * .05f * (r__1 * r__1) + 1.f;
if (temp2 == 1.f) {
if (*m - i__ > 0) {
i__3 = *m - i__;
rwork[j] = scnrm2_(&i__3, &a_ref(i__ + 1, j), &
c__1);
rwork[*n + j] = rwork[j];
} else {
rwork[j] = 0.f;
rwork[*n + j] = 0.f;
}
} else {
rwork[j] *= sqrt(temp);
}
}
/* L30: */
}
/* L40: */
}
}
return 0;
/* End of CGEQPF */
} /* cgeqpf_ */
int cunmqr_(char *side, char *trans, int *m, int *n,
int *k, complex *a, int *lda, complex *tau, complex *c__,
int *ldc, complex *work, int *lwork, int *info)
{
/* System generated locals */
address a__1[2];
int a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2], i__4,
i__5;
char ch__1[2];
/* Builtin functions */
int s_cat(char *, char **, int *, int *, unsigned long);
/* Local variables */
int i__;
complex t[4160] /* was [65][64] */;
int i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw, iws;
int left;
extern int lsame_(char *, char *);
int nbmin, iinfo;
extern int cunm2r_(char *, char *, int *, int *,
int *, complex *, int *, complex *, complex *, int *,
complex *, int *), clarfb_(char *, char *,
char *, char *, int *, int *, int *, complex *,
int *, complex *, int *, complex *, int *, complex *,
int *), clarft_(char *, char *
, int *, int *, complex *, int *, complex *, complex *
, int *), xerbla_(char *, int *);
extern int ilaenv_(int *, char *, char *, int *, int *,
int *, int *);
int notran;
int ldwork, lwkopt;
int lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CUNMQR overwrites the general complex M-by-N matrix C with */
/* SIDE = 'L' SIDE = 'R' */
/* TRANS = 'N': Q * C C * Q */
/* TRANS = 'C': Q**H * C C * Q**H */
/* where Q is a complex unitary matrix defined as the product of k */
/* elementary reflectors */
/* Q = H(1) H(2) . . . H(k) */
/* as returned by CGEQRF. Q is of order M if SIDE = 'L' and of order N */
/* if SIDE = 'R'. */
/* Arguments */
/* ========= */
/* SIDE (input) CHARACTER*1 */
/* = 'L': apply Q or Q**H from the Left; */
/* = 'R': apply Q or Q**H from the Right. */
/* TRANS (input) CHARACTER*1 */
/* = 'N': No transpose, apply Q; */
/* = 'C': Conjugate transpose, apply Q**H. */
/* M (input) INTEGER */
/* The number of rows of the matrix C. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix C. N >= 0. */
/* K (input) INTEGER */
/* The number of elementary reflectors whose product defines */
/* the matrix Q. */
/* If SIDE = 'L', M >= K >= 0; */
/* if SIDE = 'R', N >= K >= 0. */
/* A (input) COMPLEX array, dimension (LDA,K) */
/* The i-th column must contain the vector which defines the */
/* elementary reflector H(i), for i = 1,2,...,k, as returned by */
/* CGEQRF in the first k columns of its array argument A. */
/* A is modified by the routine but restored on exit. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. */
/* If SIDE = 'L', LDA >= MAX(1,M); */
/* if SIDE = 'R', LDA >= MAX(1,N). */
/* TAU (input) COMPLEX array, dimension (K) */
/* TAU(i) must contain the scalar factor of the elementary */
/* reflector H(i), as returned by CGEQRF. */
/* C (input/output) COMPLEX array, dimension (LDC,N) */
/* On entry, the M-by-N matrix C. */
/* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. */
/* LDC (input) INTEGER */
/* The leading dimension of the array C. LDC >= MAX(1,M). */
/* WORK (workspace/output) COMPLEX 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 SIDE = 'L', LWORK >= MAX(1,N); */
/* if SIDE = 'R', LWORK >= MAX(1,M). */
/* For optimum performance LWORK >= N*NB if SIDE = 'L', and */
/* LWORK >= M*NB if SIDE = 'R', where NB is the optimal */
/* blocksize. */
/* 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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
/* Function Body */
*info = 0;
left = lsame_(side, "L");
notran = lsame_(trans, "N");
lquery = *lwork == -1;
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = *m;
nw = *n;
} else {
nq = *n;
nw = *m;
}
if (! left && ! lsame_(side, "R")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "C")) {
*info = -2;
} else if (*m < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > nq) {
*info = -5;
} else if (*lda < MAX(1,nq)) {
*info = -7;
} else if (*ldc < MAX(1,*m)) {
*info = -10;
} else if (*lwork < MAX(1,nw) && ! lquery) {
*info = -12;
}
if (*info == 0) {
/* Determine the block size. NB may be at most NBMAX, where NBMAX */
/* is used to define the local array T. */
/* Computing MIN */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (unsigned long)2);
i__1 = 64, i__2 = ilaenv_(&c__1, "CUNMQR", ch__1, m, n, k, &c_n1);
nb = MIN(i__1,i__2);
lwkopt = MAX(1,nw) * nb;
work[1].r = (float) lwkopt, work[1].i = 0.f;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNMQR", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*m == 0 || *n == 0 || *k == 0) {
work[1].r = 1.f, work[1].i = 0.f;
return 0;
}
nbmin = 2;
ldwork = nw;
if (nb > 1 && nb < *k) {
iws = nw * nb;
if (*lwork < iws) {
nb = *lwork / ldwork;
/* Computing MAX */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = side;
i__3[1] = 1, a__1[1] = trans;
s_cat(ch__1, a__1, i__3, &c__2, (unsigned long)2);
i__1 = 2, i__2 = ilaenv_(&c__2, "CUNMQR", ch__1, m, n, k, &c_n1);
nbmin = MAX(i__1,i__2);
}
} else {
iws = nw;
}
if (nb < nbmin || nb >= *k) {
/* Use unblocked code */
cunm2r_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
c_offset], ldc, &work[1], &iinfo);
} else {
/* Use blocked code */
if (left && ! notran || ! left && notran) {
i1 = 1;
i2 = *k;
i3 = nb;
} else {
i1 = (*k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = *n;
jc = 1;
} else {
mi = *m;
ic = 1;
}
i__1 = i2;
i__2 = i3;
for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *k - i__ + 1;
ib = MIN(i__4,i__5);
/* Form the triangular factor of the block reflector */
/* H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i__ + 1;
clarft_("Forward", "Columnwise", &i__4, &ib, &a[i__ + i__ *
a_dim1], lda, &tau[i__], t, &c__65)
;
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = *m - i__ + 1;
ic = i__;
} else {
/* H or H' is applied to C(1:m,i:n) */
ni = *n - i__ + 1;
jc = i__;
}
/* Apply H or H' */
clarfb_(side, trans, "Forward", "Columnwise", &mi, &ni, &ib, &a[
i__ + i__ * a_dim1], lda, t, &c__65, &c__[ic + jc *
c_dim1], ldc, &work[1], &ldwork);
/* L10: */
}
}
work[1].r = (float) lwkopt, work[1].i = 0.f;
return 0;
/* End of CUNMQR */
} /* cunmqr_ */
/* Subroutine */ int cerrqr_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
real r__1, r__2;
complex q__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
static integer info;
static complex a[4] /* was [2][2] */, b[2];
static integer i__, j;
static complex w[2], x[2];
extern /* Subroutine */ int cgeqr2_(integer *, integer *, complex *,
integer *, complex *, complex *, integer *), cung2r_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *), cunm2r_(char *, char *, integer *, integer *, integer
*, complex *, integer *, complex *, complex *, integer *, complex
*, integer *);
static complex af[4] /* was [2][2] */;
extern /* Subroutine */ int alaesm_(char *, logical *, integer *),
cgeqrf_(integer *, integer *, complex *, integer *, complex *,
complex *, integer *, integer *), cgeqrs_(integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *, integer *), chkxer_(char *, integer *,
integer *, logical *, logical *), cungqr_(integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, integer *), cunmqr_(char *, char *, integer *, integer
*, integer *, complex *, integer *, complex *, complex *, integer
*, complex *, integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
#define a_subscr(a_1,a_2) (a_2)*2 + a_1 - 3
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define af_subscr(a_1,a_2) (a_2)*2 + a_1 - 3
#define af_ref(a_1,a_2) af[af_subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
CERRQR tests the error exits for the COMPLEX routines
that use the QR decomposition of a general matrix.
Arguments
=========
PATH (input) CHARACTER*3
The LAPACK path name for the routines to be tested.
NUNIT (input) INTEGER
The unit number for output.
