/* Subroutine */ int cchkbd_(integer *nsizes, integer *mval, integer *nval,
integer *ntypes, logical *dotype, integer *nrhs, integer *iseed, real
*thresh, complex *a, integer *lda, real *bd, real *be, real *s1, real
*s2, complex *x, integer *ldx, complex *y, complex *z__, complex *q,
integer *ldq, complex *pt, integer *ldpt, complex *u, complex *vt,
complex *work, integer *lwork, real *rwork, integer *nout, integer *
info)
{
/* Initialized data */
static integer ktype[16] = { 1,2,4,4,4,4,4,6,6,6,6,6,9,9,9,10 };
static integer kmagn[16] = { 1,1,1,1,1,2,3,1,1,1,2,3,1,2,3,0 };
static integer kmode[16] = { 0,0,4,3,1,4,4,4,3,1,4,4,0,0,0,0 };
/* Format strings */
static char fmt_9998[] = "(\002 CCHKBD: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002M=\002,i6,\002, N=\002,i6,\002, JTYPE=\002,i"
"6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9999[] = "(\002 M=\002,i5,\002, N=\002,i5,\002, type "
"\002,i2,\002, seed=\002,4(i4,\002,\002),\002 test(\002,i2,\002)"
"=\002,g11.4)";
/* System generated locals */
integer a_dim1, a_offset, pt_dim1, pt_offset, q_dim1, q_offset, u_dim1,
u_offset, vt_dim1, vt_offset, x_dim1, x_offset, y_dim1, y_offset,
z_dim1, z_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7;
real r__1, r__2, r__3, r__4, r__5, r__6, r__7;
/* Builtin functions
Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
double log(doublereal), sqrt(doublereal), exp(doublereal);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
static real cond;
static integer jcol;
static char path[3];
static integer mmax, nmax;
static real unfl, ovfl;
static char uplo[1];
static real temp1, temp2;
static integer i__, j, m, n;
extern /* Subroutine */ int cbdt01_(integer *, integer *, integer *,
complex *, integer *, complex *, integer *, real *, real *,
complex *, integer *, complex *, real *, real *);
static logical badmm, badnn;
extern /* Subroutine */ int cbdt02_(integer *, integer *, complex *,
integer *, complex *, integer *, complex *, integer *, complex *,
real *, real *), cbdt03_(char *, integer *, integer *, real *,
real *, complex *, integer *, real *, complex *, integer *,
complex *, real *);
static integer nfail, imode;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
static real dumma[1];
static integer iinfo;
extern /* Subroutine */ int cunt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *);
static real anorm;
static integer mnmin, mnmax, jsize, itype, jtype, iwork[1], ntest;
extern /* Subroutine */ int scopy_(integer *, real *, integer *, real *,
integer *), slahd2_(integer *, char *);
static integer log2ui;
static logical bidiag;
extern /* Subroutine */ int cgebrd_(integer *, integer *, complex *,
integer *, real *, real *, complex *, complex *, complex *,
integer *, integer *), slabad_(real *, real *);
static integer mq;
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *), claset_(char *,
integer *, integer *, complex *, complex *, complex *, integer *), xerbla_(char *, integer *);
static integer ioldsd[4];
extern /* Subroutine */ int cbdsqr_(char *, integer *, integer *, integer
*, integer *, real *, real *, complex *, integer *, complex *,
integer *, complex *, integer *, real *, integer *),
cungbr_(char *, integer *, integer *, integer *, complex *,
integer *, complex *, complex *, integer *, integer *),
alasum_(char *, integer *, integer *, integer *, integer *);
extern doublereal slarnd_(integer *, integer *);
extern /* Subroutine */ int clatmr_(integer *, integer *, char *, integer
*, char *, complex *, integer *, real *, complex *, char *, char *
, complex *, integer *, real *, complex *, integer *, real *,
char *, integer *, integer *, integer *, real *, real *, char *,
complex *, integer *, integer *, integer *), clatms_(integer *, integer *,
char *, integer *, char *, real *, integer *, real *, real *,
integer *, integer *, char *, complex *, integer *, complex *,
integer *);
static real amninv;
extern /* Subroutine */ int ssvdch_(integer *, real *, real *, real *,
real *, integer *);
static integer minwrk;
static real rtunfl, rtovfl, ulpinv, result[14];
static integer mtypes;
static real ulp;
/* Fortran I/O blocks */
static cilist io___40 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___41 = { 0, 0, 0, fmt_9998, 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_9998, 0 };
static cilist io___46 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___50 = { 0, 0, 0, fmt_9999, 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)]
/* -- 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
=======
CCHKBD checks the singular value decomposition (SVD) routines.
CGEBRD reduces a complex general m by n matrix A to real upper or
lower bidiagonal form by an orthogonal transformation: Q' * A * P = B
(or A = Q * B * P'). The matrix B is upper bidiagonal if m >= n
and lower bidiagonal if m < n.
CUNGBR generates the orthogonal matrices Q and P' from CGEBRD.
Note that Q and P are not necessarily square.
CBDSQR computes the singular value decomposition of the bidiagonal
matrix B as B = U S V'. It is called three times to compute
1) B = U S1 V', where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B.
2) Same as 1), but the singular values are stored in S2 and the
singular vectors are not computed.
3) A = (UQ) S (P'V'), the SVD of the original matrix A.
In addition, CBDSQR has an option to apply the left orthogonal matrix
U to a matrix X, useful in least squares applications.
For each pair of matrix dimensions (M,N) and each selected matrix
type, an M by N matrix A and an M by NRHS matrix X are generated.
The problem dimensions are as follows
A: M x N
Q: M x min(M,N) (but M x M if NRHS > 0)
P: min(M,N) x N
B: min(M,N) x min(M,N)
U, V: min(M,N) x min(M,N)
S1, S2 diagonal, order min(M,N)
X: M x NRHS
For each generated matrix, 14 tests are performed:
Test CGEBRD and CUNGBR
(1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
(2) | I - Q' Q | / ( M ulp )
(3) | I - PT PT' | / ( N ulp )
Test CBDSQR on bidiagonal matrix B
(4) | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'
(5) | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
and Z = U' Y.
(6) | I - U' U | / ( min(M,N) ulp )
(7) | I - VT VT' | / ( min(M,N) ulp )
(8) S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(9) 0 if the true singular values of B are within THRESH of
those in S1. 2*THRESH if they are not. (Tested using
SSVDCH)
(10) | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.
Test CBDSQR on matrix A
(11) | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )
(12) | X - (QU) Z | / ( |X| max(M,k) ulp )
(13) | I - (QU)'(QU) | / ( M ulp )
(14) | I - (VT PT) (PT'VT') | / ( N ulp )
The possible matrix types are
(1) The zero matrix.
(2) The identity matrix.
(3) A diagonal matrix with evenly spaced entries
1, ..., ULP and random signs.
(ULP = (first number larger than 1) - 1 )
(4) A diagonal matrix with geometrically spaced entries
1, ..., ULP and random signs.
(5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.
(6) Same as (3), but multiplied by SQRT( overflow threshold )
(7) Same as (3), but multiplied by SQRT( underflow threshold )
(8) A matrix of the form U D V, where U and V are orthogonal and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.
(9) A matrix of the form U D V, where U and V are orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.
(10) A matrix of the form U D V, where U and V are orthogonal and
D has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal.
(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )
(13) Rectangular matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )
Special case:
(16) A bidiagonal matrix with random entries chosen from a
logarithmic distribution on [ulp^2,ulp^(-2)] (I.e., each
entry is e^x, where x is chosen uniformly on
[ 2 log(ulp), -2 log(ulp) ] .) For *this* type:
(a) CGEBRD is not called to reduce it to bidiagonal form.
(b) the bidiagonal is min(M,N) x min(M,N); if M<N, the
matrix will be lower bidiagonal, otherwise upper.
(c) only tests 5--8 and 14 are performed.
A subset of the full set of matrix types may be selected through
the logical array DOTYPE.
Arguments
==========
NSIZES (input) INTEGER
The number of values of M and N contained in the vectors
MVAL and NVAL. The matrix sizes are used in pairs (M,N).
MVAL (input) INTEGER array, dimension (NM)
The values of the matrix row dimension M.
NVAL (input) INTEGER array, dimension (NM)
The values of the matrix column dimension N.
NTYPES (input) INTEGER
The number of elements in DOTYPE. If it is zero, CCHKBD
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 matrices are in A and B.
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 (m,n), a matrix
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.
NRHS (input) INTEGER
The number of columns in the "right-hand side" matrices X, Y,
and Z, used in testing CBDSQR. If NRHS = 0, then the
operations on the right-hand side will not be tested.
NRHS must be at least 0.
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 values of ISEED are changed on exit, and can be
used in the next call to CCHKBD to continue the same random
number sequence.
THRESH (input) REAL
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. To have
every test ratio printed, use THRESH = 0. Note that the
expected value of the test ratios is O(1), so THRESH should
be a reasonably small multiple of 1, e.g., 10 or 100.
A (workspace) COMPLEX array, dimension (LDA,NMAX)
where NMAX is the maximum value of N in NVAL.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,MMAX),
where MMAX is the maximum value of M in MVAL.
BD (workspace) REAL array, dimension
(max(min(MVAL(j),NVAL(j))))
BE (workspace) REAL array, dimension
(max(min(MVAL(j),NVAL(j))))
S1 (workspace) REAL array, dimension
(max(min(MVAL(j),NVAL(j))))
S2 (workspace) REAL array, dimension
(max(min(MVAL(j),NVAL(j))))
X (workspace) COMPLEX array, dimension (LDX,NRHS)
LDX (input) INTEGER
The leading dimension of the arrays X, Y, and Z.
LDX >= max(1,MMAX).
Y (workspace) COMPLEX array, dimension (LDX,NRHS)
Z (workspace) COMPLEX array, dimension (LDX,NRHS)
Q (workspace) COMPLEX array, dimension (LDQ,MMAX)
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,MMAX).
PT (workspace) COMPLEX array, dimension (LDPT,NMAX)
LDPT (input) INTEGER
The leading dimension of the arrays PT, U, and V.
LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).
U (workspace) COMPLEX array, dimension
(LDPT,max(min(MVAL(j),NVAL(j))))
V (workspace) COMPLEX array, dimension
(LDPT,max(min(MVAL(j),NVAL(j))))
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The number of entries in WORK. This must be at least
3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all
pairs (M,N)=(MM(j),NN(j))
RWORK (workspace) REAL array, dimension
(5*max(min(M,N)))
NOUT (input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.)
INFO (output) INTEGER
If 0, then everything ran OK.
-1: NSIZES < 0
-2: Some MM(j) < 0
-3: Some NN(j) < 0
-4: NTYPES < 0
-6: NRHS < 0
-8: THRESH < 0
-11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
-17: LDB < 1 or LDB < MMAX.
-21: LDQ < 1 or LDQ < MMAX.
-23: LDP < 1 or LDP < MNMAX.
-27: LWORK too small.
If CLATMR, CLATMS, CGEBRD, CUNGBR, or CBDSQR,
returns an error code, the
absolute value of it is returned.
-----------------------------------------------------------------------
Some Local Variables and Parameters:
---- ----- --------- --- ----------
ZERO, ONE Real 0 and 1.
MAXTYP The number of types defined.
NTEST The number of tests performed, or which can
be performed so far, for the current matrix.
MMAX Largest value in NN.
NMAX Largest value in NN.
MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal
matrix.)
MNMAX The maximum value of MNMIN for j=1,...,NSIZES.
NFAIL The number of tests which have exceeded THRESH
COND, IMODE Values to be passed to the matrix generators.
ANORM Norm of A; passed to matrix generators.
OVFL, UNFL Overflow and underflow thresholds.
RTOVFL, RTUNFL Square roots of the previous 2 values.
ULP, ULPINV Finest relative precision and its inverse.
The following four arrays decode JTYPE:
KTYPE(j) The general type (1-10) for type "j".
KMODE(j) The MODE value to be passed to the matrix
generator for type "j".