===================================================================== */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
/* Set the variables to innocuous values. */
for (j = 1; j <= 2; ++j) {
for (i__ = 1; i__ <= 2; ++i__) {
i__1 = a_subscr(i__, j);
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
a[i__1].r = q__1.r, a[i__1].i = q__1.i;
i__1 = af_subscr(i__, j);
r__1 = 1.f / (real) (i__ + j);
r__2 = -1.f / (real) (i__ + j);
q__1.r = r__1, q__1.i = r__2;
af[i__1].r = q__1.r, af[i__1].i = q__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0.f, b[i__1].i = 0.f;
i__1 = j - 1;
w[i__1].r = 0.f, w[i__1].i = 0.f;
i__1 = j - 1;
x[i__1].r = 0.f, x[i__1].i = 0.f;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Error exits for QR factorization
CGEQRF */
s_copy(srnamc_1.srnamt, "CGEQRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cgeqrf_(&c_n1, &c__0, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrf_(&c__0, &c_n1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqrf_(&c__2, &c__1, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cgeqrf_(&c__1, &c__2, a, &c__1, b, w, &c__1, &info);
chkxer_("CGEQRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQR2 */
s_copy(srnamc_1.srnamt, "CGEQR2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cgeqr2_(&c_n1, &c__0, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqr2_(&c__0, &c_n1, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cgeqr2_(&c__2, &c__1, a, &c__1, b, w, &info);
chkxer_("CGEQR2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CGEQRS */
s_copy(srnamc_1.srnamt, "CGEQRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cgeqrs_(&c_n1, &c__0, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrs_(&c__0, &c_n1, &c__0, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cgeqrs_(&c__1, &c__2, &c__0, a, &c__2, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cgeqrs_(&c__0, &c__0, &c_n1, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cgeqrs_(&c__2, &c__1, &c__0, a, &c__1, x, b, &c__2, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cgeqrs_(&c__2, &c__1, &c__0, a, &c__2, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cgeqrs_(&c__1, &c__1, &c__2, a, &c__1, x, b, &c__1, w, &c__1, &info);
chkxer_("CGEQRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNGQR */
s_copy(srnamc_1.srnamt, "CUNGQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cungqr_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungqr_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cungqr_(&c__1, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungqr_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cungqr_(&c__1, &c__1, &c__2, a, &c__1, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cungqr_(&c__2, &c__2, &c__0, a, &c__1, x, w, &c__2, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
cungqr_(&c__2, &c__2, &c__0, a, &c__2, x, w, &c__1, &info);
chkxer_("CUNGQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNG2R */
s_copy(srnamc_1.srnamt, "CUNG2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cung2r_(&c_n1, &c__0, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2r_(&c__0, &c_n1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cung2r_(&c__1, &c__2, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2r_(&c__0, &c__0, &c_n1, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cung2r_(&c__2, &c__1, &c__2, a, &c__2, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cung2r_(&c__2, &c__1, &c__0, a, &c__1, x, w, &info);
chkxer_("CUNG2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNMQR */
s_copy(srnamc_1.srnamt, "CUNMQR", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cunmqr_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunmqr_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunmqr_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunmqr_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunmqr_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmqr_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunmqr_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunmqr_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmqr_("L", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
cunmqr_("R", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &c__1, &
info);
chkxer_("CUNMQR", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* CUNM2R */
s_copy(srnamc_1.srnamt, "CUNM2R", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
cunm2r_("/", "N", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
cunm2r_("L", "/", &c__0, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
cunm2r_("L", "N", &c_n1, &c__0, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
cunm2r_("L", "N", &c__0, &c_n1, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("L", "N", &c__0, &c__0, &c_n1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("L", "N", &c__0, &c__1, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
cunm2r_("R", "N", &c__1, &c__0, &c__1, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__1, x, af, &c__2, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
cunm2r_("R", "N", &c__1, &c__2, &c__0, a, &c__1, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
cunm2r_("L", "N", &c__2, &c__1, &c__0, a, &c__2, x, af, &c__1, w, &info);
chkxer_("CUNM2R", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of CERRQR */
} /* cerrqr_ */
/* Subroutine */ int cdrvgg_(integer *nsizes, integer *nn, integer *ntypes,
logical *dotype, integer *iseed, real *thresh, real *thrshn, integer *
nounit, complex *a, integer *lda, complex *b, complex *s, complex *t,
complex *s2, complex *t2, complex *q, integer *ldq, complex *z__,
complex *alpha1, complex *beta1, complex *alpha2, complex *beta2,
complex *vl, complex *vr, complex *work, integer *lwork, real *rwork,
real *result, integer *info)
{
/* Initialized data */
static integer kclass[26] = { 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,
2,2,2,3 };
static integer kbmagn[26] = { 1,1,1,1,1,1,1,1,3,2,3,2,2,3,1,1,1,1,1,1,1,3,
2,3,2,1 };
static integer ktrian[26] = { 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,
1,1,1,1 };
static logical lasign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
TRUE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,TRUE_,TRUE_,TRUE_,TRUE_,TRUE_,FALSE_ };
static logical lbsign[26] = { FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_,TRUE_,FALSE_,FALSE_,TRUE_,TRUE_,FALSE_,FALSE_,TRUE_,FALSE_,
TRUE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,FALSE_,
FALSE_ };
static integer kz1[6] = { 0,1,2,1,3,3 };
static integer kz2[6] = { 0,0,1,2,1,1 };
static integer kadd[6] = { 0,0,0,0,3,2 };
static integer katype[26] = { 0,1,0,1,2,3,4,1,4,4,1,1,4,4,4,2,4,5,8,7,9,4,
4,4,4,0 };
static integer kbtype[26] = { 0,0,1,1,2,-3,1,4,1,1,4,4,1,1,-4,2,-4,8,8,8,
8,8,8,8,8,0 };
static integer kazero[26] = { 1,1,1,1,1,1,2,1,2,2,1,1,2,2,3,1,3,5,5,5,5,3,
3,3,3,1 };
static integer kbzero[26] = { 1,1,1,1,1,1,1,2,1,1,2,2,1,1,4,1,4,6,6,6,6,4,
4,4,4,1 };
static integer kamagn[26] = { 1,1,1,1,1,1,1,1,2,3,2,3,2,3,1,1,1,1,1,1,1,2,
3,3,2,1 };
/* Format strings */
static char fmt_9999[] = "(\002 CDRVGG: \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 CDRVGG: \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[] = "(/1x,a3,\002 -- Complex Generalized eigenvalue"
" problem driver\002)";
static char fmt_9996[] = "(\002 Matrix types (see CDRVGG for details):"
" \002)";
static char fmt_9995[] = "(\002 Special Matrices:\002,23x,\002(J'=transp"
"osed Jordan block)\002,/\002 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I"
") 5=(J',J') \002,\0026=(diag(J',I), diag(I,J'))\002,/\002 Diag"
"onal Matrices: ( \002,\002D=diag(0,1,2,...) )\002,/\002 7=(D,"
"I) 9=(large*D, small*I\002,\002) 11=(large*I, small*D) 13=(l"
"arge*D, large*I)\002,/\002 8=(I,D) 10=(small*D, large*I) 12="
"(small*I, large*D) \002,\002 14=(small*D, small*I)\002,/\002 15"
"=(D, reversed D)\002)";
static char fmt_9994[] = "(\002 Matrices Rotated by Random \002,a,\002 M"
"atrices U, V:\002,/\002 16=Transposed Jordan Blocks "
" 19=geometric \002,\002alpha, beta=0,1\002,/\002 17=arithm. alp"
"ha&beta \002,\002 20=arithmetic alpha, beta=0,"
"1\002,/\002 18=clustered \002,\002alpha, beta=0,1 21"
"=random alpha, beta=0,1\002,/\002 Large & Small Matrices:\002,"
"/\002 22=(large, small) \002,\00223=(small,large) 24=(smal"
"l,small) 25=(large,large)\002,/\002 26=random O(1) matrices"
".\002)";
static char fmt_9993[] = "(/\002 Tests performed: (S is Schur, T is tri"
"angular, \002,\002Q and Z are \002,a,\002,\002,/20x,\002l and r "
"are the appropriate left and right\002,/19x,\002eigenvectors, re"
"sp., a is alpha, b is beta, and\002,/19x,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 ulp )\002,/\002 5 = difference between (alpha,beta"
") and diagonals of\002,\002 (S,T)\002,/\002 6 = max | ( b A - a "
"B )\002,a,\002 l | / const. 7 = max | ( b A - a B ) r | / cons"
"t.\002,/1x)";
static char fmt_9992[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",0p,f8.2)";
static char fmt_9991[] = "(\002 Matrix order=\002,i5,\002, type=\002,i2"
",\002, seed=\002,4(i4,\002,\002),\002 result \002,i3,\002 is\002"
",1p,e10.3)";
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, s_dim1,
s_offset, s2_dim1, s2_offset, t_dim1, t_offset, t2_dim1,
t2_offset, vl_dim1, vl_offset, vr_dim1, vr_offset, z_dim1,
z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8, i__9,
i__10, i__11;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7, r__8, r__9, r__10, r__11,
r__12, r__13, r__14, r__15, r__16;
complex q__1, q__2, q__3, q__4;
/* Builtin functions */
double r_sign(real *, real *), c_abs(complex *);
void r_cnjg(complex *, complex *);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double r_imag(complex *);
/* Local variables */
static integer iadd, nmax;
static real temp1, temp2;
static integer j, n;
static logical badnn;