KMAGN(j) The order of magnitude ( O(1),
O(overflow^(1/2) ), O(underflow^(1/2) )
======================================================================
Parameter adjustments */
--mval;
--nval;
--dotype;
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--bd;
--be;
--s1;
--s2;
z_dim1 = *ldx;
z_offset = 1 + z_dim1 * 1;
z__ -= z_offset;
y_dim1 = *ldx;
y_offset = 1 + y_dim1 * 1;
y -= y_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1 * 1;
x -= x_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1 * 1;
q -= q_offset;
vt_dim1 = *ldpt;
vt_offset = 1 + vt_dim1 * 1;
vt -= vt_offset;
u_dim1 = *ldpt;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
pt_dim1 = *ldpt;
pt_offset = 1 + pt_dim1 * 1;
pt -= pt_offset;
--work;
--rwork;
/* Function Body
Check for errors */
*info = 0;
badmm = FALSE_;
badnn = FALSE_;
mmax = 1;
nmax = 1;
mnmax = 1;
minwrk = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = mmax, i__3 = mval[j];
mmax = max(i__2,i__3);
if (mval[j] < 0) {
badmm = TRUE_;
}
/* Computing MAX */
i__2 = nmax, i__3 = nval[j];
nmax = max(i__2,i__3);
if (nval[j] < 0) {
badnn = TRUE_;
}
/* Computing MAX
Computing MIN */
i__4 = mval[j], i__5 = nval[j];
i__2 = mnmax, i__3 = min(i__4,i__5);
mnmax = max(i__2,i__3);
/* Computing MAX
Computing MAX */
i__4 = mval[j], i__5 = nval[j], i__4 = max(i__4,i__5);
/* Computing MIN */
i__6 = nval[j], i__7 = mval[j];
i__2 = minwrk, i__3 = (mval[j] + nval[j]) * 3, i__2 = max(i__2,i__3),
i__3 = mval[j] * (mval[j] + max(i__4,*nrhs) + 1) + nval[j] *
min(i__6,i__7);
minwrk = max(i__2,i__3);
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badmm) {
*info = -2;
} else if (badnn) {
*info = -3;
} else if (*ntypes < 0) {
*info = -4;
} else if (*nrhs < 0) {
*info = -6;
} else if (*lda < mmax) {
*info = -11;
} else if (*ldx < mmax) {
*info = -17;
} else if (*ldq < mmax) {
*info = -21;
} else if (*ldpt < mnmax) {
*info = -23;
} else if (minwrk > *lwork) {
*info = -27;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CCHKBD", &i__1);
return 0;
}
/* Initialize constants */
s_copy(path, "Complex precision", (ftnlen)1, (ftnlen)17);
s_copy(path + 1, "BD", (ftnlen)2, (ftnlen)2);
nfail = 0;
ntest = 0;
unfl = slamch_("Safe minimum");
ovfl = slamch_("Overflow");
slabad_(&unfl, &ovfl);
ulp = slamch_("Precision");
ulpinv = 1.f / ulp;
log2ui = (integer) (log(ulpinv) / log(2.f));
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
infoc_1.infot = 0;
/* Loop over sizes, types */
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
m = mval[jsize];
n = nval[jsize];
mnmin = min(m,n);
/* Computing MAX */
i__2 = max(m,n);
amninv = 1.f / max(i__2,1);
if (*nsizes != 1) {
mtypes = min(16,*ntypes);
} else {
mtypes = min(17,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L170;
}
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
for (j = 1; j <= 14; ++j) {
result[j - 1] = -1.f;
/* L30: */
}
*(unsigned char *)uplo = ' ';
/* Compute "A"
Control parameters:
KMAGN KMODE KTYPE
=1 O(1) clustered 1 zero
=2 large clustered 2 identity
=3 small exponential (none)
=4 arithmetic diagonal, (w/ eigenvalues)
=5 random symmetric, w/ eigenvalues
=6 nonsymmetric, w/ singular values
=7 random diagonal
=8 random symmetric
=9 random nonsymmetric
=10 random bidiagonal (log. distrib.) */
if (mtypes > 16) {
goto L100;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.f;
goto L70;
L50:
anorm = rtovfl * ulp * amninv;
goto L70;
L60:
anorm = rtunfl * max(m,n) * ulpinv;
goto L70;
L70:
claset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
iinfo = 0;
cond = ulpinv;
bidiag = FALSE_;
if (itype == 1) {
/* Zero matrix */
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__3 = mnmin;
for (jcol = 1; jcol <= i__3; ++jcol) {
i__4 = a_subscr(jcol, jcol);
a[i__4].r = anorm, a[i__4].i = 0.f;
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, [Eigen]values Specified */
clatms_(&mnmin, &mnmin, "S", &iseed[1], "N", &rwork[1], &
imode, &cond, &anorm, &c__0, &c__0, "N", &a[a_offset],
lda, &work[1], &iinfo);
} else if (itype == 5) {
/* Symmetric, eigenvalues specified */
clatms_(&mnmin, &mnmin, "S", &iseed[1], "S", &rwork[1], &
imode, &cond, &anorm, &m, &n, "N", &a[a_offset], lda,
&work[1], &iinfo);
} else if (itype == 6) {
/* Nonsymmetric, singular values specified */
clatms_(&m, &n, "S", &iseed[1], "N", &rwork[1], &imode, &cond,
&anorm, &m, &n, "N", &a[a_offset], lda, &work[1], &
iinfo);
} else if (itype == 7) {
/* Diagonal, random entries */
clatmr_(&mnmin, &mnmin, "S", &iseed[1], "N", &work[1], &c__6,
&c_b37, &c_b2, "T", "N", &work[mnmin + 1], &c__1, &
c_b37, &work[(mnmin << 1) + 1], &c__1, &c_b37, "N",
iwork, &c__0, &c__0, &c_b47, &anorm, "NO", &a[
a_offset], lda, iwork, &iinfo);
} else if (itype == 8) {
/* Symmetric, random entries */
clatmr_(&mnmin, &mnmin, "S", &iseed[1], "S", &work[1], &c__6,
&c_b37, &c_b2, "T", "N", &work[mnmin + 1], &c__1, &
c_b37, &work[m + mnmin + 1], &c__1, &c_b37, "N",
iwork, &m, &n, &c_b47, &anorm, "NO", &a[a_offset],
lda, iwork, &iinfo);
} else if (itype == 9) {
/* Nonsymmetric, random entries */
clatmr_(&m, &n, "S", &iseed[1], "N", &work[1], &c__6, &c_b37,
&c_b2, "T", "N", &work[mnmin + 1], &c__1, &c_b37, &
work[m + mnmin + 1], &c__1, &c_b37, "N", iwork, &m, &
n, &c_b47, &anorm, "NO", &a[a_offset], lda, iwork, &
iinfo);
} else if (itype == 10) {
/* Bidiagonal, random entries */
temp1 = log(ulp) * -2.f;
i__3 = mnmin;
for (j = 1; j <= i__3; ++j) {
bd[j] = exp(temp1 * slarnd_(&c__2, &iseed[1]));
if (j < mnmin) {
be[j] = exp(temp1 * slarnd_(&c__2, &iseed[1]));
}
/* L90: */
}
iinfo = 0;
bidiag = TRUE_;
if (m >= n) {
*(unsigned char *)uplo = 'U';
} else {
*(unsigned char *)uplo = 'L';
}
} else {
iinfo = 1;
}
if (iinfo == 0) {
/* Generate Right-Hand Side */
if (bidiag) {
clatmr_(&mnmin, nrhs, "S", &iseed[1], "N", &work[1], &
c__6, &c_b37, &c_b2, "T", "N", &work[mnmin + 1], &
c__1, &c_b37, &work[(mnmin << 1) + 1], &c__1, &
c_b37, "N", iwork, &mnmin, nrhs, &c_b47, &c_b37,
"NO", &y[y_offset], ldx, iwork, &iinfo);
} else {
clatmr_(&m, nrhs, "S", &iseed[1], "N", &work[1], &c__6, &
c_b37, &c_b2, "T", "N", &work[m + 1], &c__1, &
c_b37, &work[(m << 1) + 1], &c__1, &c_b37, "N",
iwork, &m, nrhs, &c_b47, &c_b37, "NO", &x[
x_offset], ldx, iwork, &iinfo);
}
}
/* Error Exit */
if (iinfo != 0) {
io___40.ciunit = *nout;
s_wsfe(&io___40);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
return 0;
}
L100:
/* Call CGEBRD and CUNGBR to compute B, Q, and P, do tests. */
if (! bidiag) {
/* Compute transformations to reduce A to bidiagonal form:
B := Q' * A * P. */
clacpy_(" ", &m, &n, &a[a_offset], lda, &q[q_offset], ldq);
i__3 = *lwork - (mnmin << 1);
cgebrd_(&m, &n, &q[q_offset], ldq, &bd[1], &be[1], &work[1], &
work[mnmin + 1], &work[(mnmin << 1) + 1], &i__3, &
iinfo);
/* Check error code from CGEBRD. */
if (iinfo != 0) {
io___41.ciunit = *nout;
s_wsfe(&io___41);
do_fio(&c__1, "CGEBRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (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;
}
clacpy_(" ", &m, &n, &q[q_offset], ldq, &pt[pt_offset], ldpt);
if (m >= n) {
*(unsigned char *)uplo = 'U';
} else {
*(unsigned char *)uplo = 'L';
}
/* Generate Q */
mq = m;
if (*nrhs <= 0) {
mq = mnmin;
}
i__3 = *lwork - (mnmin << 1);
cungbr_("Q", &m, &mq, &n, &q[q_offset], ldq, &work[1], &work[(
mnmin << 1) + 1], &i__3, &iinfo);
/* Check error code from CUNGBR. */
if (iinfo != 0) {
io___43.ciunit = *nout;
s_wsfe(&io___43);
do_fio(&c__1, "CUNGBR(Q)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (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;
}
/* Generate P' */
i__3 = *lwork - (mnmin << 1);
cungbr_("P", &mnmin, &n, &m, &pt[pt_offset], ldpt, &work[
mnmin + 1], &work[(mnmin << 1) + 1], &i__3, &iinfo);
/* Check error code from CUNGBR. */
if (iinfo != 0) {
io___44.ciunit = *nout;
s_wsfe(&io___44);
do_fio(&c__1, "CUNGBR(P)", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (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;
}
/* Apply Q' to an M by NRHS matrix X: Y := Q' * X. */
cgemm_("Conjugate transpose", "No transpose", &m, nrhs, &m, &
c_b2, &q[q_offset], ldq, &x[x_offset], ldx, &c_b1, &y[
y_offset], ldx);
/* Test 1: Check the decomposition A := Q * B * PT
2: Check the orthogonality of Q
3: Check the orthogonality of PT */
cbdt01_(&m, &n, &c__1, &a[a_offset], lda, &q[q_offset], ldq, &
bd[1], &be[1], &pt[pt_offset], ldpt, &work[1], &rwork[
1], result);
cunt01_("Columns", &m, &mq, &q[q_offset], ldq, &work[1],
lwork, &rwork[1], &result[1]);
cunt01_("Rows", &mnmin, &n, &pt[pt_offset], ldpt, &work[1],
lwork, &rwork[1], &result[2]);
}
/* Use CBDSQR to form the SVD of the bidiagonal matrix B:
B := U * S1 * VT, and compute Z = U' * Y. */
scopy_(&mnmin, &bd[1], &c__1, &s1[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
scopy_(&i__3, &be[1], &c__1, &rwork[1], &c__1);
}
clacpy_(" ", &m, nrhs, &y[y_offset], ldx, &z__[z_offset], ldx);
claset_("Full", &mnmin, &mnmin, &c_b1, &c_b2, &u[u_offset], ldpt);
claset_("Full", &mnmin, &mnmin, &c_b1, &c_b2, &vt[vt_offset],
ldpt);
cbdsqr_(uplo, &mnmin, &mnmin, &mnmin, nrhs, &s1[1], &rwork[1], &
vt[vt_offset], ldpt, &u[u_offset], ldpt, &z__[z_offset],
ldx, &rwork[mnmin + 1], &iinfo);
/* Check error code from CBDSQR. */
if (iinfo != 0) {
io___45.ciunit = *nout;
s_wsfe(&io___45);
do_fio(&c__1, "CBDSQR(vects)", (ftnlen)13);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[3] = ulpinv;
goto L150;
}
}
/* Use CBDSQR to compute only the singular values of the
bidiagonal matrix B; U, VT, and Z should not be modified. */
scopy_(&mnmin, &bd[1], &c__1, &s2[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
scopy_(&i__3, &be[1], &c__1, &rwork[1], &c__1);
}
cbdsqr_(uplo, &mnmin, &c__0, &c__0, &c__0, &s2[1], &rwork[1], &vt[
vt_offset], ldpt, &u[u_offset], ldpt, &z__[z_offset], ldx,
&rwork[mnmin + 1], &iinfo);
/* Check error code from CBDSQR. */
if (iinfo != 0) {
io___46.ciunit = *nout;
s_wsfe(&io___46);
do_fio(&c__1, "CBDSQR(values)", (ftnlen)14);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[8] = ulpinv;
goto L150;
}
}
/* Test 4: Check the decomposition B := U * S1 * VT
5: Check the computation Z := U' * Y
6: Check the orthogonality of U
7: Check the orthogonality of VT */
cbdt03_(uplo, &mnmin, &c__1, &bd[1], &be[1], &u[u_offset], ldpt, &
s1[1], &vt[vt_offset], ldpt, &work[1], &result[3]);
cbdt02_(&mnmin, nrhs, &y[y_offset], ldx, &z__[z_offset], ldx, &u[
u_offset], ldpt, &work[1], &rwork[1], &result[4]);
cunt01_("Columns", &mnmin, &mnmin, &u[u_offset], ldpt, &work[1],
lwork, &rwork[1], &result[5]);
cunt01_("Rows", &mnmin, &mnmin, &vt[vt_offset], ldpt, &work[1],
lwork, &rwork[1], &result[6]);
/* Test 8: Check that the singular values are sorted in
non-increasing order and are non-negative */
result[7] = 0.f;
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (s1[i__] < s1[i__ + 1]) {
result[7] = ulpinv;
}
if (s1[i__] < 0.f) {
result[7] = ulpinv;
}
/* L110: */
}
if (mnmin >= 1) {
if (s1[mnmin] < 0.f) {
result[7] = ulpinv;
}
}
/* Test 9: Compare CBDSQR with and without singular vectors */
temp2 = 0.f;
i__3 = mnmin;
for (j = 1; j <= i__3; ++j) {
/* Computing MAX
Computing MAX */
r__6 = (r__1 = s1[j], dabs(r__1)), r__7 = (r__2 = s2[j], dabs(
r__2));
r__4 = sqrt(unfl) * dmax(s1[1],1.f), r__5 = ulp * dmax(r__6,
r__7);
temp1 = (r__3 = s1[j] - s2[j], dabs(r__3)) / dmax(r__4,r__5);
temp2 = dmax(temp1,temp2);
/* L120: */
}
result[8] = temp2;
/* Test 10: Sturm sequence test of singular values
Go up by factors of two until it succeeds */
temp1 = *thresh * (.5f - ulp);
i__3 = log2ui;
for (j = 0; j <= i__3; ++j) {
ssvdch_(&mnmin, &bd[1], &be[1], &s1[1], &temp1, &iinfo);
if (iinfo == 0) {
goto L140;
}
temp1 *= 2.f;
/* L130: */
}
L140:
result[9] = temp1;
/* Use CBDSQR to form the decomposition A := (QU) S (VT PT)
from the bidiagonal form A := Q B PT. */
if (! bidiag) {
scopy_(&mnmin, &bd[1], &c__1, &s2[1], &c__1);
if (mnmin > 0) {
i__3 = mnmin - 1;
scopy_(&i__3, &be[1], &c__1, &rwork[1], &c__1);
}
cbdsqr_(uplo, &mnmin, &n, &m, nrhs, &s2[1], &rwork[1], &pt[
pt_offset], ldpt, &q[q_offset], ldq, &y[y_offset],
ldx, &rwork[mnmin + 1], &iinfo);
/* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
12: Check the computation Z := U' * Q' * X
13: Check the orthogonality of Q*U
14: Check the orthogonality of VT*PT */
cbdt01_(&m, &n, &c__0, &a[a_offset], lda, &q[q_offset], ldq, &
s2[1], dumma, &pt[pt_offset], ldpt, &work[1], &rwork[
1], &result[10]);
cbdt02_(&m, nrhs, &x[x_offset], ldx, &y[y_offset], ldx, &q[
q_offset], ldq, &work[1], &rwork[1], &result[11]);
cunt01_("Columns", &m, &mq, &q[q_offset], ldq, &work[1],
lwork, &rwork[1], &result[12]);
cunt01_("Rows", &mnmin, &n, &pt[pt_offset], ldpt, &work[1],
lwork, &rwork[1], &result[13]);
}
/* End of Loop -- Check for RESULT(j) > THRESH */
L150:
for (j = 1; j <= 14; ++j) {
if (result[j - 1] >= *thresh) {
if (nfail == 0) {
slahd2_(nout, path);
}
io___50.ciunit = *nout;
s_wsfe(&io___50);
do_fio(&c__1, (char *)&m, (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))
;
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(real)
);
e_wsfe();
++nfail;
}
/* L160: */
}
if (! bidiag) {
ntest += 14;
} else {
ntest += 5;
}
L170:
;
}
/* L180: */
}
/* Summary */
alasum_(path, nout, &nfail, &ntest, &c__0);