extern /* Subroutine */ int cgegs_(char *, char *, integer *, complex *,
integer *, complex *, integer *, complex *, complex *, complex *,
integer *, complex *, integer *, complex *, integer *, real *,
integer *), cgegv_(char *, char *, integer *,
complex *, integer *, complex *, integer *, complex *, complex *,
complex *, integer *, complex *, integer *, complex *, integer *,
real *, integer *), cget51_(integer *, integer *,
complex *, integer *, complex *, integer *, complex *, integer *,
complex *, integer *, complex *, real *, real *), cget52_(logical
*, integer *, complex *, integer *, complex *, integer *, complex
*, integer *, complex *, complex *, complex *, real *, real *);
static real dumma[4];
static integer iinfo;
static real rmagn[4];
static complex ctemp;
static integer nmats, jsize, nerrs, i1, jtype, ntest, n1;
extern /* Subroutine */ int clatm4_(integer *, integer *, integer *,
integer *, logical *, real *, real *, real *, integer *, integer *
, complex *, integer *), cunm2r_(char *, char *, integer *,
integer *, integer *, complex *, integer *, complex *, complex *,
integer *, complex *, integer *);
static integer jc, nb;
extern /* Subroutine */ int slabad_(real *, real *);
static integer in, jr;
extern /* Subroutine */ int clarfg_(integer *, complex *, complex *,
integer *, complex *);
static integer ns;
extern /* Complex */ VOID clarnd_(complex *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *);
static real safmin, safmax;
static integer ioldsd[4];
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
extern /* Subroutine */ int alasvm_(char *, integer *, integer *, integer
*, integer *), claset_(char *, integer *, integer *,
complex *, complex *, complex *, integer *), xerbla_(char
*, integer *);
static real ulpinv;
static integer lwkopt, mtypes, ntestt, nbz;
static real ulp;
/* Fortran I/O blocks */
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___47 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___49 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___51 = { 0, 0, 0, fmt_9997, 0 };
static cilist io___52 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___53 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___54 = { 0, 0, 0, fmt_9994, 0 };
static cilist io___55 = { 0, 0, 0, fmt_9993, 0 };
static cilist io___56 = { 0, 0, 0, fmt_9992, 0 };
static cilist io___57 = { 0, 0, 0, fmt_9991, 0 };
#define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1
#define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)]
#define b_subscr(a_1,a_2) (a_2)*b_dim1 + a_1
#define b_ref(a_1,a_2) b[b_subscr(a_1,a_2)]
#define q_subscr(a_1,a_2) (a_2)*q_dim1 + a_1
#define q_ref(a_1,a_2) q[q_subscr(a_1,a_2)]
#define s_subscr(a_1,a_2) (a_2)*s_dim1 + a_1
#define s_ref(a_1,a_2) s[s_subscr(a_1,a_2)]
#define t_subscr(a_1,a_2) (a_2)*t_dim1 + a_1
#define t_ref(a_1,a_2) t[t_subscr(a_1,a_2)]
#define z___subscr(a_1,a_2) (a_2)*z_dim1 + a_1
#define z___ref(a_1,a_2) z__[z___subscr(a_1,a_2)]
/* -- LAPACK test routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CDRVGG checks the nonsymmetric generalized eigenvalue driver
routines.
T T T
CGEGS 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
(upper triangular), and Q and Z are unitary. It also
computes the generalized eigenvalues (alpha(1),beta(1)), ...,
(alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=T(j,j) --
thus, w(j) = alpha(j)/beta(j) is a root of the generalized
eigenvalue problem
det( A - w(j) B ) = 0
and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent
problem
det( m(j) A - B ) = 0
CGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ...,
(alpha(n),beta(n)), the matrix L whose columns contain the
generalized left eigenvectors l, and the matrix R whose columns
contain the generalized right eigenvectors r for the pair (A,B).
When CDRVGG 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, 7
tests will be performed and compared with the threshhold THRESH:
Results from CGEGS:
H
(1) | A - Q S Z | / ( |A| n ulp )
H
(2) | B - Q T Z | / ( |B| n ulp )
H
(3) | I - QQ | / ( n ulp )
H
(4) | I - ZZ | / ( n ulp )
(5) maximum over j of D(j) where:
|alpha(j) - S(j,j)| |beta(j) - T(j,j)|
D(j) = ------------------------ + -----------------------
max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|)
Results from CGEGV:
(6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of
| l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) )
where l**H is the conjugate tranpose of l.
(7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of
| (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) )
Test Matrices
---- --------
The sizes of the test matrices 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) ( 0, 0 ) (a pair of zero matrices)
(2) ( I, 0 ) (an identity and a zero matrix)
(3) ( 0, I ) (an identity and a zero matrix)
(4) ( I, I ) (a pair of identity matrices)
t t
(5) ( J , J ) (a pair of transposed Jordan blocks)
t ( I 0 )
(6) ( X, Y ) where X = ( J 0 ) and Y = ( t )
( 0 I ) ( 0 J )
and I is a k x k identity and J a (k+1)x(k+1)
Jordan block; k=(N-1)/2
(7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal
matrix with those diagonal entries.)
(8) ( I, D )
(9) ( big*D, small*I ) where "big" is near overflow and small=1/big
(10) ( small*D, big*I )
(11) ( big*I, small*D )
(12) ( small*I, big*D )
(13) ( big*D, big*I )
(14) ( small*D, small*I )
(15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and
D2 is diag( 0, N-3, N-4,..., 1, 0, 0 )
t t
(16) Q ( J , J ) Z where Q and Z are random unitary matrices.
(17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices
with random O(1) entries above the diagonal
and diagonal entries diag(T1) =
( 0, 0, 1, ..., N-3, 0 ) and diag(T2) =
( 0, N-3, N-4,..., 1, 0, 0 )
(18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 )
diag(T2) = ( 0, 1, 0, 1,..., 1, 0 )
s = machine precision.
(19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 )
N-5
(20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
(21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 )
diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 )
where r1,..., r(N-4) are random.
(22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 )
diag(T2) = ( 0, 1, ..., 1, 0, 0 )
(26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular
matrices.
Arguments
=========
NSIZES (input) INTEGER
The number of sizes of matrices to use. If it is zero,
CDRVGG does nothing. It must be at least zero.
NN (input) 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.
NTYPES (input) INTEGER
The number of elements in DOTYPE. If it is zero, CDRVGG
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. .
DOTYPE (input) 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.
ISEED (input/output) 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 CDRVGG to continue the same random number
sequence.
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. It must be at least zero.
THRSHN (input) REAL
Threshhold for reporting eigenvector normalization error.
If the normalization of any eigenvector differs from 1 by
more than THRSHN*ulp, then a special error message will be
printed. (This is handled separately from the other tests,
since only a compiler or programming error should cause an
error message, at least if THRSHN is at least 5--10.)
NOUNIT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.)
A (input/workspace) COMPLEX array, dimension (LDA, max(NN))
Used to hold the original A matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
LDA (input) INTEGER
The leading dimension of A, B, S, T, S2, and T2.
It must be at least 1 and at least max( NN ).
B (input/workspace) COMPLEX array, dimension (LDA, max(NN))
Used to hold the original B matrix. Used as input only
if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and
DOTYPE(MAXTYP+1)=.TRUE.
S (workspace) COMPLEX array, dimension (LDA, max(NN))
The upper triangular matrix computed from A by CGEGS.
T (workspace) COMPLEX array, dimension (LDA, max(NN))
The upper triangular matrix computed from B by CGEGS.
S2 (workspace) COMPLEX array, dimension (LDA, max(NN))
The matrix computed from A by CGEGV. This will be the
Schur (upper triangular) form of some matrix related to A,
but will not, in general, be the same as S.
T2 (workspace) COMPLEX array, dimension (LDA, max(NN))
The matrix computed from B by CGEGV. This will be the
Schur form of some matrix related to B, but will not, in
general, be the same as T.
Q (workspace) COMPLEX array, dimension (LDQ, max(NN))
The (left) unitary matrix computed by CGEGS.
LDQ (input) INTEGER
The leading dimension of Q, Z, VL, and VR. It must
be at least 1 and at least max( NN ).
Z (workspace) COMPLEX array, dimension (LDQ, max(NN))
The (right) unitary matrix computed by CGEGS.
ALPHA1 (workspace) COMPLEX array, dimension (max(NN))
BETA1 (workspace) COMPLEX array, dimension (max(NN))
The generalized eigenvalues of (A,B) computed by CGEGS.
ALPHA1(k) / BETA1(k) is the k-th generalized eigenvalue of
the matrices in A and B.
ALPHA2 (workspace) COMPLEX array, dimension (max(NN))
BETA2 (workspace) COMPLEX array, dimension (max(NN))
The generalized eigenvalues of (A,B) computed by CGEGV.
ALPHA2(k) / BETA2(k) is the k-th generalized eigenvalue of
the matrices in A and B.
VL (workspace) COMPLEX array, dimension (LDQ, max(NN))
The (lower triangular) left eigenvector matrix for the
matrices in A and B.
VR (workspace) COMPLEX array, dimension (LDQ, max(NN))
The (upper triangular) right eigenvector matrix for the
matrices in A and B.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The number of entries in WORK. This must be at least
MAX( 2*N, N*(NB+1), (k+1)*(2*k+N+1) ), where "k" is the
sum of the blocksize and number-of-shifts for CHGEQZ, and
NB is the greatest of the blocksizes for CGEQRF, CUNMQR,
and CUNGQR. (The blocksizes and the number-of-shifts are
retrieved through calls to ILAENV.)
RWORK (workspace) REAL array, dimension (8*N)
RESULT (output) REAL array, dimension (7)
The values computed by the tests described above.
The values are currently limited to 1/ulp, to avoid
overflow.
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. INFO is the
absolute value of the INFO value returned.
=====================================================================
Parameter adjustments */
--nn;
--dotype;
--iseed;
t2_dim1 = *lda;
t2_offset = 1 + t2_dim1 * 1;
t2 -= t2_offset;
s2_dim1 = *lda;
s2_offset = 1 + s2_dim1 * 1;
s2 -= s2_offset;
t_dim1 = *lda;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
s_dim1 = *lda;
s_offset = 1 + s_dim1 * 1;
s -= s_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;
vr_dim1 = *ldq;
vr_offset = 1 + vr_dim1 * 1;
vr -= vr_offset;
vl_dim1 = *ldq;
vl_offset = 1 + vl_dim1 * 1;
vl -= vl_offset;
z_dim1 = *ldq;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
--alpha1;
--beta1;
--alpha2;
--beta2;
--work;
--rwork;
--result;
/* Function Body
Check for errors */
*info = 0;
badnn = FALSE_;
nmax = 1;
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: */
}
/* Maximum blocksize and shift -- we assume that blocksize and number
of shifts are monotone increasing functions of N.
Computing MAX */
i__1 = 1, i__2 = ilaenv_(&c__1, "CGEQRF", " ", &nmax, &nmax, &c_n1, &c_n1,
(ftnlen)6, (ftnlen)1), i__1 = max(i__1,i__2), i__2 = ilaenv_(&
c__1, "CUNMQR", "LC", &nmax, &nmax, &nmax, &c_n1, (ftnlen)6, (
ftnlen)2), i__1 = max(i__1,i__2), i__2 = ilaenv_(&c__1, "CUNGQR",
" ", &nmax, &nmax, &nmax, &c_n1, (ftnlen)6, (ftnlen)1);
nb = max(i__1,i__2);
nbz = ilaenv_(&c__1, "CHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0, (ftnlen)
6, (ftnlen)3);
ns = ilaenv_(&c__4, "CHGEQZ", "SII", &nmax, &c__1, &nmax, &c__0, (ftnlen)
6, (ftnlen)3);
i1 = nbz + ns;
/* Computing MAX */
i__1 = nmax << 1, i__2 = nmax * (nb + 1), i__1 = max(i__1,i__2), i__2 = ((
i1 << 1) + nmax + 1) * (i1 + 1);
lwkopt = max(i__1,i__2);
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badnn) {
*info = -2;
} else if (*ntypes < 0) {
*info = -3;
} else if (*thresh < 0.f) {
*info = -6;
} else if (*lda <= 1 || *lda < nmax) {
*info = -10;
} else if (*ldq <= 1 || *ldq < nmax) {
*info = -19;
} else if (lwkopt > *lwork) {
*info = -30;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CDRVGG", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
ulp = slamch_("Precision");
safmin = slamch_("Safe minimum");
safmin /= ulp;
safmax = 1.f / safmin;
slabad_(&safmin, &safmax);
ulpinv = 1.f / ulp;
/* The values RMAGN(2:3) depend on N, see below. */
rmagn[0] = 0.f;
rmagn[1] = 1.f;
/* Loop over sizes, types */
ntestt = 0;
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
n = nn[jsize];
n1 = max(1,n);
rmagn[2] = safmax * ulp / (real) n1;
rmagn[3] = safmin * ulpinv * n1;
if (*nsizes != 1) {
mtypes = min(26,*ntypes);
} else {
mtypes = min(27,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L150;
}
++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 <= 7; ++j) {
result[j] = 0.f;
/* L30: */
}
/* Compute A and B
Description of control parameters:
KCLASS: =1 means w/o rotation, =2 means w/ rotation,
=3 means random.
KATYPE: the "type" to be passed to CLATM4 for computing A.
KAZERO: the pattern of zeros on the diagonal for A:
=1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
=4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
=6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
non-zero entries.)
KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
=2: large, =3: small.
LASIGN: .TRUE. if the diagonal elements of A are to be
multiplied by a random magnitude 1 number.
KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B.
KTRIAN: =0: don't fill in the upper triangle, =1: do.
KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
RMAGN: used to implement KAMAGN and KBMAGN. */
if (mtypes > 26) {
goto L110;
}
iinfo = 0;
if (kclass[jtype - 1] < 3) {
/* Generate A (w/o rotation) */
if ((i__3 = katype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
claset_("Full", &n, &n, &c_b1, &c_b1, &a[a_offset],
lda);
}
} else {
in = n;
}
clatm4_(&katype[jtype - 1], &in, &kz1[kazero[jtype - 1] - 1],
&kz2[kazero[jtype - 1] - 1], &lasign[jtype - 1], &
rmagn[kamagn[jtype - 1]], &ulp, &rmagn[ktrian[jtype -
1] * kamagn[jtype - 1]], &c__2, &iseed[1], &a[
a_offset], lda);
iadd = kadd[kazero[jtype - 1] - 1];
if (iadd > 0 && iadd <= n) {
i__3 = a_subscr(iadd, iadd);
i__4 = kamagn[jtype - 1];
a[i__3].r = rmagn[i__4], a[i__3].i = 0.f;
}
/* Generate B (w/o rotation) */
if ((i__3 = kbtype[jtype - 1], abs(i__3)) == 3) {
in = ((n - 1) / 2 << 1) + 1;
if (in != n) {
claset_("Full", &n, &n, &c_b1, &c_b1, &b[b_offset],
lda);
}
} else {
in = n;
}
clatm4_(&kbtype[jtype - 1], &in, &kz1[kbzero[jtype - 1] - 1],
&kz2[kbzero[jtype - 1] - 1], &lbsign[jtype - 1], &
rmagn[kbmagn[jtype - 1]], &c_b39, &rmagn[ktrian[jtype
- 1] * kbmagn[jtype - 1]], &c__2, &iseed[1], &b[
b_offset], lda);
iadd = kadd[kbzero[jtype - 1] - 1];
if (iadd != 0 && iadd <= n) {
i__3 = b_subscr(iadd, iadd);
i__4 = kbmagn[jtype - 1];
b[i__3].r = rmagn[i__4], b[i__3].i = 0.f;
}
if (kclass[jtype - 1] == 2 && n > 0) {
/* Include rotations
Generate Q, Z as Householder transformations times
a diagonal matrix. */
i__3 = n - 1;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = jc; jr <= i__4; ++jr) {
i__5 = q_subscr(jr, jc);
clarnd_(&q__1, &c__3, &iseed[1]);
q[i__5].r = q__1.r, q[i__5].i = q__1.i;
i__5 = z___subscr(jr, jc);
clarnd_(&q__1, &c__3, &iseed[1]);
z__[i__5].r = q__1.r, z__[i__5].i = q__1.i;
/* L40: */
}
i__4 = n + 1 - jc;
clarfg_(&i__4, &q_ref(jc, jc), &q_ref(jc + 1, jc), &
c__1, &work[jc]);
i__4 = (n << 1) + jc;
i__5 = q_subscr(jc, jc);
r__2 = q[i__5].r;
r__1 = r_sign(&c_b39, &r__2);
work[i__4].r = r__1, work[i__4].i = 0.f;
i__4 = q_subscr(jc, jc);
q[i__4].r = 1.f, q[i__4].i = 0.f;
i__4 = n + 1 - jc;
clarfg_(&i__4, &z___ref(jc, jc), &z___ref(jc + 1, jc),
&c__1, &work[n + jc]);
i__4 = n * 3 + jc;
i__5 = z___subscr(jc, jc);
r__2 = z__[i__5].r;
r__1 = r_sign(&c_b39, &r__2);
work[i__4].r = r__1, work[i__4].i = 0.f;
i__4 = z___subscr(jc, jc);
z__[i__4].r = 1.f, z__[i__4].i = 0.f;
/* L50: */
}
clarnd_(&q__1, &c__3, &iseed[1]);
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__3 = q_subscr(n, n);
q[i__3].r = 1.f, q[i__3].i = 0.f;
i__3 = n;
work[i__3].r = 0.f, work[i__3].i = 0.f;
i__3 = n * 3;
r__1 = c_abs(&ctemp);
q__1.r = ctemp.r / r__1, q__1.i = ctemp.i / r__1;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
clarnd_(&q__1, &c__3, &iseed[1]);
ctemp.r = q__1.r, ctemp.i = q__1.i;
i__3 = z___subscr(n, n);
z__[i__3].r = 1.f, z__[i__3].i = 0.f;
i__3 = n << 1;
work[i__3].r = 0.f, work[i__3].i = 0.f;
i__3 = n << 2;
r__1 = c_abs(&ctemp);
q__1.r = ctemp.r / r__1, q__1.i = ctemp.i / r__1;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* Apply the diagonal matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = (n << 1) + jr;
r_cnjg(&q__3, &work[n * 3 + jc]);
q__2.r = work[i__6].r * q__3.r - work[i__6].i *
q__3.i, q__2.i = work[i__6].r * q__3.i +
work[i__6].i * q__3.r;
i__7 = a_subscr(jr, jc);
q__1.r = q__2.r * a[i__7].r - q__2.i * a[i__7].i,
q__1.i = q__2.r * a[i__7].i + q__2.i * a[
i__7].r;
a[i__5].r = q__1.r, a[i__5].i = q__1.i;
i__5 = b_subscr(jr, jc);
i__6 = (n << 1) + jr;
r_cnjg(&q__3, &work[n * 3 + jc]);