return 0;
/* End of CCHKBD */
} /* cchkbd_ */
/* Subroutine */ int cdrvbd_(integer *nsizes, integer *mm, integer *nn,
integer *ntypes, logical *dotype, integer *iseed, real *thresh,
complex *a, integer *lda, complex *u, integer *ldu, complex *vt,
integer *ldvt, complex *asav, complex *usav, complex *vtsav, real *s,
real *ssav, real *e, complex *work, integer *lwork, real *rwork,
integer *iwork, integer *nounit, integer *info)
{
/* Initialized data */
static char cjob[1*4] = "N" "O" "S" "A";
/* Format strings */
static char fmt_9996[] = "(\002 CDRVBD: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002M=\002,i6,\002, N=\002,i6,\002, JTYPE=\002,i"
"6,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9995[] = "(\002 CDRVBD: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002M=\002,i6,\002, N=\002,i6,\002, JTYPE=\002,i"
"6,\002, LSWORK=\002,i6,/9x,\002ISEED=(\002,3(i5,\002,\002),i5"
",\002)\002)";
static char fmt_9999[] = "(\002 SVD -- Complex Singular Value Decomposit"
"ion Driver \002,/\002 Matrix types (see CDRVBD for details):\002"
",//\002 1 = Zero matrix\002,/\002 2 = Identity matrix\002,/\002 "
"3 = Evenly spaced singular values near 1\002,/\002 4 = Evenly sp"
"aced singular values near underflow\002,/\002 5 = Evenly spaced "
"singular values near overflow\002,//\002 Tests performed: ( A is"
" dense, U and V are unitary,\002,/19x,\002 S is an array, and Up"
"artial, VTpartial, and\002,/19x,\002 Spartial are partially comp"
"uted U, VT and S),\002,/)";
static char fmt_9998[] = "(\002 Tests performed with Test Threshold ="
" \002,f8.2,/\002 CGESVD: \002,/\002 1 = | A - U diag(S) VT | / ("
" |A| max(M,N) ulp ) \002,/\002 2 = | I - U**T U | / ( M ulp )"
" \002,/\002 3 = | I - VT VT**T | / ( N ulp ) \002,/\002 4 = 0 if"
" S contains min(M,N) nonnegative values in\002,\002 decreasing o"
"rder, else 1/ulp\002,/\002 5 = | U - Upartial | / ( M ulp )\002,/"
"\002 6 = | VT - VTpartial | / ( N ulp )\002,/\002 7 = | S - Spar"
"tial | / ( min(M,N) ulp |S| )\002,/\002 CGESDD: \002,/\002 8 = |"
" A - U diag(S) VT | / ( |A| max(M,N) ulp ) \002,/\002 9 = | I - "
"U**T U | / ( M ulp ) \002,/\00210 = | I - VT VT**T | / ( N ulp ) "
"\002,/\00211 = 0 if S contains min(M,N) nonnegative values in"
"\002,\002 decreasing order, else 1/ulp\002,/\00212 = | U - Upart"
"ial | / ( M ulp )\002,/\00213 = | VT - VTpartial | / ( N ulp "
")\002,/\00214 = | S - Spartial | / ( min(M,N) ulp |S| )\002,//)";
static char fmt_9997[] = "(\002 M=\002,i5,\002, N=\002,i5,\002, type "
"\002,i1,\002, IWS=\002,i1,\002, seed=\002,4(i4,\002,\002),\002 t"
"est(\002,i1,\002)=\002,g11.4)";
/* System generated locals */
integer a_dim1, a_offset, asav_dim1, asav_offset, u_dim1, u_offset,
usav_dim1, usav_offset, vt_dim1, vt_offset, vtsav_dim1,
vtsav_offset, i__1, i__2, i__3, i__4, i__5, i__6, i__7, i__8,
i__9, i__10, i__11, i__12, i__13, i__14;
real r__1, r__2, r__3;
/* Builtin functions */
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, j, m, n;
real dif, div;
integer ijq, iju;
real ulp;
char jobq[1], jobu[1];
integer mmax, nmax;
real unfl, ovfl;
integer ijvt;
extern /* Subroutine */ int cbdt01_(integer *, integer *, integer *,
complex *, integer *, complex *, integer *, real *, real *,
complex *, integer *, complex *, real *, real *);
logical badmm, badnn;
integer nfail, iinfo;
extern /* Subroutine */ int cunt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *);
real anorm;
extern /* Subroutine */ int cunt03_(char *, integer *, integer *, integer
*, integer *, complex *, integer *, complex *, integer *, complex
*, integer *, real *, real *, integer *);
integer mnmin, mnmax;
char jobvt[1];
integer iwspc, jsize, nerrs, jtype, ntest, iwtmp;
extern /* Subroutine */ int cgesdd_(char *, integer *, integer *, complex
*, integer *, real *, complex *, integer *, complex *, integer *,
complex *, integer *, real *, integer *, integer *);
extern doublereal slamch_(char *);
extern /* Subroutine */ int cgesvd_(char *, char *, integer *, integer *,
complex *, integer *, real *, complex *, integer *, complex *,
integer *, complex *, integer *, real *, integer *), clacpy_(char *, integer *, integer *, complex *, integer
*, complex *, integer *), claset_(char *, integer *,
integer *, complex *, complex *, complex *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int xerbla_(char *, integer *), alasvm_(
char *, integer *, integer *, integer *, integer *),
clatms_(integer *, integer *, char *, integer *, char *, real *,
integer *, real *, real *, integer *, integer *, char *, complex *
, integer *, complex *, integer *);
integer ntestf, minwrk;
real ulpinv, result[14];
integer lswork, mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___27 = { 0, 0, 0, fmt_9996, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___39 = { 0, 0, 0, fmt_9995, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___44 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9997, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CDRVBD checks the singular value decomposition (SVD) driver CGESVD */
/* and CGESDD. */
/* CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are */
/* unitary and diag(S) is diagonal with the entries of the array S on */
/* its diagonal. The entries of S are the singular values, nonnegative */
/* and stored in decreasing order. U and VT can be optionally not */
/* computed, overwritten on A, or computed partially. */
/* A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN. */
/* U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N. */
/* When CDRVBD is called, a number of matrix "sizes" (M's and N's) */
/* and a number of matrix "types" are specified. For each size (M,N) */
/* and each type of matrix, and for the minimal workspace as well as */
/* workspace adequate to permit blocking, an M x N matrix "A" will be */
/* generated and used to test the SVD routines. For each matrix, A will */
/* be factored as A = U diag(S) VT and the following 12 tests computed: */
/* Test for CGESVD: */
/* (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) */
/* (2) | I - U'U | / ( M ulp ) */
/* (3) | I - VT VT' | / ( N ulp ) */
/* (4) S contains MNMIN nonnegative values in decreasing order. */
/* (Return 0 if true, 1/ULP if false.) */
/* (5) | U - Upartial | / ( M ulp ) where Upartial is a partially */
/* computed U. */
/* (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially */
/* computed VT. */
/* (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the */
/* vector of singular values from the partial SVD */
/* Test for CGESDD: */
/* (1) | A - U diag(S) VT | / ( |A| max(M,N) ulp ) */
/* (2) | I - U'U | / ( M ulp ) */
/* (3) | I - VT VT' | / ( N ulp ) */
/* (4) S contains MNMIN nonnegative values in decreasing order. */
/* (Return 0 if true, 1/ULP if false.) */
/* (5) | U - Upartial | / ( M ulp ) where Upartial is a partially */
/* computed U. */
/* (6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially */
/* computed VT. */
/* (7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the */
/* vector of singular values from the partial SVD */
/* The "sizes" are specified by the arrays MM(1:NSIZES) and */
/* NN(1:NSIZES); the value of each element pair (MM(j),NN(j)) */
/* specifies one size. The "types" are specified by a logical array */
/* DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j" */
/* will be generated. */
/* Currently, the list of possible types is: */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A matrix of the form U D V, where U and V are unitary and */
/* D has evenly spaced entries 1, ..., ULP with random signs */
/* on the diagonal. */
/* (4) Same as (3), but multiplied by the underflow-threshold / ULP. */
/* (5) Same as (3), but multiplied by the overflow-threshold * ULP. */
/* Arguments */
/* ========== */
/* NSIZES (input) INTEGER */
/* The number of sizes of matrices to use. If it is zero, */
/* CDRVBD does nothing. It must be at least zero. */
/* MM (input) INTEGER array, dimension (NSIZES) */
/* An array containing the matrix "heights" to be used. For */
/* each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j) */
/* will be ignored. The MM(j) values must be at least zero. */
/* NN (input) INTEGER array, dimension (NSIZES) */
/* An array containing the matrix "widths" to be used. For */
/* each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j) */
/* will be ignored. The NN(j) values must be at least zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, CDRVBD */
/* 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 matrices are in A and B. */
/* 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 (m,n), a matrix */
/* 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 CDRVBD 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 IINFO not equal to 0.) */
/* A (output) COMPLEX array, dimension (LDA,max(NN)) */
/* Used to hold the matrix whose singular values are to be */
/* computed. On exit, A contains the last matrix actually */
/* used. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at */
/* least 1 and at least max( MM ). */
/* U (output) COMPLEX array, dimension (LDU,max(MM)) */
/* Used to hold the computed matrix of right singular vectors. */
/* On exit, U contains the last such vectors actually computed. */
/* LDU (input) INTEGER */
/* The leading dimension of U. It must be at */
/* least 1 and at least max( MM ). */
/* VT (output) COMPLEX array, dimension (LDVT,max(NN)) */
/* Used to hold the computed matrix of left singular vectors. */
/* On exit, VT contains the last such vectors actually computed. */
/* LDVT (input) INTEGER */
/* The leading dimension of VT. It must be at */
/* least 1 and at least max( NN ). */
/* ASAV (output) COMPLEX array, dimension (LDA,max(NN)) */
/* Used to hold a different copy of the matrix whose singular */
/* values are to be computed. On exit, A contains the last */
/* matrix actually used. */
/* USAV (output) COMPLEX array, dimension (LDU,max(MM)) */
/* Used to hold a different copy of the computed matrix of */
/* right singular vectors. On exit, USAV contains the last such */
/* vectors actually computed. */
/* VTSAV (output) COMPLEX array, dimension (LDVT,max(NN)) */
/* Used to hold a different copy of the computed matrix of */
/* left singular vectors. On exit, VTSAV contains the last such */
/* vectors actually computed. */
/* S (output) REAL array, dimension (max(min(MM,NN))) */
/* Contains the computed singular values. */
/* SSAV (output) REAL array, dimension (max(min(MM,NN))) */
/* Contains another copy of the computed singular values. */
/* E (output) REAL array, dimension (max(min(MM,NN))) */
/* Workspace for CGESVD. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all */
/* pairs (M,N)=(MM(j),NN(j)) */
/* RWORK (workspace) REAL array, */
/* dimension ( 5*max(max(MM,NN)) ) */
/* IWORK (workspace) INTEGER array, dimension at least 8*min(M,N) */
/* RESULT (output) REAL array, dimension (7) */
/* The values computed by the 7 tests described above. */
/* The values are currently limited to 1/ULP, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* -1: NSIZES < 0 */
/* -2: Some MM(j) < 0 */
/* -3: Some NN(j) < 0 */
/* -4: NTYPES < 0 */
/* -7: THRESH < 0 */
/* -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). */
/* -12: LDU < 1 or LDU < MMAX. */
/* -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ). */
/* -21: LWORK too small. */
/* If CLATMS, or CGESVD returns an error code, the */
/* absolute value of it is returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--mm;
--nn;
--dotype;
--iseed;
asav_dim1 = *lda;
asav_offset = 1 + asav_dim1;
asav -= asav_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
usav_dim1 = *ldu;
usav_offset = 1 + usav_dim1;
usav -= usav_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
vtsav_dim1 = *ldvt;
vtsav_offset = 1 + vtsav_dim1;
vtsav -= vtsav_offset;
vt_dim1 = *ldvt;
vt_offset = 1 + vt_dim1;
vt -= vt_offset;
--s;
--ssav;
--e;
--work;
--rwork;
--iwork;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
*info = 0;
/* Important constants */
nerrs = 0;
ntestt = 0;
ntestf = 0;
badmm = FALSE_;
badnn = FALSE_;
mmax = 1;
nmax = 1;
mnmax = 1;
minwrk = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = mmax, i__3 = mm[j];
mmax = max(i__2,i__3);
if (mm[j] < 0) {
badmm = TRUE_;
}
/* Computing MAX */
i__2 = nmax, i__3 = nn[j];
nmax = max(i__2,i__3);
if (nn[j] < 0) {
badnn = TRUE_;
}
/* Computing MAX */
/* Computing MIN */
i__4 = mm[j], i__5 = nn[j];
i__2 = mnmax, i__3 = min(i__4,i__5);
mnmax = max(i__2,i__3);
/* Computing MAX */
/* Computing MAX */
/* Computing MIN */
i__6 = mm[j], i__7 = nn[j];
/* Computing MAX */
i__9 = mm[j], i__10 = nn[j];
/* Computing 2nd power */
i__8 = max(i__9,i__10);
/* Computing MIN */
i__11 = mm[j], i__12 = nn[j];
/* Computing MAX */
i__13 = mm[j], i__14 = nn[j];
i__4 = min(i__6,i__7) * 3 + i__8 * i__8, i__5 = min(i__11,i__12) * 5,
i__4 = max(i__4,i__5), i__5 = max(i__13,i__14) * 3;
i__2 = minwrk, i__3 = max(i__4,i__5);
minwrk = max(i__2,i__3);
/* L10: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badmm) {
*info = -2;
} else if (badnn) {
*info = -3;
} else if (*ntypes < 0) {