q__2.r = work[i__6].r * q__3.r - work[i__6].i *
q__3.i, q__2.i = work[i__6].r * q__3.i +
work[i__6].i * q__3.r;
i__7 = b_subscr(jr, jc);
q__1.r = q__2.r * b[i__7].r - q__2.i * b[i__7].i,
q__1.i = q__2.r * b[i__7].i + q__2.i * b[
i__7].r;
b[i__5].r = q__1.r, b[i__5].i = q__1.i;
/* L60: */
}
/* L70: */
}
i__3 = n - 1;
cunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &a[a_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
cunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &a[a_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
cunm2r_("L", "N", &n, &n, &i__3, &q[q_offset], ldq, &work[
1], &b[b_offset], lda, &work[(n << 1) + 1], &
iinfo);
if (iinfo != 0) {
goto L100;
}
i__3 = n - 1;
cunm2r_("R", "C", &n, &n, &i__3, &z__[z_offset], ldq, &
work[n + 1], &b[b_offset], lda, &work[(n << 1) +
1], &iinfo);
if (iinfo != 0) {
goto L100;
}
}
} else {
/* Random matrices */
i__3 = n;
for (jc = 1; jc <= i__3; ++jc) {
i__4 = n;
for (jr = 1; jr <= i__4; ++jr) {
i__5 = a_subscr(jr, jc);
i__6 = kamagn[jtype - 1];
clarnd_(&q__2, &c__4, &iseed[1]);
q__1.r = rmagn[i__6] * q__2.r, q__1.i = rmagn[i__6] *
q__2.i;
a[i__5].r = q__1.r, a[i__5].i = q__1.i;
i__5 = b_subscr(jr, jc);
i__6 = kbmagn[jtype - 1];
clarnd_(&q__2, &c__4, &iseed[1]);
q__1.r = rmagn[i__6] * q__2.r, q__1.i = rmagn[i__6] *
q__2.i;
b[i__5].r = q__1.r, b[i__5].i = q__1.i;
/* L80: */
}
/* L90: */
}
}
L100:
if (iinfo != 0) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
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;
}
L110:
/* Call CGEGS to compute H, T, Q, Z, alpha, and beta. */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s[s_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t[t_offset], lda);
ntest = 1;
result[1] = ulpinv;
cgegs_("V", "V", &n, &s[s_offset], lda, &t[t_offset], lda, &
alpha1[1], &beta1[1], &q[q_offset], ldq, &z__[z_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, "CGEGS", (ftnlen)5);
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 L130;
}
ntest = 4;
/* Do tests 1--4 */
cget51_(&c__1, &n, &a[a_offset], lda, &s[s_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[1]);
cget51_(&c__1, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[2]);
cget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &q[
q_offset], ldq, &q[q_offset], ldq, &work[1], &rwork[1], &
result[3]);
cget51_(&c__3, &n, &b[b_offset], lda, &t[t_offset], lda, &z__[
z_offset], ldq, &z__[z_offset], ldq, &work[1], &rwork[1],
&result[4]);
/* Do test 5: compare eigenvalues with diagonals. */
temp1 = 0.f;
i__3 = n;
for (j = 1; j <= i__3; ++j) {
i__4 = j;
i__5 = s_subscr(j, j);
q__2.r = alpha1[i__4].r - s[i__5].r, q__2.i = alpha1[i__4].i
- s[i__5].i;
q__1.r = q__2.r, q__1.i = q__2.i;
i__6 = j;
i__7 = t_subscr(j, j);
q__4.r = beta1[i__6].r - t[i__7].r, q__4.i = beta1[i__6].i -
t[i__7].i;
q__3.r = q__4.r, q__3.i = q__4.i;
/* Computing MAX */
i__8 = j;
i__9 = s_subscr(j, j);
r__13 = safmin, r__14 = (r__1 = alpha1[i__8].r, dabs(r__1)) +
(r__2 = r_imag(&alpha1[j]), dabs(r__2)), r__13 = max(
r__13,r__14), r__14 = (r__3 = s[i__9].r, dabs(r__3))
+ (r__4 = r_imag(&s_ref(j, j)), dabs(r__4));
/* Computing MAX */
i__10 = j;
i__11 = t_subscr(j, j);
r__15 = safmin, r__16 = (r__5 = beta1[i__10].r, dabs(r__5)) +
(r__6 = r_imag(&beta1[j]), dabs(r__6)), r__15 = max(
r__15,r__16), r__16 = (r__7 = t[i__11].r, dabs(r__7))
+ (r__8 = r_imag(&t_ref(j, j)), dabs(r__8));
temp2 = (((r__9 = q__1.r, dabs(r__9)) + (r__10 = r_imag(&q__1)
, dabs(r__10))) / dmax(r__13,r__14) + ((r__11 =
q__3.r, dabs(r__11)) + (r__12 = r_imag(&q__3), dabs(
r__12))) / dmax(r__15,r__16)) / ulp;
temp1 = dmax(temp1,temp2);
/* L120: */
}
result[5] = temp1;
/* Call CGEGV to compute S2, T2, VL, and VR, do tests.
Eigenvalues and Eigenvectors */
clacpy_(" ", &n, &n, &a[a_offset], lda, &s2[s2_offset], lda);
clacpy_(" ", &n, &n, &b[b_offset], lda, &t2[t2_offset], lda);
ntest = 6;
result[6] = ulpinv;
cgegv_("V", "V", &n, &s2[s2_offset], lda, &t2[t2_offset], lda, &
alpha2[1], &beta2[1], &vl[vl_offset], ldq, &vr[vr_offset],
ldq, &work[1], lwork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___47.ciunit = *nounit;
s_wsfe(&io___47);
do_fio(&c__1, "CGEGV", (ftnlen)5);
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 L130;
}
ntest = 7;
/* Do Tests 6 and 7 */
cget52_(&c_true, &n, &a[a_offset], lda, &b[b_offset], lda, &vl[
vl_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[6] = dumma[0];
if (dumma[1] > *thrshn) {
io___49.ciunit = *nounit;
s_wsfe(&io___49);
do_fio(&c__1, "Left", (ftnlen)4);
do_fio(&c__1, "CGEGV", (ftnlen)5);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(real));
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();
}
cget52_(&c_false, &n, &a[a_offset], lda, &b[b_offset], lda, &vr[
vr_offset], ldq, &alpha2[1], &beta2[1], &work[1], &rwork[
1], dumma);
result[7] = dumma[0];
if (dumma[1] > *thresh) {
io___50.ciunit = *nounit;
s_wsfe(&io___50);
do_fio(&c__1, "Right", (ftnlen)5);
do_fio(&c__1, "CGEGV", (ftnlen)5);
do_fio(&c__1, (char *)&dumma[1], (ftnlen)sizeof(real));
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();
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L130:
ntestt += ntest;
/* Print out tests which fail. */
i__3 = ntest;
for (jr = 1; jr <= i__3; ++jr) {
if (result[jr] >= *thresh) {
/* If this is the first test to fail,
print a header to the data file. */
if (nerrs == 0) {
io___51.ciunit = *nounit;
s_wsfe(&io___51);
do_fio(&c__1, "CGG", (ftnlen)3);
e_wsfe();
/* Matrix types */
io___52.ciunit = *nounit;
s_wsfe(&io___52);
e_wsfe();
io___53.ciunit = *nounit;
s_wsfe(&io___53);
e_wsfe();
io___54.ciunit = *nounit;
s_wsfe(&io___54);
do_fio(&c__1, "Unitary", (ftnlen)7);
e_wsfe();
/* Tests performed */
io___55.ciunit = *nounit;
s_wsfe(&io___55);
do_fio(&c__1, "unitary", (ftnlen)7);
do_fio(&c__1, "*", (ftnlen)1);
do_fio(&c__1, "conjugate transpose", (ftnlen)19);
for (j = 1; j <= 5; ++j) {
do_fio(&c__1, "*", (ftnlen)1);
}
e_wsfe();
}
++nerrs;
if (result[jr] < 1e4f) {
io___56.ciunit = *nounit;
s_wsfe(&io___56);
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));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
real));
e_wsfe();
} else {
io___57.ciunit = *nounit;
s_wsfe(&io___57);
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));
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
real));
e_wsfe();
}
}
/* L140: */
}
L150:
;
}
/* L160: */
}
/* Summary */
alasvm_("CGG", nounit, &nerrs, &ntestt, &c__0);
return 0;
/* End of CDRVGG */
} /* cdrvgg_ */
doublereal cqrt11_(integer *m, integer *k, complex *a, integer *lda, complex *
tau, complex *work, integer *lwork)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real ret_val;
complex q__1;
/* Local variables */
static integer info, j;
extern /* Subroutine */ int cunm2r_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), slamch_(char *);
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *), xerbla_(char *,
integer *);
static real rdummy[1];
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
CQRT11 computes the test ratio
|| Q'*Q - I || / (eps * m)
where the orthogonal matrix Q is represented as a product of
elementary transformations. Each transformation has the form
H(k) = I - tau(k) v(k) v(k)'
where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form
[ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored
in A(k+1:m,k).
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A.
K (input) INTEGER
The number of columns of A whose subdiagonal entries
contain information about orthogonal transformations.
A (input) COMPLEX array, dimension (LDA,K)
The (possibly partial) output of a QR reduction routine.
LDA (input) INTEGER
The leading dimension of the array A.
TAU (input) COMPLEX array, dimension (K)
The scaling factors tau for the elementary transformations as
computed by the QR factorization routine.
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The length of the array WORK. LWORK >= M*M + M.
=====================================================================
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Function Body */
ret_val = 0.f;
/* Test for sufficient workspace */
if (*lwork < *m * *m + *m) {
xerbla_("CQRT11", &c__7);
return ret_val;
}
/* Quick return if possible */
if (*m <= 0) {
return ret_val;
}
claset_("Full", m, m, &c_b5, &c_b6, &work[1], m);
/* Form Q */
cunm2r_("Left", "No transpose", m, m, k, &a[a_offset], lda, &tau[1], &
work[1], m, &work[*m * *m + 1], &info);
/* Form Q'*Q */
cunm2r_("Left", "Conjugate transpose", m, m, k, &a[a_offset], lda, &tau[1]
, &work[1], m, &work[*m * *m + 1], &info);
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
i__2 = (j - 1) * *m + j;
i__3 = (j - 1) * *m + j;
q__1.r = work[i__3].r - 1.f, q__1.i = work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L10: */
}
ret_val = clange_("One-norm", m, m, &work[1], m, rdummy) / ((
real) (*m) * slamch_("Epsilon"));
return ret_val;
/* End of CQRT11 */
} /* cqrt11_ */
/* Subroutine */ int cgelsx_(integer *m, integer *n, integer *nrhs, complex *
a, integer *lda, complex *b, integer *ldb, integer *jpvt, real *rcond,
integer *rank, complex *work, real *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
complex q__1;
/* Builtin functions */
double c_abs(complex *);
void r_cnjg(complex *, complex *);
/* Local variables */
static integer i__, j, k;
static complex c1, c2, s1, s2, t1, t2;
static integer mn;
static real anrm, bnrm, smin, smax;
static integer iascl, ibscl, ismin, ismax;
extern /* Subroutine */ int ctrsm_(char *, char *, char *, char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *, ftnlen, ftnlen, ftnlen, ftnlen), claic1_(integer *,
integer *, complex *, real *, complex *, complex *, real *,
complex *, complex *), cunm2r_(char *, char *, integer *, integer
*, integer *, complex *, integer *, complex *, complex *, integer
*, complex *, integer *, ftnlen, ftnlen), slabad_(real *, real *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *, ftnlen);
extern /* Subroutine */ int clascl_(char *, integer *, integer *, real *,
real *, integer *, integer *, complex *, integer *, integer *,
ftnlen), cgeqpf_(integer *, integer *, complex *, integer *,
integer *, complex *, complex *, real *, integer *);
extern doublereal slamch_(char *, ftnlen);
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *, ftnlen), xerbla_(char *,
integer *, ftnlen);
static real bignum;
extern /* Subroutine */ int clatzm_(char *, integer *, integer *, complex
*, integer *, complex *, complex *, complex *, integer *, complex
*, ftnlen);
static real sminpr;
extern /* Subroutine */ int ctzrqf_(integer *, integer *, complex *,
integer *, complex *, integer *);
static real smaxpr, smlnum;
/* -- LAPACK driver routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine CGELSY. */
/* CGELSX computes the minimum-norm solution to a complex linear least */
/* squares problem: */
/* minimize || A * X - B || */
/* using a complete orthogonal factorization of A. A is an M-by-N */
/* matrix which may be rank-deficient. */
/* Several right hand side vectors b and solution vectors x can be */
/* handled in a single call; they are stored as the columns of the */
/* M-by-NRHS right hand side matrix B and the N-by-NRHS solution */
/* matrix X. */
/* The routine first computes a QR factorization with column pivoting: */
/* A * P = Q * [ R11 R12 ] */
/* [ 0 R22 ] */
/* with R11 defined as the largest leading submatrix whose estimated */
/* condition number is less than 1/RCOND. The order of R11, RANK, */
/* is the effective rank of A. */
/* Then, R22 is considered to be negligible, and R12 is annihilated */
/* by unitary transformations from the right, arriving at the */
/* complete orthogonal factorization: */
/* A * P = Q * [ T11 0 ] * Z */
/* [ 0 0 ] */
/* The minimum-norm solution is then */
/* X = P * Z' [ inv(T11)*Q1'*B ] */
/* [ 0 ] */
/* where Q1 consists of the first RANK columns of Q. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of */
/* columns of matrices B and X. NRHS >= 0. */
/* A (input/output) COMPLEX array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A has been overwritten by details of its */
/* complete orthogonal factorization. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) COMPLEX array, dimension (LDB,NRHS) */
/* On entry, the M-by-NRHS right hand side matrix B. */
/* On exit, the N-by-NRHS solution matrix X. */
/* If m >= n and RANK = n, the residual sum-of-squares for */
/* the solution in the i-th column is given by the sum of */
/* squares of elements N+1:M in that column. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,M,N). */
/* JPVT (input/output) INTEGER array, dimension (N) */
/* On entry, if JPVT(i) .ne. 0, the i-th column of A is an */
/* initial column, otherwise it is a free column. Before */
/* the QR factorization of A, all initial columns are */
/* permuted to the leading positions; only the remaining */
/* free columns are moved as a result of column pivoting */
/* during the factorization. */
/* On exit, if JPVT(i) = k, then the i-th column of A*P */
/* was the k-th column of A. */
/* RCOND (input) REAL */
/* RCOND is used to determine the effective rank of A, which */
/* is defined as the order of the largest leading triangular */
/* submatrix R11 in the QR factorization with pivoting of A, */
/* whose estimated condition number < 1/RCOND. */
/* RANK (output) INTEGER */
/* The effective rank of A, i.e., the order of the submatrix */
/* R11. This is the same as the order of the submatrix T11 */
/* in the complete orthogonal factorization of A. */
/* WORK (workspace) COMPLEX array, dimension */
/* (min(M,N) + max( N, 2*min(M,N)+NRHS )), */
/* RWORK (workspace) REAL array, dimension (2*N) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
--jpvt;
--work;
--rwork;
/* Function Body */
mn = min(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -7;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGELSX", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
/* Computing MIN */
i__1 = min(*m,*n);
if (min(i__1,*nrhs) == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters */
smlnum = slamch_("S", (ftnlen)1) / slamch_("P", (ftnlen)1);
bignum = 1.f / smlnum;
slabad_(&smlnum, &bignum);
/* Scale A, B if max elements outside range [SMLNUM,BIGNUM] */
anrm = clange_("M", m, n, &a[a_offset], lda, &rwork[1], (ftnlen)1);
iascl = 0;
if (anrm > 0.f && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info, (ftnlen)1);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
clascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info, (ftnlen)1);
iascl = 2;
} else if (anrm == 0.f) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb, (ftnlen)1);
*rank = 0;
goto L100;
}
bnrm = clange_("M", m, nrhs, &b[b_offset], ldb, &rwork[1], (ftnlen)1);
ibscl = 0;
if (bnrm > 0.f && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
clascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
clascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
ibscl = 2;
}
/* Compute QR factorization with column pivoting of A: */
/* A * P = Q * R */
cgeqpf_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &
rwork[1], info);
/* complex workspace MN+N. Real workspace 2*N. Details of Householder */
/* rotations stored in WORK(1:MN). */
/* Determine RANK using incremental condition estimation */
i__1 = ismin;
work[i__1].r = 1.f, work[i__1].i = 0.f;