*info = -4;
} else if (*lda < max(1,mmax)) {
*info = -10;
} else if (*ldu < max(1,mmax)) {
*info = -12;
} else if (*ldvt < max(1,nmax)) {
*info = -14;
} else if (minwrk > *lwork) {
*info = -21;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CDRVBD", &i__1);
return 0;
}
/* Quick return if nothing to do */
if (*nsizes == 0 || *ntypes == 0) {
return 0;
}
/* More Important constants */
unfl = slamch_("S");
ovfl = 1.f / unfl;
ulp = slamch_("E");
ulpinv = 1.f / ulp;
/* Loop over sizes, types */
nerrs = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
m = mm[jsize];
n = nn[jsize];
mnmin = min(m,n);
if (*nsizes != 1) {
mtypes = min(5,*ntypes);
} else {
mtypes = min(6,*ntypes);
}
i__2 = mtypes;
for (jtype = 1; jtype <= i__2; ++jtype) {
if (! dotype[jtype]) {
goto L170;
}
ntest = 0;
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L20: */
}
/* Compute "A" */
if (mtypes > 5) {
goto L50;
}
if (jtype == 1) {
/* Zero matrix */
claset_("Full", &m, &n, &c_b1, &c_b1, &a[a_offset], lda);
i__3 = min(m,n);
for (i__ = 1; i__ <= i__3; ++i__) {
s[i__] = 0.f;
/* L30: */
}
} else if (jtype == 2) {
/* Identity matrix */
claset_("Full", &m, &n, &c_b1, &c_b2, &a[a_offset], lda);
i__3 = min(m,n);
for (i__ = 1; i__ <= i__3; ++i__) {
s[i__] = 1.f;
/* L40: */
}
} else {
/* (Scaled) random matrix */
if (jtype == 3) {
anorm = 1.f;
}
if (jtype == 4) {
anorm = unfl / ulp;
}
if (jtype == 5) {
anorm = ovfl * ulp;
}
r__1 = (real) mnmin;
i__3 = m - 1;
i__4 = n - 1;
clatms_(&m, &n, "U", &iseed[1], "N", &s[1], &c__4, &r__1, &
anorm, &i__3, &i__4, "N", &a[a_offset], lda, &work[1],
&iinfo);
if (iinfo != 0) {
io___27.ciunit = *nounit;
s_wsfe(&io___27);
do_fio(&c__1, "Generator", (ftnlen)9);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (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;
}
}
L50:
clacpy_("F", &m, &n, &a[a_offset], lda, &asav[asav_offset], lda);
/* Do for minimal and adequate (for blocking) workspace */
for (iwspc = 1; iwspc <= 4; ++iwspc) {
/* Test for CGESVD */
iwtmp = (min(m,n) << 1) + max(m,n);
lswork = iwtmp + (iwspc - 1) * (*lwork - iwtmp) / 3;
lswork = min(lswork,*lwork);
lswork = max(lswork,1);
if (iwspc == 4) {
lswork = *lwork;
}
for (j = 1; j <= 14; ++j) {
result[j - 1] = -1.f;
/* L60: */
}
/* Factorize A */
if (iwspc > 1) {
clacpy_("F", &m, &n, &asav[asav_offset], lda, &a[a_offset]
, lda);
}
cgesvd_("A", "A", &m, &n, &a[a_offset], lda, &ssav[1], &usav[
usav_offset], ldu, &vtsav[vtsav_offset], ldvt, &work[
1], &lswork, &rwork[1], &iinfo);
if (iinfo != 0) {
io___32.ciunit = *nounit;
s_wsfe(&io___32);
do_fio(&c__1, "GESVD", (ftnlen)5);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&lswork, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
return 0;
}
/* Do tests 1--4 */
cbdt01_(&m, &n, &c__0, &asav[asav_offset], lda, &usav[
usav_offset], ldu, &ssav[1], &e[1], &vtsav[
vtsav_offset], ldvt, &work[1], &rwork[1], result);
if (m != 0 && n != 0) {
cunt01_("Columns", &mnmin, &m, &usav[usav_offset], ldu, &
work[1], lwork, &rwork[1], &result[1]);
cunt01_("Rows", &mnmin, &n, &vtsav[vtsav_offset], ldvt, &
work[1], lwork, &rwork[1], &result[2]);
}
result[3] = 0.f;
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (ssav[i__] < ssav[i__ + 1]) {
result[3] = ulpinv;
}
if (ssav[i__] < 0.f) {
result[3] = ulpinv;
}
/* L70: */
}
if (mnmin >= 1) {
if (ssav[mnmin] < 0.f) {
result[3] = ulpinv;
}
}
/* Do partial SVDs, comparing to SSAV, USAV, and VTSAV */
result[4] = 0.f;
result[5] = 0.f;
result[6] = 0.f;
for (iju = 0; iju <= 3; ++iju) {
for (ijvt = 0; ijvt <= 3; ++ijvt) {
if (iju == 3 && ijvt == 3 || iju == 1 && ijvt == 1) {
goto L90;
}
*(unsigned char *)jobu = *(unsigned char *)&cjob[iju];
*(unsigned char *)jobvt = *(unsigned char *)&cjob[
ijvt];
clacpy_("F", &m, &n, &asav[asav_offset], lda, &a[
a_offset], lda);
cgesvd_(jobu, jobvt, &m, &n, &a[a_offset], lda, &s[1],
&u[u_offset], ldu, &vt[vt_offset], ldvt, &
work[1], &lswork, &rwork[1], &iinfo);
/* Compare U */
dif = 0.f;
if (m > 0 && n > 0) {
if (iju == 1) {
cunt03_("C", &m, &mnmin, &m, &mnmin, &usav[
usav_offset], ldu, &a[a_offset], lda,
&work[1], lwork, &rwork[1], &dif, &
iinfo);
} else if (iju == 2) {
cunt03_("C", &m, &mnmin, &m, &mnmin, &usav[
usav_offset], ldu, &u[u_offset], ldu,
&work[1], lwork, &rwork[1], &dif, &
iinfo);
} else if (iju == 3) {
cunt03_("C", &m, &m, &m, &mnmin, &usav[
usav_offset], ldu, &u[u_offset], ldu,
&work[1], lwork, &rwork[1], &dif, &
iinfo);
}
}
result[4] = dmax(result[4],dif);
/* Compare VT */
dif = 0.f;
if (m > 0 && n > 0) {
if (ijvt == 1) {
cunt03_("R", &n, &mnmin, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &a[a_offset],
lda, &work[1], lwork, &rwork[1], &dif,
&iinfo);
} else if (ijvt == 2) {
cunt03_("R", &n, &mnmin, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &vt[vt_offset],
ldvt, &work[1], lwork, &rwork[1], &
dif, &iinfo);
} else if (ijvt == 3) {
cunt03_("R", &n, &n, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &vt[vt_offset],
ldvt, &work[1], lwork, &rwork[1], &
dif, &iinfo);
}
}
result[5] = dmax(result[5],dif);
/* Compare S */
dif = 0.f;
/* Computing MAX */
r__1 = (real) mnmin * ulp * s[1], r__2 = slamch_(
"Safe minimum");
div = dmax(r__1,r__2);
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (ssav[i__] < ssav[i__ + 1]) {
dif = ulpinv;
}
if (ssav[i__] < 0.f) {
dif = ulpinv;
}
/* Computing MAX */
r__2 = dif, r__3 = (r__1 = ssav[i__] - s[i__],
dabs(r__1)) / div;
dif = dmax(r__2,r__3);
/* L80: */
}
result[6] = dmax(result[6],dif);
L90:
;
}
/* L100: */
}
/* Test for CGESDD */
iwtmp = (mnmin << 1) * mnmin + (mnmin << 1) + max(m,n);
lswork = iwtmp + (iwspc - 1) * (*lwork - iwtmp) / 3;
lswork = min(lswork,*lwork);
lswork = max(lswork,1);
if (iwspc == 4) {
lswork = *lwork;
}
/* Factorize A */
clacpy_("F", &m, &n, &asav[asav_offset], lda, &a[a_offset],
lda);
cgesdd_("A", &m, &n, &a[a_offset], lda, &ssav[1], &usav[
usav_offset], ldu, &vtsav[vtsav_offset], ldvt, &work[
1], &lswork, &rwork[1], &iwork[1], &iinfo);
if (iinfo != 0) {
io___39.ciunit = *nounit;
s_wsfe(&io___39);
do_fio(&c__1, "GESDD", (ftnlen)5);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&lswork, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
return 0;
}
/* Do tests 1--4 */
cbdt01_(&m, &n, &c__0, &asav[asav_offset], lda, &usav[
usav_offset], ldu, &ssav[1], &e[1], &vtsav[
vtsav_offset], ldvt, &work[1], &rwork[1], &result[7]);
if (m != 0 && n != 0) {
cunt01_("Columns", &mnmin, &m, &usav[usav_offset], ldu, &
work[1], lwork, &rwork[1], &result[8]);
cunt01_("Rows", &mnmin, &n, &vtsav[vtsav_offset], ldvt, &
work[1], lwork, &rwork[1], &result[9]);
}
result[10] = 0.f;
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (ssav[i__] < ssav[i__ + 1]) {
result[10] = ulpinv;
}
if (ssav[i__] < 0.f) {
result[10] = ulpinv;
}
/* L110: */
}
if (mnmin >= 1) {
if (ssav[mnmin] < 0.f) {
result[10] = ulpinv;
}
}
/* Do partial SVDs, comparing to SSAV, USAV, and VTSAV */
result[11] = 0.f;
result[12] = 0.f;
result[13] = 0.f;
for (ijq = 0; ijq <= 2; ++ijq) {
*(unsigned char *)jobq = *(unsigned char *)&cjob[ijq];
clacpy_("F", &m, &n, &asav[asav_offset], lda, &a[a_offset]
, lda);
cgesdd_(jobq, &m, &n, &a[a_offset], lda, &s[1], &u[
u_offset], ldu, &vt[vt_offset], ldvt, &work[1], &
lswork, &rwork[1], &iwork[1], &iinfo);
/* Compare U */
dif = 0.f;
if (m > 0 && n > 0) {
if (ijq == 1) {
if (m >= n) {
cunt03_("C", &m, &mnmin, &m, &mnmin, &usav[
usav_offset], ldu, &a[a_offset], lda,
&work[1], lwork, &rwork[1], &dif, &
iinfo);
} else {
cunt03_("C", &m, &mnmin, &m, &mnmin, &usav[
usav_offset], ldu, &u[u_offset], ldu,
&work[1], lwork, &rwork[1], &dif, &
iinfo);
}
} else if (ijq == 2) {
cunt03_("C", &m, &mnmin, &m, &mnmin, &usav[
usav_offset], ldu, &u[u_offset], ldu, &
work[1], lwork, &rwork[1], &dif, &iinfo);
}
}
result[11] = dmax(result[11],dif);
/* Compare VT */
dif = 0.f;
if (m > 0 && n > 0) {
if (ijq == 1) {
if (m >= n) {
cunt03_("R", &n, &mnmin, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &vt[vt_offset],
ldvt, &work[1], lwork, &rwork[1], &
dif, &iinfo);
} else {
cunt03_("R", &n, &mnmin, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &a[a_offset],
lda, &work[1], lwork, &rwork[1], &dif,
&iinfo);
}
} else if (ijq == 2) {
cunt03_("R", &n, &mnmin, &n, &mnmin, &vtsav[
vtsav_offset], ldvt, &vt[vt_offset], ldvt,
&work[1], lwork, &rwork[1], &dif, &iinfo);
}
}
result[12] = dmax(result[12],dif);
/* Compare S */
dif = 0.f;
/* Computing MAX */
r__1 = (real) mnmin * ulp * s[1], r__2 = slamch_("Safe m"
"inimum");
div = dmax(r__1,r__2);
i__3 = mnmin - 1;
for (i__ = 1; i__ <= i__3; ++i__) {
if (ssav[i__] < ssav[i__ + 1]) {
dif = ulpinv;
}
if (ssav[i__] < 0.f) {
dif = ulpinv;
}
/* Computing MAX */
r__2 = dif, r__3 = (r__1 = ssav[i__] - s[i__], dabs(
r__1)) / div;
dif = dmax(r__2,r__3);
/* L120: */
}
result[13] = dmax(result[13],dif);
/* L130: */
}
/* End of Loop -- Check for RESULT(j) > THRESH */
ntest = 0;
nfail = 0;
for (j = 1; j <= 14; ++j) {
if (result[j - 1] >= 0.f) {
++ntest;
}
if (result[j - 1] >= *thresh) {
++nfail;
}
/* L140: */
}
if (nfail > 0) {
++ntestf;
}
if (ntestf == 1) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
e_wsfe();
io___44.ciunit = *nounit;
s_wsfe(&io___44);
do_fio(&c__1, (char *)&(*thresh), (ftnlen)sizeof(real));
e_wsfe();
ntestf = 2;
}
for (j = 1; j <= 14; ++j) {
if (result[j - 1] >= *thresh) {
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&iwspc, (ftnlen)sizeof(integer))
;
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&j, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[j - 1], (ftnlen)sizeof(
real));
e_wsfe();
}
/* L150: */
}
nerrs += nfail;
ntestt += ntest;
/* L160: */
}
L170:
;
}
/* L180: */
}
/* Summary */
alasvm_("CBD", nounit, &nerrs, &ntestt, &c__0);
return 0;
/* End of CDRVBD */
} /* cdrvbd_ */
/* Subroutine */ int chet22_(integer *itype, char *uplo, integer *n, integer *
m, 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;
real r__1, r__2;
complex q__1;
/* Local variables */
integer j, jj, nn, jj1, jj2;
real ulp;
integer nnp1;
real unfl;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *), chemm_(char *,
char *, integer *, integer *, complex *, complex *, integer *,
complex *, integer *, complex *, complex *, integer *), cunt01_(char *, integer *, integer *, complex *, integer
*, complex *, integer *, real *, real *);
real anorm, wnorm;
extern doublereal clanhe_(char *, char *, integer *, complex *, integer *,
real *), slamch_(char *);
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CHET22 generally checks a decomposition of the form */
/* A U = U S */
/* where A is complex Hermitian, the columns of U are orthonormal, */
/* and S is diagonal (if KBAND=0) or symmetric tridiagonal (if */
/* KBAND=1). If ITYPE=1, then U is represented as a dense matrix, */
/* otherwise the 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) = | U' A U - S | / ( |A| m ulp ) *and* */
/* RESULT(2) = | I - U'U | / ( m ulp ) */
/* Arguments */
/* ========= */
/* ITYPE INTEGER */
/* Specifies the type of tests to be performed. */
/* 1: U expressed as a dense orthogonal matrix: */
/* RESULT(1) = | A - U S U' | / ( |A| n ulp ) *and* */
/* RESULT(2) = | I - UU' | / ( n ulp ) */
/* UPLO CHARACTER */
/* If UPLO='U', the upper triangle of A will be used and the */
/* (strictly) lower triangle will not be referenced. If */
/* UPLO='L', the lower triangle of A will be used and the */
/* (strictly) upper triangle will not be referenced. */
/* Not modified. */
/* N INTEGER */
/* The size of the matrix. If it is zero, CHET22 does nothing. */
/* It must be at least zero. */
/* Not modified. */
/* M INTEGER */
/* The number of columns of U. If it is zero, CHET22 does */
/* nothing. It must be at least zero. */
/* Not modified. */
/* KBAND 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. */
/* Not modified. */
/* A COMPLEX array, dimension (LDA , N) */
/* The original (unfactored) matrix. It is assumed to be */
/* symmetric, and only the upper (UPLO='U') or only the lower */
/* (UPLO='L') will be referenced. */
/* Not modified. */
/* LDA INTEGER */
/* The leading dimension of A. It must be at least 1 */
/* and at least N. */
/* Not modified. */
/* D REAL array, dimension (N) */
/* The diagonal of the (symmetric tri-) diagonal matrix. */
/* Not modified. */
/* E REAL array, dimension (N) */
/* The off-diagonal of the (symmetric tri-) diagonal matrix. */
/* E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. */
/* Not referenced if KBAND=0. */
/* Not modified. */
/* U COMPLEX array, dimension (LDU, N) */
/* If ITYPE=1, this contains the orthogonal matrix in */
/* the decomposition, expressed as a dense matrix. */
/* Not modified. */
/* LDU INTEGER */
/* The leading dimension of U. LDU must be at least N and */
/* at least 1. */
/* Not modified. */
/* V COMPLEX array, dimension (LDV, N) */
/* If ITYPE=2 or 3, the lower triangle of this array contains */
/* the Householder vectors used to describe the orthogonal */
/* matrix in the decomposition. If ITYPE=1, then it is not */
/* referenced. */
/* Not modified. */
/* LDV INTEGER */
/* The leading dimension of V. LDV must be at least N and */
/* at least 1. */
/* Not modified. */
/* TAU 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. */
/* Not modified. */
/* WORK COMPLEX array, dimension (2*N**2) */
/* Workspace. */
/* Modified. */
/* RWORK REAL array, dimension (N) */
/* Workspace. */
/* Modified. */
/* RESULT 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 LDU is at least N. */
/* Modified. */
/* ===================================================================== */
/* .. 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;
result[2] = 0.f;
if (*n <= 0 || *m <= 0) {
return 0;
}
unfl = slamch_("Safe minimum");
ulp = slamch_("Precision");
/* Do Test 1 */
/* Norm of A: */
/* Computing MAX */
r__1 = clanhe_("1", uplo, n, &a[a_offset], lda, &rwork[1]);
anorm = dmax(r__1,unfl);
/* Compute error matrix: */
/* ITYPE=1: error = U' A U - S */
chemm_("L", uplo, n, m, &c_b2, &a[a_offset], lda, &u[u_offset], ldu, &
c_b1, &work[1], n);
nn = *n * *n;
nnp1 = nn + 1;
cgemm_("C", "N", m, m, n, &c_b2, &u[u_offset], ldu, &work[1], n, &c_b1, &
work[nnp1], n);
i__1 = *m;
for (j = 1; j <= i__1; ++j) {
jj = nn + (j - 1) * *n + j;
i__2 = jj;
i__3 = jj;
i__4 = j;
q__1.r = work[i__3].r - d__[i__4], q__1.i = work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L10: */
}
if (*kband == 1 && *n > 1) {
i__1 = *m;
for (j = 2; j <= i__1; ++j) {
jj1 = nn + (j - 1) * *n + j - 1;
jj2 = nn + (j - 2) * *n + j;
i__2 = jj1;
i__3 = jj1;
i__4 = j - 1;
q__1.r = work[i__3].r - e[i__4], q__1.i = work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
i__2 = jj2;
i__3 = jj2;
i__4 = j - 1;
q__1.r = work[i__3].r - e[i__4], q__1.i = work[i__3].i;
work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L20: */
}
}
wnorm = clanhe_("1", uplo, m, &work[nnp1], n, &rwork[1]);
if (anorm > wnorm) {
result[1] = wnorm / anorm / (*m * ulp);
} else {
if (anorm < 1.f) {
/* Computing MIN */
r__1 = wnorm, r__2 = *m * anorm;
result[1] = dmin(r__1,r__2) / anorm / (*m * ulp);
} else {
/* Computing MIN */
r__1 = wnorm / anorm, r__2 = (real) (*m);
result[1] = dmin(r__1,r__2) / (*m * ulp);
}
}
/* Do Test 2 */
/* Compute U'U - I */
if (*itype == 1) {
i__1 = (*n << 1) * *n;
cunt01_("Columns", n, m, &u[u_offset], ldu, &work[1], &i__1, &rwork[1]
, &result[2]);
}
return 0;
/* End of CHET22 */
} /* chet22_ */
/* Subroutine */ int cget24_(logical *comp, integer *jtype, real *thresh,
integer *iseed, integer *nounit, integer *n, complex *a, integer *lda,
complex *h__, complex *ht, complex *w, complex *wt, complex *wtmp,
complex *vs, integer *ldvs, complex *vs1, real *rcdein, real *rcdvin,
integer *nslct, integer *islct, integer *isrt, real *result, complex *
work, integer *lwork, real *rwork, logical *bwork, integer *info)
{
/* Format strings */
static char fmt_9998[] = "(\002 CGET24: \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_9999[] = "(\002 CGET24: \002,a,\002 returned INFO=\002,i"
"6,\002.\002,/9x,\002N=\002,i6,\002, INPUT EXAMPLE NUMBER = \002,"
"i4)";
/* System generated locals */
integer a_dim1, a_offset, h_dim1, h_offset, ht_dim1, ht_offset, vs_dim1,
vs_offset, vs1_dim1, vs1_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1;
/* Builtin functions */
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
double r_imag(complex *);
/* Local variables */
integer i__, j;
real v, eps, tol, ulp;
integer sdim, kmin;
complex ctmp;
integer itmp, ipnt[20], rsub;
char sort[1];
integer sdim1;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
integer iinfo;
extern /* Subroutine */ int cunt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *);
real anorm;
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *);
real tolin;
integer isort;
real wnorm, rcnde1, rcndv1;
extern doublereal clange_(char *, integer *, integer *, complex *,
integer *, real *), slamch_(char *);
real rconde;
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *);
extern logical cslect_(complex *);
extern /* Subroutine */ int cgeesx_(char *, char *, L_fp, char *, integer
*, complex *, integer *, integer *, complex *, complex *, integer
*, real *, real *, complex *, integer *, real *, logical *,
integer *), xerbla_(char *, integer *);
integer knteig;
real rcondv, vricmp, vrimin, smlnum, ulpinv;
/* Fortran I/O blocks */
static cilist io___12 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___13 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___17 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___18 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___21 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___22 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___25 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___26 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___27 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___28 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___29 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___30 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___31 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___32 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___33 = { 0, 0, 0, fmt_9998, 0 };
static cilist io___34 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___42 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CGET24 checks the nonsymmetric eigenvalue (Schur form) problem */
/* expert driver CGEESX. */
/* If COMP = .FALSE., the first 13 of the following tests will be */
/* be performed on the input matrix A, and also tests 14 and 15 */
/* if LWORK is sufficiently large. */
/* If COMP = .TRUE., all 17 test will be performed. */
/* (1) 0 if T is in Schur form, 1/ulp otherwise */
/* (no sorting of eigenvalues) */
/* (2) | A - VS T VS' | / ( n |A| ulp ) */
/* Here VS is the matrix of Schur eigenvectors, and T is in Schur */
/* form (no sorting of eigenvalues). */
/* (3) | I - VS VS' | / ( n ulp ) (no sorting of eigenvalues). */
/* (4) 0 if W are eigenvalues of T */
/* 1/ulp otherwise */
/* (no sorting of eigenvalues) */
/* (5) 0 if T(with VS) = T(without VS), */
/* 1/ulp otherwise */
/* (no sorting of eigenvalues) */
/* (6) 0 if eigenvalues(with VS) = eigenvalues(without VS), */
/* 1/ulp otherwise */
/* (no sorting of eigenvalues) */
/* (7) 0 if T is in Schur form, 1/ulp otherwise */
/* (with sorting of eigenvalues) */
/* (8) | A - VS T VS' | / ( n |A| ulp ) */
/* Here VS is the matrix of Schur eigenvectors, and T is in Schur */
/* form (with sorting of eigenvalues). */
/* (9) | I - VS VS' | / ( n ulp ) (with sorting of eigenvalues). */
/* (10) 0 if W are eigenvalues of T */
/* 1/ulp otherwise */
/* If workspace sufficient, also compare W with and */
/* without reciprocal condition numbers */
/* (with sorting of eigenvalues) */
/* (11) 0 if T(with VS) = T(without VS), */
/* 1/ulp otherwise */
/* If workspace sufficient, also compare T with and without */
/* reciprocal condition numbers */
/* (with sorting of eigenvalues) */
/* (12) 0 if eigenvalues(with VS) = eigenvalues(without VS), */
/* 1/ulp otherwise */
/* If workspace sufficient, also compare VS with and without */
/* reciprocal condition numbers */
/* (with sorting of eigenvalues) */
/* (13) if sorting worked and SDIM is the number of */
/* eigenvalues which were SELECTed */
/* If workspace sufficient, also compare SDIM with and */
/* without reciprocal condition numbers */
/* (14) if RCONDE the same no matter if VS and/or RCONDV computed */
/* (15) if RCONDV the same no matter if VS and/or RCONDE computed */
/* (16) |RCONDE - RCDEIN| / cond(RCONDE) */
/* RCONDE is the reciprocal average eigenvalue condition number */
/* computed by CGEESX and RCDEIN (the precomputed true value) */
/* is supplied as input. cond(RCONDE) is the condition number */
/* of RCONDE, and takes errors in computing RCONDE into account, */
/* so that the resulting quantity should be O(ULP). cond(RCONDE) */
/* is essentially given by norm(A)/RCONDV. */
/* (17) |RCONDV - RCDVIN| / cond(RCONDV) */
/* RCONDV is the reciprocal right invariant subspace condition */
/* number computed by CGEESX and RCDVIN (the precomputed true */
/* value) is supplied as input. cond(RCONDV) is the condition */
/* number of RCONDV, and takes errors in computing RCONDV into */
/* account, so that the resulting quantity should be O(ULP). */
/* cond(RCONDV) is essentially given by norm(A)/RCONDE. */
/* Arguments */
/* ========= */
/* COMP (input) LOGICAL */
/* COMP describes which input tests to perform: */
/* = .FALSE. if the computed condition numbers are not to */
/* be tested against RCDVIN and RCDEIN */
/* = .TRUE. if they are to be compared */
/* JTYPE (input) INTEGER */
/* Type of input matrix. Used to label output if error occurs. */
/* ISEED (input) INTEGER array, dimension (4) */
/* If COMP = .FALSE., the random number generator seed */
/* used to produce matrix. */
/* If COMP = .TRUE., ISEED(1) = the number of the example. */
/* Used to label output if error occurs. */
/* 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 INFO not equal to 0.) */
/* N (input) INTEGER */
/* The dimension of A. N must be at least 0. */
/* A (input/output) COMPLEX array, dimension (LDA, N) */
/* Used to hold the matrix whose eigenvalues are to be */
/* computed. */
/* LDA (input) INTEGER */
/* The leading dimension of A, and H. LDA must be at */
/* least 1 and at least N. */
/* H (workspace) COMPLEX array, dimension (LDA, N) */
/* Another copy of the test matrix A, modified by CGEESX. */
/* HT (workspace) COMPLEX array, dimension (LDA, N) */
/* Yet another copy of the test matrix A, modified by CGEESX. */
/* W (workspace) COMPLEX array, dimension (N) */
/* The computed eigenvalues of A. */
/* WT (workspace) COMPLEX array, dimension (N) */
/* Like W, this array contains the eigenvalues of A, */
/* but those computed when CGEESX only computes a partial */
/* eigendecomposition, i.e. not Schur vectors */
/* WTMP (workspace) COMPLEX array, dimension (N) */
/* Like W, this array contains the eigenvalues of A, */
/* but sorted by increasing real or imaginary part. */
/* VS (workspace) COMPLEX array, dimension (LDVS, N) */
/* VS holds the computed Schur vectors. */
/* LDVS (input) INTEGER */
/* Leading dimension of VS. Must be at least max(1, N). */
/* VS1 (workspace) COMPLEX array, dimension (LDVS, N) */
/* VS1 holds another copy of the computed Schur vectors. */
/* RCDEIN (input) REAL */
/* When COMP = .TRUE. RCDEIN holds the precomputed reciprocal */
/* condition number for the average of selected eigenvalues. */
/* RCDVIN (input) REAL */
/* When COMP = .TRUE. RCDVIN holds the precomputed reciprocal */
/* condition number for the selected right invariant subspace. */
/* NSLCT (input) INTEGER */
/* When COMP = .TRUE. the number of selected eigenvalues */
/* corresponding to the precomputed values RCDEIN and RCDVIN. */
/* ISLCT (input) INTEGER array, dimension (NSLCT) */
/* When COMP = .TRUE. ISLCT selects the eigenvalues of the */
/* input matrix corresponding to the precomputed values RCDEIN */
/* and RCDVIN. For I=1, ... ,NSLCT, if ISLCT(I) = J, then the */
/* eigenvalue with the J-th largest real or imaginary part is */
/* selected. The real part is used if ISRT = 0, and the */
/* imaginary part if ISRT = 1. */
/* Not referenced if COMP = .FALSE. */
/* ISRT (input) INTEGER */
/* When COMP = .TRUE., ISRT describes how ISLCT is used to */
/* choose a subset of the spectrum. */
/* Not referenced if COMP = .FALSE. */
/* RESULT (output) REAL array, dimension (17) */
/* The values computed by the 17 tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* WORK (workspace) COMPLEX array, dimension (2*N*N) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK to be passed to CGEESX. This */
/* must be at least 2*N, and N*(N+1)/2 if tests 14--16 are to */
/* be performed. */
/* RWORK (workspace) REAL array, dimension (N) */
/* BWORK (workspace) LOGICAL array, dimension (N) */
/* INFO (output) INTEGER */
/* If 0, successful exit. */
/* If <0, input parameter -INFO had an incorrect value. */
/* If >0, CGEESX returned an error code, the absolute */
/* value of which is returned. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Arrays in Common .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
/* Parameter adjustments */
--iseed;
ht_dim1 = *lda;
ht_offset = 1 + ht_dim1;
ht -= ht_offset;
h_dim1 = *lda;
h_offset = 1 + h_dim1;
h__ -= h_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--w;
--wt;
--wtmp;
vs1_dim1 = *ldvs;
vs1_offset = 1 + vs1_dim1;
vs1 -= vs1_offset;
vs_dim1 = *ldvs;
vs_offset = 1 + vs_dim1;
vs -= vs_offset;
--islct;
--result;
--work;
--rwork;
--bwork;
/* Function Body */
*info = 0;
if (*thresh < 0.f) {
*info = -3;
} else if (*nounit <= 0) {
*info = -5;
} else if (*n < 0) {
*info = -6;
} else if (*lda < 1 || *lda < *n) {
*info = -8;
} else if (*ldvs < 1 || *ldvs < *n) {
*info = -15;
} else if (*lwork < *n << 1) {
*info = -24;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CGET24", &i__1);
return 0;
}
/* Quick return if nothing to do */
for (i__ = 1; i__ <= 17; ++i__) {
result[i__] = -1.f;
/* L10: */
}
if (*n == 0) {
return 0;
}
/* Important constants */
smlnum = slamch_("Safe minimum");
ulp = slamch_("Precision");
ulpinv = 1.f / ulp;
/* Perform tests (1)-(13) */
sslct_1.selopt = 0;
for (isort = 0; isort <= 1; ++isort) {