i__1 = ismax;
work[i__1].r = 1.f, work[i__1].i = 0.f;
smax = c_abs(&a[a_dim1 + 1]);
smin = smax;
if (c_abs(&a[a_dim1 + 1]) == 0.f) {
*rank = 0;
i__1 = max(*m,*n);
claset_("F", &i__1, nrhs, &c_b1, &c_b1, &b[b_offset], ldb, (ftnlen)1);
goto L100;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i__ = *rank + 1;
claic1_(&c__2, rank, &work[ismin], &smin, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &sminpr, &s1, &c1);
claic1_(&c__1, rank, &work[ismax], &smax, &a[i__ * a_dim1 + 1], &a[
i__ + i__ * a_dim1], &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = ismin + i__ - 1;
i__3 = ismin + i__ - 1;
q__1.r = s1.r * work[i__3].r - s1.i * work[i__3].i, q__1.i =
s1.r * work[i__3].i + s1.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
i__2 = ismax + i__ - 1;
i__3 = ismax + i__ - 1;
q__1.r = s2.r * work[i__3].r - s2.i * work[i__3].i, q__1.i =
s2.r * work[i__3].i + s2.i * work[i__3].r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L20: */
}
i__1 = ismin + *rank;
work[i__1].r = c1.r, work[i__1].i = c1.i;
i__1 = ismax + *rank;
work[i__1].r = c2.r, work[i__1].i = c2.i;
smin = sminpr;
smax = smaxpr;
++(*rank);
goto L10;
}
}
/* Logically partition R = [ R11 R12 ] */
/* [ 0 R22 ] */
/* where R11 = R(1:RANK,1:RANK) */
/* [R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
ctzrqf_(rank, n, &a[a_offset], lda, &work[mn + 1], info);
}
/* Details of Householder rotations stored in WORK(MN+1:2*MN) */
/* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
cunm2r_("Left", "Conjugate transpose", m, nrhs, &mn, &a[a_offset], lda, &
work[1], &b[b_offset], ldb, &work[(mn << 1) + 1], info, (ftnlen)4,
(ftnlen)19);
/* workspace NRHS */
/* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
ctrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b2, &a[
a_offset], lda, &b[b_offset], ldb, (ftnlen)4, (ftnlen)5, (ftnlen)
12, (ftnlen)8);
i__1 = *n;
for (i__ = *rank + 1; i__ <= i__1; ++i__) {
i__2 = *nrhs;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0.f, b[i__3].i = 0.f;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = *n - *rank + 1;
r_cnjg(&q__1, &work[mn + i__]);
clatzm_("Left", &i__2, nrhs, &a[i__ + (*rank + 1) * a_dim1], lda,
&q__1, &b[i__ + b_dim1], &b[*rank + 1 + b_dim1], ldb, &
work[(mn << 1) + 1], (ftnlen)4);
/* L50: */
}
}
/* workspace NRHS */
/* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
work[i__3].r = 1.f, work[i__3].i = 0.f;
/* L60: */
}
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = (mn << 1) + i__;
if (work[i__3].r == 1.f && work[i__3].i == 0.f) {
if (jpvt[i__] != i__) {
k = i__;
i__3 = k + j * b_dim1;
t1.r = b[i__3].r, t1.i = b[i__3].i;
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
L70:
i__3 = jpvt[k] + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
t1.r = t2.r, t1.i = t2.i;
k = jpvt[k];
i__3 = jpvt[k] + j * b_dim1;
t2.r = b[i__3].r, t2.i = b[i__3].i;
if (jpvt[k] != i__) {
goto L70;
}
i__3 = i__ + j * b_dim1;
b[i__3].r = t1.r, b[i__3].i = t1.i;
i__3 = (mn << 1) + k;
work[i__3].r = 0.f, work[i__3].i = 0.f;
}
}
/* L80: */
}
/* L90: */
}
/* Undo scaling */
if (iascl == 1) {
clascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
clascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
lda, info, (ftnlen)1);
} else if (iascl == 2) {
clascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
clascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
lda, info, (ftnlen)1);
}
if (ibscl == 1) {
clascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
} else if (ibscl == 2) {
clascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info, (ftnlen)1);
}
L100:
return 0;
/* End of CGELSX */
} /* cgelsx_ */
/* Subroutine */ int chet21_(integer *itype, char *uplo, integer *n, integer *
kband, complex *a, integer *lda, real *d__, real *e, complex *u,
integer *ldu, complex *v, integer *ldv, complex *tau, complex *work,
real *rwork, real *result)
{
/* System generated locals */
integer a_dim1, a_offset, u_dim1, u_offset, v_dim1, v_offset, i__1, i__2,
i__3, i__4, i__5, i__6;
real r__1, r__2;
complex q__1, q__2, q__3;
/* Local variables */
integer j, jr;
real ulp;
extern /* Subroutine */ int cher_(char *, integer *, real *, complex *,
integer *, complex *, integer *);
integer jcol;
real unfl;
integer jrow;
extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *),
cgemm_(char *, char *, integer *, integer *, integer *, complex *,
complex *, integer *, complex *, integer *, complex *, complex *,
integer *);
extern logical lsame_(char *, char *);
integer iinfo;
real anorm;
char cuplo[1];
complex vsave;
logical lower;
real wnorm;
extern /* Subroutine */ int cunm2l_(char *, char *, integer *, integer *,
integer *, complex *, integer *, complex *, complex *, integer *,
complex *, integer *), cunm2r_(char *, char *,
integer *, integer *, integer *, complex *, integer *, complex *,
complex *, integer *, complex *, integer *);
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), clanhe_(char *, char *, integer *,
complex *, integer *, real *), slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *), clarfy_(char *, integer *, complex *, integer *, complex
*, complex *, integer *, complex *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHET21 generally checks a decomposition of the form */
/* A = U S U* */
/* where * means conjugate transpose, A is hermitian, U is unitary, and */
/* S is diagonal (if KBAND=0) or (real) symmetric tridiagonal (if */
/* KBAND=1). */
/* If ITYPE=1, then U is represented as a dense matrix; otherwise U is */
/* expressed as a product of Householder transformations, whose vectors */
/* are stored in the array "V" and whose scaling constants are in "TAU". */
/* We shall use the letter "V" to refer to the product of Householder */
/* transformations (which should be equal to U). */
/* Specifically, if ITYPE=1, then: */
/* RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and* */
/* RESULT(2) = | I - UU* | / ( n ulp ) */
/* If ITYPE=2, then: */
/* RESULT(1) = | A - V S V* | / ( |A| n ulp ) */
/* If ITYPE=3, then: */
/* RESULT(1) = | I - UV* | / ( n ulp ) */
/* For ITYPE > 1, the transformation U is expressed as a product */
/* V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)* and each */
/* vector v(j) has its first j elements 0 and the remaining n-j elements */
/* stored in V(j+1:n,j). */
/* Arguments */
/* ========= */
/* ITYPE (input) INTEGER */
/* Specifies the type of tests to be performed. */
/* 1: U expressed as a dense unitary matrix: */
/* RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and* */
/* RESULT(2) = | I - UU* | / ( n ulp ) */
/* 2: U expressed as a product V of Housholder transformations: */
/* RESULT(1) = | A - V S V* | / ( |A| n ulp ) */
/* 3: U expressed both as a dense unitary matrix and */
/* as a product of Housholder transformations: */
/* RESULT(1) = | I - UV* | / ( n ulp ) */
/* UPLO (input) CHARACTER */
/* If UPLO='U', the upper triangle of A and V will be used and */
/* the (strictly) lower triangle will not be referenced. */
/* If UPLO='L', the lower triangle of A and V will be used and */
/* the (strictly) upper triangle will not be referenced. */
/* N (input) INTEGER */
/* The size of the matrix. If it is zero, CHET21 does nothing. */
/* It must be at least zero. */
/* KBAND (input) INTEGER */
/* The bandwidth of the matrix. It may only be zero or one. */
/* If zero, then S is diagonal, and E is not referenced. If */
/* one, then S is symmetric tri-diagonal. */
/* A (input) COMPLEX array, dimension (LDA, N) */
/* The original (unfactored) matrix. It is assumed to be */
/* hermitian, and only the upper (UPLO='U') or only the lower */
/* (UPLO='L') will be referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at least 1 */
/* and at least N. */
/* D (input) REAL array, dimension (N) */
/* The diagonal of the (symmetric tri-) diagonal matrix. */
/* E (input) REAL array, dimension (N-1) */
/* The off-diagonal of the (symmetric tri-) diagonal matrix. */
/* E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and */