if (isort == 0) {
*(unsigned char *)sort = 'N';
rsub = 0;
} else {
*(unsigned char *)sort = 'S';
rsub = 6;
}
/* Compute Schur form and Schur vectors, and test them */
clacpy_("F", n, n, &a[a_offset], lda, &h__[h_offset], lda);
cgeesx_("V", sort, (L_fp)cslect_, "N", n, &h__[h_offset], lda, &sdim,
&w[1], &vs[vs_offset], ldvs, &rconde, &rcondv, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[rsub + 1] = ulpinv;
if (*jtype != 22) {
io___12.ciunit = *nounit;
s_wsfe(&io___12);
do_fio(&c__1, "CGEESX1", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___13.ciunit = *nounit;
s_wsfe(&io___13);
do_fio(&c__1, "CGEESX1", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
return 0;
}
if (isort == 0) {
ccopy_(n, &w[1], &c__1, &wtmp[1], &c__1);
}
/* Do Test (1) or Test (7) */
result[rsub + 1] = 0.f;
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * h_dim1;
if (h__[i__3].r != 0.f || h__[i__3].i != 0.f) {
result[rsub + 1] = ulpinv;
}
/* L20: */
}
/* L30: */
}
/* Test (2) or (8): Compute norm(A - Q*H*Q') / (norm(A) * N * ULP) */
/* Copy A to VS1, used as workspace */
clacpy_(" ", n, n, &a[a_offset], lda, &vs1[vs1_offset], ldvs);
/* Compute Q*H and store in HT. */
cgemm_("No transpose", "No transpose", n, n, n, &c_b2, &vs[vs_offset],
ldvs, &h__[h_offset], lda, &c_b1, &ht[ht_offset], lda);
/* Compute A - Q*H*Q' */
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", n, n, n, &q__1, &ht[
ht_offset], lda, &vs[vs_offset], ldvs, &c_b2, &vs1[vs1_offset]
, ldvs);
/* Computing MAX */
r__1 = clange_("1", n, n, &a[a_offset], lda, &rwork[1]);
anorm = dmax(r__1,smlnum);
wnorm = clange_("1", n, n, &vs1[vs1_offset], ldvs, &rwork[1]);
if (anorm > wnorm) {
result[rsub + 2] = wnorm / anorm / (*n * ulp);
} else {
if (anorm < 1.f) {
/* Computing MIN */
r__1 = wnorm, r__2 = *n * anorm;
result[rsub + 2] = dmin(r__1,r__2) / anorm / (*n * ulp);
} else {
/* Computing MIN */
r__1 = wnorm / anorm, r__2 = (real) (*n);
result[rsub + 2] = dmin(r__1,r__2) / (*n * ulp);
}
}
/* Test (3) or (9): Compute norm( I - Q'*Q ) / ( N * ULP ) */
cunt01_("Columns", n, n, &vs[vs_offset], ldvs, &work[1], lwork, &
rwork[1], &result[rsub + 3]);
/* Do Test (4) or Test (10) */
result[rsub + 4] = 0.f;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + i__ * h_dim1;
i__3 = i__;
if (h__[i__2].r != w[i__3].r || h__[i__2].i != w[i__3].i) {
result[rsub + 4] = ulpinv;
}
/* L40: */
}
/* Do Test (5) or Test (11) */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("N", sort, (L_fp)cslect_, "N", n, &ht[ht_offset], lda, &sdim,
&wt[1], &vs[vs_offset], ldvs, &rconde, &rcondv, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[rsub + 5] = ulpinv;
if (*jtype != 22) {
io___17.ciunit = *nounit;
s_wsfe(&io___17);
do_fio(&c__1, "CGEESX2", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___18.ciunit = *nounit;
s_wsfe(&io___18);
do_fio(&c__1, "CGEESX2", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
result[rsub + 5] = 0.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[rsub + 5] = ulpinv;
}
/* L50: */
}
/* L60: */
}
/* Do Test (6) or Test (12) */
result[rsub + 6] = 0.f;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[rsub + 6] = ulpinv;
}
/* L70: */
}
/* Do Test (13) */
if (isort == 1) {
result[13] = 0.f;
knteig = 0;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (cslect_(&w[i__])) {
++knteig;
}
if (i__ < *n) {
if (cslect_(&w[i__ + 1]) && ! cslect_(&w[i__])) {
result[13] = ulpinv;
}
}
/* L80: */
}
if (sdim != knteig) {
result[13] = ulpinv;
}
}
/* L90: */
}
/* If there is enough workspace, perform tests (14) and (15) */
/* as well as (10) through (13) */
if (*lwork >= *n * (*n + 1) / 2) {
/* Compute both RCONDE and RCONDV with VS */
*(unsigned char *)sort = 'S';
result[14] = 0.f;
result[15] = 0.f;
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("V", sort, (L_fp)cslect_, "B", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rconde, &rcondv, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[14] = ulpinv;
result[15] = ulpinv;
if (*jtype != 22) {
io___21.ciunit = *nounit;
s_wsfe(&io___21);
do_fio(&c__1, "CGEESX3", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___22.ciunit = *nounit;
s_wsfe(&io___22);
do_fio(&c__1, "CGEESX3", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L100: */
}
/* L110: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
/* Compute both RCONDE and RCONDV without VS, and compare */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("N", sort, (L_fp)cslect_, "B", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[14] = ulpinv;
result[15] = ulpinv;
if (*jtype != 22) {
io___25.ciunit = *nounit;
s_wsfe(&io___25);
do_fio(&c__1, "CGEESX4", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___26.ciunit = *nounit;
s_wsfe(&io___26);
do_fio(&c__1, "CGEESX4", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform tests (14) and (15) */
if (rcnde1 != rconde) {
result[14] = ulpinv;
}
if (rcndv1 != rcondv) {
result[15] = ulpinv;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L120: */
}
/* L130: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
/* Compute RCONDE with VS, and compare */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("V", sort, (L_fp)cslect_, "E", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[14] = ulpinv;
if (*jtype != 22) {
io___27.ciunit = *nounit;
s_wsfe(&io___27);
do_fio(&c__1, "CGEESX5", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___28.ciunit = *nounit;
s_wsfe(&io___28);
do_fio(&c__1, "CGEESX5", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform test (14) */
if (rcnde1 != rconde) {
result[14] = ulpinv;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L140: */
}
/* L150: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
/* Compute RCONDE without VS, and compare */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("N", sort, (L_fp)cslect_, "E", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[14] = ulpinv;
if (*jtype != 22) {
io___29.ciunit = *nounit;
s_wsfe(&io___29);
do_fio(&c__1, "CGEESX6", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___30.ciunit = *nounit;
s_wsfe(&io___30);
do_fio(&c__1, "CGEESX6", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform test (14) */
if (rcnde1 != rconde) {
result[14] = ulpinv;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L160: */
}
/* L170: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
/* Compute RCONDV with VS, and compare */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("V", sort, (L_fp)cslect_, "V", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[15] = ulpinv;
if (*jtype != 22) {
io___31.ciunit = *nounit;
s_wsfe(&io___31);
do_fio(&c__1, "CGEESX7", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___32.ciunit = *nounit;
s_wsfe(&io___32);
do_fio(&c__1, "CGEESX7", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform test (15) */
if (rcndv1 != rcondv) {
result[15] = ulpinv;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L180: */
}
/* L190: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
/* Compute RCONDV without VS, and compare */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("N", sort, (L_fp)cslect_, "V", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rcnde1, &rcndv1, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[15] = ulpinv;
if (*jtype != 22) {
io___33.ciunit = *nounit;
s_wsfe(&io___33);
do_fio(&c__1, "CGEESX8", (ftnlen)7);
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 *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
} else {
io___34.ciunit = *nounit;
s_wsfe(&io___34);
do_fio(&c__1, "CGEESX8", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
}
*info = abs(iinfo);
goto L220;
}
/* Perform test (15) */
if (rcndv1 != rcondv) {
result[15] = ulpinv;
}
/* Perform tests (10), (11), (12), and (13) */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
if (w[i__2].r != wt[i__3].r || w[i__2].i != wt[i__3].i) {
result[10] = ulpinv;
}
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
i__3 = i__ + j * h_dim1;
i__4 = i__ + j * ht_dim1;
if (h__[i__3].r != ht[i__4].r || h__[i__3].i != ht[i__4].i) {
result[11] = ulpinv;
}
i__3 = i__ + j * vs_dim1;
i__4 = i__ + j * vs1_dim1;
if (vs[i__3].r != vs1[i__4].r || vs[i__3].i != vs1[i__4].i) {
result[12] = ulpinv;
}
/* L200: */
}
/* L210: */
}
if (sdim != sdim1) {
result[13] = ulpinv;
}
}
L220:
/* If there are precomputed reciprocal condition numbers, compare */
/* computed values with them. */
if (*comp) {
/* First set up SELOPT, SELDIM, SELVAL, SELWR and SELWI so that */
/* the logical function CSLECT selects the eigenvalues specified */
/* by NSLCT, ISLCT and ISRT. */
sslct_1.seldim = *n;
sslct_1.selopt = 1;
eps = dmax(ulp,5.9605e-8f);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
ipnt[i__ - 1] = i__;
sslct_1.selval[i__ - 1] = FALSE_;
i__2 = i__;
sslct_1.selwr[i__ - 1] = wtmp[i__2].r;
sslct_1.selwi[i__ - 1] = r_imag(&wtmp[i__]);
/* L230: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
kmin = i__;
if (*isrt == 0) {
i__2 = i__;
vrimin = wtmp[i__2].r;
} else {
vrimin = r_imag(&wtmp[i__]);
}
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
if (*isrt == 0) {
i__3 = j;
vricmp = wtmp[i__3].r;
} else {
vricmp = r_imag(&wtmp[j]);
}
if (vricmp < vrimin) {
kmin = j;
vrimin = vricmp;
}
/* L240: */
}
i__2 = kmin;
ctmp.r = wtmp[i__2].r, ctmp.i = wtmp[i__2].i;
i__2 = kmin;
i__3 = i__;
wtmp[i__2].r = wtmp[i__3].r, wtmp[i__2].i = wtmp[i__3].i;
i__2 = i__;
wtmp[i__2].r = ctmp.r, wtmp[i__2].i = ctmp.i;
itmp = ipnt[i__ - 1];
ipnt[i__ - 1] = ipnt[kmin - 1];
ipnt[kmin - 1] = itmp;
/* L250: */
}
i__1 = *nslct;
for (i__ = 1; i__ <= i__1; ++i__) {
sslct_1.selval[ipnt[islct[i__] - 1] - 1] = TRUE_;
/* L260: */
}
/* Compute condition numbers */
clacpy_("F", n, n, &a[a_offset], lda, &ht[ht_offset], lda);
cgeesx_("N", "S", (L_fp)cslect_, "B", n, &ht[ht_offset], lda, &sdim1,
&wt[1], &vs1[vs1_offset], ldvs, &rconde, &rcondv, &work[1],
lwork, &rwork[1], &bwork[1], &iinfo);
if (iinfo != 0) {
result[16] = ulpinv;
result[17] = ulpinv;
io___42.ciunit = *nounit;
s_wsfe(&io___42);
do_fio(&c__1, "CGEESX9", (ftnlen)7);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&(*n), (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&iseed[1], (ftnlen)sizeof(integer));
e_wsfe();
*info = abs(iinfo);
goto L270;
}
/* Compare condition number for average of selected eigenvalues */
/* taking its condition number into account */
anorm = clange_("1", n, n, &a[a_offset], lda, &rwork[1]);
/* Computing MAX */
r__1 = (real) (*n) * eps * anorm;
v = dmax(r__1,smlnum);
if (anorm == 0.f) {
v = 1.f;
}
if (v > rcondv) {
tol = 1.f;
} else {
tol = v / rcondv;
}
if (v > *rcdvin) {
tolin = 1.f;
} else {
tolin = v / *rcdvin;
}
/* Computing MAX */
r__1 = tol, r__2 = smlnum / eps;
tol = dmax(r__1,r__2);
/* Computing MAX */
r__1 = tolin, r__2 = smlnum / eps;
tolin = dmax(r__1,r__2);
if (eps * (*rcdein - tolin) > rconde + tol) {
result[16] = ulpinv;
} else if (*rcdein - tolin > rconde + tol) {
result[16] = (*rcdein - tolin) / (rconde + tol);
} else if (*rcdein + tolin < eps * (rconde - tol)) {
result[16] = ulpinv;
} else if (*rcdein + tolin < rconde - tol) {
result[16] = (rconde - tol) / (*rcdein + tolin);
} else {
result[16] = 1.f;
}
/* Compare condition numbers for right invariant subspace */
/* taking its condition number into account */
if (v > rcondv * rconde) {
tol = rcondv;
} else {
tol = v / rconde;
}
if (v > *rcdvin * *rcdein) {
tolin = *rcdvin;
} else {
tolin = v / *rcdein;
}
/* Computing MAX */
r__1 = tol, r__2 = smlnum / eps;
tol = dmax(r__1,r__2);
/* Computing MAX */
r__1 = tolin, r__2 = smlnum / eps;
tolin = dmax(r__1,r__2);
if (eps * (*rcdvin - tolin) > rcondv + tol) {
result[17] = ulpinv;
} else if (*rcdvin - tolin > rcondv + tol) {
result[17] = (*rcdvin - tolin) / (rcondv + tol);
} else if (*rcdvin + tolin < eps * (rcondv - tol)) {
result[17] = ulpinv;
} else if (*rcdvin + tolin < rcondv - tol) {
result[17] = (rcondv - tol) / (*rcdvin + tolin);
} else {
result[17] = 1.f;
}
L270:
;
}
return 0;
/* End of CGET24 */
} /* cget24_ */
/* Subroutine */ int cunt03_(char *rc, integer *mu, integer *mv, integer *n,
integer *k, complex *u, integer *ldu, complex *v, integer *ldv,
complex *work, integer *lwork, real *rwork, real *result, integer *
info)
{
/* System generated locals */
integer u_dim1, u_offset, v_dim1, v_offset, i__1, i__2, i__3, i__4;
real r__1, r__2;
complex q__1, q__2;
/* Builtin functions */
double c_abs(complex *);
void c_div(complex *, complex *, complex *);
/* Local variables */
static integer i__, j;
static complex s;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int cunt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *);
extern integer icamax_(integer *, complex *, integer *);
extern doublereal slamch_(char *);
static complex su, sv;
extern /* Subroutine */ int xerbla_(char *, integer *);
static integer irc, lmx;
static real ulp, res1, res2;
#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)]
/* -- 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
=======
CUNT03 compares two unitary matrices U and V to see if their
corresponding rows or columns span the same spaces. The rows are
checked if RC = 'R', and the columns are checked if RC = 'C'.
RESULT is the maximum of
| V*V' - I | / ( MV ulp ), if RC = 'R', or
| V'*V - I | / ( MV ulp ), if RC = 'C',
and the maximum over rows (or columns) 1 to K of
| U(i) - S*V(i) |/ ( N ulp )
where abs(S) = 1 (chosen to minimize the expression), U(i) is the
i-th row (column) of U, and V(i) is the i-th row (column) of V.
Arguments
==========
RC (input) CHARACTER*1
If RC = 'R' the rows of U and V are to be compared.
If RC = 'C' the columns of U and V are to be compared.
MU (input) INTEGER
The number of rows of U if RC = 'R', and the number of
columns if RC = 'C'. If MU = 0 CUNT03 does nothing.
MU must be at least zero.
MV (input) INTEGER
The number of rows of V if RC = 'R', and the number of
columns if RC = 'C'. If MV = 0 CUNT03 does nothing.
MV must be at least zero.
N (input) INTEGER
If RC = 'R', the number of columns in the matrices U and V,
and if RC = 'C', the number of rows in U and V. If N = 0
CUNT03 does nothing. N must be at least zero.
K (input) INTEGER
The number of rows or columns of U and V to compare.
0 <= K <= max(MU,MV).
U (input) COMPLEX array, dimension (LDU,N)
The first matrix to compare. If RC = 'R', U is MU by N, and
if RC = 'C', U is N by MU.
LDU (input) INTEGER
The leading dimension of U. If RC = 'R', LDU >= max(1,MU),
and if RC = 'C', LDU >= max(1,N).
V (input) COMPLEX array, dimension (LDV,N)
The second matrix to compare. If RC = 'R', V is MV by N, and
if RC = 'C', V is N by MV.
LDV (input) INTEGER
The leading dimension of V. If RC = 'R', LDV >= max(1,MV),
and if RC = 'C', LDV >= max(1,N).
WORK (workspace) COMPLEX array, dimension (LWORK)
LWORK (input) INTEGER
The length of the array WORK. For best performance, LWORK
should be at least N*N if RC = 'C' or M*M if RC = 'R', but
the tests will be done even if LWORK is 0.
RWORK (workspace) REAL array, dimension (max(MV,N))
RESULT (output) REAL
The value computed by the test described above. RESULT is
limited to 1/ulp to avoid overflow.
INFO (output) INTEGER
0 indicates a successful exit
-k indicates the k-th parameter had an illegal value
=====================================================================
Check inputs
Parameter adjustments */
u_dim1 = *ldu;
u_offset = 1 + u_dim1 * 1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--work;
--rwork;
/* Function Body */
*info = 0;
if (lsame_(rc, "R")) {
irc = 0;
} else if (lsame_(rc, "C")) {
irc = 1;
} else {
irc = -1;
}
if (irc == -1) {
*info = -1;
} else if (*mu < 0) {
*info = -2;
} else if (*mv < 0) {
*info = -3;
} else if (*n < 0) {
*info = -4;
} else if (*k < 0 || *k > max(*mu,*mv)) {
*info = -5;
} else if (irc == 0 && *ldu < max(1,*mu) || irc == 1 && *ldu < max(1,*n))
{
*info = -7;
} else if (irc == 0 && *ldv < max(1,*mv) || irc == 1 && *ldv < max(1,*n))
{
*info = -9;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CUNT03", &i__1);
return 0;
}
/* Initialize result */
*result = 0.f;
if (*mu == 0 || *mv == 0 || *n == 0) {
return 0;
}
/* Machine constants */
ulp = slamch_("Precision");
if (irc == 0) {
/* Compare rows */
res1 = 0.f;
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
lmx = icamax_(n, &u_ref(i__, 1), ldu);
i__2 = v_subscr(i__, lmx);
if (v[i__2].r == 0.f && v[i__2].i == 0.f) {
sv.r = 1.f, sv.i = 0.f;
} else {
r__1 = c_abs(&v_ref(i__, lmx));
q__2.r = r__1, q__2.i = 0.f;
c_div(&q__1, &q__2, &v_ref(i__, lmx));
sv.r = q__1.r, sv.i = q__1.i;
}
i__2 = u_subscr(i__, lmx);
if (u[i__2].r == 0.f && u[i__2].i == 0.f) {
su.r = 1.f, su.i = 0.f;
} else {
r__1 = c_abs(&u_ref(i__, lmx));
q__2.r = r__1, q__2.i = 0.f;
c_div(&q__1, &q__2, &u_ref(i__, lmx));
su.r = q__1.r, su.i = q__1.i;
}
c_div(&q__1, &sv, &su);
s.r = q__1.r, s.i = q__1.i;
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MAX */
i__3 = u_subscr(i__, j);
i__4 = v_subscr(i__, j);
q__2.r = s.r * v[i__4].r - s.i * v[i__4].i, q__2.i = s.r * v[
i__4].i + s.i * v[i__4].r;
q__1.r = u[i__3].r - q__2.r, q__1.i = u[i__3].i - q__2.i;
r__1 = res1, r__2 = c_abs(&q__1);
res1 = dmax(r__1,r__2);
/* L10: */
}
/* L20: */
}
res1 /= (real) (*n) * ulp;
/* Compute orthogonality of rows of V. */
cunt01_("Rows", mv, n, &v[v_offset], ldv, &work[1], lwork, &rwork[1],
&res2);
} else {
/* Compare columns */
res1 = 0.f;
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
lmx = icamax_(n, &u_ref(1, i__), &c__1);
i__2 = v_subscr(lmx, i__);
if (v[i__2].r == 0.f && v[i__2].i == 0.f) {
sv.r = 1.f, sv.i = 0.f;
} else {
r__1 = c_abs(&v_ref(lmx, i__));
q__2.r = r__1, q__2.i = 0.f;
c_div(&q__1, &q__2, &v_ref(lmx, i__));
sv.r = q__1.r, sv.i = q__1.i;
}
i__2 = u_subscr(lmx, i__);
if (u[i__2].r == 0.f && u[i__2].i == 0.f) {
su.r = 1.f, su.i = 0.f;
} else {
r__1 = c_abs(&u_ref(lmx, i__));
q__2.r = r__1, q__2.i = 0.f;
c_div(&q__1, &q__2, &u_ref(lmx, i__));
su.r = q__1.r, su.i = q__1.i;
}
c_div(&q__1, &sv, &su);
s.r = q__1.r, s.i = q__1.i;
i__2 = *n;
for (j = 1; j <= i__2; ++j) {
/* Computing MAX */
i__3 = u_subscr(j, i__);
i__4 = v_subscr(j, i__);
q__2.r = s.r * v[i__4].r - s.i * v[i__4].i, q__2.i = s.r * v[
i__4].i + s.i * v[i__4].r;
q__1.r = u[i__3].r - q__2.r, q__1.i = u[i__3].i - q__2.i;
r__1 = res1, r__2 = c_abs(&q__1);
res1 = dmax(r__1,r__2);
/* L30: */
}
/* L40: */
}
res1 /= (real) (*n) * ulp;
/* Compute orthogonality of columns of V. */
cunt01_("Columns", n, mv, &v[v_offset], ldv, &work[1], lwork, &rwork[
1], &res2);
}
/* Computing MIN */
r__1 = dmax(res1,res2), r__2 = 1.f / ulp;
*result = dmin(r__1,r__2);
return 0;
/* End of CUNT03 */
} /* cunt03_ */
/* Subroutine */ int cchkbb_(integer *nsizes, integer *mval, integer *nval,
integer *nwdths, integer *kk, integer *ntypes, logical *dotype,
integer *nrhs, integer *iseed, real *thresh, integer *nounit, complex
*a, integer *lda, complex *ab, integer *ldab, real *bd, real *be,
complex *q, integer *ldq, complex *p, integer *ldp, complex *c__,
integer *ldc, complex *cc, complex *work, integer *lwork, real *rwork,
real *result, integer *info)
{
/* Initialized data */
static integer ktype[15] = { 1,2,4,4,4,4,4,6,6,6,6,6,9,9,9 };
static integer kmagn[15] = { 1,1,1,1,1,2,3,1,1,1,2,3,1,2,3 };
static integer kmode[15] = { 0,0,4,3,1,4,4,4,3,1,4,4,0,0,0 };
/* Format strings */
static char fmt_9999[] = "(\002 CCHKBB: \002,a,\002 returned INFO=\002,i"
"5,\002.\002,/9x,\002M=\002,i5,\002 N=\002,i5,\002 K=\002,i5,\002"
", JTYPE=\002,i5,\002, ISEED=(\002,3(i5,\002,\002),i5,\002)\002)";
static char fmt_9998[] = "(\002 M =\002,i4,\002 N=\002,i4,\002, K=\002,i"
"3,\002, seed=\002,4(i4,\002,\002),\002 type \002,i2,\002, test"
"(\002,i2,\002)=\002,g10.3)";
/* System generated locals */
integer a_dim1, a_offset, ab_dim1, ab_offset, c_dim1, c_offset, cc_dim1,
cc_offset, p_dim1, p_offset, q_dim1, q_offset, i__1, i__2, i__3,
i__4, i__5, i__6, i__7, i__8, i__9;
/* Local variables */
integer i__, j, k, m, n, kl, jr, ku;
real ulp, cond;
integer jcol, kmax, mmax, nmax;
real unfl, ovfl;
extern /* Subroutine */ int cbdt01_(integer *, integer *, integer *,
complex *, integer *, complex *, integer *, real *, real *,
complex *, integer *, complex *, real *, real *), cbdt02_(integer
*, integer *, complex *, integer *, complex *, integer *, complex
*, integer *, complex *, real *, real *);
logical badmm, badnn;
integer imode, iinfo;
extern /* Subroutine */ int cunt01_(char *, integer *, integer *, complex
*, integer *, complex *, integer *, real *, real *);
real anorm;
integer mnmin, mnmax, nmats, jsize, nerrs, itype, jtype, ntest;
extern /* Subroutine */ int slahd2_(integer *, char *), cgbbrd_(
char *, integer *, integer *, integer *, integer *, integer *,
complex *, integer *, real *, real *, complex *, integer *,
complex *, integer *, complex *, integer *, complex *, real *,
integer *);
logical badnnb;
extern doublereal slamch_(char *);
extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex
*, integer *, complex *, integer *);
integer idumma[1];
extern /* Subroutine */ int claset_(char *, integer *, integer *, complex
*, complex *, complex *, integer *);
integer ioldsd[4];
extern /* Subroutine */ int xerbla_(char *, integer *), clatmr_(
integer *, integer *, char *, integer *, char *, complex *,
integer *, real *, complex *, char *, char *, complex *, integer *
, real *, complex *, integer *, real *, char *, integer *,
integer *, integer *, real *, real *, char *, complex *, integer *
, integer *, integer *), clatms_(integer *, integer *, char *, integer *, char *,
real *, integer *, real *, real *, integer *, integer *, char *,
complex *, integer *, complex *, integer *);
real amninv;
integer jwidth;
extern /* Subroutine */ int slasum_(char *, integer *, integer *, integer
*);
real rtunfl, rtovfl, ulpinv;
integer mtypes, ntestt;
/* Fortran I/O blocks */
static cilist io___41 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___43 = { 0, 0, 0, fmt_9999, 0 };
static cilist io___45 = { 0, 0, 0, fmt_9998, 0 };
/* -- LAPACK test routine (new routine for release 2.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CCHKBB tests the reduction of a general complex rectangular band */
/* matrix to real bidiagonal form. */
/* CGBBRD factors a general band matrix A as Q B P* , where * means */
/* conjugate transpose, B is upper bidiagonal, and Q and P are unitary; */
/* CGBBRD can also overwrite a given matrix C with Q* C . */
/* For each pair of matrix dimensions (M,N) and each selected matrix */
/* type, an M by N matrix A and an M by NRHS matrix C are generated. */
/* The problem dimensions are as follows */
/* A: M x N */
/* Q: M x M */
/* P: N x N */
/* B: min(M,N) x min(M,N) */
/* C: M x NRHS */
/* For each generated matrix, 4 tests are performed: */
/* (1) | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P' */
/* (2) | I - Q' Q | / ( M ulp ) */
/* (3) | I - PT PT' | / ( N ulp ) */
/* (4) | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C. */
/* 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: */
/* The possible matrix types are */
/* (1) The zero matrix. */
/* (2) The identity matrix. */
/* (3) A diagonal matrix with evenly spaced entries */
/* 1, ..., ULP and random signs. */
/* (ULP = (first number larger than 1) - 1 ) */
/* (4) A diagonal matrix with geometrically spaced entries */
/* 1, ..., ULP and random signs. */
/* (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP */
/* and random signs. */
/* (6) Same as (3), but multiplied by SQRT( overflow threshold ) */
/* (7) Same as (3), but multiplied by SQRT( underflow threshold ) */
/* (8) A matrix of the form U D V, where U and V are orthogonal and */
/* D has evenly spaced entries 1, ..., ULP with random signs */
/* on the diagonal. */
/* (9) A matrix of the form U D V, where U and V are orthogonal and */
/* D has geometrically spaced entries 1, ..., ULP with random */
/* signs on the diagonal. */
/* (10) A matrix of the form U D V, where U and V are orthogonal and */
/* D has "clustered" entries 1, ULP,..., ULP with random */
/* signs on the diagonal. */
/* (11) Same as (8), but multiplied by SQRT( overflow threshold ) */
/* (12) Same as (8), but multiplied by SQRT( underflow threshold ) */
/* (13) Rectangular matrix with random entries chosen from (-1,1). */
/* (14) Same as (13), but multiplied by SQRT( overflow threshold ) */
/* (15) Same as (13), but multiplied by SQRT( underflow threshold ) */
/* Arguments */
/* ========= */
/* NSIZES (input) INTEGER */
/* The number of values of M and N contained in the vectors */
/* MVAL and NVAL. The matrix sizes are used in pairs (M,N). */
/* If NSIZES is zero, CCHKBB does nothing. NSIZES must be at */
/* least zero. */
/* MVAL (input) INTEGER array, dimension (NSIZES) */