/* (3,2) element, etc. */
/* Not referenced if KBAND=0. */
/* U (input) COMPLEX array, dimension (LDU, N) */
/* If ITYPE=1 or 3, this contains the unitary matrix in */
/* the decomposition, expressed as a dense matrix. If ITYPE=2, */
/* then it is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of U. LDU must be at least N and */
/* at least 1. */
/* V (input) COMPLEX array, dimension (LDV, N) */
/* If ITYPE=2 or 3, the columns of this array contain the */
/* Householder vectors used to describe the unitary matrix */
/* in the decomposition. If UPLO='L', then the vectors are in */
/* the lower triangle, if UPLO='U', then in the upper */
/* triangle. */
/* *NOTE* If ITYPE=2 or 3, V is modified and restored. The */
/* subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U') */
/* is set to one, and later reset to its original value, during */
/* the course of the calculation. */
/* If ITYPE=1, then it is neither referenced nor modified. */
/* LDV (input) INTEGER */
/* The leading dimension of V. LDV must be at least N and */
/* at least 1. */
/* TAU (input) COMPLEX array, dimension (N) */
/* If ITYPE >= 2, then TAU(j) is the scalar factor of */
/* v(j) v(j)* in the Householder transformation H(j) of */
/* the product U = H(1)...H(n-2) */
/* If ITYPE < 2, then TAU is not referenced. */
/* WORK (workspace) COMPLEX array, dimension (2*N**2) */
/* RWORK (workspace) REAL array, dimension (N) */
/* RESULT (output) REAL array, dimension (2) */
/* The values computed by the two tests described above. The */
/* values are currently limited to 1/ulp, to avoid overflow. */
/* RESULT(1) is always modified. RESULT(2) is modified only */
/* if ITYPE=1. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--d__;
--e;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
--tau;
--work;
--rwork;
--result;
/* Function Body */
result[1] = 0.f;
if (*itype == 1) {
result[2] = 0.f;
}
if (*n <= 0) {
return 0;
}
if (lsame_(uplo, "U")) {
lower = FALSE_;
*(unsigned char *)cuplo = 'U';
} else {
lower = TRUE_;
*(unsigned char *)cuplo = 'L';
}
unfl = slamch_("Safe minimum");
ulp = slamch_("Epsilon") * slamch_("Base");
/* Some Error Checks */
if (*itype < 1 || *itype > 3) {
result[1] = 10.f / ulp;
return 0;
}
/* Do Test 1 */
/* Norm of A: */
if (*itype == 3) {
anorm = 1.f;
} else {
/* Computing MAX */
r__1 = clanhe_("1", cuplo, n, &a[a_offset], lda, &rwork[1]);
anorm = dmax(r__1,unfl);
}
/* Compute error matrix: */
if (*itype == 1) {
/* ITYPE=1: error = A - U S U* */
claset_("Full", n, n, &c_b1, &c_b1, &work[1], n);
clacpy_(cuplo, n, n, &a[a_offset], lda, &work[1], n);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
r__1 = -d__[j];
cher_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &work[1], n);
/* L10: */
}
if (*n > 1 && *kband == 1) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
q__2.r = e[i__2], q__2.i = 0.f;
q__1.r = -q__2.r, q__1.i = -q__2.i;
cher2_(cuplo, n, &q__1, &u[j * u_dim1 + 1], &c__1, &u[(j - 1)
* u_dim1 + 1], &c__1, &work[1], n);
/* L20: */
}
}
wnorm = clanhe_("1", cuplo, n, &work[1], n, &rwork[1]);
} else if (*itype == 2) {
/* ITYPE=2: error = V S V* - A */
claset_("Full", n, n, &c_b1, &c_b1, &work[1], n);
if (lower) {
/* Computing 2nd power */
i__2 = *n;
i__1 = i__2 * i__2;
i__3 = *n;
work[i__1].r = d__[i__3], work[i__1].i = 0.f;
for (j = *n - 1; j >= 1; --j) {
if (*kband == 1) {
i__1 = (*n + 1) * (j - 1) + 2;
i__2 = j;
q__2.r = 1.f - tau[i__2].r, q__2.i = 0.f - tau[i__2].i;
i__3 = j;
q__1.r = e[i__3] * q__2.r, q__1.i = e[i__3] * q__2.i;
work[i__1].r = q__1.r, work[i__1].i = q__1.i;
i__1 = *n;
for (jr = j + 2; jr <= i__1; ++jr) {
i__2 = (j - 1) * *n + jr;
i__3 = j;
q__3.r = -tau[i__3].r, q__3.i = -tau[i__3].i;
i__4 = j;
q__2.r = e[i__4] * q__3.r, q__2.i = e[i__4] * q__3.i;
i__5 = jr + j * v_dim1;
q__1.r = q__2.r * v[i__5].r - q__2.i * v[i__5].i,
q__1.i = q__2.r * v[i__5].i + q__2.i * v[i__5]
.r;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L30: */
}
}
i__1 = j + 1 + j * v_dim1;
vsave.r = v[i__1].r, vsave.i = v[i__1].i;
i__1 = j + 1 + j * v_dim1;
v[i__1].r = 1.f, v[i__1].i = 0.f;
i__1 = *n - j;
/* Computing 2nd power */
i__2 = *n;
clarfy_("L", &i__1, &v[j + 1 + j * v_dim1], &c__1, &tau[j], &
work[(*n + 1) * j + 1], n, &work[i__2 * i__2 + 1]);
i__1 = j + 1 + j * v_dim1;
v[i__1].r = vsave.r, v[i__1].i = vsave.i;
i__1 = (*n + 1) * (j - 1) + 1;
i__2 = j;
work[i__1].r = d__[i__2], work[i__1].i = 0.f;
/* L40: */
}
} else {
work[1].r = d__[1], work[1].i = 0.f;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
if (*kband == 1) {
i__2 = (*n + 1) * j;
i__3 = j;
q__2.r = 1.f - tau[i__3].r, q__2.i = 0.f - tau[i__3].i;
i__4 = j;
q__1.r = e[i__4] * q__2.r, q__1.i = e[i__4] * q__2.i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
i__2 = j - 1;
for (jr = 1; jr <= i__2; ++jr) {
i__3 = j * *n + jr;
i__4 = j;
q__3.r = -tau[i__4].r, q__3.i = -tau[i__4].i;
i__5 = j;
q__2.r = e[i__5] * q__3.r, q__2.i = e[i__5] * q__3.i;
i__6 = jr + (j + 1) * v_dim1;
q__1.r = q__2.r * v[i__6].r - q__2.i * v[i__6].i,
q__1.i = q__2.r * v[i__6].i + q__2.i * v[i__6]
.r;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L50: */
}
}
i__2 = j + (j + 1) * v_dim1;
vsave.r = v[i__2].r, vsave.i = v[i__2].i;
i__2 = j + (j + 1) * v_dim1;
v[i__2].r = 1.f, v[i__2].i = 0.f;
/* Computing 2nd power */
i__2 = *n;
clarfy_("U", &j, &v[(j + 1) * v_dim1 + 1], &c__1, &tau[j], &
work[1], n, &work[i__2 * i__2 + 1]);
i__2 = j + (j + 1) * v_dim1;
v[i__2].r = vsave.r, v[i__2].i = vsave.i;
i__2 = (*n + 1) * j + 1;
i__3 = j + 1;
work[i__2].r = d__[i__3], work[i__2].i = 0.f;
/* L60: */
}
}
i__1 = *n;
for (jcol = 1; jcol <= i__1; ++jcol) {
if (lower) {
i__2 = *n;
for (jrow = jcol; jrow <= i__2; ++jrow) {
i__3 = jrow + *n * (jcol - 1);
i__4 = jrow + *n * (jcol - 1);
i__5 = jrow + jcol * a_dim1;
q__1.r = work[i__4].r - a[i__5].r, q__1.i = work[i__4].i
- a[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L70: */
}
} else {
i__2 = jcol;
for (jrow = 1; jrow <= i__2; ++jrow) {
i__3 = jrow + *n * (jcol - 1);
i__4 = jrow + *n * (jcol - 1);
i__5 = jrow + jcol * a_dim1;
q__1.r = work[i__4].r - a[i__5].r, q__1.i = work[i__4].i
- a[i__5].i;
work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L80: */
}
}
/* L90: */
}
wnorm = clanhe_("1", cuplo, n, &work[1], n, &rwork[1]);
} else if (*itype == 3) {
/* ITYPE=3: error = U V* - I */
if (*n < 2) {
return 0;
}
clacpy_(" ", n, n, &u[u_offset], ldu, &work[1], n);
if (lower) {
i__1 = *n - 1;
i__2 = *n - 1;
/* Computing 2nd power */
i__3 = *n;
cunm2r_("R", "C", n, &i__1, &i__2, &v[v_dim1 + 2], ldv, &tau[1], &
work[*n + 1], n, &work[i__3 * i__3 + 1], &iinfo);
} else {
i__1 = *n - 1;
i__2 = *n - 1;
/* Computing 2nd power */
i__3 = *n;
cunm2l_("R", "C", n, &i__1, &i__2, &v[(v_dim1 << 1) + 1], ldv, &
tau[1], &work[1], n, &work[i__3 * i__3 + 1], &iinfo);
}
if (iinfo != 0) {
result[1] = 10.f / ulp;
return 0;
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = (*n + 1) * (j - 1) + 1;
i__3 = (*n + 1) * (j - 1) + 1;
q__1.r = work[i__3].r - 1.f, q__1.i = work[i__3].i - 0.f;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L100: */
}
wnorm = clange_("1", n, n, &work[1], n, &rwork[1]);
}
if (anorm > wnorm) {
result[1] = wnorm / anorm / (*n * ulp);
} else {
if (anorm < 1.f) {
/* Computing MIN */
r__1 = wnorm, r__2 = *n * anorm;
result[1] = dmin(r__1,r__2) / anorm / (*n * ulp);
} else {
/* Computing MIN */
r__1 = wnorm / anorm, r__2 = (real) (*n);
result[1] = dmin(r__1,r__2) / (*n * ulp);
}
}
/* Do Test 2 */
/* Compute UU* - I */
if (*itype == 1) {
cgemm_("N", "C", n, n, n, &c_b2, &u[u_offset], ldu, &u[u_offset], ldu,
&c_b1, &work[1], n);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = (*n + 1) * (j - 1) + 1;
i__3 = (*n + 1) * (j - 1) + 1;
q__1.r = work[i__3].r - 1.f, q__1.i = work[i__3].i - 0.f;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L110: */
}
/* Computing MIN */
r__1 = clange_("1", n, n, &work[1], n, &rwork[1]), r__2 = (
real) (*n);
result[2] = dmin(r__1,r__2) / (*n * ulp);
}
return 0;
/* End of CHET21 */
} /* chet21_ */