/* The values of the matrix row dimension M. */
/* NVAL (input) INTEGER array, dimension (NSIZES) */
/* The values of the matrix column dimension N. */
/* NWDTHS (input) INTEGER */
/* The number of bandwidths to use. If it is zero, */
/* CCHKBB does nothing. It must be at least zero. */
/* KK (input) INTEGER array, dimension (NWDTHS) */
/* An array containing the bandwidths to be used for the band */
/* matrices. The values must be at least zero. */
/* NTYPES (input) INTEGER */
/* The number of elements in DOTYPE. If it is zero, CCHKBB */
/* 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. */
/* NRHS (input) INTEGER */
/* The number of columns in the "right-hand side" matrix C. */
/* If NRHS = 0, then the operations on the right-hand side will */
/* not be tested. NRHS must be at least 0. */
/* 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 CCHKBB 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 IINFO not equal to 0.) */
/* A (input/workspace) REAL array, dimension */
/* (LDA, max(NN)) */
/* Used to hold the matrix A. */
/* LDA (input) INTEGER */
/* The leading dimension of A. It must be at least 1 */
/* and at least max( NN ). */
/* AB (workspace) REAL array, dimension (LDAB, max(NN)) */
/* Used to hold A in band storage format. */
/* LDAB (input) INTEGER */
/* The leading dimension of AB. It must be at least 2 (not 1!) */
/* and at least max( KK )+1. */
/* BD (workspace) REAL array, dimension (max(NN)) */
/* Used to hold the diagonal of the bidiagonal matrix computed */
/* by CGBBRD. */
/* BE (workspace) REAL array, dimension (max(NN)) */
/* Used to hold the off-diagonal of the bidiagonal matrix */
/* computed by CGBBRD. */
/* Q (workspace) COMPLEX array, dimension (LDQ, max(NN)) */
/* Used to hold the unitary matrix Q computed by CGBBRD. */
/* LDQ (input) INTEGER */
/* The leading dimension of Q. It must be at least 1 */
/* and at least max( NN ). */
/* P (workspace) COMPLEX array, dimension (LDP, max(NN)) */
/* Used to hold the unitary matrix P computed by CGBBRD. */
/* LDP (input) INTEGER */
/* The leading dimension of P. It must be at least 1 */
/* and at least max( NN ). */
/* C (workspace) COMPLEX array, dimension (LDC, max(NN)) */
/* Used to hold the matrix C updated by CGBBRD. */
/* LDC (input) INTEGER */
/* The leading dimension of U. It must be at least 1 */
/* and at least max( NN ). */
/* CC (workspace) COMPLEX array, dimension (LDC, max(NN)) */
/* Used to hold a copy of the matrix C. */
/* WORK (workspace) COMPLEX array, dimension (LWORK) */
/* LWORK (input) INTEGER */
/* The number of entries in WORK. This must be at least */
/* max( LDA+1, max(NN)+1 )*max(NN). */
/* RWORK (workspace) REAL array, dimension (max(NN)) */
/* RESULT (output) REAL array, dimension (4) */
/* The values computed by the tests described above. */
/* The values are currently limited to 1/ulp, to avoid */
/* overflow. */
/* INFO (output) INTEGER */
/* If 0, then everything ran OK. */
/* ----------------------------------------------------------------------- */
/* Some Local Variables and Parameters: */
/* ---- ----- --------- --- ---------- */
/* ZERO, ONE Real 0 and 1. */
/* MAXTYP The number of types defined. */
/* NTEST The number of tests performed, or which can */
/* be performed so far, for the current matrix. */
/* NTESTT The total number of tests performed so far. */
/* NMAX Largest value in NN. */
/* NMATS The number of matrices generated so far. */
/* NERRS The number of tests which have exceeded THRESH */
/* so far. */
/* COND, IMODE Values to be passed to the matrix generators. */
/* ANORM Norm of A; passed to matrix generators. */
/* OVFL, UNFL Overflow and underflow thresholds. */
/* ULP, ULPINV Finest relative precision and its inverse. */
/* RTOVFL, RTUNFL Square roots of the previous 2 values. */
/* The following four arrays decode JTYPE: */
/* KTYPE(j) The general type (1-10) for type "j". */
/* KMODE(j) The MODE value to be passed to the matrix */
/* generator for type "j". */
/* KMAGN(j) The order of magnitude ( O(1), */
/* O(overflow^(1/2) ), O(underflow^(1/2) ) */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--mval;
--nval;
--kk;
--dotype;
--iseed;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--bd;
--be;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
p_dim1 = *ldp;
p_offset = 1 + p_dim1;
p -= p_offset;
cc_dim1 = *ldc;
cc_offset = 1 + cc_dim1;
cc -= cc_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
--work;
--rwork;
--result;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Check for errors */
ntestt = 0;
*info = 0;
/* Important constants */
badmm = FALSE_;
badnn = FALSE_;
mmax = 1;
nmax = 1;
mnmax = 1;
i__1 = *nsizes;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = mmax, i__3 = mval[j];
mmax = max(i__2,i__3);
if (mval[j] < 0) {
badmm = TRUE_;
}
/* Computing MAX */
i__2 = nmax, i__3 = nval[j];
nmax = max(i__2,i__3);
if (nval[j] < 0) {
badnn = TRUE_;
}
/* Computing MAX */
/* Computing MIN */
i__4 = mval[j], i__5 = nval[j];
i__2 = mnmax, i__3 = min(i__4,i__5);
mnmax = max(i__2,i__3);
/* L10: */
}
badnnb = FALSE_;
kmax = 0;
i__1 = *nwdths;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = kmax, i__3 = kk[j];
kmax = max(i__2,i__3);
if (kk[j] < 0) {
badnnb = TRUE_;
}
/* L20: */
}
/* Check for errors */
if (*nsizes < 0) {
*info = -1;
} else if (badmm) {
*info = -2;
} else if (badnn) {
*info = -3;
} else if (*nwdths < 0) {
*info = -4;
} else if (badnnb) {
*info = -5;
} else if (*ntypes < 0) {
*info = -6;
} else if (*nrhs < 0) {
*info = -8;
} else if (*lda < nmax) {
*info = -13;
} else if (*ldab < (kmax << 1) + 1) {
*info = -15;
} else if (*ldq < nmax) {
*info = -19;
} else if (*ldp < nmax) {
*info = -21;
} else if (*ldc < nmax) {
*info = -23;
} else if ((max(*lda,nmax) + 1) * nmax > *lwork) {
*info = -26;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("CCHKBB", &i__1);
return 0;
}
/* Quick return if possible */
if (*nsizes == 0 || *ntypes == 0 || *nwdths == 0) {
return 0;
}
/* More Important constants */
unfl = slamch_("Safe minimum");
ovfl = 1.f / unfl;
ulp = slamch_("Epsilon") * slamch_("Base");
ulpinv = 1.f / ulp;
rtunfl = sqrt(unfl);
rtovfl = sqrt(ovfl);
/* Loop over sizes, widths, types */
nerrs = 0;
nmats = 0;
i__1 = *nsizes;
for (jsize = 1; jsize <= i__1; ++jsize) {
m = mval[jsize];
n = nval[jsize];
mnmin = min(m,n);
/* Computing MAX */
i__2 = max(1,m);
amninv = 1.f / (real) max(i__2,n);
i__2 = *nwdths;
for (jwidth = 1; jwidth <= i__2; ++jwidth) {
k = kk[jwidth];
if (k >= m && k >= n) {
goto L150;
}
/* Computing MAX */
/* Computing MIN */
i__5 = m - 1;
i__3 = 0, i__4 = min(i__5,k);
kl = max(i__3,i__4);
/* Computing MAX */
/* Computing MIN */
i__5 = n - 1;
i__3 = 0, i__4 = min(i__5,k);
ku = max(i__3,i__4);
if (*nsizes != 1) {
mtypes = min(15,*ntypes);
} else {
mtypes = min(16,*ntypes);
}
i__3 = mtypes;
for (jtype = 1; jtype <= i__3; ++jtype) {
if (! dotype[jtype]) {
goto L140;
}
++nmats;
ntest = 0;
for (j = 1; j <= 4; ++j) {
ioldsd[j - 1] = iseed[j];
/* L30: */
}
/* Compute "A". */
/* Control parameters: */
/* KMAGN KMODE KTYPE */
/* =1 O(1) clustered 1 zero */
/* =2 large clustered 2 identity */
/* =3 small exponential (none) */
/* =4 arithmetic diagonal, (w/ singular values) */
/* =5 random log (none) */
/* =6 random nonhermitian, w/ singular values */
/* =7 (none) */
/* =8 (none) */
/* =9 random nonhermitian */
if (mtypes > 15) {
goto L90;
}
itype = ktype[jtype - 1];
imode = kmode[jtype - 1];
/* Compute norm */
switch (kmagn[jtype - 1]) {
case 1: goto L40;
case 2: goto L50;
case 3: goto L60;
}
L40:
anorm = 1.f;
goto L70;
L50:
anorm = rtovfl * ulp * amninv;
goto L70;
L60:
anorm = rtunfl * max(m,n) * ulpinv;
goto L70;
L70:
claset_("Full", lda, &n, &c_b1, &c_b1, &a[a_offset], lda);
claset_("Full", ldab, &n, &c_b1, &c_b1, &ab[ab_offset], ldab);
iinfo = 0;
cond = ulpinv;
/* Special Matrices -- Identity & Jordan block */
/* Zero */
if (itype == 1) {
iinfo = 0;
} else if (itype == 2) {
/* Identity */
i__4 = n;
for (jcol = 1; jcol <= i__4; ++jcol) {
i__5 = jcol + jcol * a_dim1;
a[i__5].r = anorm, a[i__5].i = 0.f;
/* L80: */
}
} else if (itype == 4) {
/* Diagonal Matrix, singular values specified */
clatms_(&m, &n, "S", &iseed[1], "N", &rwork[1], &imode, &
cond, &anorm, &c__0, &c__0, "N", &a[a_offset],
lda, &work[1], &iinfo);
} else if (itype == 6) {
/* Nonhermitian, singular values specified */
clatms_(&m, &n, "S", &iseed[1], "N", &rwork[1], &imode, &
cond, &anorm, &kl, &ku, "N", &a[a_offset], lda, &
work[1], &iinfo);
} else if (itype == 9) {
/* Nonhermitian, random entries */
clatmr_(&m, &n, "S", &iseed[1], "N", &work[1], &c__6, &
c_b33, &c_b2, "T", "N", &work[n + 1], &c__1, &
c_b33, &work[(n << 1) + 1], &c__1, &c_b33, "N",
idumma, &kl, &ku, &c_b41, &anorm, "N", &a[
a_offset], lda, idumma, &iinfo);
} else {
iinfo = 1;
}
/* Generate Right-Hand Side */
clatmr_(&m, nrhs, "S", &iseed[1], "N", &work[1], &c__6, &
c_b33, &c_b2, "T", "N", &work[m + 1], &c__1, &c_b33, &
work[(m << 1) + 1], &c__1, &c_b33, "N", idumma, &m,
nrhs, &c_b41, &c_b33, "NO", &c__[c_offset], ldc,
idumma, &iinfo);
if (iinfo != 0) {
io___41.ciunit = *nounit;
s_wsfe(&io___41);
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;
}
L90:
/* Copy A to band storage. */
i__4 = n;
for (j = 1; j <= i__4; ++j) {
/* Computing MAX */
i__5 = 1, i__6 = j - ku;
/* Computing MIN */
i__8 = m, i__9 = j + kl;
i__7 = min(i__8,i__9);
for (i__ = max(i__5,i__6); i__ <= i__7; ++i__) {
i__5 = ku + 1 + i__ - j + j * ab_dim1;
i__6 = i__ + j * a_dim1;
ab[i__5].r = a[i__6].r, ab[i__5].i = a[i__6].i;
/* L100: */
}
/* L110: */
}
/* Copy C */
clacpy_("Full", &m, nrhs, &c__[c_offset], ldc, &cc[cc_offset],
ldc);
/* Call CGBBRD to compute B, Q and P, and to update C. */
cgbbrd_("B", &m, &n, nrhs, &kl, &ku, &ab[ab_offset], ldab, &
bd[1], &be[1], &q[q_offset], ldq, &p[p_offset], ldp, &
cc[cc_offset], ldc, &work[1], &rwork[1], &iinfo);
if (iinfo != 0) {
io___43.ciunit = *nounit;
s_wsfe(&io___43);
do_fio(&c__1, "CGBBRD", (ftnlen)6);
do_fio(&c__1, (char *)&iinfo, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(integer))
;
e_wsfe();
*info = abs(iinfo);
if (iinfo < 0) {
return 0;
} else {
result[1] = ulpinv;
goto L120;
}
}
/* Test 1: Check the decomposition A := Q * B * P' */
/* 2: Check the orthogonality of Q */
/* 3: Check the orthogonality of P */
/* 4: Check the computation of Q' * C */
cbdt01_(&m, &n, &c_n1, &a[a_offset], lda, &q[q_offset], ldq, &
bd[1], &be[1], &p[p_offset], ldp, &work[1], &rwork[1],
&result[1]);
cunt01_("Columns", &m, &m, &q[q_offset], ldq, &work[1], lwork,
&rwork[1], &result[2]);
cunt01_("Rows", &n, &n, &p[p_offset], ldp, &work[1], lwork, &
rwork[1], &result[3]);
cbdt02_(&m, nrhs, &c__[c_offset], ldc, &cc[cc_offset], ldc, &
q[q_offset], ldq, &work[1], &rwork[1], &result[4]);
/* End of Loop -- Check for RESULT(j) > THRESH */
ntest = 4;
L120:
ntestt += ntest;
/* Print out tests which fail. */
i__4 = ntest;
for (jr = 1; jr <= i__4; ++jr) {
if (result[jr] >= *thresh) {
if (nerrs == 0) {
slahd2_(nounit, "CBB");
}
++nerrs;
io___45.ciunit = *nounit;
s_wsfe(&io___45);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer));
do_fio(&c__4, (char *)&ioldsd[0], (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&jtype, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&jr, (ftnlen)sizeof(integer));
do_fio(&c__1, (char *)&result[jr], (ftnlen)sizeof(
real));
e_wsfe();
}
/* L130: */
}
L140:
;
}
L150:
;
}
/* L160: */
}
/* Summary */
slasum_("CBB", nounit, &nerrs, &ntestt);
return 0;
/* End of CCHKBB */
} /* cchkbb_ */